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DETERMINATION OF WELD LOADS AND THROAT REQUIREMENTSUSING FINITE ELEMENT ANALYSIS WITH SHELL ELEMENT MODELS -

A COMPARISON WITH CLASSICAL ANALYSISMichael A. Weaver, P.E., Weaver Engineering, Seattle, Washington ©1997

(Paper presented in Welding Journal, Welding Research Supplement, 78(4) 116s – 126s April, 1999)

Finite element analysis (FEA) has become apractical method of predicting stresses anddeflection for loaded structures. FEA accuratelyidentifies the load path, which can be difficultusing classical analysis with complex structures.FEA shell element models are effective forpredicting loads in weldments fabricated fromplate, sheet, structural shapes, and tube.

The formulation used for a finite elementshell model is that of full penetration welds atevery joint. Although the loads carried throughjoints are calculated by FEA, they are notreadily presentable.

This article presents a method to derive theloads at weld joints from the stress results ofFEA shell element models. Additionally, usingthe calculated weld loads, weld throat stressesor size requirements are calculated usingclassical methods.

Benefits of utilizing this method are:• Accurate determination of weld loads

including distribution of weld loads alongthe joint. The weld joint loads are resolvedat each FEA node of the joint in the model.This is useful for prediction of both staticfailure and fatigue failure.

• Rapid determination of weld throatrequirements or stress levels from a solvedFEA model. The process of extractingweld loads and determining throatrequirements or stress levels can be highlyautomated.

• Shear loads induced by mismatch of lateraldeflection due to restraint/poisson effectsare included in the calculated loads. Theseloads are often ignored with classicalanalysis.

• An estimate of the ductile reserve of thejoint with respect to the hydrostatic loadstate is available. This has been proposedas a cause of non-ductile failure of weldjoints (Ref 1). Although not performed inthe implementation presented, informationuseful for this evaluation is obtained.Investigation is ongoing in this area.

Most common basic FEA packages aresuitable for this analysis. COSMOS/M wasused for the examples here. With it’s parametriccommand files, design variations are easilyevaluated. With any FEA package, accurateload estimation depends on the quality of themodel built by the analyst.

As presented, this method is standardclassical weld stress analysis except that theforces on the weld joint are determined usingFEA. The forces through the weld are dividedby the weld throat area and compared to theshear allowable of the electrode material.

There is room for improvement in failureprediction of fillet and partial penetration weldsand research is ongoing at many sites. UsingFEA, the loads at a weld joint can easily beresolved into directions associated with the weldjoint. From this, stress states at the root and toeof the weld due to applied loads can bepredicted. With this information, fractureinitiation may be better modeled and predicted.This would seem a fruitful area for research.With more accurate prediction and classificationof failure resistance, the fabrication cost for agiven structural reliability can be reduced.

Implementation:For fillet and partial penetration groove

welds, the criteria used for sizing welds is todivide the load transmitted (traction) throughthe weld by the minimum throat area andcompare that value with the electrode shearallowable. See side note A, page 7, for adescription of this criteria and the associatedsafety factors.

The applicability of this method for singlesided welds where the weld root sees tension issubject to special considerations and limitationsthat are discussed.

A welded t-joint and a lap joint are analyzedfor demonstration. First, the weld for a t-jointof a fabricated steel bracket is analyzed. Theresults will be compared to a classical analysisof the same joint. Finally, the weld of a lapjoint for an aluminum fall arrest lug is sized.

The method is presented in four steps:

Step 1 From the Finite Element Analysis, listto a file the stress tensor at each node of a weldjoint in one terminated part for both the topand bottom stresses.

Step 2 Extract the stress tractions through theweld at each weld joint node for both elementfaces (top and bottom) by multiplying the jointnormal unit vector into the shell element topand bottom stress tensors.

Step 3 From the tractions and the partthickness, solve for the normal load (lb/in),bending load (in-lb/in), and joint shear (lb/in)at each node.

Step 4 From the formulas appropriate for theweld joint (double sided fillet, double sidedpartial penetration groove, or single sidedwelds - fillet or partial penetration withlimitations) and the throat size, calculate theweld stress. Conversely, from the desiredstress level, solve for the required throat size.

Weld Size Requirement for a Steel T-JointBracket:

Figure 1 depicts a welded steel bracketloaded vertically and horizontally. Figure 2shows a fabrication detail of the bracket wherethe size of the double sided fillet weld is S.

This t-joint is subject to bending in both thestrong and weak directions, tension, and shear.

This bracket is made from ASTM A36steel and welded with matching E60XXelectrode. The required safety factor againstultimate failure is 3.0, so the allowable weldthroat “shear” stress used to size the joint was13.2 ksi (1

3 0 60 0 3 2 2. ( )( . )( . )⋅ ksi ), see Side Note

A, page 7). The objective of this analysis is todetermine the weld size, S, that results in amaximum throat stress of 13.2 ksi.

