VER Design of Anchorage to Concrete Handout

Design of Anchorage to ConcreteDesign of Anchorage to Concrete

Prepared by: Widianto, Jerry Owen, and Chandu Patel

Civil Structural

25 March 2008

Prepared by: Widianto, Jerry Owen, and Chandu Patel

Civil Structural

25 March 2008

Training Module2

Scope and Objectives

Provide general understanding about behavior of anchors in

structural concrete and design of anchorage to concrete

Present ACI 318-08 Appendix D provisions (Anchoring to Concrete)

Present common and STM approaches for designing anchor

reinforcement

Not covered in this presentation:

Shear lugs, Post-installed anchors, headed studs, tensioning,

fatigue & impact loadings, coatings / galvanizing, and

installation

Training Module3

Outline

I. Introduction

V. Design philosophy of the ACI 318-08 Appendix D

VI. Anchorage to concrete for tension loading

VII. Anchorage to concrete for shear loading

VIII. Combined loading (Tension and shear)

II. Common / existing approaches for designing anchor reinforcement

III. Strut-and-Tie Model approach for designing anchor reinforcement

IX. Summary and references

Appendix D of

ACI 318-08

IV. Example problem

Training Module4

PART I

INTRODUCTION

Pictures of anchor bolts and possible failure modes

Available design guidelines for anchor bolts

New provisions in the ACI 318-08

Basic load path for tension and shear

Training Module5

Taken from field

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Training Module7

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Directly from the field

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Taken from field

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Possible failure mode Steel failure

Wiewel (1991)

Steel failure: the concrete crushes a small amount and the stress in the anchor results in an action that causes a smooth failure plane in the stud as the steel reaches its ultimate shear capacity

Training Module14

Possible failure mode Concrete crushing

Wiewel (1991)

Concrete crushing failure: the concrete surrounding the anchor crushes near the surface allowing the anchor to displace which creates a bending load ending in a steel rupture failure. This type of failure is common for anchors manufactured from brittle steels

Training Module15

Possible failure mode Concrete breakout

Wiewel (1991)

Cone failure: the concrete fails in tension creating a shear cone. The cone starts at the bottom of the expansion mechanism and travels to the concrete surface at an angle which varies between 30 to 45 degrees. This type of failure is common when tension tests are performed on anchors installed at embedments between 4.5D and 6.0D

Training Module16

Possible failure mode Concrete breakout

Wiewel (1991)

Concrete breakout failure: this type of failure generally occurs when anchors are installed close to an edge or corner

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Possible failure mode Concrete splitting

Wiewel (1991)

Concrete splitting failure: the concrete slab/beam fails in bending, splitting the structural member.

This type of failure is common for anchors installed near an edge of a thin, unreinforcedslab or beam

Concrete failure: split structural member.

The concrete slab or beam fails in bending. This type of failure is common for anchors installed in thin slabs and beams, or for anchors installed near a corner of a slab or beam

Training Module18

Possible failure mode Side-face Blowout

DeVries (1996)

DeVries (1996)

Bashandy (1996)

Training Module19

What are the available design guidelines for anchorage to concrete ?

Appendix D of ACI 318-08

Section 1913 of IBC 2003 refer to the Appendix D of ACI 318-08

Training Module20

What are the available design guidelines for anchorage to concrete ?

Training Module21

What is new in the 2008 edition of the ACI 318, Appendix D ?

Definition of two types of reinforcement that can be used across the

potential breakout cone:

1. Supplementary reinforcement

2. Anchor reinforcement

Can be used to improve the deformation capacity for the breakout mode, and thus, enables the use of a higher -factor.

Designed to transfer the full design load from the anchors into the structural member, and thus precludes consideration of the concrete breakout failure mode.

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Section D.4.2.1 of ACI 318-08

Training Module23


Modification factor for lightweight concrete

A modification factor for concrete breakout strength is introduced to

correct the current conservative provisions for anchorages loaded

in shear and located in thin concrete members (h,V)

Training Module24

Basic Load Path

1. Tension loading (without anchor reinforcement)

Anchor (i.e. steel)

Bearing strength

of concrete

Tensile strength

of concrete

Foundation

Yielding / fracture

Anchor pullout

Concrete breakout

Mode of failure:

PLAIN CONCRETE

Side-face blowout

Concrete splitting

If close to an edge:

Training Module25

Basic Load Path cont

Basic load path:

1. Tension loading (with anchor reinforcement)

Anchor (i.e. steel)

Anchor

reinforcement

Foundation

Yielding / fracture

Pullout

Rebar yielding

Rebar pullout

Mode of failure:

REINFORCED CONCRETE

Side-face blowout

Concrete splitting


Bearing strength

of concrete

Training Module26

Fracture


Anchor (i.e. steel)

Rebar

Foundation

Pullout

Rebar yielding

Rebar pullout

Mode of failure:

Tensile strength of concrete Concrete breakoutno anchor

reinforcement

Side-face blowout

Concrete splitting


Concrete breakout

Side-face blowout

Concrete splitting

Yielding / fracture

Bearing strength

of concrete

1. Tension loading (summary)

with anchor

reinforcement

Training Module27


Basic load path:

2. Shear loading without anchor reinforcement

Anchor (i.e. steel)

Tensile strength

of concrete

Foundation

Yielding / fracture

Concrete breakout

Mode of failure:

PLAIN CONCRETE

Concrete pryout

Training Module28


Basic load path:

2. Shear loading with anchor reinforcement

Anchor (i.e. steel)

Foundation

Yielding / fracture

Yielding

Mode of failure:

REINFORCED CONCRETE

PulloutAnchor reinforcement

Bearing strength

of concreteCrushing

Training Module29

Concrete pryout


Anchor (i.e. steel)

Anchor reinforcement

Foundation

Yielding, pullout

Mode of failure:

Tensile strength of concrete Concrete breakout

Anchor failure preceded by concrete spallYielding / fracture

2. Shear loading (summary)

Concrete pryout

Bearing of concrete Crushing

Concrete breakoutno anchor

reinforcement

with anchor

reinforcement

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When both tension and shear are present

1. Design for tension

2. Design for shear

3. Check interaction

Training Module31

Common anchor bolts

PIP,

2006

Training Module32

PART II

COMMON / EXISTING APPROACH

for

DESIGNING ANCHOR REINFORCEMENT

Training Module33

Design Philosophy

Concrete contribution is neglected in proportioning the steel reinforcement.

