Pinned Base Plates

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STEEL CONSTRUCTIONJOURNAL OF THE AUSTRALIAN STEEL INSTITUTE

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Design of Pinned ColumnBase Plates

AUSTRALIAN STEEL INSTITUTE

VOLUME 36 NUMBER 2 SEPTEMBER 2002

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1 STEEL CONSTRUCTION VOLUME 36 NUMBER 2 SEPT 2002

STEEL CONSTRUCTION -- EDITORIAL

Editor: Peter Kneen

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Design of Pinned Column Base Plates

Contents

This paper deals with the design of pinned base plates. The design actions considered areaxial compression, axial tension, shear force and their combinations. The base plate isassumed to be essentially statically loaded, andadditional considerationsmay be requiredin the case of dynamic loads or in fatigue applications.

1. INTRODUCTION 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1. Design actions in accordance with AS 4100 1. . . . . . . . . . . . . . . . . . . . . . . . . . .

2. NOTATION 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3. BASE PLATE COMPONENTS 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4. AXIAL COMPRESSION 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1. INTRODUCTION 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2. BASE PLATE DESIGN -- LITERATURE REVIEW 4. . . . . . . . . . . . . . . . . . . .4.3. RECOMMENDED MODEL 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. AXIAL TENSION 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1. INTRODUCTION 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2. BASE PLATE DESIGN -- LITERATURE REVIEW 12. . . . . . . . . . . . . . . . . . . .5.3. DESIGN OF ANCHOR BOLTS -- LITERATURE REVIEW 17. . . . . . . . . . . . .5.4. RECOMMENDED MODEL 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6. SHEAR 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.1. INTRODUCTION 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2. TRANSFER OF SHEAR BY FRICTION

OR BY RECESSING THE BASE PLATE INTO THE CONCRETE --LITERATURE REVIEW 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3. TRANSFER OF SHEAR BY A SHEARKEY-- LITERATURE REVIEW 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4. TRANSFER OF SHEAR BY THE ANCHOR BOLTS --LITERATURE REVIEW 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.5. RECOMMENDED MODEL 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7. BASE PLATE AND ANCHOR BOLTS DETAILING 36. . . . . . . . . . . . . . . . . . . . . .8. ACKNOWLEDGEMENTS 38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9. REFERENCES 38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10. APPENDIX A -- Derivation of Design and Check Expressions

for Steel Base Plates Subject to Axial Compression 40. . . . . . . . . . . . . . . . . . . . . . . .11. APPENDIX B-- Derivation of Design and Check Expressions

for Steel Base Plates Subject to Axial Tension 46. . . . . . . . . . . . . . . . . . . . . . . . . . . .12. APPENDIX C -- Determination of Embedment Lengths and Edge Distances 49. . . .13. APPENDIX D -- Design Capacities of Equal Leg Fillet Welds 53. . . . . . . . . . . . . . . .14. APPENDIX E -- Design of Bolts under Tension and Shear 53. . . . . . . . . . . . . . . . . . .


Design of Pinned Column Base Plates

Gianluca RanziSchool of Civil and Environmental Engineering

The University of New South Wales

Peter KneenNational Manager TechnologyAustralian Steel Institute

1. INTRODUCTION

This paper deals with the design of pinned base plates.The design actions considered are axial compression,axial tension, shear force and their combinations asshown in Fig. 1. The base plate is assumed to beessentially statically loaded, and additionalconsiderations may be required in the case of dynamicloads or in fatigue applications.

N*t

N*c

V*x

N*t

N*c

V*y

Figure 1 Column Design Actions:Axial and Shear Loads along minorand major axes (Ref. [26])

Firstly the requirements of AS 4100 ”Steel Structures”[11] in the calculation of the design actions forconnections are outlined. Then for each design actionavailable design guidelines and/or models are brieflypresented in a chronological manner to provide anoverview on how these have improved/changed overtime. Attention has been given to try to ensure that theassumptions and/or limitations of eachmodel presentedare always clearly stated.Among thesemodels, themostrepresentative ones in the opinion of the authors are thenrecommended for design purposes. It is not intended tosuggest that models, other than those recommended,may not give adequate capacities.The design of concrete elements is outside the scope ofthe present paper. Nevertheless some designconsiderations regarding the concrete elements stillneed to be addressed, i.e. bolts’ edge distances, bolts’embedment lengths, concrete strength etc., andtherefore it is necessary to ensure that such designassumptions/considerations are included in the finaldesign of the concrete elements/structure.

1.1. Design actions in accordance with AS 4100

Pinned type column base plates may be subject to thefollowing design actions, as shown in Fig. 1:

an axial force, N*, either tension or compression;

a shear force, V* (usually acting in the directionof either principal axis or both).

Clause 9.1.4 of AS 4100 [11], which considersminimum design actions, does not specifically mentionminimum design actions for column base plates butdoes require that:

connections at the ends of tension or compressionmembers be designed for a minimum force of 0.3times the member design capacity;connections to beams in simple construction bedesigned for a minimum shear force equal to thelesser of 0.15 times the member design shearcapacity and 40 kN.

It is considered inappropriate for these provisions to beapplied to column base plates, since the design ofcolumns is usually governed by a combinations of axialloads and bending moments at other locations.

2. NOTATION

The following notation is used in this work. Othersymbols which are defined within diagrams may not belisted below. Generally speaking, the symbols will bedefined when first used.

ab = distance from centre of bolt hole to inside faceof flange

ae = minimum concrete edge distance (side cover)A1 = bearing area which varies depending upon the

assumed pressure distribution between the baseplate and the grout/concrete

A(i)1 = bearing area at the i--th iteration inMurray--Stockwell Model

A2 = supplementary area which is the largest area ofthe supporting concrete surface that isgeometrically similar to and concentric to A1

AH= assumed bearing area (in the case ofH--shapedsections it is a H--shaped area) in Murray--Stockwell Model

A(i)H = assumed bearing AH at the i--th iteration inMurray--Stockwell Model

Ai = base plate areaApsk = projected area over the concrete edge

ignoring the shear key areaAps = effective projected area of concrete under

uplift


Aps.1 = effective projected area of isolated anchorbolt (no overlapping of failure cones)

Aps.2 = effective projected area of 2 anchor boltswith overlapping of their failure cones

Aps.4 = effective projected area of 4 anchor boltswith overlapping of their failure cones. In thiscase each failure cone overlaps with all other 3failure cones

As = tensile stress area in accordance with AS1275[9]

Ask = area of the shear keybc = width of the column section (RHS and SHS)bfc = width of the column section (H--shaped

sections and channels)bfc1 = width of the column flange ignoring web

thicknessbi = width of base platebs = depth of shear keybt =distance fromfaceofweb to anchorbolt locationdc = column depthdc1 = clear depth between flanges (column depth

ignoring thicknesses of flanges)df = nominal anchor bolt diameterdh = diameter of bolt holedi = length of base plated0 = outside diameter of CHS

f′c = characteristic compressive cylinder strength ofconcrete at 28 days

f*p = uniform design pressure at the interface of thebase plate and grout/concrete

fuf = minimum tensile strength of boltfuw = nominal tensile strength of weld metalfyi = yield stress of the base plate used in design

fys = yield stress of shear key used in design

kr = reduction factor to account for length of weldedlap connection

Ld = minimum embedment length of anchor boltLh = hook length of anchor boltLs = length of shear keyLw = total length of fillet weldmp = plastic moment capacity of the base plate per

unit widthms = nominal section moment capacity of the base

plate per unit widthmsk = nominal section moment capacity per unit

width of shear key

m*c = design moment per unit width due to N*

c

m*sk = design moment to be carried by the shear keyper unit width

m*t = design moment per unit width due to N*

t

nb = number of anchor bolts part of the base plateconnection

N*c = column design axial compression load

N*b = N*

t∕nb = design axial tension load carried byone bolt

Ndes.c = design capacity of the base plate connectionsubject to axial compression

Ndes.t = design capacity of the base plate connectionsubject to axial tension

N*p = prying action

N*t = design axial tension load of the column

Ntf = nominal tensile capacity of a bolt in tension

N*0 = portion of N*

c acting over the column footprintsp = bolt pitch

Si = plastic section modulus per unit width of platetc = thickness of column sectionti = base plate thicknesstg = grout thickness

ts = thickness of shear keytt = design throat thickness of fillet weldtw = thickness of column webvdes = Ôvw = design capacity of theweld connecting

the base plate to the column per unit length

v*h and v*v= components of the loading carried by theweld between column and base plate in onehorizontal direction in the plane of the base plateand in the vertical direction respectively per unitlength

v*w = design action on fillet weld per unit lengthVdes = design shear capacity of the base plate

connection

V*s = design shear force to be transferred by meansof the shear key

Wi and We = internal and external workÔ = capacity factor

Ôf(i)b = maximum bearing strength of the concrete atthe i--th iteration in Murray--Stockwell Model

Ôfb = maximum bearing capacity of the concretebased on a certain bearing area A1

ÔNc = design axial capacity of the concretefoundation

ÔNc.lat = lateral bursting capacity of the concreteÔNcc = design pull--out capacity of the concrete

foundationÔNs = design axial capacity of the steel base plateÔNt = axial tension capacity of the base plateÔNtb = design capacity of the anchor bolt group

under tensionÔNth = tensile capacity of a hooked barÔNw= design axial capacity of the weld connecting

the base plate to the column section


Ôvw = design capacity of the fillet weld per unitlength

ÔVf = design shear capacity of the base platetransferred by means of friction

ÔVs = design shear capacity of the shear keyÔVs.c = concrete bearing capacity of the shear keyÔVs.cc = pull--out capacity of the concreteÔVs.b = shear capacity of the shear key based on its

section moment capacityÔVs.w = shear capacity of the weld between the

shear key and the base plateÔVw= design shear capacity of the weld connecting

the base plate to the columnη = ratio depth and width of columnμ = coefficient of friction

3. BASE PLATE COMPONENTS

Typical base plates considered in this paper are formedby one unstiffened plate only as shown in Fig. 3. Forhighly loaded columns or larger structures other baseplate solutions or more elaborate anchor bolt systemsmight be required. Guidelines for the design anddetailing of more complex base plates can be found in[4], [13], [14], [16] and [34].Two types of anchor bolts are usually used, which arecast--in--place or drilled--in bolts. The former are placedbefore the placing of the concrete or while the concreteis still fresh while the latter are inserted after theconcrete has fully hardened.Different types of cast--in--place anchors are shown in inFig. 2. These include anchor bolts with a head, threadedrodswith nut, threaded rodswith a platewasher, hookedbars or U--bolts. These are suitable for small to mediumsize structures considering anchor bolts up to 30 mm indiameter.

(a) Hooked Bar (b) Bolt withhead

(c) ThreadedRod with Nut

(d) Threaded rodwith plate washer

(e) U--Bolt

Filletwelds

Square plate

Figure 2 Common Forms of Holding DownBolts (Ref. [26])

There is a large variety of drilled--in anchors available,many of which are proprietary bolts whose installationand design is governed by manufacturers’specifications. References [2], [15], [17], [31] and [33]contain information on these types of anchors.This paper deals only with cast--in--place anchors, andspecifically hooked bars, anchor bolts with a head andthreaded rodswith a nut/washer/plate.Grade 4.6 anchorbolts are recommended to be utilised in base plateapplications.

sp

sg

Figure 3 Typical unstiffened base plate(Ref. [26])

4. AXIAL COMPRESSION

4.1. INTRODUCTION

The literature review presented covers only modelsregarding the design of the actual steel plate as theanchor bolts do not contribute to the strength of theconnection under this loading condition. Unless specialconfinement reinforcement is provided the maximumbearing strength of the concrete Ôfb is calculated inaccordance with Clause 12.3 of AS 3600 [10] asfollows:

Ôfb= minÔ0.85f′c A2A1 , Ô2f′c (1)

where:Ô = 0.6Ôfb = maximum bearing capacity of the concrete

based on a certain bearing area A1

f′c = characteristic compressive cylinder strength ofconcrete at 28 days

A1 = bearing area which varies depending upon theassumed pressure distribution between the baseplate and the grout/concrete

A2 = supplementary area which is the largest area ofthe supporting concrete surface that isgeometrically similar to and concentric to A1


4.2. BASE PLATE DESIGN -- LITERATUREREVIEW

Themain designmodels available in literature differ fortheir assumptions adopted regarding the pressuredistribution at the interface between the base plate andthe grout/concrete and for the relative sizes of the baseplate and the connected column. For example, the firstmodel presented, here referred to as the CantileverModel, is adequate for base plates whose dimensions(di× bi ) are much greater than those of the column(dc× bfc ), while other models, such as Fling andMurray--Stockwell Models, deal with base plates withsimilar dimensions to the ones of the connected column.

4.2.1. Cantilever Model

Historically the cantilever model was the first availableapproach for the design of base plates. It is well suitedfor the design of large base plates with the dimensionsof the base plate (di× bi)muchgreater than those of thecolumn (dc× bfc). It has been present in the AISC(US)Manuals over several editions. Its formulation issuitable for the base plate design of only H--shapedcolumns. [5]

dc 0.95dcdi

bibfc

0.8bfca2 a2

a1

a1

(a) Critical sections and assumed loaded area

N*c

bidi

Critical sectionin bending am

ti

(b) Deflection of the cantilevered plate

N*c

biditi

N*c

(c) Assumed bearing pressure

Figure 4 Cantilever Model (Ref. [26])

This model assumes that, in the case of a H--shapedcolumn, the axial load applied by the column isconcentrated over an area of 0.95dc× 0.80bfc whichcorresponds to the shaded area of Fig. 4(a). This causesthe base plate to bend as a cantilevered plate about theedges of such area as shown in Fig. 4(b). The pressureat the underside of the base plate is assumed to beuniformly distributed, as shown in Fig. 4(c), thereforeleading to a conservative design for large base plates.

a1

a2Dashed lines indicateyield lines

a1

a2

Figure 5 Cantilever Model -- Collapsemechanisms

Each of the two collapsemechanisms considered by thismodel assumes two yield lines to form at a distance a1and a2 from the edge of the plate respectively as shownin Fig. 5. Comparing the two collapse mechanisms andaccording to the rules of yield line theory the governingdesign capacity is based on the longest cantilever lengtham, being the maximum of the two cantilevered lengthsa1 and a2 shown in Fig. 4(a).

The design moment m*c and the design capacity of the

plate Ôms are calculated per unit width in accordancewith AS 4100 [11] as:

m*c=

N*cbidi

a2m2

(2)

Ôms= ÔfyiSi=0.9fyi t2i

4(3)

where:

N*c = column design axial compression load

m*c = design moment per unit width due to N*

c

ms=plate nominal sectionmoment capacity per unitwidth

fyi = yield stress of the base plate used in design

Si = plastic section modulus per unit width of plateam = max(a1, a2)a1 and a2 = cantilevered plate lengthsti, di and bi = thickness, length and width of base

plateand ensuring that the plastic section modulus of thecantilevered plate Si is able to transfer the axialcompression load N*

c to the supporting material(verified per unit width of plate):

m*c=

N*cbidi

a2m2≤

0.9fyi t2i4

= Ôms (4)

yields a maximum design axial force of:


N*c≤

0.9fyi t2i bidi2 a2m

(5)

or equivalently requires a minimum plate thickness of:

ti≥ am2N*c

0.9fyi bidi (6)

Provisions on how to extend this approach for channelsand hollow sections columns have been provided in[21], [26] and [36].The dimensions of the loaded areas and of thecantilevered lengths a1 and a2 for channels and hollowsections are shown in Figs. 6, 7 and 8 and their valuesare summarised in Table 1 based on therecommendations in [21], [26] and [36]. The values inTable 1 assume that the column iswelded concentricallyto the base plate.

Table 1 Cantilever Model -- Cantilevered platelengths a1 and a2 (refer to Figs. 4, 6, 7and 8 for the definition of the notation)

SECTION a1 a2H--shapedsection [21]

di− 0.95dc2

bi− 0.80bfc2

Channel [26] di− 0.95dc2

bi− 0.80bfc2

SHS andRHS [36]

di− dc+ ti2

bi− bc+ ti2

SHS andRHS [21]

di− 0.95dc2

bi− 0.95bc2

CHS [21] di− 0.80do2

bi− 0.80do2

a20.8bfc

a2

a1

a1

0.95dc

bibfc

dcdi

Figure 6 Cantilevered plate lengths -- Channels(Ref. [26])

0.95dc

a1

a1

a2a20.95bfc

dcdi

bi

bc

Figure 7 Cantilevered plate lengths -- RHS andSHS (Ref. [26])

a20.8do

0.8do

a1

a1

a2

dodi

bi

Figure 8 Cantilevered plate lengths -- CHS(Ref. [26])

Parker in [37] notes how other possible yield linepatterns could be investigated for hollow sections suchas the ones shown in Fig. 9. Nevertheless in [36] herecommends to investigate collapse mechanismssimilar to the ones considered by the Cantilever Modelwith values of a1 and a2 as shown in Table 1. In [36] healso recommends to specify plate thicknesses not lessthan 0.2 times the maximum cantilever length in orderto limit the deflection of the plate.Applying this model to base plates with similardimensions to the ones of connected columnwould leadto inadequate design as the capacity of the base platewould be overestimated. Utilizing equations (5) and (6)the capacity of the base plate would increase and theplate thickness ti would decrease while decreasing thecantilevered plate length am. Other design models needto be adopted in these instances.

a2

0.95dc

a1

a1

a2

0.95bc

dcdi

bibc Dashed lines

indicate yieldlines


bi

dido

0.8do

0.8do

a1

a1

a2 a2

Figure 9 Possible yield line pattern (Ref. [37])

4.2.2. Fling Model

Fling, in [25], presents adesignmodel applicable tobaseplates with similar dimensions to the ones of theconnected columnand reviews the design philosophyofthe Cantilever Model. Only H--shaped columns areconsidered in this model.He recommends to apply both a strength and aserviceability criteria to the design of base plates.Regarding the Cantilever Method, which is based on astrength criteria, he recommends to apply also aserviceability check by limiting the deflection of thecantilevered plate. He argues that, while increasing thesize of the plate, deflections of the cantilevered platewould increase reducing the ability of the mostdeflected parts of the plate to transfer the assumeduniform loading to the supporting material. Thus theload would re--distribute to the least deflected portionsof the plate which may overstress the underlyingsupport. His proposed deflection limit intends toprevent such overstressing. He also notes that such limitshould vary depending upon the deformability of thesupportingmaterial. Fling suggests 0.01 in. (0.254mm)to be a reasonable deflection limit to be imposed formost bearing plates, even if he clearly states that it isbeyond the scope of his paper to specify deflectionlimits applicable to various supporting materials. [25]Regarding the designmodel for base plates with similardimensions to the ones of the connected column herecommends to apply the following strength andserviceability checks.The strength check is based on the yield line theory andthe assumed yield line pattern is shown in Fig. 10. Theprocedure is derived for a base plate with width andlength equal to the column’s width and depth (thereforebi and di equal bfc and dc respectively).The support conditions assumed for the plate are fixedalong the web, simply supported along the flanges andfree on the edge opposite to the web.

Dashed linesindicate yield lines

βbes

β= tanθ

θ

d1bes

Figure 10 Fling Model -- Yield Line Pattern(Ref. [25])

The internal and external work produced under loadingare calculated as follows:

Wi=1bes

(2d1+ 4βbes)Ômp+ 1βbes

4besÔmp (7)

We= 2f*p(d1− 2βbes)bes12+

43 f

*pβb2es (8)

where:mp = plastic moment capacity of the baseplate per

unit width

f*p = uniform design pressure at the interface of thebase plate and grout/concrete which is assumedto be equal to the maximum bearing strength ofthe concrete Ôfb

Wi and We = internal and external work

d1, β and bes = as defined in Fig. 10

Fling introduces the following parameter λ to simplifythe notation:

λ= d1bes

(9)

Equating the internal and external work yields:

Ômp(2λ+ 4β+ 4β)= f*pb2es( λ− 2

3 β) (10)

The value of β which maximises the required momentcapacity of the base plate is as follows:

β= 34+

14λ2

− 12λ

(11)

which is obtained bydifferentiating for β the expressionof the plastic moment derived from equation (10).The requiredbaseplate thickness ti is then calculated as:[25]

ti≥ 0.43bfcβf*p

0.9fyi (1− β2)

= 0.43bfcβÔfb

0.9fyi(1− β2) (12)


where:bfc = column flange width

Equation (12) includes a safety factorof 1 and theplasticmoment capacity is increased by 10% to allow for lackof full plastic moment at the corners (as recommendedin [25]).This method assumes simultaneous crushing of theconcrete foundation and yielding of the steel base plateas the pressure at the interface of the base plate andgrout/concrete is assumed to be equal to the maximumbearing strength of the concrete Ôfb.The serviceability check verifies the adequacy of themaximum deflection of the base plate calculated fromelastic theory and assumes the same support conditionsas adopted in the strength check. The maximumdeflection occurs at the middle of the free edge of theplate (opposite to the web).