Figure 1: Depiction of Bracket Loads

Figure 2: Fabrication Detail of T-Bracket

The loads in the weld are easily determinedusing classical analysis for this bracket. Theweld size requirements will be calculated firstusing the loads from finite element analysis andthen will be compared to the results obtainedusing classical analysis.

With finite element analysis results, caremust be taken when identifying the stresses(loads) at weld joints or other discontinuities.Figure 3 depicts a finite element model of the t-joint under investigation. Figure 4 shows thefinite element stress results in part 1 (the stem ofthe “t”, see figure 2) of the joint. Figure 5shows stress results for the assembly.Comparison of figures 4 and 5 shows that thedisplayed stress in part 1 near the weld joint aredifferent in the two plots from the sameanalysis. The elements for part 1 were put on a

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separate “set” or “Layer” and the nodal stressesplotted in figure 4 are based only on thestresses in part 1. This is the most accuraterepresentation of the stress state of part 1. Thestresses at the joint of parts 1 & 2 shown infigure 5 are based on the calculated average ofthe stresses in both parts at the joint Thestresses shown in figure 5 are unrealisticallylow in part 1 and unrealistically high in part 2at the joint because of this.

Figure 3: Finite Element Model of T-Bracket

Figure 4: Von-Mises Stress Results Plottedon Part One of Bracket Only.

Figure 5: Von-Mises Stress Results Plottedfor the Entire Bracket.

Nodal stress values are calculated as theaverage stress of all of the active elements incontact with each node. At discontinuities suchas weld joints, the plotted stress is the averageof the stress in each side of the discontinuity.To identify the stresses (and loads) in a part at adiscontinuity (weld joint), the stresses must becalculated for one side of the discontinuity onlyby activating results for the area of interest only,as is shown by the comparison of figures 4 and5.

The four steps are described and applied.

Step 1 List to a file the stress tensor at eachnode of a weld joint in one terminated partfor both the top and bottom stresses.

Activate the elements for one terminatedpart of the of the weld joint and the nodes of thejoint only as shown in figure 7. For lap and Tjoints, there is only one terminated part. Refer tofigure 6. For corner and butt joints, both partsterminate and either part may be selected.

Figure 7: Element and Node Activation forListing Part Stresses at Weld Joint.

Some weld joints, such as a flare-v groovebetween two adjacent rectangular steel tubes,have no terminated part. One solution is tochamfer or round the tube corners in the finiteelement model and model the weld itself as shellelements connecting the tube walls similar tothe actual weld. These weld elements thenbecome the terminated part.

List to text files the stresses in the “top”and the “bottom” of terminated part at the activenodes.† Refer to parts A and B of figure 8. PartD of figure 8 is a list of “top” stresses at thenodes of the weld joint with the elements forboth parts one and two active - it is incorrect forextracting weld loads and corresponds to thestress plot of figure 5.

In step 2, a coordinate system aligned withthe weld joint in the terminated part isintroduced. Depending on the method ofimplementation, it may be beneficial to list the

† “Top” and “Bottom” are terms used to distinguish

the element sides, they have no significance with torespect to “Up “ or “Down”. The “Top” face of anelement is the face where the node sequence iscounter-clockwise.

top and bottom stresses in a coordinate systemaligned with the weld joint. Coordinate system3, shown in figure 7, was used for this example.

Step 2 Extract the stress tractions resultingfrom loads transmitted through the weld jointat each weld joint node for both elementfaces.

To determine the loads transmitted throughthe weld joint, as opposed to loads that runalongside the weld, the “weld joint normal” ofa selected terminated part is identified. Refer tofigure 6.

For this purpose, the weld joint normal isdefined as the direction perpendicular to theplane formed by the axis of the weld and thenormal (perpendicular) direction of the surfaceof the terminated part at the node of evaluation.Refer to figure 6. In mathematical terms,

u

u

u

u u u

s

w

j

j s w

≡≡

≡

= ×

surface normal unit vector

weld axis unit vector

weld joint normal unit vector

.

The stress traction vector, T, acting on theplane defined by the weld joint normal vector,uj, results from loads transmitted through the

weld joint. It is extracted by multiplying theweld joint normal, uj, into the stress tensor, σ‡

[ ]T uj= σIn expanded notation, the expression is:

T

T

T

u

u

u

x

y

z

xx xy xz

yx yy yz

zx zy zz

j

j

j

x

y

z

=

σ σ σσ σ σσ σ σ

One way to resolve the traction into weld jointcoordinate system, (s, w, j) is:

‡ Stress tensor mathematics are often not taught in

undergraduate engineering classes. The concepts aretaught using Mohr’s circle instead. A good referencefor stress tensor mathematics as well as failure theoryis “Mechanics of Solid Materials” by J. Lemaitre andJ.-L. Chaboche.(Ref 2)

