Combined Stresses — Worked Examples

A short column with area $60000\text{ mm}^2$ carries a concentric compressive force of $180\text{ kN}$. Determine the normal stress using tension-positive signs.

A $200\text{ mm}\times300\text{ mm}$ rectangular column carries $150\text{ kN}$ compression with eccentricity $e=50\text{ mm}$ along the $300\text{ mm}$ depth. Determine the edge stresses.

Use the same column and load as Example 2, but with $e=30\text{ mm}$. Determine the edge stresses.

Use the same $200\text{ mm}\times300\text{ mm}$ column and $150\text{ kN}$ load, but take $e=75\text{ mm}$. Evaluate the linear full-contact edge stresses.

A $100\text{ mm}\times200\text{ mm}$ rectangular member carries $100\text{ kN}$ axial tension and a bending moment of $6.0\text{ kN}\cdot\text{m}$ about the strong centroidal axis. Determine the extreme normal stresses.

A rectangular wall base is $1.20\text{ m}$ wide in the direction of eccentricity. What is the maximum eccentricity that preserves full compression under the elementary middle-third rule?

A compression resultant is $P=300\text{ kN}$ and the same load system produces $M=60\text{ kN}\cdot\text{m}$ about the section centroid. Determine the equivalent eccentricity. If the section depth is $1.50\text{ m}$, is it inside the middle third?

At a point in a beam, $\sigma_x=60\text{ MPa}$, $\sigma_y=0$, and $\tau_{xy}=30\text{ MPa}$. Determine the principal stresses.

At the extreme top fiber of an elementary beam section, the bending stress is $-80\text{ MPa}$. What transverse shear stress does the elementary free-surface model give there, and what are the in-plane principal stresses?

For the $200\text{ mm}\times300\text{ mm}$ column carrying $150\text{ kN}$ at $e=75\text{ mm}$, locate the zero-normal-stress line measured from the centroid using the linear full-contact model.

A rectangular beam section has its largest bending stress at the extreme fibers and its largest transverse shear stress at the neutral axis. Is it correct to add those two maxima directly and call the result the stress state at one material point?