1. CE579 - Structural Stability and Design
Beam-Columns
CE579 - Structural Stability and Design
Amit H. Varma
Ph. No. (765)

2. Beam-Columns
Members subjected to bending & axial compression are called beam-columns.
Beam-columns in frames are usually subjected to end forces only. However, beam-columns may also be subjected to transverse forces in addition to end-forces.
Behavior of beam-columns is similar somewhat to beams & columns.

3. Beam-Columns 4.1 Force-deformation Behavior Ry MTX Ry z P P v MBX L
y, v Ry
κM0 Ry P P v M0 θ0 θL

4. Beam-Columns

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Consider the experimental behavior of a wide-flange beam-column subjected to P=0.49Pr (concentric) & (increasing) with κ=0

6. Beam-Columns
Behavior of beam-columns is different than the behavior of beam or column.

7. Beam-Columns
Note that for beams moment is reduced due to LTB or LB buckling out-of-plane
But, for the beam-column is reached due to in-plane behavior only no LTB or LB before is reached P
M0/L v
M0/L M0 P

8. Beam-Columns
Consider, over all behavior

9. Beam-Columns 4.2 Elastic Behavior
2nd order differential equations are:
Eq. (1), (2), & (3) are coupled. Eq. (1) is also coupled through.
This means that for most general cross-sections with

10. Beam-Columns
For a singly symmetric cross-section with & moments acting in the plane of symmetry (y-z plane)

11. Beam-Columns
Differentiating these equations
Column
Beam

12. Beam-Columns
Now the final equations are (7), (8) & (11). Where, Eq. (7) is uncoupled from eq. (8) & (11).
Eq. (7) defines the in-plane bending deformations
Eq. (8) & (11) correspond to the occurrence of LTB.

13. Beam-Columns
4.2.1 IN-PLANE behavior & strength

14. Beam-Columns
4.2.1 IN-PLANE behavior & strength

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Thus, for a beam-column subjected to P & M

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4.2.2.IN-PLANE STRENGTH

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Interaction equations: effect of moment gradient κ

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25. Beam-Columns 4.2.3 Elastic Lateral-Torsional Buckling Behavior
Most general equations were (8) & (11)
The phenomenon will be identical to the lateral-torsional buckling of beams & columns.
The critical combination of loads producing it are the max. practical load that can be sustained by the member.
Eq. (8) & (11) can be solved for singly symmetric sections (x0=0) & unequal end moments (κ≠1) by numerical methods.

26. Beam-Columns For doubly symmetric sections ( ) the d.e. become
Eq. (25) & (26) are best solved by numerical or energy methods. Salvadozi used the Rayleigh-Rize method and presented the results.

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30. Beam-Columns
Effect of lateral-torsional buckling on W8X31 for

31. Beam-Columns
Another way of illustrating lateral-torsional buckling