Shear and Moment in Beams — Worked Examples

A simply supported beam has span $L=6.0\text{ m}$ and a downward point load $P=20\text{ kN}$ at midspan. Determine the reactions and maximum bending moment.

A $5.0\text{ m}$ simply supported beam carries $w=8.0\text{ kN/m}$ over its full span. Determine the reactions and maximum bending moment.

A cantilever of length $3.0\text{ m}$ carries a downward free-end load of $12\text{ kN}$. Determine the maximum shear and bending moment magnitudes.

A $3.0\text{ m}$ cantilever carries $w=4.0\text{ kN/m}$ over its entire span. Determine the fixed-end shear and moment magnitudes.

A $6.0\text{ m}$ simply supported beam carries $30\text{ kN}$ at $2.0\text{ m}$ from the left support. Find the reactions and the maximum moment.

A $5.0\text{ m}$ simply supported beam carries two $10\text{ kN}$ downward loads at $x=1.0\text{ m}$ and $x=4.0\text{ m}$. Determine the reactions and the moment between the loads.

A $4.0\text{ m}$ simply supported beam carries a triangular downward load increasing linearly from zero at the left support to $6.0\text{ kN/m}$ at the right support. Determine the reactions and the location of maximum positive moment.

Between two beam stations, shear is constant at $+6\text{ kN}$ over a distance of $2.0\text{ m}$. If the bending moment at the first station is $4\text{ kN}\cdot\text{m}$, determine the moment at the second.

A $6.0\text{ m}$ simply supported beam carries $20\text{ kN}$ at $x=3.0\text{ m}$. Write compact shear and moment expressions for $0<x<6\text{ m}$ using Macaulay brackets.

For a simply supported beam with full-span UDL, the shear equation is $V(x)=20-8x$ in $\text{kN}$ with $x$ in meters. Locate the maximum positive bending moment.

A simply supported beam carries only downward vertical loads totaling $35\text{ kN}$. The computed reactions are $R_A=18\text{ kN}$ and $R_B=15\text{ kN}$. Can the resulting shear diagram close at zero?