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Beam Analysis: Bending Moment, Shear and Deflection

A bending moment calculator is most useful when you can also see how the shear, reactions and deflected shape relate to the loading. This guide gives a hand-checkable example and explains how to reproduce it in FramePad.

Example: simply supported beam under a uniform load

Consider a prismatic 6 m beam supported by a pin at the left end (A) and a roller at the right end (B). A uniformly distributed downward load of 10 kN/m acts over the whole span.

Reference hand calculations

By vertical equilibrium and symmetry, both supports carry one-half of the total load:

With distance x measured from the left support, the conventional shear and sagging moment functions are:

The shear changes sign at midspan, which is where the positive bending moment reaches its maximum:

The maximum vertical deflection for a constant-EI Euler–Bernoulli beam is:

These are analytical reference values; sign and diagram display conventions may differ between software. Check magnitudes and physical directions, not only the plotted sign.

Reproduce this in FramePad

1. Open FramePad and choose Simply supported.
2. Check that the span is 6 m and the beam has a pin and a roller support.
3. Select the member and confirm EI = 16,000 kN·m².
4. Select the distributed load and set its magnitude to 10 kN/m downward.
5. Inspect the Moment, Shear and Deflected tabs; compare the results with the hand calculations above.

What this calculation assumes

The textbook expressions assume a straight, prismatic beam, linear-elastic material behavior, small deflections, and a static distributed load. They do not cover buckling, shear deformation, cracking, dynamic effects or code-based resistance checks. For a real structure, consider load cases, connection behavior and independent verification.