4.2.3. Murray--Stockwell Model

In 1975 Stockwell presents a design model for lightlyloaded base plates with base plate dimensions similar tothe column’s width and depth. His formulation issuitable to onlyH--shaped columns. He defines a lightlyloaded base plate as onewherein the required base platearea is approximately equal to the column flange widthtimes its depth. [40]The novelty of this model is to assume that the pressuredistribution under the base plate is not uniform but isconfined to an area in the immediate vicinity of thecolumn profile and is approximated by aH--shaped areacharacterised by the dimension a3 as shown in Fig. 11.This pressure distribution implies that in relatively thinbase plates uplift might occur at the free edge.A few years later Murray carried out a finite elementstudy to verify the possibility introduced by Stockwellof uplift at the free edge. He established, from bothmodelling and testing, that thin base plates lift off thesubgrade during loading and therefore the assumptionofuniformstressdistribution at the interface is not valid.He also concludes that experimental evidence does notsupport the need for the serviceability check introducedby Fling. [32]Murray further expanded Stockwell’s model to obtainthe model which is known today as theMurray--Stockwell Model [41] and refines thedefinition of lightly loaded base plates to be relativelyflexible plate approximately the same size as the outsidedimensions of the connected column. [32]According to Stockwell there is only a little differencebetween the procedures specified in Fling andMurray--Stockwell Models as he considers both to bevalid and logically derived. [41]

a3

di

bi

dc

bfc

a3 a3

a3

AH

Figure 11 Murray--Stockwell Model -- Assumedshape of pressure distribution.

The Murray--Stockwell Model assumes that thepressure acting over the H--shaped bearing area isuniform and equal to the maximum bearing capacity ofthe concrete Ôfb. The values of AH and Ôfb are notknown a priori and therefore an iterative procedure canbe implemented to evaluate their values. The value ofÔfb is not known a priori as it depends upon the valueof the bearing area A1which in this case is equal to AH.The area contained inside the column profile dc× bfc isused as a first approximation for the bearing area AH inthe calculation of Ôfb as shown in equation (13).

Ôf(1)b = minÔ0.85fc′ A2

A(1)1

, Ô2fc′ (13)

where:

Ôf(1)b = maximum bearing strength of the concrete atthe first iteration

A(1)1 = bearing area at the first iteration equal todc× bfc

The H--shaped bearing area AH is then calculated as thearea required to spread the applied load with a uniformpressure equal to Ôf(1)b .

A(1)H =

N*cÔf(1)

b

(14)

where:

A(1)H = assumedH--shapedbearing area AHat the firstiteration

If Ôf(1)b is equal to the maximum possible concretebearing strength Ô2f′c no further iterations are requiredand the value of the H--shaped bearing area hasconverged to A(1)

H calculated with equation (14). In thecase Ôf(1)b is less than Ô2f′c, or equivalently if the ratioof A2∕A1 is smaller than (2∕0.85)2= 5.53, the value ofthe H--shaped bearing area can be further refined.

Successive values of Ôf(i)b and A(i)H at the i--th iteration

can be calculated as follows:


Ôf(i)b = minÔ0.85f′c A2

A(i−1)1

, Ô2f′c (15)

A(i)H=

N*cÔf(i)

b

(16)

where:

Ôf(i)b = maximum bearing strength of the concrete atthe i--th iteration

A(i)1 = bearing area at the i--th iteration equal to A

(i−1)H

A(i)H = assumed H--shaped bearing AH at the i--thiteration

The value of AH can be further refined until thedifference between the values obtained from twosubsequent iterations canbeconsidered tobenegligible.The use of the iterative process allows to obtain thesmallest possible value of AH which yields thinner baseplate thicknesses. Ignoring to refine the value of AH

would simply lead to a more conservative plate design.The value of a3 is then obtained from equation (14)observing that AH can be expressed as (refer to Fig. 11):

AH= 2bfca3+ 2a3(dc− 2a3)

= 2bfca3+ 2dca3− 4a23 (17)

where:a3 = cantilevered langthAH = assumed H--shaped bearing areadc and bfc = depth and width of column

and solving for a3 yields:

a3=14(dc+ bfc)− (dc+ bfc)

2− 4AH (18)

The plate is now designed in accordance with AS4100[11] as a cantilevered plate of length a3 supporting auniform pressure equal to the converged value of themaximum bearing strength of the concrete previouslycalculated:

m*c= Ôfb

a232= N*c

AH

a232≤

0.9 fyi t2i4

= Ôms

The maximum axial load is then calculated as:

N*c≤

0.9fyi t2iAH

2a23(19)

or equivalently theminimum required plate thickness tiis determined as:

ti≥ a32N*c

0.9fyi AH (20)

The value of the cantilevered plate length a3 should bemeasured from the centre--line of the column’s plateelements as shown in Fig. 11.[21]. Nevertheless in theformulation presented here, as also carried out in [32]and [21], the full flange thickness is included in thecalculation of the cantilevered plate length a3. This onlyleads to a slightly more conservative design.

The Stockwell--Murray Method is recommended byDeWolf in Refs [21] and [22] and introduced in theAISC(US) Manuals in 1986. [7][1] notes that there are cases where the value under thesquare root of equation (18) becomes negative. In suchcases other design models should be adopted.Ref. [21] extends the application of Murray--StockwellModel to channels and hollow section members asshown in Figs. 12, 13 and 14. For these sections thevalue of the bearing area A(1)

1 (to be utilised in the firstiteration while calculating Ôf(1)b and A(1)

H ) and theexpressions of the cantilevered length a3 and of theH--shaped area AH are summarised in Table 2. [21][26]The same iterative procedure, as outlined for H--shapedsections, can be adopted to refine the value of AH if thecalculated Ôfb is less than Ô2f′c.

a3

a3

a3

Figure 12 Murray--Stockwell Model:Assumed pressure distribution --Channels (Ref. [26])

a3

a3

a3 a3

Figure 13 Murray--Stockwell Model:Assumed pressure distribution -- RHSand SHS (Ref. [26])

a3d3

do

Figure 14 Murray--Stockwell Model:Assumed pressure distribution -- CHS(Ref. [26])


4.2.4. Thornton’s Model

In [42] and [43] Thornton recommends that asatisfactory design of a base plate should be carried outcomplying with the requirements of the Cantilever,Fling (ignoring the serviceability check) andMurray--Stockwell Models.He derived a compact formulation for the designprocedure which includes all three models. Hisformulation is suitable for the design of only H--shapedcolumns.In [42] he also re--derives the collapse load based on thesame yield line pattern assumed by Fling in [25]. It isinteresting to note that while Fling applied the principleof virtual work Thornton based his results on theequilibrium equations [35]. Obviously the results areidentical. Note that Fling increased the required plateplastic moment by 10% to allow for lack of plasticmoment at the corners.The design expression proposed by Thornton in [43]and currently recommended in the AISC(US) Manual[5] is as follows:

ti= am2N*

c

0.9fyibidi (21)

where:

am= max(a1, a2, λa4)

λ= min1, 2 X

1+ 1− X a4=

14 dcbfc

N*0 = portion of N*

c acting over the column footprint

=N*cbidi

bfcdc

X=4bfcdc

(dc+ bfc)2

N*c

Ôfbdibi

= 4a25Ôfb

N*0= 4

a25ÔfbN*cdcbfcdibi

Ôfb= minÔ0.85f′c A2

dibi , Ô2f′c

a5= bfc+ dcThe concatenation of the three design models(Cantilever, Fling and Murray--Stockwell Models) isachieved in the calculation of am.The Cantilever Model is the governing criteria in thecase am equals either a1 or a2. In the case am is equal toλa4 the FlingModel would be governing if λ equals 1 orMurray--Stockwell Model would be governing if λ isless than 1. The use of λ leads to the selection of thethinner plate obtained by using the Fling Model andMurray--Stockwell Model in order not to loose theeconomy in design of the latter model in the case oflightly loaded columns. Recalling the description ofMurray--Stockwell Model no refinement in thecalculation of AH is implemented in equation (21). It isinteresting to note how this approach provides a moremathematical definition of lightly loaded columnwherea column is said to be lightly loaded if its λ is less than1, or equivalently if its X is less than (4∕5)2= 0.64.The expression of the plate thickness of Fling Model,re--derived in [42], is simplified by Thornton in [43] inorder to reduce the complexity of the yield line solution.His simplification introduces an approximation in thevalue of a4 with an error of 0% (unconservative) and17.7% (conservative) for values of dc∕bfc ranging from3/4 to 3. The value of N*

0 represents the portion of thetotal axial load N*

c acting over the column footprint(dcbfc) under the assumption of uniform bearingpressure under thebaseplate.Murray--StockwellModelis concatenated in equation (21) to carry a design axialload equal to N*

0 (not on N*c) over the assumedH--shaped

bearing area inside the column footprint.

Table 2 Murray--Stockwell Model(refer to Figs. 4, 6, 7, 8, 11, 12, 13 and 14 for the definition of the notation)

SECTION A(1)1

a3 AH

H--shaped section[21]

bfcdc (dc+ bfc)− (dc+ bfc)2− 4AH4

2bfca3+ 2a3(dc− 2a3)

Channel [26] bfcdc (2bfc+ dc)− (2bfc+ dc)2− 8AH4

2bfca3+ (dc− 2a3)a3

RHS SHS[21][26] bcdc

(dc+ bc)− (dc+ bc)2− 4AH4

dcbc− (dc− 2a3)(bc− 2a3)= 2(dc+ bc)a3− 4a23

CHS [21][26]πd204

do− d2o− 4AH∕π2

π(d2o− d23)∕4 = π(doa3− a23 )

where : d3= do− 2a3

4.2.5. Eurocode 3 Model

Clause 6.11 and Annex L of Eurocode 3 deal with thedesign of base plates. [23]

Requirement of the EC3 is to provide a base plateadequate to distribute the compression column loadover an assumed bearing area.The EC3 Model assumes an H--shaped bearing area asshown in Fig. 15(a). It requires that the pressure


assumed to be transferred at the interface baseplate/foundation should not exceed the bearing strengthof the joint fj.EC3 and the width of the bearing areashould not exceed c calculated as follows:

c= tifyi

3fj.EC3γMO (22)

where:fj.EC3 = bearing strength of the joint

=βjkjfcdβj = 2/3 provided that the characteristic strength of

the grout is not less than 0.2 times thecharacteristic strength of the concrete foundationand the thickness of the grout is not greater than0.2 times the smallestwidth of the steel base plate

kj = concentration factor and may be taken as 1 or

otherwise asa1b1ab

a1 and b1 = dimensions of the effective area asshown in Fig. 16

a1 = mina+ 2ar, 5a, a+ h, 5b1 ≥ a

b1 = minb+ 2br, 5b, b+ h, 5a1 ≥ b

fcd = design value of the concrete cylindercompressive strength = fck∕γc

fck = characteristic concrete cylinder compressivestrength (in accordance with Eurocode 2)

γc = partial safety factor for concrete materialproperties (in accordance with Eurocode 2)

γMO = 1.1 (boxed value from Table 1 of [23])In the case of large or short projections the bearing areashould be calculated as shown in Figs. 15(b) and (c).[23][23] requires that the resistance moment mRd per unitlength of a yield line in the base plate should be taken as:

mRd=t2ifyi6γMO

(23)

No specific expression for the sizing of the steel baseplate are provided.

N*c

c

ccc

This area not includedin bearing area

Bearing area

(a) General Case

≤ c≤ c

≤ c

(b) Short Projection (c) Large Projection

c c

c

c

Figure 15 Assumed bearing pressuredistributions specified in EC3 [23]

h Concretefoundation

Baseplate

Elevation

Plan

N*c

b1

a1

b

br

ar a

Figure 16 Column base layout [23]

4.3. RECOMMENDED MODEL

4.3.1. Design considerations

The recommended design model is a modified versionof the one proposed by Thornton in [43] and alsoadjusted to suit Australian Codes AS 3600 [10] and AS4100 [11]. The Thornton Model is currentlyrecommended by the AISC(US) Manual [5].Unfortunately the Thornton Model presented in [5],[42] and [43] is suitable for the design of H--shapedcolumns only. His formulation has been here modifiedfor H--shaped sections and extended for channels andhollows sections adopting a similar approach as in [43]which is outlined in Section 10.The modification to the Thornton Model introducedhere regards the manner in which Murray--StockwellModel is implemented. It is in the authors’ opinion thatthe calculation of AH and consequently of λ (refer to theliterature review for further details regarding thenotation) should be calculated based on N*

c (total axialcompression load) and not N*

0 (portion of the total loadN*

c acting over the column footprint under theassumption of uniform bearing pressure). This intendsto ensure that Murray--Stockwell Model would governthe design only for base plates of similar dimensions tothe ones of the connected columns and for lightly loadedcolumns, which represents the actual base plate layoutfor which the model has been developed. The designwould then be based on only one assumed pressure


distribution. Calculating AH based on N*0 could lead to

the design situation for lightly loaded columns wherethe plate thickness is governed by Murray--StockwellModel even for plate dimensions larger than those of theconnected columns as the model would select thethinner plate between the ones calculated with FlingModel and with Murray--Stockwell Model.It is interesting to note how the assumed bearing area(H--shaped in the case of H--shaped column sections)could extend also beyond the footprint of the columnsection as shown in Fig. 17 in the case of H--shapedsections and hollow sections. [34] No specific designguidelines are provided in [34]. A similar pressureditribution is considered in the Eurocode 3 Model. [23]Nevertheless in the recommended model theapplication of Murray--Stockwell Model is alwayscarried out based on assumed bearing areas inside thecolumn footprint even for base plates with dimensionsgreater than the column’s depth and width as otherbearing distributions need to be validated by testings.

aaa aaa

bb

bb

b bb b

Ineffective areas

Figure 17 Possible assumed bearing areas (Ref.[34])

4.3.2. Design criteria

There are two different design scenarios which areconsidered here:

the column is prepared for full contact inaccordance with Clause 14.4.4.2 of AS 4100 [11]and the axial compression may be assumed to betransferred by bearing. Design requirements are asfollows:

Ndes.c= [ÔNc ; ÔNs]min≥ N*c (24)

the end of the column is not prepared for fullcontact and the welds shall have sufficientstrength to carry the axial load. The designrequirements are as follows:

Ndes.c= [ÔNc ; ÔNs ; ÔNw]min≥ N*c (25)

where:Ndes.c = design capacity of the base plate connection

subject to axial compressionÔNc = design axial capacity of the concrete

foundationÔNs = design axial capacity of the steel base plateÔNw= design axial capacity of the weld connecting

the base plate to the column section

N*c = design axial compression load

4.3.3. Design Concrete Bearing Strength

The maximum bearing strength of the concrete Ôfb isdetermined in accordance with Clause 12.3 of AS 3600[10].


A1

, Ô2f′c (26)

where:Ô = 0.6A1 = bidi

The axial capacity of the concrete foundation ÔNc isthen obtained multiplying the maximum concretebearing strength Ôfbby thebaseplate area Ai as follows:

ÔNc= ÔfbAi

It is interesting to note from equation (26) thatincreasing the supplementary area A2 increases theconcrete confinement which yields larger designcapacities ÔNc. The loss of bearing area due to thepresence of the anchor bolt holes is normally ignored.[21]

4.3.4. Steel Base Plate Design

The base plate thickness required to resist a certaindesign axial compression N*

c is calculated as follow:

ti= am2N*c

0.9fyi di bi (27)

where:


λ= min1, k X

1+ 1− X X= YN*

c

a1, a2, a4, k and Y are tabulated in Table 3.

When X is greater than 1, λ should be taken as 1.


Table 3 Values for the design and check specified by the recommended model for axial compression.

Section a1 a2 a4 k Y a5

H--shapedsections

di− 0.95dc2

bi− 0.80bfc2

dcbfc4 2

dibidcbfc 4N*

c

Ôfba25bfc+ dc

Channels di− 0.95dc2

bi− 0.80bfc2

2dcbfc3

32

dibidcbfc 8N*

c

Ôfba252bfc+ dc

RHS di− 0.95dc2

bi− 0.95bc2

2dibi23 1.7

dibidcbfc 4N*

c

Ôfba25bc+ dc

SHS di− 0.95bc2

bi− 0.95bc2

bc3

32dibibc

4N*c

Ôfba252bc

CHS di− 0.80d02

bi− 0.80do2

d02 3

2 dibid0

4N*c

Ôfbπd20−

Thicknesses of base plates with dimensions similar tothose of the connected column section calculated withequation (27) might be quite thin, especially in the caseof lighlty loaded columns (where Murray--StockwellModel applies). It is therefore recommended to specifyplate thicknesses not less than 6mm thick for generalpurposes and not less than 10mm for industrialpurposes.Similarly a procedure to evaluate/check the capacity ofan existing plate is carried out as follows:

ÔNs=0.9fyi dibi t2i

2a′m2 (28)

where:

λ′ = max1,1k22 k a4ti Y

20.9fyidibi − 1

a′m= maxa1, a2,a4λ

a1, a2, a4, k and Y are tabulated in Table 3.This model is applicable to column sections as outlinedin Table 3 with the exception of H--shaped sections forwhich bfc∕2 is greater than dc as a different yield linepattern from those considered would occur.

4.3.5. Weld design at the column base

The design of the weld at the base of the column iscarried out in accordance with Clause 9.7.3.10 of AS4100. [11] The weld is designed as a fillet weld and itsdesign capacity ÔNw is calculated as follows:

ÔNw= ÔvwLw= Ô0.6fuwttkrLw (29)

where:Ôvw = design capacity of the fillet weld per unit

lengthÔ = 0.8 for all SP welds except longitudinal fillet

welds on RHS/SHS with t < 3 mm (Table 3.4 ofAS 4100)0.7 for all longitudinal SP fillet on RHS/SHSwith t < 3 mm (Table 3.4 of AS 4100)

0.6 for all GP welds (Table 3.4 of AS 4100)fuw = nominal tensile strength of weld metal (Table

9.7.3.10(1) of AS 4100)tt = design throat thicknesskr = 1 (reduction factor to account for length of

welded lap connection)Lw = total length of fillet weld

Refer to Section 13. for tabulated values of the designcapacity of fillet welds Ôvw.

5. AXIAL TENSION

5.1. INTRODUCTION

There is notmuchguidance available in literature for thedesign of unstiffened base plates subject to uplift.The literature presented here outlines the availableguidelines for the design of base plates and of anchorbolts. Twomodels presented here for the design of baseplates for hollowsections,which are the IWIMMModel(named here after its authors) and Packer--BirkemoeModel, were firstly derived for bolted connectionsbetween hollow sections. [37] and [36] suggest theirsuitability also for the design of base plates. Thesemodels include also guidelines for determining therequired number of anchor bolts. Such guidelines areincorporated in the literature review for the design of thesteel base plates as their application is only suitable forthe particular base plate model they refer to and as theydo not account for the interaction between the anchorbolts and the concrete foundation, which is dealt with inthe literature review on anchor bolts.

5.2. BASE PLATE DESIGN -- LITERATUREREVIEW

The models presented here differ for their assumptionsregarding the failure modes investigated. It isinteresting to note that the design guidelines currentlyavailable deal with a limited number of base platelayouts.For each model outlined here, the column sections andthe number of bolts considered by the model arespecified after the model name.


