Deflection of a Beam: Solving for vB using the Double-Integration Method

[Name15]

Homework Statement

For the simply supported steel beam [E = 200 GPa; I = 129 × 10^6 mm4], use the double-integration method to determine the deflection vB at B. Assume L = 4 m, P = 60 kN, and w= 40 kN/m.

Can someone please help, when I insert x=2m into the equation i derived for M, and then insert M into equation 1, I do not get the correct answer (-8.27 mm).

Homework Equations

E.I.y''=M (eq. 1)
M=F.d (eq. 2)

The Attempt at a Solution

[/B]

 

[SteamKing]

Check your equation for the bending moment in the beam. I would split the problem up into calculating the BM due to the central point load plus the BM due to the distributed load.

In order to avoid confusion, draw the shear and bending moment diagrams for this beam. Because the beam is symmetrically loaded, these can almost be done by inspection.