When a non-ductile design is permitted, the reinforcement should be designed to resist the factored design load.

When a ductile design is required, the reinforcement should be proportioned to develop the strength of the anchor. If the anchor is sized for more than 2.5 times factored tension design loads, it is permitted to design the reinforcement to carry 2.5 times the factored design load, where 2.5 is an overstrength factor.

When reinforcement is used to restraint concrete breakout, the overall anchorage design should ensure that there is sufficient strengthcorresponding to other failure modes (pullout failure, side-face blowout failure, and pryout failure).

Training Module34

Designing Anchor Reinforcement for Tension

35

hef

dmax hef /3

ld

db

Pier height

cover

dmax

ldh

Construction jointSide cover

T

What is the max. distance from anchor head to the reinforcement to be considered effective, dmax ?

Cannon et al. (1981): dmax = hef /3 (clear distance from anchor head)Section RD.5.2.9 of ACI 318-08: dmax = hef /2

(measured from the anchor centerline)

What is the required development length, ld ?

Use Section 12.2 of the ACI 318-08

The development length may be reduced when excess reinforcement is provided per section 12.2.5 of the ACI 318-08 (but cannot be less than 12)Reduction in the development length cannot be applied in the areas of moderate or high seismic risk.

In order to limit the embedment length of anchor, a larger number of smaller-size reinforcing bars is preferred over fewer, larger-size reinforcing bars.

Training Module35


35

hef

dmax hef /3

ld

db

Pier height

cover

dmax

ldh

Construction jointSide cover

T

How to determine the required area of steel, Ast ?

When a non-ductile failure is permitted:y

ust f

TA

When a ductile failure is required:y

utasest f

fAA

However, the anchor is sized for more than 2.5 Tu, it is permitted to design the reinforcement to carry 2.5 Tu to satisfy IBC 2006 and ASCE 7-05 requirements for SDC C and above where ductility cannot be achieved.

y

ust f

TA

5.2

Design for anchor ductility requires that the necessary conditions for elongation over a reasonable gage length are fulfilled (i.e., that strain localization will not limit the yield strain).

where: 9.0=

where: 9.0=

If the available development length is less than the required length to fully develop the anchor reinforcement, reduce the bar size or use the stress that can be developed fs (< fy).

ACI 318-08 use = 0.75

ACI 318-08 use = 0.75

Training Module36


What does the Appendix D of ACI 318-08 recommend ?

75.0=

Commentary RD.5.2.9:

This recommendation is limited to anchor reinforcement with maximum diameter similar to a #5 bar.

It is beneficial for the anchor reinforcement to enclose the surface reinforcement.

In sizing the anchor reinforcement, the use of =0.75 is recommended as is used for the strut-and-tie models.

As a practical matter, the use of anchor reinforcement is generally limited to cast-in-place anchors.

Training Module37

Designing Anchor Reinforcement for Shear

23

V

V

dtie

35

How many anchors are effective to carry V ?

If welded washers are used, all anchors will be effective.

Otherwise, only some anchors will be effective (due to oversize holes)

Where is the origin of the shear cracks ?

Questionableld or ldh

ld or ldh

Training Module38


23

V

V

dtie

35

How to determine the required area of steel, Atie ?

How many legs are available ?

Try to carry all shear forces using the first two sets of shear reinforcement.

y

utie f

VA

ld or ldh

ld or ldh

where: 9.0=

If the available development length is less than the required length to fully develop the anchor reinforcement, use smaller rebar size or use the stress that can be developed fs (< fy).

ACI 318-08 use = 0.75

Training Module39

Designing Anchor Reinforcement for ShearWhat does the Appendix D of ACI 318-08 recommend ?

75.0=


Based on research with max. diameter similar to a #5 bar.

Enclosing anchor reinforcement should be in contact with the anchor and placed as close as practicable to the concrete surface.

In sizing the anchor reinforcement, the use of = 0.75 is recommended as is used for the strut-and-tie models.


Training Module40


What does the Appendix D of ACI 318-08 recommend ?


The reinforcement could also consist of stirrups and ties (as well as hairpins) enclosing the edge reinforcement embedded in the breakout cone and placed as close to the anchors as practicable

Only reinforcement spaced < the lesser of 0.5 ca1 and 0.3 ca2 from the anchor centerline should be included as anchor reinforcement.

The anchor reinforcement must be developed on both sides of the breakout surface.

Based on research with the max. size of #6 bar

In sizing the anchor reinforcement, the use of = 0.75 is recommended as is used for the strut-and-tie models.

For equilibrium reasons, an edge reinforcement must be present.


Training Module41

PART III

STRUT-and-TIE MODEL APPROACH

for

DESIGNING ANCHOR REINFORCEMENT

Training Module42

Problems with the existing design approach

Variation of breakout cone angle Some of anchor

reinforcements may not be effective

Anchor reinforcement will only be effective after breakout cone

cracks have been developed. Even though the breakout cone

capacity is commonly smaller than service loads, cracks on

concrete pedestals are rarely seen. Better explanation on load

transfer is needed

For shear - There are many applications where the shape of

concrete breakout cone is not obvious. In a group of anchor, the

location where the shear crack starts is not always obvious

For shear reinforcement - enclosing anchors with hairpin is not

always feasible.

Training Module43

What is the Strut-and-Tie Model (STM) ?

A strut-and-tie model (STM) is an ultimate strength design method based on the formation of a hypothetical truss that transmits forces from loading points to supports.

