Chapter 8, Problem 14P

In structural engineering, the secant formula defines the force per unit area, $P/A$, that causes a maximum stress ${\sigma }_m$ in a column of given slenderness ratio $L/k$:

$\frac{P}{A}=\frac{{\sigma }_m}{1+\left(ec/k^2\right)\sec \left[0.5\sqrt{P/\left(EA\right)\left(L/k\right)}\right]}$

where $ec/k^2=$ the eccentricity ratio and $E=$ the modulus of elasticity. If for a steel beam, $E=200,000\text{MPa, }ec/k^2=0.2,\text{ and }{\sigma }_m=250\text{ MPa, compute }P/A\text{ for }L/k=100$. Recall that sec $x=1/\text{cos}x$.