Solving the Truss Bridge Problem

[BridgeBuilder]

First time poster, long time reader...

Consider the truss bridge as shown in the attached diagram (Each member is the same length) A force of 1000N is applied 3/4 of the way across the bridge. We get:

R1 = 250 N
R2 = 750 N

Resolving from the left we get:

T1 = 250 / sin 60
T1 sin 60 = T3 sin 60 so T1 = T3
T4 = T1 cos 60 + T3 cos 60

so T4 = T1 = T3 = 250 / sin 60

However, resolving from the right we get:

T7 = 750 / sin 60
T7 sin 60 = T5 sin 60 so T7 = T5
T4 = T5 cos 60 + T7 cos 60

so T4 = T5 = T7 = 750 / sin 60

Why do we get two different values for T4? I cannot see my mistake.

Many thanks.

 

[MrMatt2532]

Forces must be applied at joints. You could break up the 1000 N to 500 N on both joints for that member. You will see that the solution you found in your analysis from the left side is correct.

 

[pongo38]

The forces don't have to be applied to the joints. You can cut the structure right down the middle. Using the method of sections, and taking moments for each side about the centre bottom joint gives consistent values of T4.