Support Conditions and End Moments in Beams Consider a prismatic, linearly elastic, simply supported beam without end restraints (i.e., pin–roller or pin–pin). State whether the bending moment at each support (beam ends) is zero under external transverse loading.

Introduction:
In elementary structural analysis, the relationship between boundary conditions and internal actions is fundamental. A simply supported beam has supports that do not restrain rotation; therefore, the end moments are generally expected to be zero. This item checks your understanding of how ideal support types (pins/rollers) influence bending moments at the boundaries.

Given Data / Assumptions:

• Beam behavior is linear elastic, small deflection.
• Supports are ideal: no rotational restraint (pin and/or roller).
• Loads are transverse (point loads, uniformly distributed loads, etc.).
• No externally applied end couple at the supports.

Concept / Approach:
For a simply supported beam, rotations at the supports are free. The internal bending moment is related to curvature and rotational restraint. With free rotation, the boundary bending moment is zero unless an explicit couple is applied at the end. Shear forces at the supports can be non-zero, but bending moment values at those points vanish for the ideal model.

Step-by-Step Solution:
1) Identify support type: pin/roller implies zero resisting moment.2) Draw bending moment diagram for common loads (point, UDL): the diagram starts and ends at zero.3) Recognize exceptions only arise if an external end couple is applied (not part of typical “simply supported” definition).

Verification / Alternative check:
From equilibrium and compatibility, the boundary condition for a free-rotation support is M = 0 at that node, which is consistent with classical solutions and textbook bending moment diagrams.

Why Other Options Are Wrong:

• “No” is incorrect because ideal simple supports cannot sustain end moment.
• “Only under UDL” is false; point-load cases also show zero end moments.
• “Only when span is symmetric” is irrelevant; symmetry is not required.
• “Only when deflection is zero at ends” confuses displacement with rotational restraint.

Common Pitfalls:
Mixing up shear (which is often maximum at supports) with bending moment, and assuming end fixity where there is none.

Final Answer:
Yes