#77 Draw the free body diagram - civil engineering

Draw the free-body diagram - Civil Engineering

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Free Chegg Question

#77 Draw the free-body diagram - Civil Engineering

Free Chegg Answer

Step 1

Draw the free body diagram.

Step 2

Take moments about.

Here,  is the tension in the cable .

Step 3

Consider the free body diagram at the joint .
Resolve forces vertically.

Here,  is the force in the member .
Substitute  for .

Hence, the force in the member  is 

Step 4

Resolve forces horizontally.

Here,  is the force in the member .
Substitute  for .

Hence, the force in the member  is .

Step 5

Consider the free body diagram at the joint .
Resolve forces vertically.
 ...... (1)
Here,  is the force in the member , and  is the angle made by the cross members in the bridge.
Calculate the value of .

Substitute  for , and  for  in the equation (1).

Hence, the force in the member  is .

Step 6

Resolve forces horizontally at the joint .

Here,  is the force in the member .
Substitute  for , and  for .

Hence, the force in the member  is .

Step 7

Consider the free body diagram at the joint .
Resolve forces horizontally.

Here,  is the force in the member .
Substitute  for ,  for , and  for .

Hence, the force in the member  is .