Beam Mechanics – Purlin under Uniformly Distributed Load For a purlin of span L subjected to a uniformly distributed load ω (per unit length), what is the maximum bending moment assumed for a simply supported condition?

Introduction / Context:
Purlins span between roof trusses or rafters and carry roofing loads idealized as uniform line loads. Determining the maximum bending moment for a given support condition is a fundamental step in sizing the purlin section and its connections.

Given Data / Assumptions:

• Span: L (simply supported).
• Loading: uniform line load ω (force per unit length along the span).
• Objective: compute the maximum bending moment magnitude for design.

Concept / Approach:

For a simply supported beam under uniform load, reactions are equal at supports and the bending moment diagram is a parabola with a peak at midspan. The standard closed-form result for the midspan moment is ω L^2 / 8, widely used in preliminary and detailed design.

Step-by-Step Solution:

Verification / Alternative check:

Area-under-shear-diagram or energy methods yield the same value. Standard tables of beam formulas list ω L^2 / 8 for this case, confirming the result.

Why Other Options Are Wrong:

• ω L^2 / 12 and ω L^2 / 16: Too low; these belong to other support/load cases.
• ω L^2 / 10: Not a standard exact result for classical boundary conditions.

Common Pitfalls:

Confusing simply supported with continuous purlins (which reduce peak moment due to continuity), or neglecting load components from roof slope and cladding self-weight.

Final Answer:

ω L^2 / 8