Subject :- Structural Analysis II

Title :- Plastic Analysis

Difficulty:- Medium

1) Elastic Analysis:-

$Z_e = \frac{I_{NA}}{Y_{max}} = \frac{\frac{bh^3}{36}}{\frac{2h}{3}}$

$Z_e = \frac{bh^2}{12}$

2) Plastic Analysis:-

$Z_p = \frac{A}{2}[Y_1 + Y_2]$

For part 1:-

$A_1 = \frac{1}{2}*b_1*h_1$

[By Similar triangle (A)]

$\frac{2}{h} = \frac{b_1}{h_1}$

$b_1 = \frac{b}{(2)^\frac{1}{2}}$

$h_1 = \frac{h}{(2)^\frac{1}{2}}$

$Y_1 = \frac{h_1}{3} = \frac{h}{3(2)^\frac{1}{2}}$

$Y = \frac{x}{3}*(\frac{a+2b}{(a+b)})$ ==> Standard Formulae

$Y_2 = \frac{h - h_{\frac{1}{2}}}{3}*(\frac{b_1 + 2b}{b_1 + 2})$

$Y_2 = 0.1548h$

$Z_P = \frac{A(y_1 + y_2)}{2}$

$Z_P = 0.3905*\frac{h^2b}{4}$

3) $S = \frac{Z_P}{Z_e}$

[s = 2.343];[Sharp factor = 2.343]