Subject : Structural Analysis 1

Topic : Deflection of Beam

Difficulty : High

1. Calculation support reaction:

$ \sum M_A=0(\circlearrowright+ve)\\ 160+120\times4-V_B\times8=0\\ \boxed{V_B=80\ kN}$

$ \sum F_Y=(\uparrow+ve)\\ V_A-120+40\\ \boxed{V_A=40\ kN}$

2. Using Macaulay's Method:

Let, Taking A as origin and using Macaulay's Method, the bending moment at any section x at a distance x from A.

$ BM_x=EI\frac{d^2y}{dx^2}=80x+160(x-3)^0-15x\frac{x}{2}$

$ = 80x+160(x-3)^0-15\frac{x^2}{2}$ --- (1)

Integrating …