Calculating Bending Moments with UDL's

[mm391]

Homework Statement

The T-beam is loaded as shown in Figure attached Find the maximum transverse shear stress at the location of the maximum bending moment.

Homework Equations

Forces in Y direction = 0 for it to be in equilibrium
Moments about a point = 0 for it to be in equilibrium

The Attempt at a Solution

Ra = Reactions at A
Rb = Reactions at B

ƩForces in Y direction = Ra - 20kN - (8)(3) + Rb
ƩForces about Ra = 20*2+((8*3)*4.5)-Rb*6

Rb = 24.6kN
Ra = 19.4kN

Now I tried to work out the bending moments from the left hand side:

1> Ra*x = 19.4x
2> 19.4x -20(x-2) = 0.6x-40
3> 19.4x-20x-40+((8(x-4)^2)/2)

Are these right? Do I also need a moment for Rb if so how would I include it? Do I work it out from the right hand side. If so how, as I have been trying but can't figure it out.

Thanks

 

[SteamKing]

Try working out the shear diagram first. Once you have that, the bending moment diagram should follow easily.