For a simply supported beam carrying a uniformly distributed load of w per unit length over the entire span, what is the qualitative shape of the shear force diagram?

Introduction / Context:Internal shear force and bending moment diagrams are fundamental for beam design. Recognising their shapes for common loadings lets engineers size members quickly and check results by inspection.

Given Data / Assumptions:

• Simply supported beam (pin and roller supports).
• Uniformly distributed load (UDL) = w per unit length across entire span L.
• Static, prismatic beam in the usual sign convention (upward reactions positive).

Concept / Approach:Shear force V(x) equals the algebraic sum of vertical forces to the left (or right). Under a UDL, dV/dx = −w, so V varies linearly. For symmetry, reactions are equal (wL/2 each). The diagram is a straight line decreasing from +wL/2 at the left support to −wL/2 at the right support—i.e., a right-angled triangle.

Step-by-Step Solution:

Verification / Alternative check:The slope of the bending moment diagram equals V; since V is linear, moment is quadratic (parabolic), consistent with standard beam theory.

Why Other Options Are Wrong:Two triangles or equilateral forms do not match the single linear ramp imposed by constant w.

Common Pitfalls:Misplacing signs at supports; forgetting that UDL produces linear shear and parabolic moment.

Final Answer:

A single right-angled triangle (linear variation across the span)