Figure 6:THE WELD JOINT COORDINATE SYSTEM OF THE TERMINATED PART

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T

T

T

s

w

j

=•••

T usT u wT u j

Where Ts represents the shear acting

perpendicular to the terminated part, Twrepresents the weld joint longitudinal shear,and Tj represents the tension or compression in

the terminated part through the weld joint.For a lap joint, Tj also represents the

transverse shear. If the joint is loaded in plane,(Ts = 0 ) and there is a transverse component

to the load (Tj ≠ 0), the 1996 AWS D1.1

Structural Welding Code – Steel (Ref 3) hasalternate increased weld load allowables basedon transverse/longitudinal load orientation(Paragraph 2.14.4). Thistransverse/longitudinal orientation is availablewith these results.1

For the t-bracket, the stresses are listed incoordinate system 3 which has the z axisaligned with the weld joint normal. Thepreceding analysis simplifies as follows:

u uj z=

T

T

T

x

y

z

xx xy xz

yx yy yz

zx zy zz

xz

yz

zz

=

=

σ σ σσ σ σσ σ σ

σσσ

0

0

1

For node 340 of the t-joint (refer to figure 8),the top and bottom stress tractions through theweld joint are:

T

T

T

T

T

T

x

y

z TOP

x

y

z TOP

=−−

− −

=−−

340

340

0 384 8 390 2

384 8 4 468 2 530

390 2 2 530 19 560

0

0

1

390 2

2 530

19 560

. .

. , ,

. , ,

.

,

,

T

T

T

T

T

T

x

y

z BOT

x

y

z BOT

=−−

− −

=−−

340

340

0 384 8 390 2

384 8 2 531 1 210

390 2 1 210 7 884

0

0

1

390 2

1 210

7 884

. .

. , ,

. , ,

.

,

,

The extraction of stress tractions resultingfrom loads transmitted through the weld joint iscomplete.

1 A note of warning: Although joints with transverse -in plane loading have greater strength, they have lessductility and energy absorption than longitudinallyloaded joints. Refer to Commentary Figure C2.6,“Load Deformation Relationship for Welds”, ofAWS D1.1-96.

Step 3 From the tractions and the partthickness, solve for the normal load (lb/in),bending load (in-lb/in), and joint shear (lb/in).

The equations used to determine part topand bottom stress due to bending, normal, andshear loads are easily reversed to determinebending, normal, and shear loads from thestresses. For node 340, the calculation ispresented in figure 9.

This calculation determines the loads perinch of weld joint. Columns two through fourin part C of figure 8 show the results of thesecalculations for the t-joint of the steel bracket.For comparison with classical analysis, thevalues for joint normal load, P, and joint shearload, V, are divided by two to obtain load perinch of weld since there are two welds in thejoint.

Step 4 From the formulas appropriate forthe weld joint and the desired stress level,solve for the required throat size.

Three weld configurations are considered.They are: 1) double sided fillet weld, 2) doublesided partial penetration groove weld, and 3)single sided welds - fillet or partial penetrationgroove welds. The expressions for weld throatstress are different for each of these three. Theycover most cases.

The analysis will be presented first bydeveloping the expression for weld throat stressgiven the weld loads, the joint geometry and theweld size. Then the solution for the weld throat

Figure 8:

tb

σ

σt

b

Resolution of Weld Loads, Node 340:

t b.3

8in Base Material Thickness

σ t.19560 psi Normal Stress at Top of Joint

σ b.7884 psi Normal Stress at Bottom of Joint

τ zx_avg.390.2 psi Average Shear Stress in Joint

τ yz_avg.2530 psi .1210 psi

2

τ avg τ zx_avg2 τ yz_avg

2=τ avg 1910 psi

Joint Normal Load:

P .σ t σ b

2t b =P 5146

lbf

in

Joint Bending Load:

M .σ t σ b

2

t b2

6=M 136.8

.in lbf

in

Joint Shear Load:

V .τ avg t b =V 716.4lbf

in

Figure 9: Load Calculation for One Node

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size given the allowable stress will be described.Finally, the weld size requirements for the steelbracket t-joint will be evaluated.

WELD SECTION PROPERTIES:Figure 10 presents the expressions used for

weld area and section modulus about the weldaxis for the three categories considered.

DOUBLE SIDED FILLET WELD PROPERTIES:The section modulus for the double sided

fillet weld is unique in this presentation becauseit is calculated assuming the centroid of the ofthe weld throat on each side is at the part outeredge instead at the physical centroid of thethroat. See figure 10. This is drawn from theclassical method of treating the weld as a line todevelop properties (Ref 4).

When developing the properties for a weldgroup using classical analysis, the method oftreating a weld as a line does not differ muchfrom calculating the properties using the actualweld centroid because compared to the overallgeometry, the distance from the weld centroid tothe part wall is small. Treating the weld as aline results in a much simpler calculation Witha double sided fillet weld of a plate in a t-joint,however, the difference between the twomethods is significant.

The resulting calculated stresses frombending loads in double sided fillet weldstreated as lines is more conservative. There is adearth of references on this subject - mostpublished investigations of fillet weld strengthinvolve lap joints loaded in plane (Ref 5). In theabsence of illumination, the safer path waschosen.

