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

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S cornwell asked 1 year ago

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

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Sazid Ahmad answered 1 year ago

Step: 1

Draw the free body diagram of the Howe roof truss.

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Step: 2

Since the truss is symmetrical about the member , the forces in the following members are equal in magnitude.

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Step: 3

Calculate the angle  by using the following relation:

Consider  to be the reaction force at point  due to the roller support, and ,  to be the reactions force in the  and  directions respectively at point  due to the pin support.
Write the force equilibrium equation in the  direction.

Consider the moment about point .

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Step: 4

Write the force equilibrium equation in the direction.

Substitute for .

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Step: 5

Draw the free body diagram at joint A.

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Step: 6

Consider the force equilibrium equation equilibrium in the direction.

Substitute for .

Therefore, the force acting in each member AB and FH are .

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Step: 7

Write the force equilibrium equation in the  direction.

Substitute  for .

Therefore, the force acting in each member AC and  is .

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Step: 8

Draw the free body diagram of the joint C.

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Step: 9

Write the force equilibrium equation in the direction.

Substitute for .

Therefore, the force acting in each member CE and is .

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Step: 10

Write the force equilibrium equation in the direction.

Therefore, force acting in each member BC and is .

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Step: 11

Draw the free body diagram of the joint B.

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Step: 12

Write the force equilibrium equation in the direction.

Substitute for .
…… (1)

Step: 13

Write the force equilibrium equation in the  direction.

Substitute  for .

Substitute  for .

Therefore, force acting in each member BE and  is .
Substitute  for  in equation (1).

Therefore, the force acting in each member BD and  is .