Step: 1

Draw the free body diagram of the Pratt roof truss.

 

Step: 2
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Let  be the forces in the members.  respectively.
By the symmetry of the truss,




 and

 

Step: 3

From triangle ADE,

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, 

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Step: 9

Draw the free body diagram of the joint B,

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Step: 10

Taking the condition of equilibrium,



Substitute  for .

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

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Step: 11

Taking the condition of equilibrium,


Substitute  for ,  for , and  for .


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

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Step: 12

Draw the free body diagram of the joint C,

 

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Step: 13

Taking the condition of equilibrium,
 


Substitute  for  and  for .



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

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Step: 14

Taking the condition of equilibrium,


Substitute  for ,  for , and  for .



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

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Step: 15

Draw the free body diagram of the joint E,

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Step: 16

Taking the condition of equilibrium,


Therefore, the force in the member DE is .