# Determine the force in each member of the Pratt roof truss shown. State whether each member is in tension or compression.

Question-AnswerCategory: Engineering MechanicsDetermine the force in each member of the Pratt roof truss shown. State whether each member is in tension or compression.
S cornwell asked 1 year ago

Determine using the method of joints the force in each member of the Howe roof truss shown. State whether each member is in tension or compression.

Step: 1

Draw the free body diagram of the Howe roof truss.

Step: 2

Since the truss is symmetrical about the member , the forces in the following members are equal in magnitude.

Step: 3

Calculate the angle  by using the following relation:

Consider  to be the reaction force at point  due to the roller support, and  to be the reactions force in the  and  directions respectively at point  due to the pin support.
Write the force equilibrium equation in the  direction.

Consider the moment about point .

Step: 4

Write the force equilibrium equation in the  direction.

Substitute  for .

Step: 5

Draw the free body diagram at joint A.

Step: 6

Consider the force equilibrium equation equilibrium in the  direction.

Substitute  for .

Therefore, the force acting in each member AB and FH are .

Step: 7

Write the force equilibrium equation in the  direction.

Substitute  for .

Therefore, the force acting in each member AC and  is .

Step: 8

Draw the free body diagram of the joint C.

Step: 9

Write the force equilibrium equation in the  direction.

Substitute  for .

Therefore, the force acting in each member CE and is .

Step: 10

Write the force equilibrium equation in the  direction.

Therefore, force acting in each member BC and  is .

Step: 11

Draw the free body diagram of the joint B.

Step: 12

Write the force equilibrium equation in the  direction.

Substitute  for .
…… (1)

Step: 13

Write the force equilibrium equation in the  direction.

Substitute  for .

Substitute  for .

Therefore, force acting in each member BE and  is .
Substitute  for  in equation (1).

Therefore, the force acting in each member BD and  is .

Step: 14

Draw the free body diagram of the joint E.