Mumbai University > Civil Engineering > Sem 5 > Structural Analysis – II

Marks: 8 Marks

Year: May 2015

Number of plastic hinges , n = r + 1 = ( R – E ) + 1 = ( 6 - 3 ) + 1 = 4

Plastic Hinges Location , N = 6

N > n …………………………… Partial collapse mechanism

Let , beam AB collapse

Using virtual work principle

Σw * δ = Σ Mp * Θ

40 * δ = Mp * Θ + Mp *( Θ + Θ ) + Mp * Θ

But , Θ = δ/2

δ = 2 Θ

40 * 2 Θ = 4 Mp Θ

Mp = 80 / 4 = 20 KN-m

Let , beam BC collapse

Using virtual work principle

Σw * δ = Σ Mp * Θ

20 * δ = Mp * Θ + Mp *( Θ + α ) + Mp * α

But , Θ = δ/1 , Θ = δ

α = δ / 3 , α = Θ / 3

20 * Θ = Mp Θ + Mp * (Θ + Θ / 3 ) + Mp * Θ / 3

20 * Θ = 2.67 Mp * Θ

Mp = 20 / 2.67 = 7.49 KN-m

Let , Span CD collapse ,