Calculating the maximum bending moment on a bridge

[Kasthuri]

Homework Statement

Calculate the maximum bending moment on the bridge section using the values given.

(REFER TO DIAGRAM ATTACHED)

mass of bridge = 9250 kg
mass of car = 2250 kg
length of bridge section = 26 m

Homework Equations

I worked out previously that:
Reaction at A = reaction at B = 56407.5 N , which I got right

ƩFx = 0;
ƩFy = 0;
ƩM = 0;

The Attempt at a Solution

I know the maximum Bending Moment is at x = 13m (because shear force = 0 ant x = 13m)weight of bridge = 6250 x 9.81 = 90742.5 N
weight of car = 22072.5 N

I tried three ways, I know the 1st is wrong.

1st method:

Bending Moment max:
= 90742.5N x 13m + 22072.5N x 13m
= 1466595 N.m

2nd method:

Bending Moment max:
make a cut at 0≤x<13m , (shear force) v = 56407.5 N
so integrate this to get BM at x = 13m:
BM = 56407.5x
so at x = 13m:
Bending Moment max = 56407.5 x 13 = 733297.5 N.m

3rd method:

Bending Moment max
= wL/4 (for point load car) + wL^2/8 (uniformly distributed load of bridge)
= 22072.5 x 26/4 + 90742.5 x (26 x 26)/8
= 7811212.5 N.m

So, I'm quite stuck on the method.

Thank you so much for any help!

 

[SteamKing]

In the third bending moment calculation, you have used the entire weight of the bridge rather than the weight per meter for w.

 

[Kasthuri]

Thanks!
I did what you said and got it right :D