Beam Engineering Guide

How to Calculate Beam Reactions, Shear, Moment & Deflection

A useful beam analysis follows a sequence: define supports and loads, solve equilibrium, trace shear and bending moment, then evaluate deformation using the member stiffness EI.

1. Define the structural model

Start with the span, support condition, elastic modulus E and second moment of area I. The support model controls the boundary conditions, so a simply supported beam and a cantilever with the same span and loading will not produce the same response.

2. Resolve the applied loads

Point loads act at a specified location. A uniformly distributed load acts over a length and may cover the entire span or only part of it. Keep force units and distributed-load units dimensionally distinct.

3. Solve support reactions

Use static equilibrium for the modeled support system. Reaction forces must balance the applied vertical loads, and the corresponding moment equilibrium must also be satisfied.

4. Build the shear-force response

Moving along the beam, concentrated forces create jumps in shear while distributed loads change shear continuously over their loaded interval.

5. Build the bending-moment response

Bending moment follows from the shear response and the selected sign convention. Critical bending locations commonly occur where shear changes sign or at structural boundaries, depending on the load case.

6. Evaluate deflection

For the V1 linear-elastic model, deformation is related to bending response through EI stiffness and the boundary conditions. Multiple supported loads are combined by linear superposition.

7. Interpret, do not over-claim

A calculated reaction, moment or deflection is not by itself a code-compliance conclusion. Real design may also require strength, stability, serviceability, connection and load-combination checks under the applicable standard.

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