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

Step: 1

Draw the free body diagram of the Pratt roof truss.

Step: 2

Let  be the forces in the members.  respectively.
By the symmetry of the truss,

and

Step: 3

Substitute 2.4 m for DE and  for AE.

From triangle CDE,

Substitute 2.4 m for DE and 3.2 m for CE.

Step: 4

Taking the moment about point A,

Step: 5

Taking the condition of equilibrium,

Taking the condition of equilibrium,

Substitute  for .

Step: 6

Draw the free body diagram of the joint A,

Step: 7

Taking the condition of equilibrium,

Substitute  for  and  for .

Therefore, the member AB is subjected to a compressive force, .

Step: 8

Taking the condition of equilibrium,

Substitute 0 for  for , and  for .

Therefore, the member AC is subjected to a tensile force,

Step: 9

Draw the free body diagram of the joint B,

Step: 10

Taking the condition of equilibrium,

Substitute  for .

Therefore, the member BD is subjected to a compressive force, .

Step: 11

Taking the condition of equilibrium,

Substitute  for  for , and  for .

Therefore, the member BC is subjected to a compressive force, .

Step: 12

Draw the free body diagram of the joint C,

Step: 13

Taking the condition of equilibrium,

Substitute  for  and  for .

Therefore, the member CD is subjected to a tensile force, .

Step: 14

Taking the condition of equilibrium,

Substitute  for  for , and  for .

Therefore, the member CE is subjected to a tensile force, .

Step: 15

Draw the free body diagram of the joint E,