The STM utilizes concrete struts to resist compression and reinforcing ties to carry tension. Design using STM involves calculating the required amount of reinforcement to serve as the tension ties and then checking that the compressive struts and nodal zone (joints) are sufficiently large enough to support the forces.

Training Module44

STM for tension

25

25

ACI 318-08:

Mechanism of force transfer between opposing lapped headed bars (Thompson et al., 2006)

Training Module45

STM for tensionIn order to make it consistent with the CCD method, the angle of

strut is assumed to be 35 from horizontal.

Concrete strut

Steel tie

35

How to determine the tie force ?

Tie Tie

T

T/4

Tie force per side = [ T/4 cos (55) ] cos (35) = T/4 0.47 = 0.12 T

Training Module46

STM for tension

T

35 25

25

Design tie to carry 0.12 T

If one layer of tie at 35 is insufficient,

place additional tie layers within this

region only

Training Module47

Assumptions for STM - shear Concrete strength

Concrete strength for struts and bearing 0.85 fc

Training Module48

Assumptions for STM Bearing area

VV

V

Concrete strut

Grout

2

3

do

8do

1.51

Rebar

Anchor

Tie

Hairpin

T1

T2T2

T1

Concrete strut

Anchor

V : Shear force per anchor

T1 : Tension force on tie

T2 : Tension force on hairpin

do : Diameter of anchor

Note:

Section 7.10.5.6 of the ACI 318-08:

The lateral reinforcement shall surround at least four vertical bars, shall be distributed within 5 of the pedestal, and shall consist of at least two #4 or three #3 bars.

Section D.6.2.2 of the ACI 318-08: the maximum load bearing length of the anchor for shear is 8 do.

Bearing area of anchor = (8 do) do = 8 do2

Bearing area of the rebar is shown on the left

Training Module49

Only the top most two layers of ties (assume 2-#4 within 5of top of pedestal per Section 7.10.5.6 of the ACI 318-08) are effective

23

Layer A

Layer B

V

Layer A

Layer B

1 2 3

4 5

6 7 8

V

6dtie 3

dtie

Assumptions for STM Tie reinforcement

1 2 3

4 5

6 7 8

lah V

6dtie 3dtie

Tie reinforcement should consist of tie with seismic hooks. If internal ties are required, hairpins could be used. As an alternative, diamond-shaped ties can also be used.

The location of hooks and the direction of hairpins should be alternated

If the available length of hairpin lah < the required straight development length for a fully developed hairpin ld, the maximum stress that can be developed in hairpin is

d

ahy l

lf

If lah is shorter than 12 (i.e. the minimum development length based on Section 12.2.1 of the ACI 318-08), hairpin should not be used.

Training Module50

At the nodes away from the hook, the tie is assumed to be fully developed. (For example, under the shear force V, the tie on layer A can develop fy at the nodes 1 and 6)

23

Layer A

Layer B

V

Layer A

Layer B

1 2 3

4 5

6 7 8

V

6dtie 3

dtie

Assumptions for STM Tie reinforcement cont

1 2 3

4 5

6 7 8

lah V

6dtie 3dtie At the node where the hook is located, the tie cannot

develop fy. (For example, under the shear force V, while the tie on layer A can develop fy at the node 6, the tie on layer B cannot develop fy because the hook of tie B is located at the node 6)

Training Module51

Compare the stiffness of the following two cases:

Layer B

1 2 3

4 5

6 7 8

V

6dtie 3

dtie

V

V

Tie

Hairpin

T2T2

T1

Anchor

Concrete strutHow to account for contribution from tie Layer B to the tension tie at the node 6?


CASE 1: smooth rebar with 180 hook bearing in concrete (Fabbrocino et al., 2005) T

T

CASE 2: the conventional single-leg stirrup with reinforcing bars inside the bends (Leonhardt and Walther, 1965 as cited in Ghali and Youakim, 2005)

Even though the capacity of CASE 2 may be higher than the capacity of CASE 1 due to bearing on the heavier rebar, the contact will not always present because of common imprecise workmanship. When the contact is not present, the CASE 2 is assumed to behave as CASE 1. Training Module52

In order to fully-develop fy on the bends of 90, 135, and 180 hooks when engaging heavier bars lodged inside the bends (CASE 2), there was a slip about 0.2 mm (Leonhardt and Walther, 1965).

How to account for contribution from tie Layer B to the tension tie at the node 6?


The stress at the hook that was developed at the smooth rebar with 180 hook bearing in concrete (CASE 1) when it slipped 0.2 mm was about 20 ksi (Fabbrocino et al., 2005)

T

T

Therefore, it is assumed that the tie can only develop 20 ksi at the node where the hook is located. 1 2 3

4 5

6 7 8

V

6dtie 3

dtie1 2 3

4 5

6 7 8

V

6dtie 3

dtie

Training Module53

VV

V

Tie

Hairpin

T1

T2T2

T1

Concrete strut

Anchor


T1 : Tension force on tie

T2 : Tension force on hairpin

do : Diameter of anchor

With internal ties :

Typical STM for shear loading

VV

V

Tie

T

T


T : Tension force on tie

Anchor

Concrete strutT

T

V

V

Without internal ties :

Training Module54

PART IV

EXAMPLE PROBLEM

Training Module55

Example problemPedestal

c1 s1 c1

c2

s2

c2

Vua_XAnchor

Shear reinforcement

Reinforcing bars

b2

X

Y

b1

Vua_Y

Pier height

hef

do

db

Side cover

Concrete cover

Grout

Design the anchor for the steel column located at the top of concrete pedestals. Anchors resist tension and shear forces.

