Stresses in Beams — Worked Examples

A rectangular timber beam is $100\text{ mm}$ wide and $200\text{ mm}$ deep. It carries a bending moment of $15\text{ kN}\cdot\text{m}$. Determine the extreme-fiber bending stress magnitude.

A $150\text{ mm}\times250\text{ mm}$ rectangular beam carries $V=40\text{ kN}$. Determine the maximum transverse shear stress.

A beam section must carry $M=30\text{ kN}\cdot\text{m}$ while the stated allowable bending stress is $150\text{ MPa}$. Determine the required section modulus.

Use the beam from Example 1. Determine bending stress magnitude at a point $50\text{ mm}$ from the neutral axis.

A rectangular beam remains $100\text{ mm}$ wide and carries $15\text{ kN}\cdot\text{m}$. Its depth is increased from $200\text{ mm}$ to $300\text{ mm}$. Determine the new extreme-fiber bending stress.

A $150\text{ mm}\times250\text{ mm}$ rectangular beam carries $40\text{ kN}$ shear. Determine $\tau$ at $y=50\text{ mm}$ above the neutral axis.

A rectangular section is $150\text{ mm}$ wide and requires $S=2.50\times10^5\text{ mm}^3$. Determine the required depth from the elastic section-modulus equation.

A $100\text{ mm}\times200\text{ mm}$ rectangle can bend about either centroidal axis. Compare the elastic section moduli.

For an ordinary solid beam section under the elementary beam-shear model, evaluate the transverse shear stress at the top free surface.

A linear flexure calculation predicts an extreme-fiber stress of $300\text{ MPa}$ in a steel beam whose stated yield strength is $250\text{ MPa}$. Can the purely linear-elastic stress distribution be treated as valid through the full section at that load?