5.2.1. Murray Model(H--shaped sections with 2 bolts)

In [32] Murray presents a design procedure for baseplates of lightly loaded H--shaped columns with onlytwo anchor bolts subject to uplift. He also notes that tohis knowledge no studies have been published on thedesign of lightly loaded column base plate subjected touplift loading prior to his [32]. His design model isbased on yield line analysis and the yield line patternassumed is shown in Fig. 18.The expressions of the internal and externalwork can bewritten as follows:

Wi= Ômp 2bfc 2b′ + 1b′ 4

2bfc

= Ômp4b′2+ 2b2fc

b′bfc(30)

We=N*

t

2sg22bfc=

N*t sg

2bfc(31)

where:

N*t = design tension axial load

sg and b′ = as defined in Fig. 18Equating the external and internal work the expressionof Ômp can be written as follows:

Ômp=N*

t

2sgbfc

b′bfc4b′2+ 2b2fc

(32)

The value of b′ which maximises the required plateplastic capacity is obtaineddifferentiating equation (32)for b′ and is equal to:

b′ =bfc2

(33)

Thepresence of the flanges requires b′ to remain alwaysless or equal to dc∕2 and therefore the value of b′whichmaximises the plate plastic capacity varies dependingupon the column cross--sectional geometry as follows:

b′ =bfc2

forbfc2≤ dc

2(34)

b′ = dc2

forbfc2≥ dc

2(35)

Theminimumplate thicknesses required under a certainaxial load N*

t are obtained substituting equations (34)and (35) into equation (32) as shown below:

ti≥N*tsg 2

0.9fyibfc4 for

bfc2≤ dc

2(36)

ti≥N*tsgdc

0.9fyi(d2c+ 2b2fc)

forbfc2≥ dc

2(37)

Murray carried out a finite element study to investigatethe adequacy of the proposed model. He also validatedthe reliability of equations (36) and (37) using limited

experimental results, which consisted of 4 base platespecimenswith dimensions ranging from8” x 6” (203.2x 152.4 mm) to 12” x 8” (304.8 x 203.2 mm) andthicknesses varying from 0.364 in. (9.246mm) to 0.377in. (9.576 mm).This method is included in the design modelrecommended by the current AISC(US) Manual [5].

bfc∕2

bfc∕2

dc∕2 dc∕2

b′b′

b′ = 2 (bfc∕2)≤ dc∕2

bfc∕2b′ b′

sg∕2sg∕2

1 unit

Figure 18 Murray Model Assumed Yield LinePatterns (Ref. [32])

5.2.2. Tensile Cantilever Model(Generic Model)

Tensile Cantilever Method, as it is referred here,assumes that the tension in the anchor bolts spreads outto act over an effective width of plate (be) which isassumed to act as a cantilever in bending ignoring anystiffening action of the column flanges.

dh

11

bt bt

bt

be

Figure 19 Tensile Cantilever Model (Ref. [26])

It can be applied to generic base plate layouts.Nevertheless it provides conservative designs as itignores the two way action of the base plates.Reference [47] suggests a 45 degree angle of dispersionas shown in Fig. 19. This is based on considerations ofelastic plate theory as described in reference [13].The designmoment and the designmoment capacity arethen calculated as:

m*t =

N*t

nbbt (38)

Ôms=0.9be t2i fyi

4(39)

where:

m*t = design moment per unit width due to N*

t


nb = number of anchor boltsbt =distance fromfaceofweb to anchorbolt locationdh = diameter of the bolt holebe = 2bt+ dh

The axial capacity of the base plate can then bedetermined equating the designmoment and the sectionmoment capacity as follows:

N*t ≤

0.9fyibet2i4

nbbt

(40)

or equivalently the minimum base plate thickness tiunder a certain loading condition is calculated as:

ti=4N*

t bt0.9fyi be nb (41)

5.2.3. IWIMMModel(CHS with varying number of bolts)

The IWIMM Model has been named here after theinitials of the authors of the model. [27] The model wasfirstly derived for the design of CHS boltedconnections. [37] and [36] suggest its use also for thedesign of base plates of CHS columns.The base plate layout considered by thismodel is shownin Fig. 20.The plate thickness is calculated based on the designaxial tension load N*

t as follows:

ti≥2N*

tÔfyi π f3 (42)

where:Ô = 0.9d0 = outside diameter of a CHStc = thickness of column section

f3=12k1k3+ k23− 4k1

k1= lnr2r3k3= k1+ 2

r2=d02+ a1

r3=d0− tc

2a1 and a2 as defined in Fig. 20

[27] recommends to keep the value of a1 as small aspossible, i.e. between 1.5df and 2df (where df is thenominal diameter of the bolts), while ensuring aminimum of 5 mm clearance between the nut face andthe weld around the CHS.

N*t

a1do

ti ti

a2

N*t

Figure 20 Bolted CHS Flange--plate Connection(Ref. [36])

[27] also recommends to determine the number ofrequired anchor bolts as follows:

nb≥N*t

ÔNtf1− 1

f3+ 1

f3 lnr1r2

(43)

where:Ô= 0.9Ntf = nominal tensile capacity of the bolt

r1=d02+ 2a1

r2=d02+ a1

a1= a2This procedure does not verify the capacity of theconcrete foundation and its interaction with the anchorbolts needs to be checked.Assumptions adopted by this model are an allowancefor prying action equal to 1/3 of the ultimate capacity ofthe anchor bolt (at ultimate state), a continuous baseplate, a symmetric arrangement of the bolts around thecolumn profile and a weld capacity able to develop thefull yield strength of the CHS.[28] notes that adopting the above prying coefficient forthe bolted CHS connection in the base plate design isconservativedue to thegreater flexibility of the concretefoundation when compared to the steel to steelconnection. [36]

5.2.4. Packer--Birkemoe Model(RHS with varying number of bolts)

The Packer--Birkemoe Model is here named after theauthors of the model. [36] This model deals with baseplate for RHS as shown in Fig. 21 and it has beenvalidated only for base plates with thickness varyingbetween 12mm and 26mm.The model includes prying effects in the designprocedure. The prying action decreases whileincreasing a2as shown inFig. 21.Thevalueof a2shouldbe kept less or equal to 1.25 a1, as no benefit in the baseplate performance would be provided beyond suchvalue. a1 is defined as the distance between the bolt lineand the face of the hollow section.Generally 4--5 bolt diameters are used as spacing of thebolts sp but shorter spacing are also possible.

Based on the design loads the required number ofanchor bolts should be calculated assuming that the


prying action absorbs about 20--40% of the anchor boltcapacity. The coefficient δ is then calculated as follows:

δ= 1−dhsp (44)

where:sp = bolt pitch as defined in Fig. 21

The designer should then select a preliminary platethickness in the following range:

KN*b

1+ δ ≤ ti≤ KN*

b (45)

where:

K=4a3103

Ôfyisp(where fyi is in MPa)

a3= a1− df∕2+ tcN*b = design axial tension load carried by one bolt

=N*t

nbdf = nominal anchor bolt diameter

The value of α represents the ratio of the bendingmoment per unit width of plate at the bolt line to thebending moment per unit width at the inner hoggingplastic hinge. In the case of a rigid base plate α is equalto 0 while for a flexible base plate with plastic hingesforming at both the bolt line and at the inner face of thecolumn (see Fig. 21) α is equal to 1. From equilibrium,the value α for preliminary base plate layout iscalculated as follows:

α= KÔNtft2i− 1 a2+ df∕2

δ(a2+ a1+ tc) (46)

α should be taken as 0 if its value calculated withequation (46) is negative.The capacity of the steel base plate is then calculated asfollows:

ÔNt=t2i(1+ δα)nb

K (47)

where:ÔNt = axial tension capacity of the base plate

ÔNt calculated with equation (47) must be greater thanN*t. The actual tension in one bolt, including prying

effects, is determined as follows:

N*b≈

N*t

nb1+ a3

a4 δα1+ δα (48)

where:

α= KN*t

t2i nb− 1 1

δ

a4= min1.25a1, a2+df2

The value of α previously calculated in equation (46)does not have to equal the value of α calculated fromequation (48) as the former assumes the bolts to beloaded to their full tensile capacity.It interesting to note how equation (48) provides anestimate of the prying action present in the base plate.

a1

a3

= = = =

tc

N*t

= =

N*t

sp

a2

a4

sp

Figure 21 Packer--Birkemoe Model (Ref. [36])

5.2.5. Eurocode 3 Model(H--shaped sections with varyingnumber of bolts)

The Eurocode 3 does not provide a specific designprocedure for the design of base plates subject totension. Nevertheless it provides very useful guidelinesfor the design of bolted beam--to--column connections(Appendix J.3 of [23]) which can be adapted for thedesign of base plates considering all anchor bolts asbolts on the tension side of the beam--to--columnconnection.The design of the end plate or of the column flange ofthe beam--to--column connection is carried out in termsof equivalent T--stubs as shown in Fig. 22.

eme

m 0.8a 2

a

emin

tf

tf

0.8re m

emin

r

l

Figure 22 T--stub connection in EC3 (Ref. [23])

EC3 considers that the capacity of a T--stub may begoverned by the resistence of either the flange, or thebolts, or the web or the weld between flange and web ofT--stub. The failure modes considered are three asshown in Fig. 23. The axial capacity is calculated asfollows:


Ft.Rd= minFt.Rd1, Ft.Rd2, Ft.Rd3 (49)

where:

Ft.Rd1=4Mpl.Rdm

Ft.Rd2=2Mpl.Rd+ nΣBt.Rd

m+ nFt.Rd3= ΣBt.Rd

Mpl.Rd=0.25lt2ffyγMO

n= emin≤ 1.25ml = equivalent effective length calculated in

equations (50), (51), (52) and (53)

ΣBt.Rd = tensile capacity of bolt groupγMO = partial safety factor

= 1.10 (boxed value from Table 1 of [23])Ft.Rd1, Ft.Rd2 and Ft.Rd3 = tensile capacities of the

T--stub based on failure modes 1, 2 and 3respectively

Mode 1: Completeflange yielding

Mode 2: Bolt failurewith flange yielding

Mode 3: Bolt failure

Ft

Ft

Ft

Q Q

QQ

Ft2 + Q Ft

2 + Q

Bt∕2Bt∕2

Bt∕2Bt∕2

Figure 23 Failure modes of a T--stub flange(Ref. [23])

It is interesting to note that the amount of prying actionfor a certain baseplate layout canbeobtained as the ratioFt.Rd∕ΣBt.Rd as shown in Fig. 24.

2λ1+ 2λ

2λ1+ 2λ

1 2

Mode 3

Mode 2

Mode 1

1

FBt.Rd

λ = n∕m β =4MplRd

mBt.Rd

=l t2f fy∕γMOmBt.Rd

β

Figure 24 Prying action in T--stub for the threefailure modes considered in (Ref.[23])

The tension zone of the end plate should be consideredto act as a series of equivalentT--stubswith a total lengthequal to the total effective length of the bolt pattern inthe tension zone, as shown in Fig. 26.[23] The length tobe utilised in the design of the equivalent T--stub iscalculated as follows:

for bolts outside the tension flange of the beam

leff.a= min0.5bp, 0.5w+2mx+0.625ex,4mx+1.25ex, 2πmx) (50)

for first row of bolts below the tension flange ofthe beam

leff.b= min(αm, 2πm) (51)

for other inner bolts

leff.c= minp, 4m+ 1.25e, 2πm (52)

for other end bolts

leff.d=min(0.5p+2m+0.625e, 4m+1.25e, 2πm) (53)

where:α = as defined in Fig. 27

It is interesting to note that the failuremodes consideredfor example by equations (52) and (53) are the same asthose considered to evaluate the capacity of anunstiffened flange. The yield line patterns of suchfailure modes are shown in Fig. 25.


em

p p

Centreline of web

Centreline of web

Centreline of web

(a) Combined bolt group action

(b) Separate bolt patterns

(c) Circles around each bolt

Figure 25 Yield line patterns for unstiffenedflange (Ref. [23])

Transformation of extension to equivalent T--stub

Equivalent T--stubfor extension

Portion between flanges

bpw

exmx

p

p

e mme

ex mx

leff.a

leff.b

leff.c

leff.d

bp bp∕2 leff.a

leff.a

Figure 26 Effective lengths of equivalent T--stubflanges representing an end plate(Ref. [23])

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

2π 65.554.75

4.54.45

λ2

α

λ1=m1

m1+ e

λ2=m2

m1+ e

e m1

m2

λ1

Figure 27 Value of Effective lengths of α tocalculate equivalent T--stub flanges(Ref. [23])

5.3. DESIGN OF ANCHOR BOLTS --LITERATURE REVIEW

Available design guidelines regarding the behaviour ofanchor bolts in tension distinguish between thebehaviour of anchor bolts with an anchor head and ofhooked anchor bolts and therefore these will bediscussed here separately. For the purpose of this paperan anchor head is defined as a nut, flat washer, plate, orbolt head or other steel component used to transmitanchor loads from the tensile stress component to theconcrete by bearing. [2]

5.3.1. Anchor bolts with anchor head

The first detailed guidance on the design of anchor boltsis provided by the American Concrete InstituteCommittee 349 in 1976 in [3]. These recommendationsare produced for the design of nuclear safety relatedstructures. Some of the ACI Committee 349 members,very active in the preparation of [3], publish an article[17] where the guidelines provided in [3] are modifiedto suit concrete structures in general.


The design criteria at the base of [2] and of [17] is thatanchor bolts should be designed to fail in a ductilemanner, therefore the anchor bolt should reach yieldingprior to the concrete brittle failure. This is achieved byensuring that the calculated concrete strength exceedsthe minimum specified tensile strength of the steel.[2][17]Typical brittle failure of an isolated anchor bolt is bypulling out of a concrete cone radiating out at 45 degreesfrom the bottom of the anchor as shown in Fig. 28. [2]and [17] recommend to calculate its nominal concretepull--out capacity based on the tensile strength Ô4 f′c(where f′c is in psi) or Ô0.33 f′c (where f′c is in MPa)acting over an effective area which is the projected areaof the concrete failure cone.In both [3] and [17] it is recommended to use a capacityreduction factorof0.65 in the calculationof the concretecone capacity,which can be increased to 0.85 in the casethe anchor head is beyond the far face reinforcement.The value of 0.65 applies to the case of an anchor boltin plain concrete. This intends to be a simplification ofa very complex problem. [3][17]In the current version of ACI349 [2] the capacityreduction factor is equal to 0.65 unless the embedmentis anchored either beyond the far face reinforcement, orin a compression zone or in a tension zone where theconcrete tension stress (based on an uncracked section)at the concrete surface is less than the tensile strength ofthe concrete 0.4 f′c subjected to strength loadcombinations calculated in accordance with currentloading codes (i.e. AS1170.0 [8]) in which cases acapacity reduction factor of 0.85 can be used. [2] Anembedment is defined in [2] as that steel componentembedded in the concrete used to transmit applied loadsto the concrete structure. The ACI Committee 349recognises that there is not sufficient data to definemoreaccurate values for the strength reduction factor. [2]Experimental results have generally verified the resultsof this approach. [31]

The value of Ô0.33 f′c represents an average value ofthe concrete stress on the projected area accounting forthe stress distribution which occurs along the failurecone surface varying from zero at the concrete surfaceto a maximum at the bolt end. [31] In calculating theprojected area of the failure cone the area of the anchorhead should be disregarded as the failure cone initiatesat the outside periphery of the anchor head. [2]Experimental results have shown that the head of astandard bolt, without a plate or washer, is able todevelop the full tensile strength of the bolt provided, asspecified in [2], that there is a minimum gross bearingarea of at least 2.5 times the tensile stress area of theanchor bolt and provided there is sufficient side cover,

that the thickness of the anchor head is at least 1.0 timesthe greatest dimension from the outermost bearing edgeof the anchor head to the face of the tensile stresscomponent and that the bearing area of the anchor headis approximately evenly distributed around theperimeter of the tensile stress component. [2]The placing of washers or plates above the bolt head toincrease the concrete pull--out capacity should beavoided as it only spreads the failure cone away from thebolt--line which may cause overlapping of cones withadjacent anchors or edge distance problems. [31]

Ld

Ld

45o

Failureplane

Projected surface

Figure 28 Concrete failure cone (Ref. [26])

If reinforcement in the foundation is extended into thearea of the failure cone additional strength would bepresent in practice since the nominal capacity of thefailure cone is based on the strength of unreinforcedconcrete.The concrete pull--out capacity of a bolt group iscalculated as the average concrete tensile strengthÔ0.33 f′c times the effective tensile area of the boltgroup. This effective area is calculated as the sum of theprojected areas of each anchor part of the bolt group ifthese projected areas do not overlap; when overlappingoccurs overlapped areas should be considered only oncein the calculation of the effective tensile area, thusleading to a smaller concrete pull--out capacity ifcompared to the sum of the concrete pull--out capacitiesof each anchor in the bolt group considered in isolation.[2][17]


= πL2d−

2cos−1 s2LdπL2

d

3600+ s

2 L2d−

s24

ShadedArea

(a) Two Intersecting Failure Cones

LdLd

ss

= πL2d−

2cos−1 s2LdπL2

d

3600+ s

2 L2d−

s24

Area

Circle -- Sector + Triangle(b) Failure Cone Near an Edge

s2

Ld

Ld

− Ld

+ Ld

=

(Note: the inverse cosine term listed in theequations is in degrees)

Figure 29 Calculation of the projected area oftwo intersecting failure cones or onefailure cone near an edge (Ref. [30])

Simple procedures to calculate the effective tensileareas of bolt groups are provided in [30], i.e. theprocedure to calculate two intersecting cones is shownin Fig. 29. [30]Depending upon the bolt group layout other possiblefailure modes could take place such as the one shown inFig. 30 where an entire part of the concrete foundationwould pull--out. In such cases the effective tensile areashould be calculated selecting the smallest projectedarea due to the possible concrete failure surfaces asshown in Fig. 30. A similar average tensile strength asin the case of the pull--out cones can be adopted. [2][17]

Tension Force

Figure 30 Potential Failure Modewith limited depth (Ref. [2])

Transverse splitting is another failure mode which canoccur between anchor heads of an anchor bolt groupwhen their centre--to--centre spacing is less than theanchor bolt depth and is shown in Fig. 31. This failuremodeoccurs at a load similar to theone required to causea pull--out cone failure in uncracked concrete andtherefore no additional design checks need to beconsidered. [2][17]

Tension Force

Transversesplitting

Figure 31 Transverse splitting failure mode(Ref. [2])

It is interesting to note that in the case of shallow anchorbolts the angle at the bolt head formed by the failurecone tends to increase from 90 degrees to 120 degrees.An anchor bolt is classified as shallow when its lengthis less than 5in. (127 mm). Nevertheless for designpurposes caution should be applied is using anglesgreater than 90 degrees as cracksmight be present at theconcrete surface. It is recommendednot use anglesotherthan 90 degrees. [2][17]The previous considerations assume the concreteelement to be stress--free and only subjected to theanchor bolts loading. [2] and [17] consider the casewhen there is a state of biaxial compression and tensionin the plane of the concrete. The former loadingcondition would be beneficial to the anchor bolt’sstrength while the latter loading state would lead to asignificantly decrease in strength. Nevertheless, it is inthe opinion of the ACI 349 Committee that a failurecone angle of 90 degrees can still be utilised as it isassumed that any cracking would be controlled by themain reinforcement designed in accordance withcurrent concrete codes, i.e. AS 3600 [10].The design procedure proposed by ACI 349 and [17] isalso recommended by DeWolf in [21].[21] notes that the use of cored holes, such as shown inFig. 32, should not reduce the anchorage capacity basedon the failure cone, provided that the coredhole doesnotextend near the bottom of the bolt. This situation shouldbe avoided if the dimensions shown in Fig. 32 arefollowed. [26]

but≥ 75mm

df

3df

Ld

Projection

Figure 32 Suggested layout for Cored Holesto Permit Minor Adjustments inPosition on Site (Ref. [26])


45o Blow outcone

Failuresurface

45o

Figure 33 Failure Surface of Blow--out Conedue to Lateral Bursting of theConcrete (Ref. [31])

Lateral bursting of the concrete can occur when ananchor bolt is located close to the concrete edge asshown in Fig. 33, which is caused by a lateral forcepresent at the bolt head location.This lateral force may be conservatively assumed to beone--fourth of the nominal tensile capacity of the anchorbolt for conventional anchor heads which can becalculated in accordancewithClause9.3.2.2ofAS4100[11] as follows:

Ntf= Asfuf= 0.75A0fuf= 0.75d2f π4

fuf (54)

where:As = tensile stress area in accordance with AS1275

[9] and conservatively approximated with 0.75A0

A0=d2f π4

= shank area

fuf = minimum tensile strength of a boltThe failure surface has the shape of a cone whichradiates at 45 degrees from the anchor head towards theconcrete edge.The concrete capacity is calculated as theaverage concrete tensile strength Ô0.33 f′c appliedover the projected cone area as follows: [2][3][17]

ÔNc.lat= Ô0.33 f′c π a2e (55)

where:Ô = 0.65 in Ref. [3], 0.85 in Refs. [2] and [17]ÔNc.lat = lateral bursting capacity of the concreteae = side cover

Equating the assumed lateral force (equal to 0.25 Ntf) tothe concrete lateral bursting capacity allows to expressthe minimum required side cover as a function of boththe concrete and anchor bolt strengths as shown below:

0.25Ntf= ÔNc.lat= Ô0.33 f′c π a2e (56)

and solving equation (56) for ae yields:

ae= dffuf

Ô7 f′c (57)

where:

Ô = 0.65 in Ref. [3],= 0.85 in Refs. [2] and [17]

Adopting the capacity reduction factor Ô equal to 0.85the minimum side cover to avoid lateral bursting of theconcrete can be calculated as follows:

ae= dffuf

6 f′c (58)

Equation (58) has also been recommended in [26] and[47].

Tension Force

Spiralreinforcement

PotentialFailureZone

Figure 34 Reinforcement Against LateralBursting of Concrete Foundation(Ref. [2])

Based on the guidelines provided in reference [3],simplified design guidelines regarding minimumembedment lengths and minimum edge distances arepresented in reference [39]. These minimumembedment lengths are calculated with an additionalsafety factor of 1.33 when compared to the guidelinespresented in reference [3]. These simplified guidelinesare as follows:

for Grade 250 bars and Grade 4.6 bolts:Ld ≥ 12dfae = min(100, 5df)for Grade 8.8 bolts:Ld ≥ 17dfae = min(100, 7df)

where:Ld = minimum embedment length

Theseminimumembedment lengths and edge distanceshave also been recommended in references [18], [21]and [26].Reinforcement needs to be specified in the case anchorbolts are located too close to a concrete edge (the edgedistance ae is less than the one required by equation(58)) or their embedment length is less than the onerequired to develop the bolt’s full tensile strength. Suchreinforcement should be designed and located tointersect potential cracks ensuring full developmentlength of the reinforcement onboth sides of such cracks.The placement of the reinforcement should beconcentric with the tensile stress field. [2]


In the specific case of insufficient embedment length apossible reinforcement layout to enhance the concretepull--out capacity is detailed in Fig. 35 using hairpinreinforcement. The hairpins need to be placed asspecified in Fig. 35 in order to effectively interceptpotential failure planes. Other reinforcementconfigurations can be specified in accordance with AS3600 while still complying with the specificationspreviously outlined for hairpin reinforcement toconsider the reinforcement to be effective. Thesespecifications are the maximum distance from theanchor head and theminimum embedment length equalto 8 reinforcement diameters.