Maximum total factored loads:

Tension: Nua_total 80kip:=

Maximum shear in the X-direction: Vua_total_X 20kip:=

Maximum shear in the Y-direction: Vua_total_Y 20kip:=

Training Module56

c1 s1 c1

c2

s2

c2

Vua_XAnchorb2

X

Y

b1

Vua_Y

Pier height

hef

do

db

Side cover

Concrete cover

c1 s1 c1

c2

s2

c2

Vua_XAnchorb2

X

YY

b1

Vua_Y

Pier height

hef

do

db

Side cover

Concrete cover

Assumptions:

1. Untorqued, cast-in anchors2. No sleeve is used3. Low seismic risk and capacity design is not considered4. Tension force is distributed equally among all anchors5. Shear force is assumed to be carried by two anchorsbecause of oversize holes in the base plate

Note: All code section numbers referred in this example are inthe ACI 318-08

Pier / Pedestal Data:

Specified compressive strength of concrete: f'c 4000psi:= (Blocks are input data)

Height: Pier_height 28in:= Concrete_cover 1.5in:= Side_cover 2in:=

Note: In many cases, the height of the pier is a design constraint.

Cross-section dimensions: b1 24in:= b2 26in:=

Edge Distance: C1 8 in:= C2 8in:=

Anchor Spacing: S1 8in:= S2 10in:=

Training Module57

Anchors:

Specification: ASTM F1554, A36 fya 36ksi:= futa 58ksi:=

ASTM F1554, A36 is a ductile steel (Table 2.1). Therefore: T 0.75:= (tension loads) V 0.65:= (shear loads) (D.4.4.a)

Note: Load combinations shall be per Chapter 9 (or ASCE 7-05, Chapter 2)

Reinforcing bars: Grade 60 steel: fy_rebar 60ksi:=

Vertical (longitudinal rebars): #6 db 0.75in:= Asb 0.44in2:=Shear reinforcement: #4 dtie 0.5in:= Astie 0.2in

2:=

Design assumptions:

1. The tension and the shear forces in the anchors are transfered to the longitudinal rebars and shear reinforcement, respectively,which will be designed as anchor reinforcement. Therefore, the concrete breakout strength in tension and shear (D.5.2 and D.6.2)is not checked. The concrete pryout strength in shear (D.6.3) is assumed OK by inspection because it is usually critical for shortand stiff anchors. 2. When welded washers are not used, it is not likely that all anchors are effective in resisting shear due to oversize holes in thebase plate. For this case, it is conservative to assume that only the bolts on the critical face are engaged. For this example, onlytwo anchors are assumed to be effective for resisting shear.

Training Module58

1. Determine the size of anchors

The size of anchors is determined based on the steel strength of anchor in tension and shear. Since the tension force isassumed to be distributed equally, each anchor carries 80 kip / 4 = 20 kip. There are two anchors in both X and Y directions (i.e. half of the total number of anchors) are effective in resisting shear, the maximum shear force carried by one anchor is 20 kip / 2 = 10 kip. If there is any shear in the X-direction acting simultaneously, it may be added here.

Try 1.25-in. anchor: do 1.25in:= (Threads per inch: nt 7:= )

Effective cross-sectional area: Ase

4do

0.9743 innt

2:=

Ase 0.969 in2

=

The steel strength of one anchor in tension: Nsa Ase futa:= (D.5.1.2) T Nsa 42.156kip= > Nua 20kip:= (OK !)

The steel strength of one anchor in shear: Vsa 0.8 0.6 Ase futa:= (D.6.1.2.b) V Vsa 17.537kip= > Vua 10kip:= (OK !)

Note: Shear strength of anchors with grout pads shall be multiplied by 0.8 (D.6.1.3).

Since Nf > 0.2TNsa and Vf > 0.2VVsa , check interaction equation based on D.7.3:

NuaT Nsa

VuaV Vsa

+ 1.045= < 1.2 , OK !

The minimum effective embedment depth of the non-sleeve 1.25-in anchor: hef,min =12do=15 inNote: Since the pier height is 28 inches, try h ef=24 in. This effective embedment depth will be checked if it is sufficient forthe required development length of vertical reinforcing bars.

Training Module59

2. Check the pullout resistance of anchor in tension (D.5.3.4)

Section D.5.3.4 indicates the load at which the concrete above the anchor head begins to crush. Since the local crushingabove the head will greatly reduce the stiffness of the connection, and generally will be the beginning of a pullout failure. Thepullout resistance of anchor in tension must be ensured to be larger than the factored tension load (Nua). If the capacitydesign (which is not considered herein) is performed, the pullout resistance of anchor in tension should be larger than thetensile capacity of the anchor (T Nsa).Use the heavy hex nut (on the anchor head) with the flat-to-flat dimension of 2 inches.

Abrg 0.866 22

54

1.252:=Bearing area: Abrg 1.51in2

:=

The pullout resistance in tension of a single headed bolt: Npn = c_P 8 Abrg fc' (D.5.3.1 and D.5.3.4)Assume concrete cracks: c_P 1:= Npn = (1)8(3.68)(4) = 117.8 kip

Strength reduction factor for anchor governed by pullout, assuming condition A (supplementary reinforcement is provided to tiethe failure prism): = 0.75 (D.4.4.(c))

Therefore: Npn = (0.75)(117.8) = 88.4 kip > Nua OK !

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3. Check the side-face blowout resistance of anchor in tension (D.5.3.4)

Consider side-face blowout on face 1 because c1 = c2 and s1 < s2

Check if the corner effect and close spacing have to be considered:

Corner effect: c2 < 3 c1 --> Consider corner effect

Nsb 160 C1 Abrg fc1

C2C1

+

4:= fc Nsb 49.7kip:=

Close spacing: s1 < 6 c1 --> Consider close spacing

Nsbg 1S1

6 C1+

Nsb:= Nsbg 57.983kip=

These Nsbg is for the two anchors located on side 1.

Therefore: Npn = (0.75)(58) = 43.5 kip > 2* Nua OK !

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4. Transfer of Anchor Load to Vertical Rebars

4.1 Amount of vertical reinforcing steel

In order to be considered effective for resisting anchor tension, vertical reinforcing steel must be located within hef / 3 = 8inches from the anchor head or edge of washer. The number of pier vertical rebars that are effective for resisting anchor tensionis 3.

