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DISTORTIONAL BUCKLING OF C AND Z MEMBERS IN BENDING. Progress Report to AISI. Cheng Yu, Benjamin W. Schafer The Johns Hopkins University February 2004. Overview. Test Summary Notable Tests Comparison with Local Buckling Tests Comparison with Design Specifications

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distortional buckling of c and z members in bending
DISTORTIONAL BUCKLING OF C AND Z MEMBERS IN BENDING

Progress Report to AISI

Cheng Yu, Benjamin W. Schafer

The Johns Hopkins University

February 2004

overview
Overview
  • Test Summary
  • Notable Tests
  • Comparison with Local Buckling Tests
  • Comparison with Design Specifications
  • Finite Element Modeling
  • Conclusions
notable tests
Notable Tests

1. Test D8C097 – with lower lateral-torsional buckling strength

Local

Distortional

Lateral-torsional

slide4

Notable Tests - Continued

Continued. Test D8C097 – with lower lateral-torsional buckling strength

Actuator load-displacement

D8C097-5E4W-standard

D8C097-5E4W-angle added

Actuator load P=10350 lbs

Actuator load P=12751 lbs

84% of DSM_d

99% of DSM_d

slide5

Notable Tests - Continued

2. Test D8.5Z059-6E5W – failed outside constant moment region

Purlin buckled

Actuator load-displacement

Beam failed at 83% of distortional strength by DSM

slide6

Notable Tests - Continued

3. Test D3.62C054-3E4W – failed by yielding

Observed large deflection

Mtest= 34 kips-in.

My = 33 kips-in.

McrD = 66 kips-in. (first mode)

slide7

Notable Tests - Continued

4. Test D8C033-1E2W – failed in local buckling mode

Mtest= 32.8 kips-in.

My = 40 kips-in.

McrL = 30 kips-in.

McrD = 61 kips-in.

direct comparison with local bucking tests
Direct Comparison with Local Bucking Tests

9 pairs of tests having nominally identical geometry and material yield stresses

slide9

Direct Comparison with Local Bucking Tests - Continued

Test 8.5Z092

Local buckling test

Distortional buckling test

Test 8.5Z082

Local buckling test

Distortional buckling test

slide10

Direct Comparison with Local Bucking Tests - Continued

Test 8C043

Local buckling test

Distortional buckling test

Test 12C068

Local buckling test

Distortional buckling test

comparison with design codes
Comparison with Design Codes

(consider controlling specimens only)

Compared with North American Spec (NAS 2001) prediction

Local buckling tests average Mtest/MNAS=1.02

Distortional buckling tests average Mtest/MNAS=0.87

direct strength method vs tests
Direct Strength Method vs. tests

Local buckling tests

Mtest/MDSL=1.03

Distortional buckling tests

Mtest/MDSD=1.01*

*formulas similar to AS/NZS Spec.

finite element modeling
Finite Element Modeling

displacement control at loading point.

automatic stabilization technique applied.

slide14

Finite Element Modeling - Continued

Shell element (S4R)

Solid element (C3D8)

Pin connection between Load

beam and tube

Tie connection between purlin

and tube

1

Shell element (S4R)

Tie connection between purlin

and panel

2

1

2

slide15

Finite Element Modeling - Continued

Link connection between two

nodes to simulate the angle at

tension flanges

3

  • Material properties of beams use tension test results.
  • Panel is pure elastic.
  • High elastic modulus is assumed for tubesand load beam.

3

2

slide16

d

d

Type 1 Type 2

(local) (distortional)

Finite Element Modeling – Continued

geometric imperfection

Geometric imperfection is generated by the superposing two eigenmodes which

are calculated by finite strip method. The magnitudes are corresponding to

25% and 75% CDF of maximum imperfection.

CDF of Maximum Imperfection

conclusions
Conclusions
  • Tests that separate local and distortional buckling are necessary for understanding bending strength
  • Current North American Specifications are adequate only for local buckling limit states
  • The Direct Strength expressions work well for strength in local and distortional buckling
  • Local buckling failure could control the strength of beams with loose restraint
  • Nonlinear finite element analysis with proper imperfections provides a good simulation
  • More work on restraint and influence of moment gradients has been initialized
acknowledgments
Acknowledgments
  • Sponsors
    • MBMA and AISI
    • VP Buildings, Dietrich Design Group andClark Steel
  • People
    • Sam Phillips - undergraduate RA
    • Tim Ruth - undergraduate RA
    • Jack Spangler – technician
    • James Kelley – technician
slide21

Finite Element Modeling - Continued

comparison with tests

Local buckling tests

Distortional buckling tests

Ptest: tested actuator load

P25%: load of simulation with 25% CDF

P75%: load of simulation with 75% CDF

slide22

Comparison with Design Codes - Continued

μ: meanσ: standard deviation

test summary
Test Summary

Total 19 completed tests were included in the progress report.

9 Z beams

10 C beams

Tensile tests are underway for additional performed 5 tests.

D6C063-2E1W D8C045-1E2W D8C085-2E1W

D10C048-1E2W D10C056-3E4W