Tension Force

Ld

Ld

3

Ld

3

8x diameter of thehairpin reinforcement

Development lengthfrom AS3600

Maximum distance fromanchor head for reinforcementto be considered effective

Locate legs of hairpinreinforcement in this region

Figure 35 Possible Placement of Reinforcementfor Direct Tension (Ref. [2])

In the case of insufficient side cover ae there are noexperimental results to validate a design procedure toinclude reinforcement to avoid lateral bursting of theconcrete. The ACI 349 Committee recommends the useof spiral reinforcement as shown in Fig. 34 while alsosuggesting to refer to accepted practices for prestressinganchorages to resist the lateral bursting force. [2][2] and [17] recommend that if proper anchorage of thereinforcement cannot be accomplished in the availabledimensions, the anchorage configuration should bechanged.

5.3.2. Hooked bars

There are different opinions regarding the ability ofhooked anchor bolts to carry tensile loading. Someauthors do not recommend to use them to resist upliftloads, while others have provided some designguidelines.The major concern regarding the use of hooked bars intension is that they tend to fail by straightening andpulling out of the concrete as shown by research carriedout by the PCI.[24][24] and [31] discuss the behaviour of smooth anchorbolts and recommend to use hooked anchor bolts witha bearing head as smooth bars are less able to developtheir strength along their length than deformed bars.[24] recommends to use the following formula todetermine thepull--out capacityof ahookedanchorbolt:

ÔNth= 0.7f′cdf Lh (59)

where:Ô = 0.80 (as recommended in [26])ÔNth = tensile capacity of a hooked bardf = nominal diameter of the hooked barLh = length of the hook

DeWolf in [22] recommends to use hooked anchor boltsonly under compressive axial loading, and where nofixity is needed at the base except during erection. Evenfor this case he recommends to design the hook to resisthalf thedesign tensile capacityof thebolt usingequation(59). He also recommends to use anchor bolts with amore positive anchorage which is formed when bolts orrods with threads and nut are used. [22] Similar designconsiderations are presented in reference [47].The recommendations of the AISC(US) Manuals havechangedover time. In reference [6] thedesign ofhookedanchor rods under tension is recommended to be carriedout based on the design procedure presented in [24] asoutlined in equation (59) while in reference [5] the useof hooked anchor rods is recommended only for axiallyloaded members subject to compression only.


5.4.1. Introduction

Available design guidelines have been included in therecommended design models where possible.Additional design models/provisions are here providedfor those instances, to the knowledge of the authors, notcovered by available design guidelines. Their use hasbeen clearly stated and their derivations are illustratedin Section 11.It is interesting to note that depending upon themagnitude of the plate flexural deformation and the boltelongation which occur in the loaded base plateconnection, a prying action might be present.The possible collapse mechanisms which can occur aresimilar to those which can occur in bolted connections.These are shown in Fig. 36.

N*tN*

bN*t N*

tN*b N*

b

N*p N*

p

Schematic failure modes

Bending moment diagramsshowing plastic hinges

Figure 36 Possible plate deformationsand anchor bolt elongations(modified from Ref.[13])

In the case the plate flexural deformation is smaller thanthe bolt elongation no prying actionwould take place asshown in Fig. 36(a). In the case the plate flexural


deformation is of similar or of greater magnitude as thebolt elongation, as shown in Fig. 36(b) and (c), pryingactions N*

p should be accounted for in the design.Possible bending moment diagram occurring in theplate in all three collapsemechanisms are also shown inFig. 36. [13]For design purposes the use of a prying factor of 1.4 isconservatively recommended as suggested in [37] and[36].

5.4.2. Design Criteria

The recommended model for axial tension is based onthe following design criteria:

Ndes.t= [ÔNt ; ÔNw ; Ô ÔpNtb]min≥ N*t (60)

with the following constraint to ensure a ductile failureof the anchorage system (connection of anchor bolt toconcrete):

ÔNcc> ÔNtb (61)

and complying with the anchor bolts’ embedmentlengths and concrete edge distances specified inSections 5.4.5. and 5.4.6. andwhere:

Ndes.t = design capacity of the base plate connectionsubject to axial tension

ÔNt = design tensile axial capacity of the steel baseplate

ÔNw= design axial capacity of the weld connectingthe base plate to the column

ÔNtb = design capacity of the anchor bolt groupunder tension

Ôp = 1/1.4 = 0.72 prying reduction factor asrecommended in references [36] and [37] unlessnoted otherwise in 5.4.3.

ÔNcc = design pull--out capacity of the concretefoundation

N*t = design axial tension load

5.4.3. Anchor bolt design

The tensile design capacity of the anchor bolt groupÔNtb is calculated in accordance with Clause 9.3.2.2 ofAS4100 [11] as the sum of the design capacities of eachsingle bolt ÔNtf.

ÔNtb= nbÔNtf= nbÔAsfuf (62)

where:Ô = 0.8

Refer to Section 14. for tabulated values of the tensilecapacities of anchor bolts.In the case the base plate is designed based onPacker--Birkemoe Model the preliminary number ofbolts required is obtained from equation (62) which isthen refined in the section describing the steel plate

design. Once the steel plate design is complete thecapacity of the anchor bolt groups needs to bere--checked. The value of Ôp to be adopted in the Packer-- Birkemoe model is specified in equation (95).In the case the design of the base plate is carried out baseon IWIMM Model (refer to Section 5.4.7.) the tensiledesign capacity of the anchor group should becalculated as follows:

ÔNtb=nbÔNtf

1− 1f3+ 1

f3 lnr1r2(63)

where:Ô= 0.9Ôp= 1 to be used in equation (60) as prying effects

are already included in equation (63)

r1=d02+ 2a1

r2=d02+ a1

a1= a2 (condition to apply equation (63))

f3=12k1k3+ k23− 4k1

k1= lnr2r3k3= k1+ 2

r2=d02+ a1

r3=d0− tc

2a1, a2 and d0 are defined in Fig. 20

5.4.4. Design of concrete pull--out capacity

The pull--out capacity of the concrete ÔNcc variesdepending upon the anchor bolts layout and it can becalculated in accordance with AS 3600 as follows:

ÔNcc= Ô0.33 f′c Aps (64)

where:Ô = 0.7 (based on Ô required for Clause 9.2.3 of AS

3600)Aps = effective projected area

Equation (64) is similar to the expression provided inClause 9.2.3 of AS 3600 to calculate the concretecapacity of a slab against punching shear, whichinvolves a similar failure mechanism as the one of thepull--out cone.Thevalueof βh tobecalculated inClause9.2.3 of AS 3600 would be equal to 1 as the shape of theeffective loaded area is a circle. AS 3600 recommendsa strength reduction factor under shear of 0.7 (Table 2.3of AS 3600).The capacities of a few common bolt layouts as shownin Fig. 37 are here outlined. [47]


L1

L145o

Projectedarea

L2

L2

s

Single Cone Two Intersecting Cones(a) (b)

L4

s

L4

Four IntersectingCones

(c)

Figure 37 Common bolt layouts (Ref. [47])

The effective projected areas of each anchor bolt layoutshown in Fig. 37 is calculated as follows:Aps.1 = effective projected area of isolated anchor bolt

(nooverlappingof failure cones) as shown inFig.37(a)

= πL21

Aps.2 = effective projected area of 2 anchor bolts withoverlapping of their failure cones as shown inFig. 37(b);

= πd22×1− 2 cos−1(s∕2L2)360+ s

2L22− s2∕4

Aps.4 = effective projected area of 4 anchor bolts withoverlapping of their failure cones. In this caseeach failure cone overlaps with all other 3 failurecones as shown in Fig. 37(c).

= πd240.75− 2 cos−1(s∕2L4)360

+ s2

L24− s2∕4 + s2∕4

where the inverse cosine term is in degrees.

5.4.5. Concrete cover requirements

The cover requirements for an anchor bolt aredetermined in accordance with [2] and [17] in order toprevent lateral bursting of the concrete which can occurwhen a bolt is located close to a concrete edge as shownin Fig. 33.The minimum cover to be provided is calculated asfollows: [17][2]

ae= max100, dffuf

6 f′c (65)

Tabulated values of equation (65) are presented inSection 12.The following simplified expressions, which have beenderived in Section 12., can be used in place of equation(65) leading to slightly more conservative side coversthan those calculated with equation (65).

for Grade 4.6 bolts and Grade 250 rodsae = 4 df when f′c = 20, 25 and 32 MPa≥ 100 when f′c = 20, 25 and 32 MPa

for Grade 8.8 boltsae = 6 df when f′c = 20 and 25 MPa

= 5 df when f′c = 32 MPa≥ 100 when f′c = 20, 25 and 32 MPa

The requirement of a minimum side cover of 100mm isbased on recommendations of [21], [26] and [39].

5.4.6. Minimum embedment lengths

The recommended minimum embedment length Ld ofan anchor bolt is determined in accordance with thedesign guidelines specified in [2] adjusted to suit AS3600.

Edge of ConcreteFoundation

ae

Ld

Lh

Figure 38 Hook, embedment lengths and edgedistances for anchor bolts (Ref. [26])

The minimum embedment length Ld for an isolatedanchor bolt should be calculated as follows: (refer toFig. 38)

Ld=− d2f+ d2f+ 4γ

2 ≥ 100 (66)where:

Ô = 0.7 (based on Ô in Clause 9.2.3 of AS 3600)

γ =fufAs

Ô0.33 f′c π

Even if it has been observed that for shallow anchors theangle at the bolt head formed by the concrete failurecone tends to increase from 90 degrees to 120 degrees(therefore increasing the concrete pull--out capacity) aminimum limit of 100mm is here introduced in equation(66) as cracks might be present at the concrete surface.Refer to Section 12. for the derivation of equation (66)and of the simplified expressions shown below whichcan be used in place of equation (66).

for Grade 4.6 bolts and Grade 250 rods


Ld = 9 df when f′c = 20, 25 and 32MPafor Grade 8.8 boltsLd = 13 df when f′c = 20 MPa

= 12 df when f′c = 25 MPa= 11 df when f′c = 32 MPa

Hooked anchor bolts, as shown in Fig. 38, need to bedetailed with a minimum embedment length asspecified for bolts with an anchor head of same nominaldiameter (specified by equation (66) or by its alternativesimplified expressions) and with a minimum hooklength calculated as follows:[24][26]

Lh≥Asfuf0.7f′cdf

(67)

where:Lh = hook length of anchor bolt

The anchorage length (embedment length and hooklength) should be such as to prevent bond failurebetween the anchor bolt and concrete prior to yieldingof the bolt. When possible, a more positive anchorageshould be adopted at the end of the hook, for example bymeans of a nut.

5.4.7. Design of the Steel Base Plate

The recommended procedure to design or check thesteel base plate varies depending upon the columnsection and number of bolts considered.Recommended models are illustrated below for thefollowing combinations of column section and numberof bolts:

H--shaped column section -- 2 anchor bolts (*)H--shaped column section -- 4 anchor bolts (*)Channel -- 1 anchor bolt (*)Channel -- 2 anchor bolts (*)Hollow section (RHS, SHS, CHS) -- 2 anchorbolts (*)Hollow section (RHS, SHS) -- 4 anchor bolts (*)Hollow section (CHS) -- varying no. of anchorbolts (IWIMM Model described in the literaturereview)Hollow section (RHS) -- varying no. of anchorbolts (Packer--Birkemoe Model described in theliterature review)

The derivation of the models marked with (*) isillustrated in Section 11. It is important to note that,similarly to Murray Model, in the case of open sectionsthe derivedmodels to determine the capacity of the steelbase plate capacity account only for the strength of platepresent inside the column footprint.The reduction in plate capacity due to the bolt hole hasbeen included in the model. The yield line patternsconsidered for open sections are assumed to developinside the internal faces of the column profile.

H--SHAPED COLUMN -- 2 anchor bolts

The yield line pattern considered by the recommendedmodel is shown in Fig. 39 and is similar to the oneconsidered inMurrayModelmodified to account for thereduction in plate capacity due to the anchor bolt holes.

s

y

y

bfc

dc12

dc12

Figure 39 Yield line pattern -- H--shaped columnsection with 2 anchor bolts

Theplate thickness required to resist a design axial forceÔN*

t is calculated as follows:

ÔNt= 0.9fyit2iα (68)

ti≥N*t

0.9fyiα (69)

y= mindc12 ,bfc1− dh

2 bfc1 (70)

where:ÔNt = axial tension capacity of the base platebfc1 = width of the column flange ignoring web

thickness= bfc− tw

dc1 = clear depth between flanges (column depthignoring thicknesses of flanges)

tw = thickness of webdh = diameter of bolt hole

α=2b2fc1− 2bfc1dh+ 4y2

4syy and s = as defined in Fig. 39

In this model the reduction in plate capacity due to thepresenceof a bolt hole along theyield lineperpendicularto the web has been included.Further reductions due to other yield lines intersectingbolt holes have not been considered as they are veryunlikely to occur and amore detailed analysis should becarried out in such situation.The critical yield line pattern is a function of the valueof y calculated from equation (70). To ensure that noneof the oblique yield lines intersects the bolt hole, asassumed in the model derived, the following conditionneeds to be satisfied:

y> l2 (71)

where:

l1=dh2 1−

d2h4s2

l2=

l1l3

s−d2h4 − l21


and the notation is defined in Fig. 40.

d2h∕4− l21

l1

l2

s

diameter of hole = dhWeb

Edge of plate

l3

Figure 40 Yield line layout near the bolt hole

H--SHAPED COLUMN -- 4 anchor bolts

The yield line patterns considered by the recommendedmodel are shown in Figs. 41, 42, 43, 44 and 45.In the case of yield line patterns (a), (b) and (c) thederived model does not assume that the oblique linesintersect the bolt hole. This should be verified andconsidered in a similarmanner as previously outlined inthe case of H--shaped column with 2 anchor bolts (referto equation (71) and Fig. 40).The recommended design procedure is as follows:


ti≥N*t

0.9fyiα (73)

y=bfc1− dh

2 bfc1 (74)

and the value of α is calculated as follows:

α = max(αa,αb) when y<sp2

= αb when y<sp2and y> ab

= max(αc,αd,αe) when y≥sp2

where:

αa=2b2fc1− 2bfc1dh+ 4y2

2sy

αb=bfc1(bfc1− dh)(ab+ y)+ 2(y+ ab)aby

2saby

αc=b2fc1− dhbfc1+ 2y2c+ spyc

2syc

αd=bfc1s− dhs+ 2y2d+ spyd− dhyd

syd

αe=bfc1s− 2dhs+ 4a2b+ 2absp− 2abdh

2abs

yc= minab, y

yd= minab, bfc1− dh2 s

ab = distance from bolt hole to inside face offlange

s

y

y

bfc

dc12

dc12

Figure 41 Yield line pattern (a) H sections

y

y

s

y

y

bfc

ab

spy

y ab

Figure 42 Yield line pattern (b) H sections

ab

y

s

y

bfc

ab

spy

Figure 43 Yield line pattern (c) H sections

y

s

y

bfc

ab

sp

y ab

Figure 44 Yield line pattern (d) H sections


y

s

bfc

ab

sp

y ab

Figure 45 Yield line pattern (e) H sections

s

bfc

ab

sp

ab

Figure 46 Yield line pattern (f) H sections

CHANNEL -- 1 anchor bolt

The yield line pattern considered by the recommendedmodel is shown in Fig. 47 and is similar to the oneconsidered in the case of H--shaped sections with 2anchor bolts.The derived model does not assume that the obliquelines intersect the bolt hole. This should be verified andconsidered in a similarmanner as previously outlined inthe case of H--shaped column with 2 anchor bolts (referto equation (71) and Fig. 40).

s

y

y

bfc

dc12

dc12

Figure 47 Yield line pattern -- Channel with 1anchor bolt

Theplate thickness required to resist a design axial forceÔN*

t is calculated as follows:


ti≥N*t

0.9fyiα (76)

y= mindc12, (2bfc1− dh)bfc1 (77)

where:

α=2b2fc1− bfc1dh+ y2

2syy and s = as defined in Fig. 47

CHANNEL -- 2 anchor bolts

The yield line patterns considered by the recommendedmodel are shown in Figs. 48, 49, 50, 51 and 52.In the case of yield line patterns (a), (b) and (c) thederived model does not assume that the oblique linesintersect the bolt hole. This should be verified andconsidered in a similarmanner as previously outlined inthe case of H--shaped column with 2 anchor bolts (referto equation (71) and Fig. 40).The recommended design procedure is as follows:


ti≥N*t

0.9fyiα (79)

y= (2bfc1− dh)bfc1 (80)


α = max(αa,αb) when y<sp2

= αb when y<sp2and y> ab

= max(αc,αd,αe) when y≥sp2

where:

αa=2b2fc1− bfc1dh+ y2

sy

αb=bfc1(2bfc1− dh)(ab+ y)+ (y+ ab)aby

2saby

αc=4b2fc1− 2dhbfc1+ 2y2c+ spyc

4syc

αd=2bfc1s− dhs+ 2y2d+ spyd− dhyd

2syd

αe=bfc1s− dhs+ 2a2b+ absp− abdh

2abs

yc= minab, y

yd= minab, 2bfc1− dh2 s


y

y

s

y

y

bfc

ab

spy

y ab

Figure 48 Yield lines (a) Channels, 2 bolts

y

s

y

bfc

ab

spy

ab

Figure 49 Yield lines (b) Channels, 2 bolts

y

s

bfc

ab

sp

y ab

Figure 50 Yield lines (c) Channels, 2 bolts

y

s

bfc

ab

sp

y ab

Figure 51 Yield lines (d) Channels, 2 bolts

s

bfc

ab

sp

ab

Figure 52 Yield lines (e) Channels, 2 bolts

HOLLOW SECTION (RHS, SHS, CHS) --2 anchor bolts

The yield line patterns considered by the recommendedmodel are shown in Figs. 53 and 54.In the case of yield line pattern (a) the derived modeldoes not assume that the oblique lines intersect the bolthole. This should be verified and considered in a similarmanner as previously outlined in the case of H--shapedcolumn with 2 anchor bolts (refer to equation (71) andFig. 40).The recommended design procedure is as follows:


ti≥N*t

0.9fyiα (82)

y= (2s2− dh)s2 (83)


α = max(αa,αb) when y≤li2= αb when y>

li2

where:

αa=2s22− dhs2+ y2

ys1

αb=li2s3

s3 = distance from centerline of bolt hole to yieldline location specified by s4s4 = cantilevered lengths a1 or a2 of CantileverModel depending uponorientation of the columnsection

s1

y

y

s2

li


y

yli

s2s1

y

s1

y

s2

li

Figure 53 Yield lines (a) Hollows, 2 bolts

s4

s3li

s4

s3

li

s3

li

s4

Figure 54 Yield lines (b) Hollows, 2 bolts

HOLLOW SECTION (RHS and SHS) --4 anchor bolts

The yield line patterns considered by the recommendedmodel are shown in Figs. 55 and 56.

In the case of yield line pattern (a) the derived modeldoes not assume that the oblique lines intersect the bolthole. This should be verified and considered in a similarmanner as previously outlined in the case of H--shapedcolumn with 2 anchor bolts (refer to equation (71) andFig. 40).The recommended design procedure is as follows:


ti≥N*t

0.9fyiα (85)

y= (2s2− dh)s2 (86)


α = max(αa,αb) when y≤li− sp2

= αb when y>li− sp2

where:

αa=4s22− 2dhs2+ 2y2+ spy

2ys1

αb=li2s3

y

y

sp li

s2s1

s1

s2

li

y

y

sp

Figure 55 Yield lines (a) Hollows, 4 bolts


li

s4s3

s3

li

s4

Figure 56 Yield lines (b) Hollows, 4 bolts

HOLLOW SECTION (CHS) --varying no. of anchor bolts(IWIMMModel)

The recommended model for the design of base platesof CHS with a symmetric arrangement of bolts aroundthe column profile as shown in Fig. 20 is based onIWIMM Model previously outlined in the literaturereview.The recommended design procedure is as follows:

ÔNt=Ôfyi π f3t2i

2(87)

ti≥2N*

tÔfyi π f3 (88)

where:Ô = 0.9

f3=12k1k3+ k23− 4k1

k1= lnr2r3k3= k1+ 2

r2=d02+ a1

r3=d0− tc

2a1, a2 and d0 are defined in Fig. 20

[27] recommends to keep the value of a1 as small aspossible, i.e. between 1.5df and 2df (where df is thenominal diameter of the bolts), while ensuring aminimum of 5 mm clearance between the nut face andthe weld around the CHS.Assumptions adopted by this model are a continuousbase plate and a weld capacity able to develop the fullyield strength of the CHS.