Since capacity design is not considered (for a low seismic risk), determine the required number of vertical rebar to resist Nua :

For capacity that is governed by yielding of rebars: s 0.75:= (D.5.2.9)n_requiredNua

s fy_rebar Asb:=

n_required20

0.75( ) 60( ) 0.44( ):= n_required 1:=< provided effective number of rebar, OK !

Training Module62

4.2 Development lengthThe vertical rebar should be developed on either side of the potential failure plane. The part of the rebar above the failure surfaceis commonly straight and the part of the rebar that goes into the mat is commonly bent (as shown in Figure 9). Therefore, thedevelopment length for straight bar applies to the part of the rebar above the failure surface and the development length for the90-degree hooked bar can be applied to the part of the rebar below the failure surface. Since the development length for the90-degree hooked bar (below the failure surface) is part of the pier/foundation design, it is not considered in this calculation.

Development length for straight bars above the failure surface:

The minimum development length, ld (> 12 in), is determined based on the 12.2.2 and 12.2.4 as follows:

Bar location factor: t 1:= (for vertical bar)

Coating factor: e 1:= (for uncoated bar)

Concrete density factor: 1:= (for normal concrete)

For #6 and smaller bars, use:ld

fy_rebar t e ( )

25 f'c

db:= ld = 28.5 in

Available development length based on the pier height and the embedment depth of the anchor bolt:

Available_length hef Side_cover dmax tan 35deg( ):=From Figure 2, dmax = 5.7 in Available_length = 24 - 1.5 - 5.7 tan(35deg) = 18.5 in < ld

However, since the provided number of effective rebar is significantly more than the required number of rebars and for low seismicrisks, l d can be reduced using the excess reinforcement factor per 12.2.5 but cannot be less than 12 in per 12.2.1.

ld_reduced ldAs_requiredAs_provided:= ld_reduced 28.5

0.83

:= = 7.6 in (12 in. governs in this case)

< Available_length OK !

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5. Design of shear reinforcement

Say Lda = 10.7 in

The required straight development length to fully-develop theties:

t 1.3:= (for top ties)

ldfy_rebar t e ( )

25 f'c

dtie:= ld 24.7in:=

The steel stress : fs 26ksi:=

Required area of ties: Atie20

0.75 26:=

Atie 1in2

:=

Requires 5 legs of #4 tie

Training Module64

STRUT-AND-TIE APPROACH

Assumptions:

1. Strut-and-tie modeling (Figure 10) is used to analyze shear transfer to concrete pedestal and to design the required amountof shear reinforcement. 2. Since the shear forces in both directions are the same and the total number of anchors resisting the total shear forces inboth directions are the same, only the shear in the X-direction is presented in this example problem.

Figure 10

Training Module65

5.1 Check a geometry of the truss model to see if a direct strut can develop

Since the angles between the axes of all struts and ties entering a single node is larger than 25 degrees, direct struts candevelop (Section A.2.5 of the ACI 318-05).

5.2 Develop a truss model and calculate member forces

The truss model and member forces are shown in Figure 10.

5.3 Check strength of bearing

Assume concrete strength for checking the strength of bearing and compression struts: f cu = 0.85 f'c

5.3.a. Bearing of the anchor

Bearing area: Abrg_anc 8 do do:=

Abrg_anc 12.5 in2

=

Strength: fcu 0.85 f'c( ):=

fcu 3400psi= >13.3kipAbrg_anc

1064psi= OK !

5.3.b. Bearing of the reinforcing barsBy inspection, bearing on the rebar at the node D (Fig. 11) governs (shorter length and larger force):

The clear distance between the nodes B and D, l BD : lbd 5 in( )2 5.125 in( )2+do2

db2

:=

lbd 6.16 in=

Bearing area: Abrg_rebar 8 do 1.5 lbd+ Concrete_cover( ) db:=

Abrg_rebar 13.305 in2

=

Strength: fcu 0.85 f'c( ):=

fcu 3400psi= >9.5kip

Abrg_rebar714.017psi= OK !

Training Module66

Figure 11

5.4. Check strength of struts

Since it is assumed that the strength of strut is the same as the bearing strength (fcu = 0.85 fc') and the available area forstruts is typically larger than the available area for bearing, the bearing strength governs over the strength of struts. Therefore,if the bearing strengths at the anchor and rebar are OK, the strength of struts does not need to be checked.

Training Module67

5.5. Select tie reinforcement

Assumptions:

1. Only the top most two layers of ties (within 5" of pedestal as required by Section 7.10.5.6 of the ACI 318-05), shown in Fig. 12, are effective. 2. Tie reinforcement consists of tie with seismic hooks. Hairpins are used as internal ties.3. The location of hooks and the direction of hairpins are alternated as shown in Fig. 12. 4. At the nodes away from the hook, the tie is assumed to be fully developed.5. At the node where the hook is located, the contribution of the hoop to the tension ties T is T1 = Astie*(20 ksi)

T1 Astie 20 ksi:= T1 4 kip=

Thook T1:=

Figure 12 Training Module68

Ties a and b (see Figure 11):

Ties a and b are resisted by exterior ties.

Assuming that one layer of the exterior tie can develop f y and the other layer can provide T hook :

Total resistance: Rtot_ab As tie fy_rebar Thook+:=

Rtot_ab 16kip= > 6.6 kip OK !

Tie c (see Figure 11):

Tie c is resisted by a hairpin. Diameter of hairpin: dhairpin 0.5in:= Ashairpin

4dhairpin

2:=

Yield stress of hairpin: fy_hairpin 60ksi:=Check the stress that can be developed in the hairpin:

Check available length of the hairpin: la_hairpin 26in 2 Side_cover 2 dtie:=

la_hairpin 21in=

Required straight development length for a fully developed hairpin:

Bar location factor: t 1.3:=

Coating factor: e 1:= (for uncoated bar)

Concrete density factor: 1:= (for normal concrete)

For #6 and smaller bars, use:ld_hairpin

fy_rebar t e ( )

25 f'c

dhairpin:=

ld_hairpin 25in:= cannot be less than 12 in per Section 12.2.1 of the ACI 318-05.

