In structural engineering, the secant formula defines the force per unit area, P/A, that causes a maximum stress m in a column of given

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

P/A = σ_m/1 + (ec/k²) sec [0.5√P/(EA) (L/k)]

Where ec/k² = the eccentricity ratio and E = the modulus of elasticity. If for a steel beam, E = 200,000 MPa, ec/k² = 0.4, and σ_m = 250 MPa, compute P/A for L/k = 50. Recall that sec x = l / cos x.