HOLLOW SECTION (RHS) --varying no. of anchor bolts(Packer--Birkemoe Model)

RHS COLUMNS -- varying no. of boltsThe model recommended here is Packer--BirkemoeModel. This model is applicable only to base platesbetween 12mm and 26mm.Thedesignprocedure is as follows (refer to the literaturereview for further details regarding the model and toFig. 21 regarding the notation):

a preliminary number of bolts required isdetermined from equation (62)a bolt spacing sp equal to 4--5 df should be used(even if smaller spacing are possible) and that:a2≤ 1.25a1 (89)

Calculate δ:

δ= 1−dhsp (90)

The designer should then select a preliminaryplate thickness in the following range:

KN*b

1+ δ ≤ ti≤ KN*

b (91)

where:

K=4a3103

Ôfyisp(where fyi is in MPa)

a3= a1− df∕2+ tccalculate α:

α= KÔNtft2i− 1 a2+ df∕2

δ(a2+ a1+ tc) (92)

with the constraint of α≥ 0The capacity of the steel base plate is then calculated asfollows:

ÔNt=t2i(1+ δα)nb

K (93)

And ÔNt calculated with equation (93) must be greaterthan N*

t.The actual tension in the anchor bolt group,including prying effects, is determined as follows:

N*tb≈ N*

t1+ a3a4 δα1+ δα (94)

where:N*tb = design tension in anchor bolt group includingprying effects

α= KN*t

t2inb− 1 1

δ

a4= min1.25a1, a2+ df2

Theanchorbolt group capacity calculatedwith equation(62) needs to be greater than the axial loads applied tothe bolt group calculated with equation (94). This is


achieved adopting a value Ôp to be used in equation (60)equal to:

Ôb= 1+ a3a4 δα1+ δα−1

≤ 1 (95)

The evaluation of the capacity of an existing base plateis carried out following the design procedure previouslyoutlined. Instead of the preliminary values the actualnumber of bolts and plate thickness are utilised.

5.4.8. Design of weld at column base

The design of the weld at the base of the column iscarried out in accordance with Clause 9.7.3.10 of AS4100. Theweld is designed as a filletweld and its designcapacity ÔNw is calculated as follows:

ÔNw= ÔvwLw= Ô0.6fuw tt krLw (96)

where:Ô = 0.8 for all SP welds except longitudinal fillet

welds on RHS/SHS with t < 3 mm (Table 3.4 ofAS 4100)0.7 for all longitudinal SP fillet on RHS/SHSwith t < 3 mm (Table 3.4 of AS 4100)0.6 for all GP welds (Table 3.4 of AS 4100)

kr = 1 (reduction factor to account for length ofwelded lap connection)

Refer to Section 13. for tabulated values of Ôvw.The fillet weld is recommended to be placed all aroundthe column section profile.

6. SHEAR

6.1. INTRODUCTION

The shear actionmay be assumed to be transferred fromthe column to the concrete base either:1. by friction between between base plate and

concrete/grout base or by recessing the baseplate into the concrete footing;

2. by a shear key (or shear lug);3. by the anchor bolts;4. by a combination of two or more of the above.Available design information regarding the transfer ofshear by each of these means with and without axialloading is now outlined. It is interesting to note howthere are still very different opinions regarding theability of anchor bolts to transfer shear actions. Forclarity, the literature review regarding the behaviour ofanchor bolts is further divided into the case of anchorbolts subject to shear only or to shear and axialcompression and the case of anchor bolts subject toshear and axial tension.

6.2. TRANSFER OF SHEAR BY FRICTIONOR BY RECESSING THE BASE PLATEINTO THE CONCRETE --LITERATURE REVIEW

There is general agreement regarding the determinationof the shear capacity of a base plate which can be

transferred by means of friction when the column issubject to axial compression loading. The shearcapacity is calculated as follows:

ÔVf= ÔμN*c (97)

where:Ô = 0.8μ = coefficient of frictionÔVf = shear capacity of the base plate transferred by

frictionCoefficients of friction μ available in literature areshown in Fig. 57 and are specified as follows:[2][21][22]

0.9 -- concrete or grout against as--rolled steelwhen the contact plane is the full base platethickness below the concrete surface (i.e.recessed);0.7 -- for concrete or grout placed against theas--rolled steel surface with the contact planecoincidental with the concrete surface;0.55 -- for grouted conditions with the contactplane between the grout and the as--rolled steelexterior to the concrete surface (normalcondition).

μ= 0.9

μ= 0.7 μ= 0.55

Figure 57 Coefficients of Friction (Ref. [26])

6.3. TRANSFER OF SHEAR BY A SHEARKEY-- LITERATURE REVIEW

Available design guidelines agree that in the presence ofa shear key, the shear force is transferred through theshear key acting as a cantilever and bearing against theconcrete surface as shown in Fig. 58 while no bearing isassumed to occur against the grout. The bearingcapacity of the concrete is calculated in accordancewithAS 3600 [10]. Uniform bearing pressure is assumed tooccur at the interface between the shear key and theconcrete equal to the maximum bearing capacity of theconcrete. The shear key is designed as a cantilever tocarry the assumed bearing pressure. [26]The required area of the shear key is determined basedon the bearing concrete strength 0.85Ôf′c as shown inFig. 58:

Ask=V*s

0.85Ôcf′c(98)

where:Ô = 0.8Ask = area of the shear key


V*s = design shear force to be transferred by meansof the shear key

The actual length of the shear key Ls is then determinedbased on the available plate depth in contact with theconcrete, which, referring to Fig. 58, is equal to(bs− tg). The design moment per unit width of platem*sk carried by the shear key can then be calculated as

follows:

m*sk=

V*sLs

bs+ tg2 (99)

where:

m*sk = design moment to be carriedto the shear key

Ls = length of shear keybs = depth of shear keytg = grout thickness

Equating the design moment to the plastic nominalsection moment capacity of the shear key the followingis obtained (per unit width of plate):

m*sk=

V*sLs

bs+ tg2 =

0.9fys t2s4 = Ômsk (100)

where:msk = nominal section moment capacity per unit

width of shear keyfys = yield stress of shear key used in design

ts = thickness of shear keyfromwhich theminimum thickness for the shear key tskcan be calculated in accordance with AS4100 asfollows:

ts=4m*

sk0.9fys = V*s

Ls2bs+ tg0.9fys

(101)

or equivalently the shear capacity of a shear key iscalculated as:

ÔVs=0.9fysbs+ tg

t2sLs2 (102)

where:ÔVs = design shear capacity of the shear key

ts

Shear Keybstg

0.85f′c

V*c

Figure 58 Forces acting on Shear Keys(Ref. [26])

In the presence of combined shear and axialcompression actions, the shear key is normally assumed

to resist the part of the design shear force that cannot beresisted by friction.For shear keys located near a free concrete edge itshould be verified that the concrete is able to carry theapplied shear action. The possible failure surface is theone which radiates at 45 degrees from the shear key’sedges towards the concrete edge. The concrete capacityshould be determined by multiplying the effectiveconcrete stress area, determined as the projected area ofthe failure surface on the concrete edge ignoring theshear key area, by the average concrete tensile stress ofÔ0.33 f′c (where f′c is inMPa) with Ô is equal to 0.85.[2]Theweld of the shear key shall be designed to carry bothdesign shear and moment actions acting on the shearkey.It is interesting to note that the shear key can be weldedto the underside of the base plate at any angle even if itis common to choose directions parallel to one or bothof the principal axes of the column as these are usuallythe axes along which the shear needs to be transferred.Reference [26] extends this design procedure for shearkeys in two orthogonal directions applying the samedesign procedure in both orthogonal directions.

6.4. TRANSFER OF SHEAR BY THEANCHOR BOLTS -- LITERATUREREVIEW

6.4.1. Shear only or Shear and AxialCompression

An anchor bolt located away from a concrete edge andwith sufficient embedment length would typicallytransfer the shear through bearing at the surface of theconcrete and testing has shown that this transfer modecould cause a concrete wedge to form as shown in Fig.59. It has been observed that the depth of the concretewedge can be approximated to be one quarter of theanchor bolt diameter. In the presence of a base plate thetranslation of the concrete wedge is prevented by aclamping force provided by the base plate and anchorbolts. While the anchor’s behaviour remains in theelastic range the clamping force applied by the anchorbolt and base plate is proportional to the shear force.

df∕4

df

Applied Shear

Concrete Wedge

Figure 59 Concrete wedge failure mode underanchor bolt shear force (Ref. [31])

Locating an anchor bolt near the concrete free edgecould lead to another failure mode to occur as shown inFig. 60. The concrete failure surface is determined byradiating at 45 degrees from the anchor bolt at the


concrete surface towards the free edge. The concretecapacity is calculated by multiplying the projected areaof the failure surface at the concrete edgeby the concreteaverage tensile strength of Ô0.33 f′c .

Applied Shear

SideFailureSurface Front

Figure 60 Concrete failure surface under boltshear force near a concrete edge (Ref.[31])

The minimum side cover required to ensure a ductilefailure requires the concrete wedge capacity to carry ashear load equal to the nominal shear capacity of theanchor bolt.The concrete capacity of the wedge cone can becalculated as follows:

ÔVu.c= Ô0.33 f′cπa2e2

(103)

where:Ô = 0.65 in [3] and 0.85 in [17]ÔVu.c = concrete capacity against wedge cone

failureExperimental results have shown that equation (103)provides agood estimate of the concretewedge capacityusing Ô equal to 0.65. [44][45]Based on [2], [3] and [17] the nominal shear capacity ofthe anchor bolt is calculated assuming that the shear istransferred by friction between the steel and theconcrete with a friction coefficient of 0.7:

Vu.b= 0.7πd2f4

fuf (104)

where:Vu.b = nominal shear capacity of an anchor bolt

assumed to be transferred by friction betweenanchor and concrete with a friction coefficient of0.7

Theminimumside cover ae to be adopted for the anchorbolt to avoid the concrete wedge failure can bedetermined ensuring that the concrete capacity againstwedge failure ÔVu.c is able to carry the shear capacityof the bolt transferred by friction Vu.b and equatingequation (103) to equation (104): [2]

ÔVu.c= Ô0.33 f′cπa2e2

= 0.7πd2f4

fuf= Vu.b (105)

and solving equation (105) for ae:

ae≥ dffuf

Ô0.94 f′c (106)

where:Ô = 0.65 in [3] and 0.85 in [17]

Based on the guidelines provided in reference [3],simplified design guidelines of the minimum edgedistances calculated with equation (106) using Ô equalto 0.65 are presented in reference [39] which are asfollows:

for Grade 250 bars and Grade 4.6 bolts:ae ≥ 12dfminimum bolt spacing ≥ 16dffor Grade 8.8 bolts:ae ≥ 17dfminimum bolt spacing ≥ 24df

These minimum bolt spacings intend to avoidoverlapping of anchors’ concrete failure cones. Thesehave also been recommended in reference [26].For completeness minimum edge distances have beenderived in Section 12. based on equation (106) with Ôequal to 0.65 and0.85.Also simplified expressionshavebeen derived as shown in Tables 4 and 5.Table 4 Grade 4.6 bolts and 250 Grade rods

Ô f′c ae

0.65 20 13 df0.65 25 12 df0.65 32 11 df0.85 20 11 df0.85 25 10 df0.85 32 10 df

Table 5 Grade 8.8 bolts

Ô f′c ae

0.65 20 18 df0.65 25 17 df0.65 32 16 df0.85 20 16 df0.85 25 15 df0.85 32 14 df

References [26] and [47] recommend edge distancesbased on Ô values equal to 0.85.In the case the side cover is less than ae (calculatedwithequation (106)) caution should be placed in the designand positioning of the reinforcement. The shearcapacity of an anchor bolt located at a distance less thanae∕3 from a concrete edge should be ignored. Adoptinga similar reinforcement layout as suggested in Fig. 35 toresist direct tensile loading it has been observed bylimited testing that concrete failure would occur when


anchor bolts are located with a side cover less than2ae∕3.Apossible reinforcement layout to beutilised in the casethe side cover is in between ae∕3 and 2ae∕3 is shown inFig. 61. Allowance for the full development of thereinforcement should be allowed for in accordancewithAS3600 regardless of the reinforcement layout adoptedand in the case such allowance is not feasible the shearcapacity of the anchor bolt with edge distance problemsshould be disregarded. [2][17]Experimental studies have shown that possible failuremodes which can occur by transferring shear actions bymeans of anchor bolts are concrete failure with andwithoutwedgecone, concrete failurewithpull--out coneand shear failure of the anchor bolt. [45]

Shear force

Potentialfailure zone

* -- Developmentlength from AS3600

*

*

Figure 61 Reinforcement for ShearNear an Edge of ConcreteFoundation (Ref. [2])

[45] notes that by ensuring sufficient embedment lengthof the anchor bolt no concrete pull--out can occur. Theconcrete edge cone failure can be prevented if either anedge distance ae as determined in equation (106) oradequate reinforcement are provided. From test data,[45] concludes that among available guidelines the oneof [3], outlined in equation (106), is the mostappropriate.[45] shows that equation (106) is not applicable toanchor bolt groups as it can lead to unsafe designparticularly for large edge distances and that thenominal concrete capacity is related to both edgedistance and bolt spacing. [45] provides no alternativedesign guidelines but notes that from experimentalresults the nominal capacity of a two bolt group mayonly be 60%more than that of a single bolt for the sameedge distance.[45]No guidance is currently available for calculating thenominal shear capacity of anchor bolt groups.It is interesting to note that for the casewhere a grout padexists between the base plate and the concrete, the groutpad allows bending deformation of the anchor bolt tooccur under an applied shear force. The lateral

deformation of the bolt leads to tensile stress in the boltbut this is generally insufficient to cause pullout. [38]Some authors do not recommend that shear be resistedby the anchor bolts.Ricker in [38] specificallynotes that anchorbolts shouldnot be used to resist shear forces in a column base. In hisopinion bolts have a low bending resistance and that ifa plate eases sideways to bear against a bolt, bending isinduced in the boltwhich acts as a cantileverwith a leverarm equal to the grout thickness plus an additionaldistance should the concrete foundation crush locally.Fischer in [24] notes that in his opinion no more thantwo anchor bolts for each anchor group would transfershear. He explains that under normal loading conditiononly one bolt would be carrying shear in bearing asshown in Fig. 62. The columnwould then rotate subjectto a shear action till a second anchor would go intobearing. Due to the oversize holes specified in baseplates it is not possible to ensure that the bolts of the boltgroup would deform sufficiently to allow all bolts to gointo bearing. [24]Ref. [31] considers that, in the case of base plates, thereis not enough data available to precisely quantify theshear strength of an individual anchor bolt, much less agroup of anchor bolts.

Figure 62 Transfer of shear by bearing ofanchor bolts

DeWolf in [22] recommends to avoid the use of anchorbolts to resist shear and suggests that the transfer ofshear through anchor bolts takes place by either shearfriction or bearing.In the former instance the transfer of shear occurs oncea clamping force is developed to the base plate. [22]Even if the anchor bolts are not tightened properly theclamping force can still develop as a consequence of awedge concrete failurewhichwould tend to lift the baseplate up and therefore tensioning the anchor bolts. [31]No specific guidelines are available to evaluate thecontribution of the clamping force to the shearresistance of the bolt and in practice this clamping forcemay not necessary be available.The other transfer mode of anchor bolts described byDeWolf is by bearing between the anchor and the bolthole, but he regards this very unlikely to occur inpractice in more than one or two anchors as the boltholes of base plates are usually oversized holes. [22] Healso notes that a more reliable method of shear transferthrough the anchor bolts can be achieved bywelding thenuts to the base plate or by providing special washers


with normal size holes (bolt dia + 2 mm) which fit overthe oversize holes and are welded to the base plate. [21]

Anchor bolt

Projected areaof wedge cone

Anchor bolt

ae

aeα= 45o

Top ofconcreteblock

Overlappedarea

Anchor bolts

ae

ae45oα

Figure 63 Concrete edge failure cones(Ref. [45])

Ref. [34] notes that it is common and successfulindustrial practice to use anchor bolts of pinned--baseportals to resist the shear forces while recommendingthe following design guidelines:

if shear force is less than 20% of the axial load,then no special provisions are required;for higher levels of shear force, it suggests thatgreat attention be paid to ensuring good groutingunder the base plate and around the anchor boltsusing a mix of minimum shrinkage;excessive clearance between the anchor bolts andthe holes in the base plate should be avoided;to avoid possible horizontal deformation of thecolumn the shear actions should be transferredeither by recessing the base plate into concrete, orby means of a shear key or by tying the steelcolumns to share the load among adjacentcolumns.

6.4.2. Shear and Axial Tension

The ability of anchor bolts to transfer shear actions wasconsidered in the previous paragraph. Here onlyavailablemodels to describe the interaction of shear andtension are considered.[39] notes that most references suggest the use of aparabolic interaction equation, similar to the oneadopted for conventional bolts as also specified in AS

4100 [11], for the design of the anchor bolts. Shipp andHaninger suggest in [39] that the total area of anchorbolt required should be the sum of that required to resisttension and that required to resist shear. They argue thatthe shear force causes a bearing failure near the concretesurface and translates the shear load on the anchor boltinto an effective tension load by friction, so that the boltmust have enough tension capacity to resist both effects.[30] notes that for an anchor bolt subject to both shearforce and axial tension, design difficulties exist becausethe interaction of shear and tension is not understoodand generally a straight line interaction relationship isassumed, which requires the total steel bolt area beobtained by adding the area required for shear force andthe area required for tension. [30] notes that thisapproach is conservative but is warranted since test dataconcerning combined shear and tension are lacking formost anchors.Reference [20] suggests an elliptical interactionrelationship between tension and shear for the design ofanchor bolts while considering the linear interactionrelationship to be conservative.References [2] and [17] recommend, in the case ofanchor bolts subject to combined shear and tension, toadopt the design recommendations regardingminimumembedment length and edge distances provided in thecase of anchor bolts subject to tension and shearseparately.


6.5.1. Introduction

The recommended design model allows shear action tobe transferred by friction between the base plate and theconcrete/grout base, by recessing the base plate into theconcrete footing, by a shear key or by a combination ofthe above.It is in the authors’ opinion that due to the uncertaintyregarding the ability of anchor bolts to transfer shear itis left up to designer to decide whether or not to designthe anchor bolts to carry shear actions.

6.5.2. Design criteria

The recommended model for the design of base platesubject to shear or combined shear and axial actions isbase on the following design criteria:

Vdes= ÔVf+ ÔVs,ÔVwmin≥ V* (107)

Ndes.c≥ N*c

Ndes.t≥ N*t

vdes= Ôvw≥ v*w

where:Vdes = design shear capacity of the base plate

connectionÔVf = design shear capacity of the base plate

transferred by means of frictionÔVs = design shear capacity of the shear key


ÔVw= design shear capacity of the weld connectingthe base plate to the column

Ndes.t = design capacity of the base plate connectionsubject to axial tension as determined in Section5.4.

Ndes.c = design capacity of the base plate connectionsubject to axial compression as determined inSection 4.3.

N*t = design axial tension load

N*c = design axial compression load

vdes = Ôvw = design capacity of theweld connectingthe base plate to the column per unit length ofweld

v*w = design load per unit length acting on the weldconnecting the base plate to the column. Itsdirection depends upon the combined shear andaxial loading

The additional check on theweld capacity is required asthe critical action acting on the weld (between columnand base plate) is caused by a combination of shear andaxial loading.

6.5.3. Design of shear transfer by frictionand by recessing the base plate in theconcrete

The design shear capacity of the base plate transferredbymeans of friction and by recessing the base plate intothe concrete footing is calculated as follows:

ÔVf= ÔμN*c (108)

where:Ô = 0.8μ = coefficient of friction

= 0.9 -- concrete or grout against as--rolled steelwhen the contact plane is the full base platethickness below the concrete surface (i.e.recessed)= 0.7 -- for concrete or grout placed against theas--rolled steel surface with the contact planecoincidental with the concrete surface= 0.55 -- for grouted conditions with the contactplane between the grout and the as--rolled steelexterior to the concrete surface (normalcondition)

6.5.4. Design of the column weld

The design action applied to the weld between thecolumn and the base plate is calculated as follows:

v*w= v*h2+ v*v

2 (109)

where:

v*h and v*v= components of the loading carried by theweld between column and base plate in onehorizontal direction in the plane of the base plateand in the vertical direction respectively per unitlength

v*h= V*

Lw

v*v =N*cLw

if the column end is not prepared for full

contact= 0 if the column end is prepared for fullcontact (under axial compression only)

The fillet weld capacity between the column and thebase plate Ôvw is designed in accordance with Clause9.7.3.10 of AS 4100 [11] as follows:

Ôvw= Ô0.6fuwttkr (110)

where:Ô = 0.8 for all SP welds except longitudinal fillet

welds on RHS/SHS with t < 3 mm (Table 3.4 ofAS 4100)0.7 for all longitudinal SP fillet on RHS/SHSwith t < 3 mm (Table 3.4 of AS 4100)0.6 for all GP welds (Table 3.4 of AS 4100)

Refer to Section 13. for tabulated values of the filletweld capacity Ôvw.

6.5.5. Design of shear transfer by a shear key

The shear capacity of a shear key can be calculated oncethe bearing and pull--out capacity of the concrete, theshear capacity of the shear keydue to its nominal sectionmoment capacity and the weld capacity between theshear key and the base plate are determined as shownbelow.

