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

Step: 1

Draw the free body diagram of the entire truss.

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Step: 2

From the geometry of the figure,

From

From similar triangles

Calculate the angle of inclination .

Step: 3

From similar triangles

Step: 4

Take moment about A as follows:

Step: 5

Apply the equilibrium condition as follows:

Step: 6

Free body diagram of the joint A:

Step: 7

Apply the equilibrium condition as follows:

Therefore, the force acting in the member AB is

Step: 8

Apply the equilibrium condition as follows:

Therefore, the force acting in the member AC is .

Step: 9

Draw the free body diagram of the joint B:

Step: 10

Apply the equilibrium condition as follows:

…… (1)

Step: 11

Apply the equilibrium condition as follows:

Step: 12

Substitute for in equation (1).

Therefore, the force acting in the member BC is .

Therefore, the force acting in the member BD is .

Step: 13

Free body diagram of the joint C:

Step: 14

Apply the equilibrium condition as follows:

Therefore, the force acting in the member CD is .

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Step: 15

Apply the equilibrium condition as follows:

Therefore, the force acting in the member CE is .

Step: 16

Draw the free body diagram of the joint D:

Step: 17

Apply the equilibrium condition as follows:

…… (2)

Step: 18

Apply the equilibrium condition as follows:

…… (3)

Step: 19

Solve equations (2) and (3).

Therefore, the force acting in the member DF is .

Therefore, the force acting in the member DE is .

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Step: 20

Draw the free body diagram of the joint E:

Step: 21

Apply the equilibrium condition as follows:

Therefore, the force acting in the member EF is .