The stress that can be developed in the hairpin:

fs_hairpinla_hairpinld_hairpin

fy_hairpin:= fs_hairpin 50.4ksi=

Since the direction of hairpin is alternated, only one layer of hairpin can be accounted as tie reinforcement.

Total resistance: Rtot_c 2As hairpin fs_hairpin:= (Note: 2 legs per hairpin)

Rtot_c 19.792kip= > 13.5 kip OK !

Training Module69

6. Check the minimum distance requirements to preclude splitting failure

The following minimum distances for anchors shall be satisfied unless reinforcement is provided to control splitting.

I. Center-to-center spacing (D.8.1): Smin_untorqued 4 do:= = 5 in < min (S1,S2) OK !

II. Minimum edge distance (D.8.2):

For untorqued cast-in anchors, the minimum edge distances shall be based on minimum cover requirements.

Cmin_untorqued = cover = 1.5 in < min (C1,C2) OK !

Training Module70

T

35 25

25

Design tie to carry 0.12 T = 0.12 (80) = 9.6 kip

STM for tension

2in 21.00)6( .750

6.9=tieA

Use 2 layers of #4 tie

Use 2 layers of #4 tie @ 4 spacing

Training Module71

PART V

DESIGN PHYLOSOPHY

of

APPENDIX D ACI 318-08

Training Module72

Strength Design

Nominal strength Factored Design Load

- factorsLoad factors

Chapter 9 (Based on ASCE-7) Section D.4.4

Appendix C (older) Section D.4.5

Training Module73

- factors

Cast-in-place anchor or post-installed anchor ?

- factors are determined based on :

Condition A or Condition B ?

Category 1, Category 2 or Category 3 ? (ONLY for post-installed

anchor)

Tension loads or shear loads ?

Training Module74

- factors from Section D.4.4 of ACI 318-08

Condition A :- For concrete breakout or side-face blowout governs, when supplementary reinforcement is provided

Condition B :- For concrete breakout or side-face blowout govern, when supplementary reinforcement is not provided

- For pullout or pryout strength governs

Training Module75

PART VI

ANCHORAGE TO CONCRETE

for

TENSION LOADING

Training Module76

ACI NotationsFor tension: ca1 ca2

ca1 s1

ca2

s2

For shear:

ca1 is taken in the

direction of the applied

shear

Training Module77

Strength Design for Tension Loading

uan NN

utaNsesa fAnN ,=

=nN the least of

bNcpNcNedNco

Nccb NA

AN ,,,

=

bNcpNcNedNecNco

Nccbg NA

AN ,,,,

=

pPcpn NN ,=

( ) ' 160 1 cbrgasb fAcN =

sba

sbg Nc

sN 6

11

+=

Training Module78

Lightweight Concrete New ACI 318-08 provision

'cf

Section 8.6.1 of the ACI 318-08

To account for the use of lightweight concrete, a modification factor appears as a multiplier of in all applicable equations and sections.

= 1.0 for normal-weight concrete

= 0.85 for sand light-weight concrete

= 0.75 for all light-weight concrete

If the average splitting tensile strength of light-lightweight concrete, fct, is specified:

0.1'7.6=

c

ct

ff

Training Module79

Steel strength of anchor in tension

utaNsesa fAnN ,=n = number of anchors in groupAse,N = effective cross-sectional area of anchorfuta = specified tensile strength of anchor steel

< the smaller of 1.9 fya and 125,000 psi

For threaded bolts:

2

,

9743.04

=

taNse

ndA

da = outside diameternt = number of threads per inch

Section D.5.1 of the ACI 318-08

Training Module80

Concrete breakout strength in tension

bNcpNcNedNco

Nccb NA

AN ,,,

=For a single anchor:


For a group of anchors: bNcpNcNedNecNco

Nccbg NA

AN ,,,,

=

Basic concrete breakout strength

Modification factors

Eccentricity

ed : For edge effectsc : For cracked / uncracked concretecp : For splitting of post-installed anchors

Modification factors:

Training Module81


DeVries, pp. 43

Training Module82


5.1 ' efccb hfkN =

The basic concrete breakout strength

kc = coefficient based on test results (has been adjusted for cracked concrete)= 24 for cast-in anchors= 17 for post-installed anchors

Alternatively, for cast-in headed studs and headed bolts with

11 hef 25, Nb shall not exceed:

3/5 ' 16 efcb hfN =

Training Module83


,Nc

1.25 ,=Nc

1.0 ,

=Nc

Modification factor for cracked concrete (D.5.2.6):

kc = coefficient based on test results (has been adjusted for cracked concrete)= 24 for cast-in anchors= 17 for post-installed anchors

This is related to kc as follows:

For cracked concrete:

kc represents a coefficient that was determined by testing anchors in uncracked concrete.

kc values were then adjusted to provide kc values in cracked concrete.

For uncracked concrete:

Cast-in anchors:

1.4 ,=NcPost-installed anchors: (when kc is 17)

At service load levels !

Training Module84


Nco

Nc

AA

NcoNc AnA

Modification to account for geometry:

ANc = projected concrete failure area for anchor/group of anchor under consideration

ANco = maximum projected area for a single anchor

2 9 efNco hA =

Training Module85


(D.5.2.8): Where a plate / washer is added at the head of the anchor,

the failure surface can be projected outward 1.5 hef from the effective

perimeter of the plate / washer.

Training Module86

Concrete breakout strength in tensionModification factor for eccentric loads (D.5.2.4): 0.1

3' 21

1

,

+

=

ef

N

Nec

he

(Only for a group of anchor)

How to define eN ?

Training Module87


Only anchors in tension shall be considered when determining eN

Training Module88


ef

a

Ned hc

5.1 0.3 0.7 min,

,+=

efa hc 1.5 min, 2.5 ca1Deep embedment and close to an edge: (Previous edition of ACI: ca1 < 0.4 hef )

Furche & Eligehausen (1991) found:1. The critical ratios of (c/h) at which the failure mode changed from blowout to concrete cone were between 0.2 and 0.4.2. The diameter of the lateral concrete cone was 6 to 8 times the edge distance.