ÔVs= ÔVs.c; ÔVs.cc; ÔVs.b; ÔVs.wmin≥ V* (111)

where:ÔVs = design shear capacity of the shear keyÔVs.c = concrete bearing capacity of the shear keyÔVs.cc = pull--out capacity of the concreteÔVs.b = shear capacity of the shear key based on its

section moment capacityÔVs.w = shear capacity of the weld between the

shear key and the base plateThe concrete bearing capacity of the shear key ÔVs.c iscalculated as follows:

ÔVs.c= Ô0.85fc′Ls(bs− tg) (112)

where:Ô = 0.6Ls and bs = length and depth of the shear key as

shown in Fig. 64

tg

ts

Shear Keybs

Ls

Figure 64 Shear Key Details (Ref. [26])

In the case the shear key is located near a concrete edgethe capacity of the concrete could be reduced by the


formation of a failure surface radiating at 45 degreesfrom the shear key’s edges towards the concrete edge.The concrete capacity calculated over the projected areaof such failure surface ignoring the shear key area isdetermined as follows:

ÔVs.cc= Ô0.33 fc′ Apsk≤ ÔVs.c (113)

where:Ô = 0.7 (based on as Ô required for Clause 9.2.3 of

AS3600)Apsk = projected area over the concrete edge

ignoring the shear key areaThe shear capacity of the shear key based on its nominalsectionmoment capacity ÔVs.b is calculated as follows:

ÔVs.b=0.9fysbs+ tg

t2sLs2 (114)

The capacity of the fillet weld connecting the shear keyto the base plate ÔVs.w calculated in the directionperpendicular to the shear key is determined as follows(assuming the shear key is welded all around):

ÔVs.w=Ôvw2Ls

1+bs+ts

2

ts (115)

where:Ôvw = design capacity of the fillet weld per unit

length (as calculated in equation (110) or astabulated in Section 13.)

7. BASE PLATE AND ANCHOR BOLTSDETAILING

Typical base plate layouts considered in this paper areshown in Figs. 65, 66, 67 and 68.Typical anchor bolts used in base plate applications arecast--in anchors of category 4.6/S and of diameter eitherM16, M20, M24 or M30. Masonry anchors of diameterM16, M20, M24 may also be used.

Componentto suit

Grout pad

sg

Typical

Typical

Figure 65 2--bolt base plate to UB /UC column(Ref. [26])

sp

sg

Figure 66 4--bolt base plate to UB/UC column(Ref. [26])

sp

Figure 67 2--bolt base plate to channel column(Ref. [26])

Anchor Bolt LocationHole to allow groutegress

Legend:

Figure 68 2--bolt base plate to hollow columns(Ref. [26])

Preferred anchor bolt gauge (sg) and pitch (sp) are givenin Reference [12].The ”weld all round” philosophy sometimes adopted inthe weld design of base plates can lead to over--weldingand can become very expensive. The details shown inFigs. 65, 66, 67 and 68 can, if designed for lightloadings, tend to the other extreme and some fabricatorsmay prefer to increase the amount ofwelding above thatshown on the design drawings in order to preventdamage during handling and shipping. There is usuallya compromise possible between these two extremes.Another design consideration is the likelihood of anominally pinned base being subjected to somebendingmoment in a real situation. [26]Prior to erecting the column/base plate assembly, thelevel of thebaseplate area shouldbe surveyed and shimsplaced to indicate the correct level of the underside ofthe base plate as shown in Fig. 69. For heavier column/baseplate assemblies, levelling--nut arrangementsmaybe used in order to allow accurate levelling of the baseplate as outlined in [7] and [38].Hole sizes in base plates


may be up to 6mm larger than the anchor bolt diameterin accordance with Clause 14.3.5.2 of AS 4100 [11].

Level of U/SBaseplate

Concrete surfaceShims

Figure 69 Use of shims for levelling purposes(Ref. [26])

Holes require a special plate washer of 4 mmminimumthickness under thenut if thebolt hole ismore than3mmlarger than the anchor bolt diameter.Base plates should be provided with at least one groutinspection hole through which the grout will riseindicating a satisfactory grouting operation.Anchor bolts are usually galvanized, even for an interiorapplication, in order to avoid corrosion during theconstruction period where the steel columns may standfor some time in the open air.The size and location of any permanent steel shimsunder the base plate should be shown on the drawings.Temporary packers which are used for erectionpurposes until the underside of the base plate is groutedor concreted should be left to the erector to detail.The minimum space between the underside of the baseplate and the concrete foundation should be:

25 mm for grouting;50 mm for mortar bedding;75 mm for concrete bedding.

Tolerances on anchor bolt positions and level of baseplate should conform to the provisions ofClause 5.12 ofAS 4100.[11][24] notes that possible design and detailing problemsfor base plates include:

inadequate development of the anchor bolts fortension and of concrete reinforcing steel;improper selection of anchor bolt material;inadequate base plate thickness;poor placement of anchor bolts;shear and fatigue loading on anchor bolts.

Based on a survey carried out in the UK [29] notes thatpoor fit of base plates onto holding down bolts is amongone of the four most commonly reported problems oflack of fit on site.To ensure that the bolt centres match the nominatedcentres and the hole centres drilled in the base plate, thebolts are often caged into a group as shown in Fig. 70.Also useful is the provision of cored holes usuallyformed by using polystyrene which allow theadjustment of anchor bolt positions once the concrete iscast in order to exactlymatch the hole centres in the baseplate as already shown in Fig. 32.Anchor bolt centresmust complywith the tolerances setout in Clause 15.3.1 of AS 4100 as shown in see Fig. 71.

Tack weld 10mmreinforcing bars toform cage -- notacks on HS bolts.

Figure 70 Locating Holding Down Boltswith a Cage (Ref. [26])

1 2 3

Specified dimension (+/-- 6 in every 30mbut not greater than +/-- 25 overall)

Max deviation +/-- 6

Detail of off--centrelocation of anchor bolts

C/L Anchor bolts


+/-- 3

+/-- 3

C/L Grid

C/L Grid

C/L Anchor bolts


Unless otherwisespecified, dimensionsare in millimetres

4

Max deviation +/-- 6 ifcolumn offset from maincolumn line.

MaincolumnC/L grid

Figure 71 Tolerances in Anchor Bolt Locationafter AS 4100 (Ref. [26])

[19] and [38] present a discussion of a number ofpractical aspects of the use of anchor bolts and shouldbe referred to if problems arise on site. [19] deals withgeneral aspects regarding design, installation,anchorage, corrosion of anchor bolts, bedding andgrouting as well as the responsibilities of all parties in


the construction process but no firm recommendationsare made on design however.

8. ACKNOWLEDGEMENTS

This paper started from thevery significantworkcarriedout by Tim Hogan and Ian Thomas who collated themajority of the research results on steel connectionsfrom around the world in Ref [26]. Valuable input andsupport for this current work has come from OneSteel-- in particular AnthonyNg,GaryYumandNick van derKreek. TheASI StateManagers -- LeighWilson, RupertGrayston, John Gardner and Scott Munter have allcontributed industry insights. Several overseasresearchers, notably Jeffery Packer and John DeWolf,havecontributed significantly in this area and theirworkand comments are acknowledged.

9. REFERENCES

[1] Ahmed, S. and Kreps, R.R., “Inconsistencies inColumn base Plate design in the New AISCASD Manual”, Engineering Journal, AmericanInstitute of Steel Construction, Vol. 27, No. 3,1990, pp 106 -- 107.

[2] American Concrete Institute, ”CodeRequirements for Nuclear Safety RelatedStructures”, ACI 349 -- 90, Manual of ConcretePractice (1994).

[3] American Concrete Institute, ”CodeRequirements for Nuclear Safety RelatedStructures”, ACI 349 -- 1976, Manual ofConcrete Practice.

[4] American Institute of Steel Construction,“Detailing for Steel Construction”, SecondEdition, 2002.

[5] American Institute of Steel Construction,“Manual of Steel Construction -- Load andResistance Factor Design”, Third Edition,2001.

[6] American Institute of Steel Construction,“Manual of Steel Construction -- Volume IIConnections”, Ninth Ed./First Edition, 1992.

[7] American Institute of Steel Construction,“Manual of Steel Construction -- Load andResistance Factor Design”, First Edition, 1986.

[8] AS/NZ 1170.0:2002 -- “Structural designactions -- Part 0: General principles”, 2002

[9] AS 1275 -- ”Metric Screw Threads forFasteners”, 1985.

[10] AS 3600 -- ”Concrete Structures”, 2001.[11] AS 4100 -- ”Steel Structures ”, 1998.[12] Australian Institute of Steel Construction,

”Standardized Structural Connections”, ThirdEdition, 1985.

[13] Ballio, G. and Mazzolani, F.M., “Theory andDesign of Steel Structures”, Chapman andHall, 1983.

[14] Bangash, M.Y.H., “Structural detailing inSteel”, Thomas Telford, 2000

[15] Bickford, J.H. and Nassar, S., Handbook ofBolts and Bolted joints”, Marcel Dekker, 1998

[16] Blodgett, O., Design of Welded Structures”,The James F Lincoln Arc Welding Foundation,Fifth Printing, 1972, Section 3.3.

[17] Cannon, R.W., Godfrey, D.A. and Moreadith,F.L., ”Guide to the Design of Anchor Bolts andOther Steel Embedments”, ConcreteInternational, July 1981, pp 28 -- 41.

[18] Chen, W.F., “Handbook of StructuralEngineering”, CRC Press, 1997

[19] Concrete Society/British ConstructionalSteelwork Association/Constructional SteelResearch and Development Organisation,”Holding Down Systems for Steel Stanchions”,1980.

[20] Cook, R. and Klingner, R., “Behaviour ofDuctile Multiple--Anchor Steel--to ConcreteConnections with Surface--MountedBaseplates”, from “Anchors in Concrete --Design and Behavior” edited by Senkiw, G.A.and Lancelot III, H.B., American ConcreteInstitute, 1991

[21] DeWolf, J.T, ”Column Base Plates”, AmericanInstitute of Steel Construction, Design GuideSeries No. 1, 1990. (Publication also containsRefs. [38] and [42])

[22] DeWolf, J.T, ”Column Anchorage Design”,American Institute of Steel Construction,National Eng Conf., New Orleans,Proceedings, Paper 15, April/May 1987.

[23] Eurocode 3: Design of steel structures DDENV 1993--1--1 Part 1.1 General rules andrules for buildings, 1992

[24] Fischer, J.M., “Structural details in Industrialbuildings”, Engineering Journal, AmericanInstitute of Steel Construction, Vol. 18, No. 3,1981, pp 83--89.

[25] Fling, R.S., ”Design of Steel Bearing Plates”,Engineering Journal, American Institute ofSteel Construction, Vol. 7 No. 2, April 1970,pp 37 -- 40.

[26] Hogan, T.J. and Thomas, I.R., “Design ofstructural connections”, Fourth Edition,Australian Institute of Steel Construction,1994.

[27] Igarashi, S., Wakiyama, K., Inove, R.,Matsumoto, T. and Murase, Y., “Limit Designof high strength Bolted Tube Flange joint --Parts 1 -- 2”, Journal of Structural andConstruction Engineering Transactions of AIJ,Department of Architecture reports, OsakaUniversity, Japan, 1985.

[28] Jaspart, J.P. and Vandegans, D., “Application ofthe component method to column bases”,Proceedings of the International Conference on


Advances in Steel Structures, Hong Kong,Vol.1, 1996, pp 139--144.

[29] Mann, A.P. and Morris, L.J., “Lack of fit insteel structures”, CIRIA Report 87, 1981

[30] Marsh M.L. and Burdette, E.G., ”Multiple BoltAnchorages: Method for Determining theEffective Projected Area of Overlapping StressCones”, Engineering Journal, AmericanInstitute of Steel Construction, Vol. 22 No. 1,1985, pp 29 -- 32.

[31] Marsh, M.L. and Burdette, E.G., ”Anchorageof Steel Building Components to Concrete”,Engineering Journal, American Institute ofSteel Construction, Vol. 22 No. 1, 1985, pp 33-- 39.

[32] Murray, TM., Design of Lightly Loaded SteelColumn Base Plates”, Engineering Journal,American Institute of Steel Construction, Vol.20 No. 4, 1983, pp 143 -- 152.

[33] National Institute of Standards and Technology,“Post--Installed Anchors -- A LiteratureReview”, NISTIR 6096, 1998.

[34] Owens, G.W. and Cheal, B.D., ”StructuralSteelwork Connections”, Butterworths,London, 1989.

[35] Park, R. and Gamble, W.L., “ReinforcedConcrete Slabs”, Wiley, 1980.

[36] Parker, J.A. and Henderson, J.E., “Hollowstructural section connections and trusses -- Adesign guide”, Second Edition, CanadianInstitute of Steel Construction, 1997.

[37] Parker, J.A., “Design with structural steelhollow sections -- Australian Institute of SteelConstruction Seminar”, Australian Institute ofSteel Construction, March 1996.

[38] Ricker, D.T, ”Some Practical Aspects ofColumn Base Selection”, Engineering Journal,American Institute of Steel Construction, Vol.26 No. 3, 1989, pp 81 -- 89.

[39] Shipp, J.G. and Haninger, E.R., ”Design ofHeaded Anchor Bolts”, Engineering Journal,American Institute of Steel Construction, Vol.20 No. 2, 1983, pp 58 -- 69.

[40] Stockwell, F.W., ”Preliminary Base PlateSelection”, Engineering Journal, AmericanInstitute of Steel Construction, Vol. 12 No. 3,1975, pp 92 -- 93.

[41] Stockwell, F.W., ”Base Plate Design”,American Institute of Steel Construction,National Eng Conf, Proceedings, Paper 49,April/May 1987.

[42] Thornton W.A., ”Design of Small base Platesfor Wide Flange Columns”, EngineeringJournal, American Institute of SteelConstruction, Vol. 27, No. 3, 1990, pp108--110.

[43] Thornton W.A., ”Design of Base Plates forWide Flange Columns -- A ConcatenationMethod”, Engineering Journal, AmericanInstitute of Steel Construction, Vol. 27, No. 4,1990, pp 173--174.

[44] Ueda, T, Kitipornchai, S. and Ling, K.,”Experimental Investigation of Anchor BoltsUnder Shear”, Journal of StructuralEngineering, 1990

[45] Ueda, T, Kitipornchai, S. and Ling, K., ”AnExperimental Investigation of Anchor BoltsUnder Shear”, University of Queensland, Deptof Civil Eng., Research Report No. CE93, Oct.1988.

[46] Wood, R.H. and Jones, L.L., “Yield--lineanalysis of slabs”, Thames and hudson, Chatto& Windus, London, 1967.

[47] Woolcock, S.T, Kitipornchai, S. and Bradford,M.A., ”Limit State Design of Portal FrameBuildings”, Second Edition, AustralianInstitute of Steel Construction, 1993.


10. APPENDIX A -- Derivation of Designand Check Expressions for Steel BasePlates Subject to Axial Compression

The design model for base plates subject to axialcompression recommended in this paper is a modifiedversion of Thornton Model presented in [43] which issuitable for H--shaped columns only. Its derivation hasalso been extended here for channels and hollowsections.The recommended model concatenates the Cantilever,Fling and Murray--Stockwell Models as follows:

ti≥ am2N*c

0.9fyi di bi


For clarity themodel which describes the design of baseplates subject to uniform pressure using yield linetheory is referred to throughout this section as YieldLine Model. In the case of H--shaped sections FlingModel and theYieldLineModel coincide. The assumedyield line patterns are based on the external dimensionsof the column profile.Values of a1 and a2 are available in [21], [26] and [36]for H--shaped columns, channels and hollow sectionswhile values of λ and a4 are available in [5] and [43] foronly H--shaped sections.In the recommendedmodel presented here the values ofλ and a4 have been re--derived and modified forH--shaped sections and have been derived for channelsand hollow sections.Thederivationof suchvalues is outlinedbelowbasedona procedure similar to the one utilised by Thornton in[43]. The values of λ and a4 allow the inclusion in therecommended model of the results obtained withMurray--Stockwell Model and with the Yield LineModel respectively. It is important to note that, similarlyto Thornton Model, the recommended model alwaysadopts the thinnest plate determined usingMurray--Stockwell Model and the Yield Line Model.In the following derivation the values of a4 are firstlydetermined to include theYieldLineModel and then thevalue of λ to include Murray--Stockwell Model isdetermined.

A.1 DERIVATION FOR DESIGN PURPOSES-- H--SHAPED SECTIONS

A.1.1 DETERMINATION OF a4(Yield Line Model -- Fling Model)

The base plate is designed assuming a yield line patternas shown in Fig. 72. The present derivation is suitablefor H--shaped sections for which bfc∕2 is less than dc asa different yield line pattern would otherwise occur.


θ

d1bes

Figure 72 Yield line pattern for H--shapedsections

The base plate is considered to be simply supportedalong the flanges, fixed along theweb and free along theedge opposite to the web. Solutions from yield linetheory are available for this kind of support conditionscarrying a uniformly distributed load f*p and based onthe results presented in [35]:

f*p=

24Ômp1+ 4+48η2 −24η2

b2fc3− 4+48η2 −24η2

(116)

where:

η = dc∕bfcIn this case the uniform load f*p is calculated as follows:

f*p=N*cdibi

The required design plastic moment Ômp to support auniform pressure of f*p is obtained by re--arrangingequation (116) as follows:

Ômp= f*pb2fc24

6η2− 1+ 12η2 + 1

2η2+ 1+ 12η2 − 1

= 18 f

*pb2fcα

2 (117)

where:

α2= 136η2− 1+ 12η2 + 1

2η2+ 1+ 12η2 − 1

The value of α2 introduced in equation (117) isapproximated by the following expressionwith an errorof --0% (unconservative) and+17.7% (conservative) forvalues of η (which is equal to dc∕bfc) between 3/4 and3:

α= 12 η (118)

The required plate thickness to support f*p can bedetermined by equating the nominal section momentcapacity of the plate Ôms (per unitwidth) to the requireddesign plastic capacity (per unit width) as follows:


Ôms=0.9fyit2i4≥ 1

8f*pb2fcα

2= Ômp (119)

and re--arranging equation (119) in terms of the requiredplate thickness yields:

ti=14

dcbfc 2f*p0.9fyi

= a42N*c

0.9fyidibi (120)

where:

a4=14 dcbfc

A.1.2 DETERMINATION OF λ(Murray--Stockwell Model)

The thickness of the base plate calculated according toMurray--Stockwell Model is determined as follows:

ti= a32N*c

0.9fyiAH (121)

It is interesting to note how, in the formulationpresentedin [5], [42] and [43], the load adopted in equation (121)would have been equal to N*

0 instead of N*c, where N*

0is the portion of full column load N*

c acting over thecolumn footprint under the assumption of uniformbearing pressure, while in the derivation presented thefull column load N*

c is assumed to be applied on theH--shaped area AH.Referring to Fig. 11 the H--shaped bearing area AH canbe expressed as follows:

AH= 2a3a5− 4a23 (122)

where:a5 = bfc+ dc

In this derivation, similarly to Thornton Model, theiterative procedure for the calculation of AH and Ôfbdescribed in the literature review is not implementedand is terminated at the first iteration. The value of themaximum bearing strength of the concrete Ôfb iscalculated as follows:


A1

, Ô2f′c (123)

where:Ô= 0.6A1 = bearing area equal to the base plate area Ai

The H--shaped area AH is defined as the area able tosupport the applied axial compression load N*

c at auniform pressure of Ôfb.

AH=N*cÔfb

(124)

Substituting equations (122) and (123) into equation(124) and solving for a3 the following expression for a3is obtained:

a3=Ôfba5− (Ôfba5)2− 4ÔfbN*c

4Ôfb

=a541− 1− X (125)

where:

X= 4N*cÔfba

25

Substituting the value of a3 calculated in equation (125)into equation (122) yields, after simplifying, thefollowing expression for the H--shaped bearing areaAH:

AH=a25X

4 (126)

The required plate thickness can now be calculatedsubstituting the values of AH and a3 calculated fromequations (125) and (126) into equation (121).

ti=a541− 1− X 8N*c

0.9fyi a25X

= λa4

2N*c0.9fyidibi (127)

where:

λ= 2dibidcbfc X

1+ 1− X

A.2 DERIVATION FOR DESIGN PURPOSES-- CHANNELS

A.2.1 DETERMINATION OF a4(Yield Line Model)

The yield line pattern assumed in the case of channels issimilar to the one assumed in the case of H--shapedcolumn sections as shown in Fig. 73 and it is suitable forchannels with bfc less than dc, as a different yield linepattern would otherwise occur.