DOUBLE SIDED PARTIAL PENETRATIONGROOVE WELD PROPERTIES:

The section modulus for a double sided

partial penetration groove weld is calculatedusing the geometrical section of the weld throat.The formulation shown is for the simple case ofa weld with the weld size on both sides of thejoint being equal and no fillet weldreinforcement.

SINGLE SIDED WELDS:No differentiation is made between fillet andpartial penetration groove welds for analyzingsingle sided welds. The section modulus for asingle weld is calculated using the geometricalsection of the weld throat. WELD THROAT STRESS:

From the weld load componentsdetermined in step three and the weld sectionproperties for a given weld size, the weld throatstress components can be determined as follows:

Stress due to normal load

fP

Anormalw

=

Stress due to bending:

fM

Sbendingw

=

Stress due to shear:

fV

Ashearw

=

Total stress magnitude:

( ) ( )f f f fweld bending normal shear= + +2 2

Refer to figure 11. Note in the aboveequation that the bending and normal stressesare combined so that their magnitudes areadditive. This is because this will always be thecase on one side of the joint.

For evaluation of the weld size, the totaltraction magnitude is compared to the electrode

shear allowable, Fa.

fweld

f + fnormal bending f

shear

weld throat

Figure 11: Components of Weld Throat StressTraction.

The calculation for the total weld throattraction just presented is of practical use fordetermining stress levels of existing designs.For new design, a method of calculating throatsize requirements is presented.

DETERMINATION OF WELD SIZE:Given the weld loads determined in step 3,

the joint type and geometry, and the allowableshear stress, there will exist a throat size wherethe calculated magnitude of the weld throatstress traction will equal the allowable shearstress. For double sided fillet welds treated aslines, Aw and Sw are linear with respect to tw, andthis can be solved explicitly for the requiredthroat size:

For the double sided fillet weld on the steelbracket at node 340, the formulation is asfollows:

Figure 10: Weld Section Properties

Double Sided Fillet Weld Double Sided Partial PenetrationGroove Weld

Single Sided Weld, Fillet or PartialPenetration Groove

Weld Throat Area: A tw w= ⋅2 Weld Throat Area: A tw w= ⋅2 Weld Throat Area: A tw w=

Moment of Inertia: It t

ww b=

⋅ 2

2Moment of Inertia: I

t t ttw

w b ww= +

−⋅

3 2

6 2

( )Moment of Inertia: I

tw

w=3

12

Section Modulus: S t tw w b= ⋅ Section Modulus: St

tt t tw

w

bw w b= ⋅ − +

4

32

32 Section Modulus: s

tw

w=2

6

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tF

M

t

P V

tin

psi

t in

wa b

w

in lbin

lbin

lbfin

w

MIN

MIN

MIN

= ⋅ +

+

=

+

+

=

−

1

2 2

137

375

5146

2

716 4

2

13 200

0 224

2 2

2 2

.

.

,

.

For an equal leg fillet weld, the weld size,S, is equal to the square root of 2 times thethroat,

S t

in

in or in

w= ⋅

= ⋅

=

2

2 0 224

0 317 0 32

( . )

. . .

This is the value for S that should be used forthe joint callout in figure 2.

Figure 8 part C displays the results of theabove calculation for every node in the joint.Figure 12 shows a plot of the weld throat stressas a function of the weld throat size.

Double Sided Fillet Weld

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.455000

1 104

1.5 104

2 104

2.5 104

3 104

f w(t )w

psi

13200

t w

in

.224

Figure 12: Plot of Weld Throat Stress vs.Weld Throat Size for Double SidedFillet Weld at Node 340.

Double Sided Partial Penetration Groove Weld

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.455000

1 104

1.5 104

2 104

2.5 104

3 104

3.5 104

13200

t w

in

.304

f w(t )w

psi

root f t psi inw w( ( ) , ) .− ⋅ = ⋅13 200 304

Figure 13: Plot of Weld Throat Stress vs.Weld Throat Size for Double SidedPartial Penetration Groove Weld atNode 340.

An explicit expression for a double sidedpartial penetration groove weld requiressolution of a sixth order polynomial while asingle sided weld results in a fourth orderpolynomial that must be solved. Rather thanpursue these, it was more expedient toimplement an iterative search in the computerprogram. The weld throat size, tw, is adjusteduntil the calculated throat traction equals theallowable shear stress for the electrode. Thismethod is employed for both double sidedpartial penetration groove welds and singlesided welds. Figure 13 shows a plot of the weldthroat stress as a function of the weld throat size

at node 340 of the t-joint if it were a doublesided partial penetration groove weld. Theresulting throat size for a maximum throattraction of 13,200 psi is .304 inches.

This concludes the calculation of the weldthroat size of the steel bracket t-joint based onthe results of finite element analysis. Forcomparison, the same joint is now analyzedusing classical methods.

