- #1
Kasthuri
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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!
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