# 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. 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. Write the force equilibrium equation in the direction. Substitute for and for . Therefore, the force acting in the member ED is .