Figure 73 Yield line pattern for Channels


The base plate is considered to be simply supportedalong the flanges and the web and free at the edgeopposite to the web. Available solutions as proposed in[35] for a uniformly distributed load f*p are utilised.

f*p=

8Ômp 4+9η2 −2η2

b2fc3− 434+9η2 −2η2

(128)

where:

η = dc∕bfcSimilarly to the case of H--shaped column sections theuniform load f*p is calculated as follows:

f*p=N*cdibi

The required design plastic moment Ômp to support auniform pressure of f*p is obtained by re--arrangingequation (128) as follows:

Ômp= f*pb2fc9η2− 4 4+ 9η2 + 8

24 4+ 9η2 − 2

= f*pb2fcα2 (129)

where:

α2=9η2− 4 4+ 9η2 + 8

24 4+ 9η2 − 48

The value of α2 introduced in equation (129) can beapproximated by the following expressionwith an errorof --0% (unconservative) and +6.7% (conservative) forvalues of η (which is equal to dc∕bfc) between 1.25 and4 (which include the channel sections available inAustralia):

α= 13 η (130)


Ôms=0.9fyit2i4≥ f*pb2fcα

2= Ômp (131)


ti=2dcbfc3

2f*p0.9fyi

= a42N*c

0.9fyidibi (132)

where:

a4=2dcbfc3


The thickness of the base plate calculated according toMurray--Stockwell Model is determined as follows:

ti= a32N*c

0.9fyiAH (133)

Referring to Fig. 12 the assumedbearing area AHcan beexpressed as follows:

AH= a3a5− 2a23 (134)

where:a5 = 2bfc+ dc

The value of the maximum bearing strength of theconcrete Ôfb is calculated as follows:


A1

, Ô2f′c (135)


The assumed area AH is defined as the area able tosupport the applied axial compression load N*


AH=N*cÔfb

(136)


a3=Ôfba5− (Ôfba5)2− 8ÔfbN*c

4Ôfb

=a541− 1− X (137)

where:

X= 8N*cÔfba

25

Substituting the value of a3 calculated in equation (137)into equation (134) yields, after simplifying, thefollowing expression for the assumed bearing area AH:

AH=a25X

8 (138)

The required plate thickness can now be calculatedsubstituting the values of AH and a3 calculated fromequations (137) and (138) into (133).

ti=a541− 1− X 16N*c

0.9fyi a25X


= λa42N*c

0.9fyidibi (139)

where:

λ= 32

dibidcbfc X

1+ 1− X

A.3 DERIVATION FOR DESIGN PURPOSES-- RECTANGULAR HOLLOW SECTION

A similar procedure to the ones adopted in the case ofH--shaped sections and channels is adopted forrectangular hollow sections.

A.3.1 DETERMINATION OF a4(Yield Line Model)

The yield line pattern considered in the case ofrectangular hollow sections is shown in Fig. 74 and therequired design plastic moment Ômp under a uniformpressure f*p can be expressed as follows (based on [35]):

Ômp= f*pb2c 1+ 3η2 − 12

24η2= f*pb2cα2 (140)

where:

α2= 1+ 3η2 − 12

24η2

f*p=N*cdibi

η = dc∕bc

bc

dc

Figure 74 Yield line pattern for RectangularHollow Sections

The plate is assumed to be simply supported along allthe edges.

The value of α2 introduced in equation (140) can beapproximated by the following expressionwith an errorof --0% (unconservative) and+11.1% (conservative) forvalues of η (which is equal to dc∕bc) between 3/4 and4:

α= η23 (141)


Ôms=0.9fyit2i4≥ f*pb2cα2= Ômp (142)


ti=2dcbc23 2f*p

0.9fyi

= a42N*c

0.9fyidibi (143)

where:

a4=2dcbc23



AH= 2a3a5− 4a23 (144)

where:a5 = bc+ dc



A1

, Ô2f′c (145)




AH=N*cÔfb

(146)


a3=2Ôfba5− 4(Ôfba5)2− 16ÔfbN*c

8Ôfb

=a541− 1− X (147)

where:

X= 4N*cÔfba

25

Substituting the value of a3 calculated in equation (147)into equation (144) yields, after simplifying, thefollowing expression for the assumed bearing area AH:


AH=a25X

4 (148)

The required plate thickness can now be calculatedutilising the values of AH and a3 calculated fromequations (147) and (148) as previously carried out forH--shaped sections and channels.

ti=a541− 1− X 8N*c

0.9fyi a25X

= λa4


where:

λ=dibidcbc 23

8 X

1+ 1− X

≈ 1.7dibidcbc X

1+ 1− X

A.4 DERIVATION FOR DESIGN PURPOSES-- SQUARE HOLLOW SECTION

A similar procedure to the one previously adopted iscarried out for square hollow sections.A.4.1DETERMINATIONOF a4 (YieldLineModel)The yield line pattern considered in the case ofrectangular hollow sections is shown in Fig. 75 and therequired design plastic moment Ômp under a uniformpressure f*p can be expressed as follows (based on [35]and [46]):

Ômp=f*pb2c21.4

(150)

where:

f*p=N*cdibi

bc

bc

Figure 75 Yield line pattern for Square HollowSections



Ôms=0.9fyit2i4≥

f*pb2c21.4

= Ômp (151)


ti=1

10.7 bc

2f*p0.9fyi

= a42N*c

0.9fyidibi (152)

where:

a4=1

10.7 bc≈ 1

3bc



AH= 2a3a5− 4a23 (153)

where:a5 = 2bc



A1

, Ô2f′c (154)




AH=N*cÔfb

(155)

In a similar manner as previously carried out the valueof a3 can be determined as follows:

a3=bc21− 1− X (156)

where:

X= 4N*cÔfba

25

and the value of the assumed bearing area AH can beexpressed as follows:

AH=a25X

4 = b2cX (157)

The required plate thickness can now be calculated.

ti=bc21− 1− X 2N*c

0.9fyi b2cX


= λa42N*c

0.9fyidibi (158)

where:

λ= 32

dibibc

X

1+ 1− X

A.5 DERIVATION FOR DESIGN PURPOSES-- CIRCULAR HOLLOW SECTION

A similar procedure to the one previously adopted iscarried out for circular hollow sections.

A.5.1 DETERMINATION OF a4(Yield line theory)

The yield line pattern considered in the case of circularhollow sections is shown in Fig. 76 and the requireddesign plasticmoment Ômpunder a uniformpressure f*pcan be expressed as follows (based on [35]):

Ômp=f*pd2024

(159)

where:

f*p=N*cdibi

do

Figure 76 Yield line pattern for CircularHollow Sections



Ôms=0.9fyit2i4≥

f*pd2024= Ômp (160)


ti=d02 3

2f*p0.9fyi = a4


where:

a4=d02 3


Referring to figure 14 the assumed bearing area AH canbe expressed as follows:

AH=π4[d20− (d0− 2a3)

2]= π(a3d0− a23) (162)



A1

, Ô2f′c (163)




AH=N*cÔfb

(164)

In a similar manner as previously carried out the valueof a3 can be determined as follows:

a3=d021− 1− X (165)

where:

X= 4N*cd20πÔfb

and the value of the assumed bearing area AH can beexpressed as follows:

AH= πd20X4

(166)

The required plate thickness can now be calculated.

ti=d021− 1− X 8N*c

0.9fyi πd20X

= λa4


where:

λ= 12π dibi

d0X

1+ 1− X

≈ 2dibid0

X

1+ 1− X

A.6 DERIVATION FOR CHECK PURPOSES-- ALL SECTIONS

The base plate capacity for a given base plate accordingto eachModel considered is first determined and then aunique expression which concatenates them is derived.


The following notation is used in the derivation:ÔNc.1=designcapacitybasedon a1of theCantilever

ModelÔNc.2=designcapacitybasedon a2of theCantilever

ModelÔNc.3 = design capacity based on the Yield Line

ModelÔNc.4 = design capacity based on Murray --

Stockwell Model

ÔNc.1=0.9fyidibit2i

2a21(168)


2a22(169)


2a24(170)

The calculation of the design capacity ÔNc.4 based onMurray--Stockwell model requires the followingderivation:

ti= λa42ÔNc.40.9fyidibi

=ÔNc.4 Y

1+ 1− ÔNc.4Y ka42

0.9fyidibi (171)

where:

λ= k X

1+ 1− X

X= ÔNc.4Y

and re--arranging equation (171) yields:

ÔNc.4=0.9fyibidi2a24

t2i λ′ (172)

where:

λ′ = 1k22ka4ti Y

2

0.9fyibidi − 1

The design capacity of the base plate is then calculatedas follows:

ÔNc= min(ÔNc.1, ÔNc.2, ÔNc.5) (173)

where:

ÔNc.5= max(ÔNc.3, ÔNc.4)

and ÔNc.1, ÔNc.2, ÔNc.3 and ÔNc.4 area calculated asshown in equations (168), (169), (170) and (172).

11. APPENDIX B-- Derivation of Design andCheck Expressions for Steel BasePlates Subject to Axial Tension

The derivation of the expressions for the design andcheck of base plate subject to axial tensile loading hasbeen here carried out for common base plate layoutswhen no design guidelines were found in literature.Yield line theory, based on conservative yield linepatterns (in the authors’ opinion), has been utilised inthe derivation.The plate moment capacity per unit length of yield linehas been calculated here based on the plastic sectionmodulus of the plate as also carried out inAustralian andAmerican guidelines [5], [21] and [26]. It is interestingto note that [23] recommends to use the elastic sectionmodulus.The reduction of plate capacity due to the anchor boltholes has been accounted for. Ignoring the effects of boltholes is a substantial simplification as also noted in [37].Murray Model, which considers the design of baseplates for lightly loaded H--shaped columns with twoanchor bolts, has been here re--derived and modified toinclude the plate reduction capacity due to bolt holes.Here the yield lines are conservatively assumed toremain inside the internal faces of the column profile,while in Murray Model they extend to the centerline ofthe web and to the outside faces of the flanges.The derivations of the capacity or required thickness forthe yield line patterns considered have been carried outfor various combinations of column sections andnumber of anchor bolts as listed in Section 5.4.7. Thederivation for the case of a H--shaped column withanchor bolts, as shown in Fig. 77, is outlined below. Allother cases are considered in a similar manner and therelevant expressions of their derivation are summarisedin Table 6. Similar considerations outlined for thevalidity of the Yield Line Model for the case of aH--shaped column section with 2 bolts can be applied tothe other base plate configurations considered.

B.1 H--SHAPED COLUMNWITH 2ANCHOR BOLTS

In the case of H--shaped column sections with twoanchor bolts the yield line pattern assumed is shown inFig. 77. It is the same as the one considered in MurrayModel. The base plate dimensions are conservativelyassumed to be equal to the outside column dimensionsunless noted otherwise.


s

y

y

bfc

dc12

dc12

tw

Figure 77 Yield line pattern: H--shaped columnwith 2 bolts

Considering the symmetry about the column web thederivation of the internal work and external work iscarried out only considering half the plate area:

Wi= Ômp1y4 bfc12 − 2dh+ 2bfc1

2y= Ômp2bfc1− 2dh

y + 4ybfc1 (174)

We= 2N*bsbfc1

(175)

where:bfc1= bfc− twy and s are defined in Fig.77

Equating the internal and external work the expressionof the design axial tension load per bolt N*

b is obtainedas follows:

N*b=

bfc12s2bfc1− 2dh

y + 4ybfc1Ômp (176)

Thevalueof ywhichminimises N*b (or equivalently that

maximises the required Ômp) is determineddifferentiating equation (176) for y.

dN*b

dy=−

2bfc1− 2dhy2

+ 4bfc1= 0 (177)

Solving equation (177) for y yields:

y=bfc1− dh

2 bfc1 (178)

The presence of the flanges requires the value of y to bealways less or equal to dc∕2 and therefore y isre--defined as follows:

y= mindc12 ,bfc1− dh

2 bfc1 (179)

The design axial tension capacity of the base plate ÔNtis then obtained re--arranging equation (176) as follows:

ÔNt= 2b2fc1− 2bfc1dh+ 4y20.9fyit2i4sy

(180)

where:y = as calculated from equation (179)

or equivalently the minimum plate thickness requiredfor a certain design tension load N*

t:

ti≥4syN*

t

0.9fyi2b2fc1− 2bfc1dh+ 4y2 (181)

In this model the reduction in plate capacity due to thepresenceof a bolt hole along theyield lineperpendicularto the web has been included.Further reductions due to other yield lines intersectingbolt holes have not been considered as they are veryunlikely to occur and amore detailed analysis should becarried out in such situation.The critical yield line pattern is a function of the valueof y calculated from equation (179). To ensure that noneof the oblique yield lines intersects the bolt hole, asassumed in the model derived, the following simplifiedcondition needs to be satisfied:

y> l2 (182)

where:

l1=dh2 1−

d2h4s2

l2=

l1l3

s−d2h4 − l21

and the notation is defined in Fig. 78.

d2h∕4− l21

l1

l2

s

diameter of hole = dhWeb

Edge of plate

l3

Figure 78 Yield line layout near the bolt hole

Substituting a nil value for the diameter of the bolt holedh in equations (179) and (181) would lead to thedetermination of plate thicknesses ti similar to thoseobtained with Murray Model.


Table 6 Summary of Internal and External Work for the Various Base Plate Configurations(refer to figures of Section 5.4.7. to view the yield line patterns considered)

Section /No. Bolts

Wi We y Restraints

H--shapedsection2--bolts

Ômp2bfc1− 2dhy + 4y

bfc1 2N*

bsbfc1 mindc12 ,

bfc1--dh2 bfc1

H--shapedsection

4--bolts (a)2Ômp2bfc1− 2dh

y + 4ybfc1 4N*

bsbfc1

bfc1− dh2 bfc1 y≤ ab, sp2

H--shapedsection

4--bolts (b)Ômp2bfc1--2dhab

+2bfc1--2dh

y +4y+4abbfc1 4N*

bsbfc1

bfc1− dh2 bfc1 y≤

sp2

H--shapedsection

4--bolts (c)Ômp2bfc1− 2dh

y +4y+ 2spbfc1 4N*

bsbfc1 minab, bfc1--dh

2 bfc1 H--shapedsection

4--bolts (d)Ômp2bfc1− 2dh

y +4y+ 2sp− 2dh

s 2N*b

minab, bfc1--dh2 s

H--shapedsection

4--bolts (e)Ômpbfc1− 2dh

ab+

4ab+ 2sp− 2dhs 2N*

b

Channel2--bolts Ômp4bfc1− 2dh

y + 2ybfc1 N*

bsbfc1 mindc12 , (2bfc1--dh)bfc1

Channel4--bolts (a) 4Ômp2bfc1− 2dh

y + 2ybfc1 2N*

bsbfc1

(2bfc1− dh)bfc1 y≤ ab, sp2 Channel4--bolts (b) Ômp4bfc1--2dhab

+4bfc1--2dh

y +2y+2abbfc1 2N*

bsbfc1 (2bfc1− dh)bfc1 y≤

sp2

Channel4--bolts (c) Ômp4bfc1− 2dh

y +2y+ spbfc1 2N*

bsbfc1 minab, (2bfc1--dh)bfc1

Channel4--bolts (d) Ômp4bfc1− 2dh

y +4y+ 2sp− 2dh

s 2N*b

minab, 2bfc1− dh2 s

Channel4--bolts (e) Ômp2bfc1− 2dh

ab+

4ab+ 2sp− 2dhs 2N*

b

Hollow2--bolts (a) Ômu4s2− 2dh

y + 2ys2 N*

bs1s2

(2s2− dh)s2 2y≤ li

Hollow2--bolts (b) Ômp

lis4

N*bs3s4

Hollow4--bolts (a) Ômu4s2− 2dh

y +2y+ sp

s2 2N*

bs1s2

(2s2− dh)s2 2y+ sp≤ li

Hollow4--bolts (b) Ômp

lis2

2N*bs3s4


12. APPENDIX C -- Determination ofEmbedment Lengths and EdgeDistances

The recommended guidelines regarding the minimumembedment lengths and concrete edge distances arehere derived in a similar manner as carried out inreferences [39] and [47]. The guidelines derived in [39]are also recommended in [21] and [26]. Differencesbetween the derivations carried out here and thosepresented in references [39] and [47] are noted.

C.1 MINIMUM EMBEDMENT LENGTHOF ANCHOR BOLTS

The recommended model requires the anchoragesystem (anchor to concrete connection) to fail in aductile manner. This is achieved by ensuring that theconcrete capacity is greater than the tensile capacity ofthe anchor bolt. [2]Minimum embedment lengths are here derived,similarly to [39], for isolated anchor bolts. Anchor boltsin bolt groups might require longer embedment lengthsdue to overlapping of the concrete failure envelopes.The calculation of the concrete capacity is based on theprocedure described in the recommended model. Theconcrete cone projected area is calculated ignoring thearea of the bolt calculated using the nominal boltdiameter df. In [39] the projected area is calculatedignoring the area of a circle equivalent to the projectedarea of a heavy hexagonal head. Comparing the ratiosLd∕df (where Ld is the minimum embedment lengthrequired and df is the nominal bolt diameter) regardingthe same types of bolts, the results obtained here appearto be of the order of 1%more conservative than the onesobtained in [39]. The further simplification of simplyconsidering the cone as starting at the embedded end ofthe anchor bolt has been adopted in reference [47].The concrete capacity is calculated as follows:

ÔNcc= Ô0.33 f′c Aps (183)

where:Ô = 0.7 (based Ô required for Clause 9.2.3 of AS

3600) instead of 0.65 as adopted in references[39] and [47]

Aps = πLd+ df22− πdf2

2

=

= π(L2d+ dfLd)

The tensile capacity of the anchor bolt is determined inaccordance with Clause 9.3.2.2. of AS 4100 as follows:

Ntf= Asfuf (184)

where:As = tensile stress area in accordance with AS 1275

[9]Theminimumembedment length is calculated equatingequations (183) and (184) as follows:

Ô0.33 f′c πL2d+ dfLd = Asfuf (185)

and solving for Ld:

Ld=− df+ d2f+ 4γ

2 ≥ 100 (186)

where:

γ=fufAs

Ô0.33 f′c π

The minimum embedment lengths derived andrecommended in [39] have been calculated adding anadditional safety factor of 1.33. The recommendedembedment lengths recommended here do not includethe additional safety factor of 1.33 (similarly toreference [47]). For completeness the embedmentlengths have been here calculated with and without thesafety factor of 1.33.The calculation of theminimumembedment lengths foranchors with different bolts tensile strengths and fordifferent concrete strengths is carried out in Tables 7and 8 in order to explicitly show how this additionalsafety factor of 1.33 introduced in references [39] isincorporated in the results.The tabulated results are smaller than those presented inreference [47] due to the different procedure utilised todetermine theprojected area even if here a Ô equal to 0.7has been adopted.Including the additional factor of safety Ôsf= 1.33recommended in reference [39] equation (186) can bere--written as :

Ld= Ôsf− d2f+ d2f+ 4γ

2 ≥ 100 (187)

where:Ôsf= 1.33

γ=fufAs

Ô0.33 f′c π


Table 7 Minimumembedment lengths forGrade4.6 bolts and Grade 250 rods(fuf = 400 MPa)

BoltType

dfmm

Asmm2

f’cMPa

Ldmm

MinratioLd/df

1.33Ldmm

1.33Ld/df

M12 12 84.3 20 100.0 8.4 127.8 10.7

M16 16 157 20 131.3 8.2 174.7 10.9

M20 20 225 20 164.1 8.2 218.2 10.9

M24 24 324 20 196.9 8.2 261.9 10.9

M30 30 519 20 248.4 8.3 330.3 11.0

M36 36 759 20 299.8 8.3 398.8 11.1

M12 12 84.3 25 100.0 8.4 120.5 10.0

M16 16 157 25 123.8 7.7 164.7 10.3

M20 20 225 25 154.6 7.7 205.7 10.3

M24 24 324 25 185.6 7.7 246.9 10.3

M30 30 519 25 234.1 7.8 311.4 10.4

M36 36 759 25 282.6 7.9 375.9 10.4

M12 12 84.3 32 100.0 8.4 112.8 9.4

M16 16 157 32 115.9 7.2 154.2 9.6

M20 20 225 32 144.8 7.2 192.6 9.6

M24 24 324 32 173.8 7.2 231.2 9.6

M30 30 519 32 219.3 7.3 291.6 9.7

M36 36 759 32 264.7 7.4 352.1 9.8

Table 8 Minimum embedment lengthsforGrade 8.8 bolts (fuf = 830MPa exceptfuf = 800 MPa for M12 bolts )

BoltType

dfmm

Asmm2

f’cMPa

Ldmm

MinratioLd/df

1.33Ldmm

1.33Ld/df

M12 12 84.3 20 138.3 11.5 183.9 15.3

M16 16 157 20 192.5 12.0 256.1 16.0

M20 20 225 20 240.5 12.0 319.9 16.0

M24 24 324 20 288.7 12.0 384.0 16.0

M30 30 519 20 364.1 12.1 484.2 16.1

M36 36 759 20 439.5 12.2 584.5 16.2

M12 12 84.3 25 130.5 10.9 173.5 14.5

M16 16 157 25 181.7 11.4 241.6 15.1

M20 20 225 25 226.9 11.3 301.8 15.1

M24 24 324 25 272.4 11.4 362.3 15.1

M30 30 519 25 343.5 11.5 456.9 15.2

M36 36 759 25 414.7 11.5 551.5 15.3

M12 12 84.3 32 122.3 10.2 162.7 13.6

M16 16 157 32 170.3 10.6 226.6 14.2

M20 20 225 32 212.8 10.6 283.0 14.2

M24 24 324 32 255.4 10.6 339.7 14.2

M30 30 519 32 322.1 10.7 428.4 14.3

M36 36 759 32 388.8 10.8 517.1 14.4

Observing the results of Tables 7 and 8 the embedmentlengths requirements can be simplified as shownbelow.

