Question

example 3 determine the critical pressure of the following slender compressive columns. knowing: l=0.5m and e=200gpa. (45×45×6) equal-leg angle steel

Explanation:

Step1: Identify column end conditions

For Fig(a): fixed at base, free at top → $K=2$. For Fig(b): fixed at base, free at top → $K=2$.

Step2: Find minimum moment of inertia for angle section

Equal-leg angle $45×45×6$: $I_{\text{min}} = I_y = I_z = 1.29×10^{-8}\,m^4$ (standard value).

Step3: Apply Euler's formula for critical load

Euler's formula: $P_{\text{cr}} = \frac{\pi^2EI}{(KL)^2}$
Substitute $E=200×10^9\,Pa$, $I=1.29×10^{-8}\,m^4$, $K=2$, $L=0.5\,m$:
$P_{\text{cr}} = \frac{\pi^2×200×10^9×1.29×10^{-8}}{(2×0.5)^2}$

Step4: Calculate critical pressure

$P_{\text{cr}} = \frac{9.8696×200×10^9×1.29×10^{-8}}{1} ≈ 25500\,N = 25.5\,kN$

Answer:

$25.5\,kN$