Determination of T-Joint Weld Size UsingClassical Analysis:

The t-joint double sided fillet weld will beevaluated using the method of treating a weld asa line as described in Omer Blodgett’s “Designof Weldments” (Ref 4) among others (Refs 6-7).

Refer to figures 2 and 3 for the jointgeometry and loads. The classical calculationis:

Section Properties:A d

in

in

Sd

in

in

S b d

in in

in

w

w x

w y

= ⋅= ⋅=

=

=

== ⋅

=

=

2

2 5

10

3

5

3

8 33

375 5

188

2

2

2

2

( )

( )

.

(. )( )

.

Applied Loads:

Normal Load, P:

P lb= 3000

Shear Load, V:

V lb lb

lb

= + −

=

( ) ( )146 2810

2814

2 2

Bending Load About x, Mx:

M lb in

in lb

x =

= −

( )( )2810 5

14050

Bending Load About y, My:

M lb in

in lb

y =

= −

( )( )146 5

730

Weld Loads :

Normal Load, fnormal:

fP

A

lb

in

lb in

normalw

=

=

=

3000

10

300 /

Shear Load, fshear:

fV

A

lb

in

lb in

shearw

=

=

=

2814

10

281 /

Bending Load About x, fbx:

fM

S

in lb

in

lb in

bxx

w x=

=−

=

14050

8 33

1690

2.

/

Bending Load About y, fby:

fM

S

in lb

in

lb in

byy

w y=

=−

=

730

188

388

2.

/

Total Weld Load, fw:

f f f f f

lb in

w normal bx by shear

lbin

lbin

lbin

lbin

= + + +

= + + +

=

( ) ( )

( ) ( )

/

2 2

2 2300 1690 388 281

2390

Required Weld Throat Size, tw:

tf

F

lb

psi

in

ww

a=

=

=

2390

13200

0188.

Figure 14: Comparison of Weld Loads AlongJoint from FEA and ClassicalCalculations

The required weld throat size as calculatedusing classical analysis is 20% smaller that thevalue calculated using the loads from the FEA.Figure 14 compares the weld loads calculatedusing FEA and classical analysis. The resultsare reasonably close. Some causes of thedifference are:

1) Poisson Effect: Part 2 (Figure 2, 0.75 inthick) restrains part 1(0.375 in thick) fromthe lateral contraction/expansion associatedwith the Poisson Ratio due to normal loadsat the weld joint. This induces a shear loadthat is carried through the weld. The loads

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obtained from FEA account for this forfnormal while it is not accounted for in withthe beam formulas used with classicalanalysis. (With the current implementation,the Poisson effect due to bending about theweld weak axis is ignored because the shearstresses are opposite and they cancel eachother in the shear load calculation.)

2) Uneven distribution of the load path due tothe bolts and the non-linear effects of out-of-plane forces on part 2.

3) End effects.

The FEA accounts for these effects while theclassical analysis used does not. The differencebetween these methods for this joint design isnot great and this steel t-bracket is a goodcandidate for classical evaluation.

The finite element analysis method ofdetermining weld loads becomes useful whenestimating weld loads using classical analysis isdifficult.

For a quick, simple example, figure 15shows the same 0.375 thick part 1 bracketwelded to a matching 5 x 9 lb/ft channel. Byinspection, most of the applied normal andbending load will be transferred from the part 1bracket to the channel near the channel flanges.

Figure 15: T-Joint Welded to MatchingChannel

Figure 16: Von-Mises Stresses in Part 1Welded to Channel

Figures 16 and 17 confirm this. Thisdesign is not suitable for the classical beamformulas. More advanced classical analysissimilar to that presented for rectangular tubularstructures in the AWS D1.1 Structural WeldingCode (Ref 3) would be appropriate.

Note on design of single sided weldsDesign of single sided welds where the

root of the weld is subject to tension requirescareful study of joint restraint, loadinggeometry, and has limitations.

Figure 17: Weld Loads in T-Joint withChannel.

Figure 18 depicts a pipe welded in a t-jointloaded in bending. This is an acceptable singlesided joint with the root in tension. Figure 19 isa diagram of the joint, loading, and restraintthrough the top section where the single sidedweld is subject to tension. The weld in thissection is not subject severe bending becausethe section of the pipe adjacent to the weld isrestrained from rotating. The loading on thisweld joint is similar to the weld loading on adouble lap joint.

S

Figure 18: Pipe T-Joint Welded on One Side,Loaded in Bending

Figure 19: Section Through Top of Pipe T-Joint, Loaded in Tension.

In contrast, the steel t-joint bracket underinvestigation , Figures 1 through 5, is notrecommended for a single sided joint withoutcareful consideration of the applied loads andthe resulting resistance to failure. The threeloading directions will be considered separately.

If Px can put the root of the joint in tensionand is unrestrained, no amount of deformationwill take the weld out of bending and stop

continued deformation. This condition has thelowest resistance against failure.

When Px puts the root of the weld incompression, the weld will not have degradedresistance based on calculated weld stresses.