Table 9 Grade 4.6 bolts and 250 grade rodswhere Ôsf is a safety factor introduced inreference [39]

Ôsf f′c (MPa) Ld

1 20 9 df1 25 9 df1 32 9 df

1.33 20 12 df1.33 25 11 df1.33 32 10 df

Table 10 Grade 8.8 bolts where Ôsf is a safetyfactor introduced in reference [39]

Ôsf f′c (MPa) Ld

1 20 13 df1 25 12 df1 32 11 df

1.33 20 17 df1.33 25 16 df1.33 32 15 df

C.2 MINIMUM CONCRETE EDGEDISTANCES --Anchor bolt subject to tension

[2] provides a design procedure to determine theminimum concrete edge distances to avoid lateralbursting of the concrete as discussed in the literaturereview of anchor bolts subject to tension. This has beenincluded in the recommended model. The minimumedge distance is calculated as follows:

ae= dffuf

6 f′c (188)

The required minimum edge distances ae calculatedwith equation (188) are tabulated inTables 11 and 12 fordifferent combinations of anchor bolts and concretestrengths.


Table 11 Minimum concrete edge distances foranchor bolts Grade 4.6 bolts and Grade250 rods (fuf = 400 MPa)subject to tension

Bolttype

df (mm) f’c(MPa)

ae(mm)

ae / df

M12 12 20 46.3 3.9M16 16 20 61.8 3.9M20 20 20 77.2 3.9M24 24 20 92.7 3.9M30 30 20 115.8 3.9M36 36 20 139.0 3.9M12 12 25 43.8 3.7M16 16 25 58.4 3.7M20 20 25 73.0 3.7M24 24 25 87.6 3.7M30 30 25 109.5 3.7M36 36 25 131.5 3.7M12 12 32 41.2 3.4M16 16 32 54.9 3.4M20 20 32 68.7 3.4M24 24 32 82.4 3.4M30 30 32 103.0 3.4M36 36 32 123.6 3.4

Table 12 Minimum concrete edge distancesfor anchor bolts Grade 8.8 bolts(fuf = 830 MPa except fuf = 800 MPa forM12 bolts ) subject to tension

Bolttype

df (mm) f’c(MPa)

ae(mm)

ae / df


The values of minimum edge distances requiredexpressed in terms of df can be summarised as follows:

for Grade 4.6 bolts and Grade 250 rodsae = 4 df when f′c = 20, 25 and 32 MPafor Grade 8.8 bolts

ae = 6 df when f′c = 20 and 25 MPa= 5 df when f′c = 32 MPa

The recommended model requires the minimum edgedistance ae to be always at least equal to 100mm asrecommended in [21], [26] and [39]. Minimum edgedistance recommended in reference [47] is 50mm.

C.3 MINIMUM CONCRETE EDGEDISTANCES --Anchor bolt subject to shear

Guidelines onminimumedge distances to be adopted inthe case of bolts in shear are provided in [2], [3], [17],[26], [39] and [47].These are all based on the design procedure presented in[2], [3] and [17] which requires the minimum edgedistance to be calculated as (refer equation (106)):

ae≥ dffuf

Ô0.94 f′c (189)

where:Ô = 0.65 according to references [3] and [39]

= 0.85 according to references [17], [26] and [47]For completeness edge distances calculated with bothvalues of Ô have been considered and tabulated here. Itis up to designer to decide whether or not to design theanchor bolts to carry shear and to select a value of Ô.These values of ae are tabulated in tables 13, 14, 15 and16 for different combinations of anchor bolts andconcrete strengths and for different values of Ô.Table 13 Minimum concrete edge distances

for anchor bolts Grade 4.6 bolts andGrade 250 rods (fuf = 400 MPa)subject to shear with Ô = 0.65

Bolttype

df (mm) f’c(MPa)

ae(mm)

ae / df



Table 14 Minimum concrete edge distancesfor anchor bolts Grade 8.8 bolts(fuf = 830 MPa except fuf = 800 MPa forM12 bolts) subject to shear with Ô = 0.65

Bolttype

df (mm) f’c(MPa)

ae(mm)

ae / df


Table 15 Minimum concrete edge distancesfor anchor bolts Grade 4.6 bolts andGrade 250 rods (fuf = 400 MPa)subject to shear with Ô = 0.85

Bolttype

df (mm) f’c(MPa)

ae(mm)

ae / df


Table 16 Minimum concrete edge distancesfor anchor bolts Grade 8.8 bolts(fuf = 830 MPa except fuf = 800 MPa forM12 bolts) subject to shear with Ô = 0.85

Bolttype

df (mm) f’c(MPa)

ae(mm)

ae / df


Re--arranging equation (189) the ratios ae∕df fordifferent combinationsof concrete andbolt strengths fordifferent values of Ô are obtained as shown below.Table 17 Grade 4.6 bolts and 250 Grade rods

Ô f′c (MPa) ae

0.65 20 13 df0.65 25 12 df0.65 32 11 df0.85 20 11 df0.85 25 10 df0.85 32 10 df

Table 18 Grade 8.8 bolts

Ô f′c (MPa) ae

0.65 20 18 df0.65 25 17 df0.65 32 16 df0.85 20 16 df0.85 25 15 df0.85 32 14 df


13. APPENDIX D -- Design Capacities ofEqual Leg Fillet Welds

Table 19 Category SP, Ô =0.8, kr=1.0

Weld size (mm) Design Capacity per unit lengthof fillet weld except for RHS/SHS with thickness less than 3

mm (kN/mm)tw tt E41XX/W40X E48XX/W50X2 1.41 0.278 0.3263 2.12 0.417 0.4894 2.83 0.557 0.6525 3.54 0.696 0.8156 4.24 0.835 0.9788 5.66 1.11 1.3010 7.07 1.39 1.6312 8.49 1.67 1.96

fuw=410 MPa fuw=480 MPa

Table 20 Category SP, Ô =0.7, kr=1.0

Weld size (mm) Design Capacity per unit length oflongitudinal fillet weld in RHS/SHS with t < 3mm (kN/mm)

tw tt E41XX/W40X E48XX/W50X2 1.41 0.244 0.2853 2.12 0.365 0.4284 2.83 0.487 0.5705 3.54 0.609 0.713


Table 21 Category GP, Ô =0.6, kr=1.0

Weld size (mm) Design Capacity per unit lengthof fillet weld (kN/mm)

tw tt E41XX/W40X E48XX/W50X2 1.41 0.209 0.2443 2.12 0.313 0.3674 2.83 0.417 0.4895 3.54 0.522 0.6116 4.24 0.626 0.7338 5.66 0.835 0.97810 7.07 1.04 1.2212 8.49 1.25 1.47


Table 22 Minimum Fillet Weld Sizes

Thickness of thickestpart t (mm)

Minimum size of a filletweld tw (mm)

t≤ 7 3

7< t≤ 10 4

10< t≤ 15 5

15< t 6

14. APPENDIX E -- Design of Bolts underTension and Shear

Table 23 Design Capacities Commercial Bolts4.6/S Bolting Cat. fuf=400MPa, Ô =0.8

BoltSi

AxialT i

Shear (single shear)Size Tension

ÔNtf(kN)

Threadsincluded inshear plane NÔVfn (kN)

Threadsexcluded fromshear plane XÔVfx (kN)

M12 27.0 15.1 22.4

M16 50.1 28.6 39.9

M20 78.3 44.7 62.3

M24 113 64.3 89.8

M30 179 103 140

M36 261 151 202

4.6N/S 4.6X/S

Table 24 Design Capacities High StrengthStructural Bolts8.8/S, 8.8/TB, 8.8/TF Bolting Categorys,Ô =0.8

BoltSi

Min.T il

AxialT i

Shear (single shear)Size Tensile

Strengthof Boltfuf

(MPa)

TensionÔNtf(kN)

Threadsincludedin shearplane NÔVfn (kN)

Threadsexcludedfromshearplane XÔVfx (kN)

M12 800 53.9 30.3 44.9

M16 830 104 59.3 82.8

M20 830 163 92.7 129

M24 830 234 133 186

M30 830 372 214 291

8.8N/S 8.8X/S


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ASI Members -- The best in Steel Fabrication

New South Wales and ACTAlmar Industries Pty Ltd9 Cheney Place Mitchell ACT 2911 02 6241 3391Baxter Engineering Pty LtdPO Box 643 Fyshwick ACT 2609 02 6280 5688Ace High Engineering Pty Ltd67 Melbourne Rd Riverstone 2765 02 9627 2500Algon Steel P/L9 Arunga Drive Beresfield 2322 02 4966 8224Align Constructions & Engineering Pty LtdPO Box 747 Moss Vale 2577 02 4869 1594Allmen Engineering35--37 Anne St St Marys 2760 02 9673 0051Antax Steel Constructions P/L93 Bellambi Lane Bellambi 2518 02 4285 2644B & G Welding Pty Ltd12 Bessemer St Blacktown 2148 02 9621 3189Beltor Engineering Pty LtdPO Box 4187 Edgeworth 2285 02 4953 2444Bosmac Pty Ltd64--68 Station Street Parkes 2870 02 6862 3699Boweld Constructions Pty LtdPO Box 52 Bomaderry 2541 02 4421 6781Charles Heath Industries18 Britton Street Smithfield 2164 02 9609 6000Combell P/LPO Box 5038 Prestons 2170 02 9607 3822Coolamon SteelworksPO Box 102 Coolamon 2701 02 6927 3296Cooma Steel Co. Pty LtdPO Box 124 Cooma 2630 02 6452 1934Cosme--Australia Stainless Steel Fab Pty Ltd19 Lasscock Road Griffith 2680 02 6964 1155Davebilt Industries116 Showground Rd NGosford 2250 02 4325 7381Designed Building Systems144 Sackville Street Fairfield 2165 02 9727 0566Edcon Steel Pty Ltd52 Orchard Rd Brookvale 2100 02 9905 6622Flame--Cut Pty LtdPO Box 6367 Wetherill Park 2164 02 9609 3677Gale Bros Engineering Pty LtdPO Box 6013 South Penrith 2750 02 4732 1133Jeskah Steel Products23 Arizona Rd Charmhaven 2263 02 4392 7022Kermac Welding & EngineeringCemetery Street Goulburn 2580 02 4821 3877Leewood WeldingPO Box 1767 Orange 2800 02 6362 8797Lifese Engineering Pty Ltd5 Junction Street Auburn 2144 02 9748 0444Mario & Sons (NSW) Pty Ltd189--193 Newton Road,Wetherill Park 2164 02 9756 3400Mecha Engineering Pty LtdPO Box 477 Wyong 2259 02 4351 1877Morson Engineering Pty LtdPO Box 244 Wyong 2259 02 4352 2188National Engineering Pty Ltd72--74 Bayldon Road,Queanbeyan 2620 02 6299 1844

National Engineering Pty LtdPO Box 437 Young 2594 02 6382 1499Piper & Harvey Steel FabricationsPO Box 821 Wagga Wagga 2650 02 6922 7527Ripa Steel Fabrication Pty Ltd4 Warren Place Silverdale 2752 02 4774 0011Riton Engineering Pty Ltd101 Gavenlock Road,Tuggerah 2259 02 4353 1688Romac EngineeringPO Box 670 Armidale 2350 02 6772 3407Saunders International Pty LtdPO Box 281 Condell Park 2200 02 9792 2444Steeline FabricationsPO Box 296 Woy Woy 2256 02 4341 9571Tenze EngineeringPO Box 426 Greenacre 2190 02 9758 2677Tri--Fab Engineering Pty LtdLot 1 Ti--Tree Street,Wilberforce 2756 02 4575 1056UEA Industrial Engineers Pty LtdPO Box 6163 Queanbeyan 2620 02 6299 3238Universal Steel Construction52--54 Newton Road,Wetherill Park 2164 02 9756 2555Walpett Engineering Pty Ltd52 Hincksman Street,Queanbeyan 2620 02 6297 1277Weldcraft Engineering ACT Pty Ltd79 Thuralilly Street,Queanbeyan 2620 02 6297 1453Z Steel Fabrications Pty LtdPO Box 7274 Lismore Heights 2480 02 6625 1717

Northern TerritoryM&J Welding And EngineeringGPO Box 2638 Darwin 0801 08 8932 2641Trans Aust Constructions P/LPO Box 39472 Winnellie 0821 08 8984 4511

QueenslandAG Rigging & Steel Pty LtdPO Box 9154 Wilsonton,Toowoomba 4350 07 4633 0244Alltype WeldingPO Box 1418 Beenleigh 4207 07 3807 1820Apex Fabrication & Construction164--168 Cobalt Street,Carole Park 4300 07 3271 4467Austin Engineering P/L173 Cobalt Street,Carole Park 4300 07 3271 2622Beenleigh Steel Fabrications P/L41 Magnesium Drive,Crestmead 4132 07 3803 6033Belconnen Steel Pty Ltd11 Malton Street The Gap 4061 07 3300 2444Brisbane Steel FabricationPO Box 7087 Hemmant 4174 07 3893 4233Cairns Steel Fabricators P/LPO Box 207b Bungalow 4870 07 4035 1506Casa Engineering (Qld) Pty LtdPO Box Ge 80 Garbutt East 4814 07 4774 4666

Central Engineering Pty Ltd19 Traders Way Currumbin 4223 07 5534 3155D A Manufacturing Co Pty Ltd7 Hilldon Court Nerang 4211 07 5596 2222Darra Welding Works Pty LtdPO Box 47 Richlands 4077 07 3375 5841Factory Fabricators Pty Ltd63 Factory Road Oxley 4075 07 3379 8811Fritz Steel (Qld) Pty LtdPO Box 12 Richlands 4077 07 3375 6366J K Morrow SalesPO Box 59 Earlville 4870 07 4035 1599

M C EngineeringPO Box 381 Burpengary 4505 07 3888 2144MilfabPO Box 3056 Clontarf 4019 07 3203 3311Morton Steel Pty Ltd47 Barku Court Hemmant 4174 07 3396 5322Noosa Engineering & Crane HirePO Box 356 Tewantin 4565 07 5449 7477Oz--Cover Pty Ltd35 Centenary Place,Logan Village 4207 07 5546 8922Pacific Coast Engineering Pty LtdPO Box 7284 Garbutt 4814 07 4774 8477Podevin Engineering Co P/LPO Box 171 Archerfield 4108 07 3277 1388Queensbury Steel Pty Ltd3 Queensbury Avenue,Currumbin Waters 4223 07 5534 7455Rimco Building Systems Pty Ltd20 Demand Avenue Arundel 4214 07 5594 7322Spaceframe Buildings Pty Ltd360 Lytton Road Morningside 4170 07 3370 6500Stewart & Sons Steel11 Production St Bundaberg 4670 07 4152 6311Sun Engineering Pty Ltd113 Cobalt St Carole Park 4300 07 3271 2988Taringa Steel P/L17 Jijaws St Sumner Park 4074 07 3279 4233Thomas Steel FabricationPO Box 147 Aitkenvale,Townsville 4814 07 4775 1266W D T Engineers Pty LtdPO Box 115 Acacia Ridge 4110 07 3345 4000Walz Construction Company Pty LtdPO Box 1713 Gladstone 4680 07 4972 4799

South AustraliaAdvanced Steel Fabrications61--63 Kapara Rd Gillman 5013 08 8447 7100Ahrens Engineering Pty LtdPO Box 2 Sheaoak Log 5371 08 8524 9045Bowhill EngineeringLot 100, Weber Road Bowhill 5238 08 8570 4208Magill Welding Service Pty Ltd33 Maxwell Road Pooraka 5095 08 8349 4933Manuele Engineers Pty LtdPO Box 209 Melrose Park 5039 08 8374 1680RC & Ml Johnson Pty Ltd671 Magill Road Magill 5072 08 8333 0188

ASI Members -- The best in Steel Fabrication

TasmaniaDowling Constructions Pty Ltd46 Formby Road Devonport 7310 03 6423 1099

Haywards Steel Fabrication & ConstructionPO Box 47 Kings Meadows 7249 03 6391 8508

VictoriaAlfasi Steel Constructions12--16 Fowler Road,Dandenong 3175 03 9794 9207

AMS Fabrications Pty Ltd18 Healey Road Dandenong 3175 03 9706 5988

Bahcon Steel Pty LtdPO Box 950 Morwell 3840 03 5134 2877

Downer PTR195 Wellington Rd Clayton 3168 03 9560 9944

F & B Skrobar Engineering Pty LtdPO Box 1578 Moorabbin 3189 03 9555 4556

Fairbairn Steel Pty LtdPO Box 2057 Seaford 3198 03 9786 2866

G F C Industries Pty Ltd42 Glenbarry Road,Campbellfield 3061 03 9357 9900

Geelong Fabrications Pty Ltd5/19 Madden Avenue,North Shore Geelong 3214 03 5275 7255

GVP Fabrications Pty Ltd25--35 Japaddy Street,Mordialloc 3195 03 9587 2172Monks Harper Fabrications P/L25 Tatterson Road,Dandenong South 3164 03 9794 0888Preston Structural Steel140--146 Barry Road,Campbellfield 3061 03 9357 0011Riband Steel (Wangaratta) Pty Ltd69--81 Garden Road Clayton 3168 03 9547 9144Rosebud Engineering13 Henry Wilson Drive,Rosebud 3939 03 5986 6666Stanley Welding23 Attenborough Street,Dandenong 3175 03 9555 5611Stilcon Holdings Pty LtdPO Box 263 Altona North 3025 03 9314 1611Vale Engineering Co Pty Ltd170 Gaffney Street Coburg 3058 03 9350 5655

Western AustraliaC Bellotti & CoPO Box 1284 Bibra Lake 6965 08 9434 1442Cays EngineeringLot 21 Thornborough Road,Mandurah 6210 08 9581 6611

Devaugh Pty Ltd12 Hale St Bunbury 6230 08 9721 3433Fremantle Steel Fabrication CoPO Box 3005 Jandakot 6964 08 9417 9111Highline Building Constructions9 Felspar Street Welshpool 6106 08 9451 5366H’var Steel Services Pty Ltd56 Cooper Rd Jandakot 6164 08 9414 9422Italsteel W.A.PO Box 206 Bentley 6102 08 9356 1566JV Engineering (WA) Pty Ltd159 Mcdowell Street Kewdale 6105 08 9353 3377Leblanc Comm\ Aust P/LPO Box 40 Belmont 6984 08 9277 8866Pacific Industrial CompanyPO Box 263 Kwinana 6966 08 9410 2566Park Engineers Pty LtdPO Box 130 Bentley 6102 08 9458 1437Scenna Constructions43 Spencer Street Jandakot 6164 08 9417 4447United KGPO Box 219 Kwinana 6167 08 9499 0499Uniweld Structural Co Pty Ltd61A Coast Road Beechboro 6063 08 9377 6666Wenco Pty Ltd1 Ladner Street Oconnor 6163 08 9337 7600

ASI Manufacturing Members -- The best quality steel

BHP SteelBHP Tower, 600 Bourke Street,Melbourne VIC 3000(GPO Box 86A, Melbourne 3001) 03 9609 3756Bisalloy Steels Pty LtdResolution Drive, Unanderra NSW 2526(PO Box 1246, Unanderra 2526) 02 4272 0444Commonwealth Steel Company LimitedMaud Street, Waratah NSW 2298(PO Box 14) 02 4967 0457Graham Group117--151 Rookwood Road, Yagoona NSW 2199(PO Box 57) 02 9709 3777Industrial Galvanizers Corporation Pty Ltd20--22 Amax Avenue, Girraween NSW 2145(PO Box 576, Toongabbie 2146) 02 9636 8244Martin Bright SteelsCliffords Road, Somerton VIC 3062(PO Box 39 MDC) 03 9305 4144

OneSteel Pty LtdLevel 23, 1 York Street, Sydney NSW 2000(GPO Box 536) 02 9239 6666

Palmer Tube Mills (Aust) Pty Ltd46 Ingram Road, Acacia Ridge QLD 4110(PO Box 246, Sunnybank 4109) 07 3246 2600

Smorgon Steel Group LtdGround Floor, 650 Lorimer Street,Port Melbourne VIC 3207 03 9673 0400

Stramit Industries6--8 Thomas Street, Chatswood NSW 2067(PO Box 295, Chatswood 2057) 02 9928 3600

J Blackwood & Son Steels and Metals Pty Ltd165--169 Newton Road, Wetherill Park NSW 2164(PO Box 6427) 02 9203 1100

Coil Steels Group Pty Ltd16 Harbord Street, Granville NSW 2142(PO Box 166) 02 9682 1266

G A M Steel Pty LtdLynch Road, Brooklyn VIC 3025(PO Box 159, Altona North 3025) 03 9314 0855Midala Steel Pty Ltd49 Pilbara Street, Welshpool WA 6106(PO Box 228, Welshpool 6986) 08 9458 7911Southern Steel Group319 Horsley Road, Milperra NSW 2214(PO Box 342, Panania 2213) 02 9792 2099Smorgon Steel Distribution88 Ricketts Road, Mount Waverley VIC 3149(PO Box 537) 03 9239 1844Metalcorp Steel103 Ingram Road,Acacia Ridge QLD 4110 07 3345 9488OneSteel DistributionCnr Blackwall Point & Parkview Roads,Five Dock NSW 2046(PO Box 55) 02 9713 0350

AUSTRALIAN STEEL INSTITUTE

Level 13, 99 Mount StreetNorth Sydney NSW 2060

Telephone (02) 9929 6666Website: www.steel.org.au

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