# Determine the force in each member of the truss shown.

Question-AnswerCategory: Engineering MechanicsDetermine the force in each member of the truss shown.
S cornwell asked 1 year ago

Determine the force in each member of the truss shown.

Step: 1

Draw the free body diagram of the entire truss.

Step: 2

Calculate the angle  from the geometry of the figure.

Calculate the angle  from the geometry of the figure.

Step: 3

Apply the equilibrium condition along the vertical direction.

Now apply the equilibrium condition along the horizontal direction.

Step: 4

Draw the free body diagram of the joint A:

Step: 5

Apply the equilibrium condition along the horizontal axis.

Substitute  for

Therefore, the force acting in the member AB is .

Step: 6

Apply the equilibrium condition along vertical direction.

Substitute  for .

Therefore, the force acting in the member AE is .

Step: 7

Consider the force at joint point E:

Step: 8

Apply the equilibrium condition along the horizontal direction.

Substitute  for  , for and  for .

…… (1)

Step: 9

Apply the equilibrium condition along the y direction.

Substitute  for  , for and  for

…… (2)

Step: 10

Solve the equations (2) and (1) to get the forces in members BE and EF.

Therefore, the tensile force acting in the member EF is.
Therefore, the compressive force acting in the member BE is .

Step: 11

Consider the forces acting at joint B:

Step: 12

Apply the equilibrium condition along the vertical direction.

Substitute  for  , for  and  for .

Therefore, the force acting in the member BC is .

Step: 13

Apply the equilibrium condition along the horizontal direction.

Therefore, the tensile force acting in the member BF is .

Step: 14

Consider the triangles  and .

Now consider the triangle .

Step: 15

Consider the forces acting at point F:

Step: 16

Consider the equilibrium condition along the x direction.

Substitute  for  , for  and  for
…… (3)
Apply the equilibrium condition along vertical direction.

Substitute  for  , for , for and  for .

…… (4)

Step: 17

Solve the equation (3) & (4).

Therefore, the tensile force acting in the member FG is .
Therefore, the tensile force acting in the member CF is .

Step: 18

Free body diagram of the joint C:

Step: 19

Apply the equilibrium condition.

Therefore, the tensile force acting in the member CD is .

Step: 20

Apply the equilibrium condition.

Therefore, the compressive force acting in the member CG is .

Step: 21

Free body diagram of the joint D