The application of a tensile Pz load againputs the weld in bending with the root intension. The bending load will be equal to theload times the distance between the centerline ofthe part and the weld centroid. Therefore, filletwelds will see more severe induced bendingthan a partial penetration groove weld. Of notewith this loading is that the joint will seebending deformation only until the applied loadis in line with the weld centroid. Theapplication of Py puts the joint in bending aboutit’s strong axis. One end of the joint willexperience tension and the other will seecompression. The moment from the load offsetat the tensile end will induce the part to rotateso that the weld root opens while the load offsetat the compression end will induce the part torotate so that the weld root closes. This creates awarping, twisting load in the part. A shorter,stubbier part will provide more restraint againstopening the weld root at the tensile end thanwill a long thin part. Again, specialinvestigation of the joint against the desiredresistance to failure is required.

Configurations with one sided fillet weldswhere the root is in unconstrained tension aregood candidates for redesign.

Figure 20: Welds of double fillet welded lapjoint are evaluated individually.

The single sided formulation is used fordouble fillet welded lap joints as shown infigure 20. Even though this is a double weldjoint, each weld is evaluated individually.

. Weld Size Requirement for a Lap Joint of aFall Arrest Lug:

Figure 21 is a depiction of a fall arrestplatform. This platform is designed towithstand the most severe type of fall arrestsystem - that of a simple lanyard allowing amaximum free-fall of six feet. OSHA 1910.66Appendix C (Ref 8) stipulates by the simplestmethod that the structure for such a fall arrestsystem must withstand a lanyard load of 5000pounds without failure.

This structure is fabricated from 5086-H112 Aluminum with 5356 electrode. Thepublished minimum tensile strength of5086-H112 is 31,500 psi and the publishedminimum shear strength for 5356 electrode is17 ksi (Ref 9).

There were 54 welds evaluated for 13 loadcases. Ten load cases were used to evaluate fallarrest loads at various locations and three loadcases were used to evaluate the

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Figure 21: Finite Element Model of FallArrest Platform

floor and structure for the fatigue loadingof day to day usage. This analysis was highlyautomated, and numerous platform materialsizing and geometry variations could beevaluated overnight with batch processing.

Weld #01 of the fillet welds in the lapjoint between the fall arrest lug (part 1) and thesupport post side (part 4) is analyzed fordemonstration. See figure 22 detail A. This isthe inside weld between the Lug (part 1) andthe post side (part 4).

Figure 22: Details of the Fall Arrest Anchorand Post.

SIDE NOTE A: STRESS CRITERIA FOR FILLET WELDS WITH AWS D1.1The following is the author’s method and rational of applying the requirements of AWS D1.1

for weld size determination.The shear stress allowable for static loading in the Structural Welding Code, AWS D1.1 (Ref

3), is 0.3 times the electrode tensile strength for fillet welds and partial penetration groove weldsnot in bearing, except fillet welds of lap joints loaded in plane with a transverse load componenthave an increased allowable per paragraph 2.14 of AWS D1.1-96. See also Lesik (Ref 10). Theincreased allowable is new with the 1996 code. There are no directly published shear strengthsfor steel electrodes in AWS D1.1 or AWS electrode specifications, however, the commentary forsection 2 (section 8 for pre-1996 versions of AWS D1.1) does reveal that the allowable stress isbased on a safety factor ranging from 2.2 for in plane longitudinal shear to 4.6 for in planetransverse loads based on test results (Ref 5). These tests were performed on lap joints loaded in-plane. Based on this datum, the minimum ultimate shear strength for steel electrode used foranalysis is taken as 0.66 (= 0.3 x 2.2) times the electrode minimum tensile strength. . Because outof plane loading was not evaluated in the testing referenced by the AWS D1.1, and very fewtesting results of out of plane loading have been published, the lower safety factor of 2.2 is used toestimate joint strength by the author for all joints loaded out of plane. For E60XX electrode, thisresults in an ultimate shear strength of 39.6 ksi. For tubular structure welded with 60 or 70 ksielectrode, the strength is taken as 2.67 times the allowable stress, per paragraph 2.40.1.3.

This is useful when designing for compliance with codes and specifications requiring othersafety factors for static loading. For example, ANSI/ALI B153.1-1990, the “American NationalStandard for Automotive Lifts -Safety Requirements…” requires a safety factor of 3.0 againstultimate failure for ductile material while deferring to “ANSI/AWS D1.1-90 Sections 1 through 7,Section 8 where applicable, …”, “… and the Commentary on Structural Welding Code - Steel,(Part of ANSI/AWS D1.1).” for welding techniques and weld joint design. The resultingallowable weld throat shear stress used for design with this code is 13.2 ksi (= 39.6 ksi/3.0) forE60XX electrode.