3. The blowout failure depends on the edge distance, the bearing area of the anchor head, and the concrete strength

ca1

Section A-A Elevation

6 ca1

3 ca1 3 ca1A

A Training Module110

Concrete side-face blowout strength cont

4

11

2

+

a

a

c

c

How to account for the effects of corner bars and close spacing ?

61

1

+

ac

s

1. If ca2 < 3 ca1

Multiply Nsb with:

where: 0.30.11

2 a

a

c

c

ca1


6 ca1

ca2 3 ca1

2. If s < 6 ca1

Multiply Nsb with:

ca1


6 ca1

3 ca1 3 ca1s

A

AA

A

Training Module11

1

1. Given: 1. Edge distance

2. Bearing area

3. Concrete strength

Calculate the side-face blowout capacity:

( ) ' 160 1 cbrgasb fAcN =

Bearing head should have sufficient stiffness !

2. If it is insufficient, design transverse reinforcement to carry

30% of the vertical load 25% increase in capacity if its

bearing based on test result

Important design consideration: Development length and

stiffness of transverse reinforcement

Concrete side-face blowout strength cont

Training Module11

2

Alternatives to increase side-face blowout strength

Shear reinforcement

Spiral reinforcement to increase bearing strength

c

c : edge distance

Potential failure surface

6c 8c

Training Module11

3

Effect of Head Thickness / Flexibility

DeVries (1996)

1. Too thick waste of materials Cost

2. Too thin reduce effective bearing area smaller capacity

Inelastic deformation of thin headsTraining Module

11

4

Effect of Head Thickness / Flexibility cont

Based on the tests on bearing capacity of concrete prisms by

applying a load with a punch through flexible plates, Hawkins

(1968) concluded that the flexibility of plates did decrease the

bearing capacity compared to rigid plates.

Training Module11

5

Effect of Head Thickness / Flexibility

DeVries (1996)

recommended the

use of cantilever

beam / footing model

to determine the

required head

thickness

Hasselwander et al.

(1977) recommended

the minimum washer

thickness of

1/8(washer diameter)

to prevent excessive

flexibility of the washer

Training Module11

6

PART VII

ANCHORAGE TO CONCRETE

for

SHEAR LOADING

Training Module11

7

Strength Design for Shear Loading

uan VV

utaVsesa fAnV ,=

=nV the least of bVhVcVedVco

Vccb VA

AV ,,,

=

bVhVcVedVecVco

Vccbg VA

AV ,,,,

=

cbcpcp NkV =

For cast-in headed studs

utaVsesa fAnV 0.6 ,= For cast-in headed bolts, hooked bolts

cbgcpcpg NkV =

Training Module11

8

Steel strength of anchor in shear

n = number of anchors in groupAse,V = effective cross-sectional area of anchorfuta = specified tensile strength of anchor steel

< the smaller of 1.9 fya and 125,000 psi

For threaded bolts:

2

,,

9743.04

==

taNseVse

ndAA

da = outside diameternt = number of threads per inch


utaVsesa fAnV ,=

utaVsesa fAnV 0.6 ,=

For cast-in headed studs :

For cast-in headed bolts, hooked bolts :

Training Module11

9

Concrete breakout strength in shear

For a single anchor:


For a group of anchors:

Basic concrete breakout strength

Modification factors

Eccentricity

bVhVcVedVco

Vccb VA

AV ,,,

=

bVhVcVedVecVco

Vccbg VA

AV ,,,,

=

For shear force perpendicular to the edge:

ed : For edge effectsc : For cracked / uncracked concreteh : For shallow members

Modification factors:

Training Module12

0

Concrete breakout strength in shearSection D.6.2 of the ACI 318-08

For shear force parallel to the edge:

Use twice of the Vcb for the shear perpendicular to the edge

(defined on the previous slide)

Use d,V = 1.0

Training Module12

1


( ) 5.11

2.0

' 7 acaa

eb cfdd

lV

=

The basic concrete breakout strength

le = load-bearing length of the anchor for shear ( 8 da)= hef for anchors with constant stiffness over hef

(i.e. headed studs / post-installed anchors with one tubular shell over hef)= 2 da for torque-controlled expansion anchors with a distance sleeve

separated from expansion sleeveca1 = edge distance in the direction of shear force

For a single anchor in cracked concrete:

Training Module12

2

Concrete breakout strength in shearThe basic concrete breakout strength

For cast-in headed studs, headed/hooked bolts that are continuously

welded to steel attachments having a minimum thickness of the

greater of (3/8 and da/2), can use:

( ) 5.11

2.0

' 8 acaa

eb cfdd

lV

=

Provided:

Training Module12

3


Vco

Vc

AA

VcoVc AnA

Modification to account for geometry:

AVc = projected concrete failure area for anchor/group of anchor under considerationAVco = maximum projected area for a single anchor

21 5.4 aNco cA =

Training Module12

4


Some examples for Avc calculations:

Training Module12

5


Avc calculations for two rows of anchors in the direction of shear:

Evaluate the both cases 1 and 2 to determine the controlling case !

