Calculating the Shear Lag Effects in Tension Member Connections...

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Calculating the Shear Lag Effects in Tension Member ConnectionsDominique Bauer

SSEF Architecture and Engineering Educators Meeting 2006March 3-4, 2006, Telus Centre, University of alberta, Edmonton

Dominique Bauer

Presentation Summary

• Introduction• Finite Element Model• Finite Element Model• Shear Stresses in Welds• Stresses in the Connection• The Analytical Method• Comparisons between F.E.A., CAN/CSA-

March 3-4, 2006Dominique Bauer 2

S16-01 and the Analytical Method• Conclusions

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Introduction• Shear Lag : “Phenomenon that creates a loss

in resistance in a tension member connected thro gh onl part of its cross section”through only part of its cross-section”

• Complex problem which has been under study for many years– McKibben 1906– Davis and Boomsliter 1934– Gibson and Wake 1942

Chesson and Munse 1963


– Chesson and Munse 1963– Easterling and Gonzalez Giroux 1993, Wu and

Kulak 1993, Tremblay 2001, Petretta 1999, Abi-Saad, Benaddi, Bauer 2002-2005, etc.

• Parameters:– Type of cross-section– Size of cross-section– Type of connectionyp– Length of welds– Length of member– Joint eccentricities– etc.


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Finite Element Model

• ANSYS Solid 95: 20 nodes (8 at the corners, 12 at the mid edges)12 at the mid edges)

• Kinematic hardening• Static analysis• Large displacements• Plastic material properties



Isotropic Hardening(neglects completely the Baushinger effect)

Kinematic Hardening(considers the Baushinger effect to its full extent)

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E = 200 GPaFy = 350 MPaEst = 7.5 GPaEst 7.5 GPaFu = 540 MPaεy = 0.00175εst = 0.02εf = 0.20ν = 0.3


• 6500 elements• Results differed by 3% when using a finer

mesh with elements half the size• Execution time from 0 5 to 12 hours and more• Execution time from 0.5 to 12 hours and more

• Applied stresses at free end of bar• 100 MPa, 200 MPa, 300 MPa, maximum

value for which F.E.A. would converge


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2 Critical Section


Shear Stresses in Welds


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Gusset plate thickness = 10 mm


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Gusset plate thickness = 20 mm



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Stresses in the Tension Bar

L = 50 mmLoad = 262 MPa σVM = 532 MPa


von Mises stresses

L = 100 mmLoad = 350 MPa


von Mises stresses

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L = 50 mm

L = 100 mm


Principal stressesL = 200 mm

The Analytical Method

The analytical method was proposed by theauthors, based on an assumed distribution ofauthors, based on an assumed distribution offorces along inclined lines in the memberends, somewhat similar to the Whitmore’sconcept used with gusset plates for bracingmembers (Abi-Saad and Bauer 2004).


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F.E.A.


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F.E.A.



F.E.A.


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Predicted tensile resistances of the welded connections

F.E.M.F.E.M.


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Conclusions

1. The shear stresses in the longitudinal weldswere found to be significantly higher at thewere found to be significantly higher at theends of the welds than the average valuealong the length of the weld. This aspect willbe investigated further as it might affect thestrength of the connection in regards withfracture at the critical section.


2. von Mises contour plots clearly showedregions of stress concentrations. However,the information contained in these plots isnot sufficient for predicting the strength ofg gthe connections.


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3. Vector plots revealed that the maximumprincipal stresses in the bars make an angleof approximately 30° with the longitudinalaxis of the member. This observationvalidates the assumption made in theanalytical method. Also, the vector plotsshowed that the resultant stresses arelongitudinal in the region where stressesfrom either side of the connection overlap.Thi b ti ld b d i fi i


This observation could be used in refiningthe analytical method.

4. Stress distributions at the critical sectionassumed in the analytical method comparesreasonably well with the distributionsobtained from the finite element analysis.yThis observation confirms the validity of theanalytical method. Also, it will help inmaking adjustments to the method in orderto improve it.


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5. For the three models studied, the resistancespredicted using F.E.M., CAN/CSA-S16-01and the analytical method compare well.


6. The information provided by the finite elementmethod would have been be difficult to obtain bylaboratory tests or otherwise. However, carrying thenon-linear finite element analyses was timeconsuming and difficult for the following reasons:

– F.E.A. are quite complex. Non-linear analyses requirepractice and mastery of a software that may take severalweeks to acquire.

– Even with a very simple model, the non-linear analysesran for hours, sometimes several days.

– The convergence of the f.e.a. is difficult to obtain at loadsapproaching the ultimate resistance of the model. Severalruns had to be done at various load levels, in a trial and


,error fashion, in order to determine the maximum load forwhich a solution converged, making the process very timeconsuming. Such an approach would not be suitable fordesign.

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7. The finite element analysis was used tovalidate the analytical method proposed bythe authors and gave some insight into thebehaviour of the connections which will beused for improving the analytical method.However, further validation of the analyticalmethod should be done against finiteelement analyses and laboratory tests.


Acknowledgments

The present research was made possible by grants from :grants from :

• Steel Structures Education Foundation of the Canadian Institute of Steel Construction

• National Sciences and Engineering Research Council of Canada (No 238967-01)

• École de technologie supérieure


• École de technologie supérieure

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