Of note is the evaluation of only the stresses due to loads carried through the weld joint.Stresses along the axis of the weld from loads not passing through the weld are not used ( See note3 in Table 2.3 of AWS D1.1-96). With respect to static loading resistance, these axial stresseswill participate in the onset of yield, increasing or decreasing the load at which yield initiatesdepending on the load geometry. A justification for this approach can be made for fillet and partialpenetration welds where the weld cross section is less than the base metal cross section for axialloads and the weld sizes are not great. As far as the weld is concerned, these axial stresses areseen as applied axial strains and a small amount of yielding will relieve the stresses associatedwith them while the base metal remains in an elastic state. This is true because the weld will beconstrained to strain in the axial direction by the same amount as the base material adjacent to theweld. If the weld cross section is significant compared to the base metal cross section for axialload, this assumption will be attenuated and further investigation is suggested. Also, in the case ofplastic design where the base material is expected to see large deformation, the combined effectsof axial and through weld elongation must be considered in the resistance of the joint. A high,tensile hydrostatic stress state (associated with large welds combined with severe cross section orload path discontinuities, such as mismatched base metal sizes) will cause a crack to propagateacross the joint before it’s theoretical ductile limit is reached. It is good to remember that filletand partial penetration welds are brought into this world with the equivalent of a crack at the root

The method used to size fillet welds against ductile failure is based on the practical approach ofcomparing the magnitude of the stress resulting from loads passing through the weld joint to theelectrode and base metal shear strengths. From the standpoint of the mechanics discipline ofphysics, this approach is close for a joint in pure longitudinal shear only. In general, for otherloading geometries, this approach results in a more conservative (earlier failure) prediction thanother ductile failure theories. However, factors such as the high stress concentration at the weldroot, residual stresses and distortion induced by the welding process, and weld defects call for aconservative approach.

Per AWS D1.1-96 for dynamically loaded structures (fatigue), the allowables for stress range inthe fillet weld are also in terms of shear on the weld throat (Category F, Table 2.4 and Figures 2.9and 2.10). The values for redundant structures correspond to the underlying study referenced inthe commentary (Refs 11-12), where the recommendations are drawn for a 95% survival rate at a95% confidence level from the underlying test data. These studies are oriented directly at bridgeconstruction. The total stress state in a fillet weld - not just the traction through the throat - willcontribute to fatigue failure, however, the traction through the throat is subject to the stressconcentration at the root and toe while stresses along the weld axis are not. Because the root isessentially a crack, the weld is born into stage 2 fatigue with respect to loads through the weldwhile the weld is closer to stage 1 fatigue for loads along the weld axis. Additionally, there areseparate allowables for stresses in the base metal adjacent to weld joints that are near the samerange as the allowables for the weld throat shear (Categories B through E, Table 2.4 ofAWS D1.1-96). These account for the load path discontinuity at the welds and notch effects.

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The geometry of this joint has somefeatures that increase the load in this weld.Specifically, because the post is fabricated ofplates with overhang of part 4 with respect topart 2, the x direction load combined with theoverhang induce a bending moment in the weakdirection of the single sided weld. Refer tofigure 23. The distribution of the loadtransmitted through weld #01 (V14 and M14)along the joint is difficult to calculate usingclassical analysis. Conservative assumptionswould be required resulting in larger welds andthicker material requirements.

Free Body Diagram at Loaded Section of Part 4 Post Side

Loading Diagram at Section Through Fall Arrest Lug Connection

4

1

23

4

Figure 23: Loading Diagram of the Fall ArrestPost Side.

Special care is required when creating afinite element model of lap joints with eithershell or solid elements. It must be ensured thatonly the nodes of the weld joint in the two partsare merged (joined). The nodes on the fayingsurfaces that are not part of the weld joint mustbe removed from the selection set or layerbefore merging is performed. See Figure 24.

Figure 24: Finite Element Model of Lap Joint

For weld 1, the terminated piece is part 4,the post side (figure 22). Coordinate system 15was used to evaluate the loads in weld 1. Seefigure 25. The elements of part 4 and the nodesof weld 1 are shown in figure 26. The resultsare plotted in figure 27.

Finite element analysis provided a reasonableestimation of loads for this analysis that wouldhave been difficult to estimate using classicalmethods. Also, FEA was of value determiningthe configuration of the lug to avoid hot spots atthe top and bottom.

Figure 25: Coordinate Systems used for PostWeld Joints.

Figure 26: Von Mises Stresses in Part 4 PostSide Plate with Nodes of Weld01Displayed.

Figure 27: Calculated Throat Requirement forWeld01.

Note on Intermittent WeldsOn the first cut when modeling structures withintermittent welds, it is expedient to merge(connect) all of the nodes along the weld joint.The results of the weld analysis will predict arequired weld size for a continuous weld. Thisgives the designer the distribution of the loadalong the joint for refinement of weld depositrequirements. If the joint is uniformly loadedand designed against static failure, it may bereasonable to use this result to size the

intermittent weld by providing the same throatarea as the predicted continuous weld.

On the other hand, if the loads exhibit non-uniform distribution or the structure is to becyclically loaded, it is recommended that furthermodels be built with the nodes merged at onlythe locations of welded connection.