Training Module12

6


directioneither in 5.12ac

When anchors are influenced by three or more edges, what is ca1 ?

ca1 the max: 5.1ah

1/3 of max. spacing between anchors within the group

Training Module12

7


,VecModification factor for eccentric loading (D.6.2.5):

(Only for a group of anchor)

Consider only anchors that are loaded

in shear in the same direction

+

=

1

,

3' 21

1

a

VVec

c

e

Training Module12

8


,VedModification factor for edge effects (D.6.2.6):

ca1

ca2

V

Training Module12

9


,Vc

1.4 ,=Vc

1.4 ,=Vc

Modification factor for cracked / uncracked concrete (D.6.2.7):

To account for :

Cracked / uncracked at service loads

The amount of supplementary / edge reinforcement

If uncracked at service loads:

If cracked at service loads and :

with no supplementary / edge reinforcement < #4 bar : 1.0 ,=Vc

1.2 ,=Vcwith supplementary reinforcement of #4 bar between the anchor and the edge :

with supplementary reinforcement of #4 bar between the anchor and the edge, and with the supplementary reinforcement enclosed within stirrups spaced 4 :

Training Module13

0


,VhModification factor for thin concrete (D.6.2.8):

NEW provision introduced in the ACI 318-08

For ha < 1.5 ca1 :

a

aVh h

c 1,

1.5 =

Training Module13

1

PART VIII

COMBINED LOADING

(Tension and Shear)

Training Module13

2

Combined Loadings (Tension & Shear)

McMackin et al. (1973) recommended: 13

53

5

=

+

uu VV

PP

P: applied tension load

V: applied shear load

Pu: Tensile capacity of the anchor = u As

Vu: Shear capacity of the anchor

Training Module13

3


121

=

+

p

u

p

u VV

PP

The Task Group on Steel Embedment (1984) and CEB (1991) recommended p1 = p2 = 5/3

Based on the test results on two-anchor connections on a rigid baseplate under eccentric shear with both anchors on the tension side, Cook (1989) recommended p1 = p2 = 5/3.

General elliptical interaction formula:

Based on the tests results of several types of anchors under oblique loading, Lotze and Klingner (1997) found that p1 and p2 values between 1.67 and 1.8 could describe the steel failure load appropriately.

The general elliptical interaction formula can be used for both steel and concrete failureShaikh and Whayong (1985) recommended: p1 = p2 = 2.0Cook and Klingner (1992) recommended: p1 = p2 = 5/3

Training Module13

4


Section D.7 of ACI 318-08

Section D.4.3 of ACI 318-08 indicated that any other interaction expression that is in substantial agreement with results comprehensive tests can be used.

Training Module13

5

PART IX

SUMMARY

and

REFERENCES

Training Module13

6

What weve discussed today ?I. Introduction

V. Design philosophy of the ACI 318-08 Appendix D

VI. Anchorage to concrete for tension loading

VII. Anchorage to concrete for shear loading

VIII. Combined loading (Tension and shear)

II. Common / existing approaches for designing anchor reinforcement

III. Strut-and-Tie Model approach for designing anchor reinforcement

IX. Summary and references

Appendix D of

ACI 318-08

IV. Example problem

Training Module13

7

References

Cannon, R.W., Godfrey, D.A., and Moreadith, F.L. (1981). Guide to the Design of Anchor Bolts and Other Steel Embedments, Concrete International, July, pp. 28-41.

CEB. (1991). Fastenings to Reinforced Concrete and Masonry Structures: State-of-Art Report, Part 1, Euro-International-Concrete Committee (CEB), August, 1991.

Cook, R. A. (1989). Behavior and Design of Ductile Multiple-Anchor Steel-to-Concrete Connections , Ph.D. Dissertation, The University of Texas at Austin, May, 1989.

Cook, R.A. and Klingner, R.E. (1992). Ductile Multiple-Anchor Steel-to-Concrete Connections, Journal of Structural Engineering, V. 118, No. 6, pp. 1645-1665.

Fabbrocino, G., Verderame, G.M., and Manfredi, G. (2005). Experimental behavior of anchored smooth rebars in old type reinforced concrete buildings, Engineering Structures, Vol. 27, pp. 1575-1585.

Training Module13

8

References

Furche, J. and Eligehausen, R. (1991). Lateral Blow-out Failure of Headed Studs Near a Free Edge, Anchors in ConcreteDesign and Behavior, SP-130, American Concrete Institute, Farmington Hills, Mich., pp. 235-252.

Ghali, A. and Youakim, S.A. (2005). Headed Studs in Concrete: State of the Art, ACI Structural Journal, V. 102, No. 5, pp. 657-667.

Hasselwander, G.B., Jirsa, J.O., Breen, J.E., and Lo, K. (1977). Strength and Behavior of Anchor Bolts Embedded Near Edges of Concrete Piers, Research Report 29-2F, Center for Highway Research, The University of Texas at Austin.

Leonhardt, F. and Walther, R. (1965). Welded Wire Mesh as Stirrup Reinforcements Shear Tests on T-Beams and Anchorage Tests, Bautechnik, V. 42, October. (in German)

Lotze, D. and Klingner, R. E. (1997), Behavior of Multiple-Anchor Connections to Concrete From the Perspective of Plastic Theory, PMFSEL Report No. 96-4, The University of Texas at Austin, March.

McMackin, P.J., Slutter, R.G., and Fisher, J.W. (1973). Headed Steel Anchor under Combined Loading, Engineering Journal, AISC, Vol. 10, No. 2, April, 1973.

Training Module13

9

References

Shaikh, A. and Whayong, Y. (1985). In-place Strength of Welded Headed Studs, Journal of the Prestressed Concrete Institute, pp. 56-81.

Swirsky, R.A., Dusel, J.P., Crozier, W.F., Stoker, J.R., and Nordlin, E.F. (1977). Lateral Resistance of Anchor Bolts Installed in Concrete, Report FHWA-CA-ST-4167-77-12, California Department of Transportation, Sacramento, May.

Task Group on Steel Embedment. (1984). State of Art Report on Steel Embedment,Structural Engineering in Nuclear Facilities, Proceedings, J. J. Ucciferro, Ed., North Carolina State University, Raleigh, 1984, pp. 1080-1218.

Thompson, M.K., Ledesma, A, Jirsa, J.O., and Breen, J.E. (2006). Lap Splices Anchored by Headed Bars. ACI Structural Journal, V. 103, No. 2, pp. 271-279.

Wiewel, H. (1991). Design Guidelines for Anchorage to Concrete, Anchors in ConcreteDesign and Behavior, SP-130, American Concrete Institute, Farmington Hills, Mich., pp. 1-18.

VER Design of Anchorage to Concrete Handout

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