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

Question-Answer › Category: Engineering Mechanics › Determine the force in each member of the roof truss shown. State whether each member is in tension or compression.
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S cornwell asked 1 year ago

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

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Sazid Ahmad answered 1 year ago

Step: 1

Free body diagram of the truss is as shown.
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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.
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Step: 5

Consider triangle ADE.

Consider triangle BDE.

 

Step: 6

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


Therefore, force in the member CE is .
 

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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 .

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