Learning topic
Support Reactions and Internal Forces in Beams
Calculate support reactions in statically determinate beams, then use the section method to find shear force V/Q and bending moment M at any section.
Support reactions and internal forces are treated here as a concise review of tools needed throughout structural mechanics. The introductory theory of supports, external and internal forces, and the section method also belongs to mechanics of materials.
Support reactions
After replacing supports by their reaction components, equilibrium equations are written for the entire beam. A suitable moment center often eliminates several unknowns at once. Calculated reactions should be checked with an independent equilibrium equation.
Internal force resultants
A general section of a planar beam may carry axial force $N$, shear force $V$ or $Q$, and bending moment $M$. In common transverse-bending problems the primary quantities are shear and bending moment.
Section method
The beam is cut at the required location and equilibrium is written for one of the two parts. Choosing the side with fewer external actions usually simplifies the calculation. The sign convention for internal forces must be applied consistently.
Verification
An error in the reactions propagates through all subsequent diagrams. Before constructing $V(x)$ and $M(x)$, check global equilibrium, dimensions, and whether the resulting reaction directions are mechanically plausible.
About this topic
This topic covers beam idealization, support reactions, and the use of sections to determine shear force and bending moment in statically determinate beams.