Subject: Structure Analysis 2

Topic: Determination of collapse load for beans

Difficulty: Hard

1)

2)

3)

1)

No of plastic = r+ 1

$r =D_s (Degree of static indeterminancy)$

$D_s = r-2 = 4-2 = 2 [Neglecting Axial deformation]$

No of plastic hing = r = 1 = 2 + 1 = 3

where it will formed:

[In kinamatic we have to draw deformation Dig]

[Using virtual work Principle]

EWD = IWD

$P*\gamma = M_P\theta + 2M_P\theta + M_P\theta$

$W*\frac{L\theta}{2} = 4M_P\theta$

$M_P = \frac{W*L}{8}$

2)

No of plastic = r+ 1

$r =D_s (Degree of static indeterminancy)$

$D_s = 2 + 1 = 3 [Neglecting Axial deformation]$

[Using virtual work Principle]

EWD = IWD

Intensity of UDL*Area of plastic deformation = $Σ(M_P\theta)$

$P*\frac{1}{2}*L*\gamma =4M_P\theta$

$M_P = \frac{W*L^2}{16}$

3)

No of PH

$D_s = r - 2 = 3 - 2 = 1$

Using virtual work Principle

EWD = IWD

$w*\frac{1}{2}*L*\gamma =M_P\theta + M_P(\gamma + \alpha)$

$\theta = \frac{\gamma}{0.586L}$

$\alpha = \frac{\gamma}{0.414L}$

$w*\frac{1}{2}*\gamma*L = \frac{\gamma}{L}(2M_P*1.706 + M_P*2.415)$

$M_P = \frac{W*L^2}{11.65}$