BeamColumns CE 579 Structural Stability and Design Amit

Beam-Columns CE 579 - Structural Stability and Design Amit H. Varma Ph. No. (765) 496 3419 Email: ahvarma@purdue. edu

Beam-Columns n n n 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.

Beam-Columns Ry 4. 1 Force-deformation Behavior Ry MTX z P MBX P v L y, v Ry Ry P P v M 0 θ 0 κM 0 θL

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Beam-Columns n Consider the experimental behavior of a wide-flange beam-column subjected to P=0. 49 Pr (concentric) & (increasing) with κ=0

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

Beam-Columns n n 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 M 0/L v M 0/L M 0 P

Beam-Columns n Consider, over all behavior

Beam-Columns 4. 2 Elastic Behavior n 2 nd order differential equations are: n Eq. (1), (2), & (3) are coupled. Eq. (1) is also coupled through. n This means that for most general cross-sections with

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

Beam-Columns n Differentiating these equations Column Beam

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

Beam-Columns 4. 2. 1 IN-PLANE behavior & strength

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

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Beam-Columns 4. 2. 2. IN-PLANE STRENGTH

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Beam-Columns n Interaction equations: effect of moment gradient κ

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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 (x 0=0) & unequal end moments (κ≠ 1) by numerical methods.

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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Beam-Columns n Effect of lateral-torsional buckling on W 8 X 31 for

Beam-Columns n Another way of illustrating lateral-torsional buckling