Shear Diagram

A shear diagram is a graphical representation showing how shear forces are distributed along a beam's length. Engineers use it to visualize internal force patterns in beams subjected to perpendicular loads. This diagram helps identify critical sections where shear stress is highest, essential for structural design and safety assessment.

Start by drawing a free-body diagram of the beam and calculating reaction forces using equilibrium equations. Apply the method of sections at different points along the beam. For each section, draw a free-body diagram and use equilibrium conditions to determine shear force values. Plot these values to create the shear diagram.

The method of sections allows you to isolate portions of the beam and analyze shear forces at arbitrary points. In each region, the shear force remains constant until a load is encountered. The shear value changes at load points and ultimately returns to zero at the beam's end to maintain equilibrium.

In the first section of a beam from the support, the shear force equals the reaction force at that support. For example, if the reaction force at support A is 24 kN, the shear force in the adjacent section is also 24 kN. This relationship comes directly from applying equilibrium equations to the isolated section.

Shear force changes when perpendicular loads act on the beam. Between load points, shear remains constant. At each load application, the shear value shifts by the magnitude of that load. This variation is captured in the shear diagram and reflects how internal forces redistribute along the beam's length.

At the beam's end, no external forces act beyond that point, so the shear force must equal zero to satisfy force equilibrium. This boundary condition is fundamental to beam mechanics and serves as a verification check when constructing shear diagrams. If calculated shear does not approach zero at the free end, an error exists in the analysis.

The free-body diagram isolates a beam section and shows all external forces and internal reactions acting on it. By applying equilibrium equations to this isolated section, you can solve for the internal shear force. This systematic approach works at any arbitrary distance along the beam, enabling construction of the complete shear diagram.