steel circular bar

[logistic_guy]

A steel circular bar (\(\displaystyle \sigma_{yp} = 250 \ \text{MPa}\)) of \(\displaystyle d = 60\)-\(\displaystyle \text{mm}\) diameter is acted upon by combined moments \(\displaystyle M\) and axial compressive loads \(\displaystyle P\) at its ends. Taking \(\displaystyle M = 1.5 \ \text{kN}\cdot\text{m}\), determine, based on the maximum energy of distortion theory of failure, the largest allowable value of \(\displaystyle P\).

 

[logistic_guy]

We will let the axial loads be along the \(\displaystyle x\)-axis, so there is no normal stress along the \(\displaystyle y\)-axis.

This gives:

\(\displaystyle \sigma_y = 0\)

And we have a beautiful formula for the stress along the \(\displaystyle x\)-axis.

\(\displaystyle \sigma_x = -\frac{P}{A} - \frac{M_yy}{I_y}\)