Applicability and Limitations:This form of design evaluation is

based on elastic behavior only. Depending onthe expected failure mode and the definition offailure, elastic analysis is either a reasonablemodel or is conservative (in terms of rupturestrength). Elastic stress ranges are a verymeaningful predictor of resistance to fatigue.For static, ductile failure resistance, thedefinition of failure determines the applicabilityof elastic analysis. For design wheremeaningful change in geometry would causeloss of function (as for most mechanicalequipment), elastic analysis is entirelyappropriate and accurately predicts the onset ofyield. For applications where loss of functionoccurs when load bearing capacity is lost, butlarge plastic deformation can be tolerated andmay be desired, such as in seismic design orautomotive frames, elastic analysis with a safetyfactor against ultimate strength will generateconservative strength results and is not likely toprovide an accurate prediction of the behaviorof the structure regarding the design intent.Under this latter case, non-linear plastic analysisor the use of tabulated plastic factoredresistances provide a better prediction ofbehavior.

The Choice of Shell Elements:An alternative to using shell elements forgeneric analysis of weldments with fea is the useof solid elements.

Reasons for Not Modeling Welds with SolidElements:

1) The published strength data for static andfatigue failure is in terms of nominal throatstress. This information is not easilypresented or extracted from a solid elementmodel

2) The size of the weld would have to beknown a priori. The benefit of using shellelements as presented is that the requiredweld size can be calculated from the resultsof the fea analysis.

3) The effort required to build solid models ofwelds and the computational resourcesneeded to solve such models make their useuneconomic for most designs within mostorganizations.

Situations Where a Solid Model of the Weld isAppropriate:

1) Solid modeling can provide usefulpredictions of notch stresses for fatigueevaluation if the weld profile andpenetration can be modeled to accurately

2) For structures where the stiffness differencebetween the actual weld geometry and a

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shell element representation of the jointwould be meaningful.

3) For situations where plastic behavior of theweld itself is of interest.

The Present SystemPresently, this analysis is performed

external to the finite element analysis software.A database of welds is created that contains thenecessary information: part thickness, weldtype, allowable throat stress, and definition ofthe shell elements and nodes by surfaces andweld end points to be evaluated for weld loads.Refer to figure 28. A database such as thisorganizes the work to automate many of thetasks, however improvements in productivitycan be obtained from improvements in themodeling environment. More of the manualeffort of building the database can beautomated.

Future DevelopmentWith the information that the finite element

analysis results readily provide, that is, theorientation and magnitude of the traction at theroot and face of the weld, improved failureprediction may be possible compared to themethod of comparing the weld shear allowableto the magnitude of the traction divided by thethroat area. This would result in more efficientdesigns - less material used for a givenreliability.

SolicitationThe author is interested in comments on

this method and recommendations forimprovement. He can be reached through emailat mw@weavereng.com or at WeaverEngineering, 1219 Westlake Avenue N, Suite210, Seattle, WA 98109. Related information isavailable on the internet atwww.weavereng.com.

References:1. Blodgett, O.W. 1995 Details to Increase Ductility in SMRF Connections. The Welding Innovation Quarterly XII (2). The

James F. Lincoln Arc Welding Foundation.2. Lemaitre, J. and Chaboche, J. -L. 1990. Mechanics of Solid Materials. Cambridge University Press.3. The American Welding Society. 1996. ANSI/AWS D1.1-96. Structural Welding Code – Steel.4. Blodgett, O.W. 1963. Design of Weldments. The James F. Lincoln Arc Welding Foundation.5. Higgins, T. R. and Preece, F. R. 1968. Proposed Working Stresses for Fillet Welds in Building Construction. Welding

Journal 47 (10): 429s to 432s.6. Shigley, J. E. and Mischke, C. R. 1989 Mechanical Engineering Design. Fifth Edition. McGraw-Hill Book Company.7. American Welding Society. 1987. Welding Handbook. Eighth Edition. Volume 1.8. Occupational Safety and Health Administration. 1997. 29 CFR 1910.66 Appendix C. Office of the Federal Register,

National Archives and Records Administration. U.S. Government Printing Office.9. The Aluminum Association. 1986. Specifications for Aluminum Structures. Fifth Edition.10. Lesik, D. F., and Kennedy, D. J. L., 1990. Ultimate Strength of Fillet Welded Connections Loaded in Plane. Canadian

Journal of Civil Engineering. 17: pp 55 to 67.11. Fisher, J. W., Frank, K. H., Hirt, M. A., and McNamee, B. M. 1970. Effect of Weldments on Fatigue Strength of Steel

Beams. Report No. 102. National Cooperative Highway Research Program, Transportation Research Board, NationalAcademy of Sciences.

12. Fisher, J. W., Albrecht, P. A. Yen, B. T., Klingerman, D. J., and McNamee, B. M. 1974. Fatigue Strength of Steel Beamswith Welded Stiffeners and Attachments. Report No. 147... National Cooperative Highway Research Program,Transportation Research Board, National Academy of Sciences.

Figure 28: FEWELD Database.