Simple Stresses — Worked Examples

A steel tie with a net area of $600\text{ mm}^2$ carries a tensile force of $120\text{ kN}$. Determine the average normal stress.

A circular rod with diameter $20\text{ mm}$ carries $50\text{ kN}$ in tension. Determine the average normal stress.

A $16\text{ mm}$ diameter bolt transfers a $40\text{ kN}$ load through two effective shear planes. Determine the average shear stress in the bolt.

A $20\text{ mm}$ bolt transfers $60\text{ kN}$ through a plate $12\text{ mm}$ thick. Determine the average bearing stress in the plate.

A plate is $100\text{ mm}$ wide and $10\text{ mm}$ thick with one $20\text{ mm}$ diameter hole across the critical section. It carries $120\text{ kN}$ in tension. Determine the average net-section stress.

A steel member is fully restrained against axial expansion. Take $E=200\text{ GPa}$, $\alpha=12\times10^{-6}/{}^\circ\text{C}$, and a temperature increase of $40{}^\circ\text{C}$. Determine the thermal stress.

A steel member has a yield strength of $250\text{ MPa}$ and is checked using a factor of safety of $1.67$. If its area is $1200\text{ mm}^2$, determine the allowable stress and corresponding axial load.

A single bolt transfers $50\text{ kN}$. The allowable bolt shear stress is $100\text{ MPa}$. The connected plate is $10\text{ mm}$ thick with allowable bearing stress $150\text{ MPa}$. Determine the minimum bolt diameter from both checks.

A circular rod carries a fixed axial load. Its radius is doubled while the load remains unchanged. Determine the ratio of the new average normal stress to the original stress.

A $20\text{ mm}$ bolt in single shear connects a $14\text{ mm}$ plate. The applied load is $45\text{ kN}$. Check the bolt against an allowable shear stress of $120\text{ MPa}$ and the plate against an allowable bearing stress of $180\text{ MPa}$.