Compression Members MCQ with answer and solution

Concept

Causes of second-order moments in beam-columns

Formula

NONE

Step-by-step solution

1. In beam-columns, axial force P acts on deformed structural geometries causing second-order moments. 2. The P-δ effect accounts for member curvature deformation along its length relative to its chord. 3. The P-Δ effect accounts for relative lateral displacement between member ends. 4. Therefore, second-order moments are created due to both P-δ and P-Δ effects. Answer: C

Explanation

Beam-columns experience secondary bending moments due to lateral displacements combined with axial compressive forces. The lower-case p-delta effect arises from member curvature along its length, whereas upper-case P-Delta arises from global relative displacement between member ends. Because both member deflection and joint sway generate second-order moments, option C is correct.

Why the other options are wrong

A) P-δ effects account for member curvature deflections but exclude global joint displacements. B) P-Δ effects model lateral story drift displacements but omit member-level curvature between nodes. D) Second-order moments are produced by the combined actions of both P-δ and P-Δ non-linear geometric effects.

Shortcut

Second-order moments account for both member deflection (P-δ) and frame sway (P-Δ).

Common mistake

Selecting either P-δ or P-Δ effect individually instead of recognizing that second-order moments involve both member and structure displacements.