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

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

Determine the force in members AD. CD. and CE of the truss shown.

Step: 1

Free body diagram of the truss is as shown.

Step: 2

Let  be the forces in the members  respectively
Consider algebraic sum of moments about point K to be zero.

Step: 3

Consider the algebraic sum of forces along the horizontal direction to be zero.

Consider the algebraic sum of forces along the vertical direction to be zero.

Step: 4

Cut the truss through the members to analyze the forces in them.

Step: 5

Consider triangle BDE.

Step: 6

Consider algebraic sum of moments about point D to be zero.

Therefore, force in the member CE is .

Step: 7

Taking condition of equilibrium along the vertical direction,

Step: 8

Therefore, the force in the member CD is .

Step: 9

Taking condition of equilibrium along the horizontal direction,

Therefore, force in the member AD is .