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6.5: Method of Joints: Problem Solving II

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Mechanical Engineering

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Method of Joints: Problem Solving II
 
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6.5: Method of Joints: Problem Solving II

Consider a truss structure with frictionless joints fixed to a wall and roller support. If a force of 150 N is applied to joint A, the forces in each member of the truss can be determined using the method of joints.

Figure 1

The angle between members AC and AB can be found by taking the inverse tangent of the ratio of the lengths of BC and AB, and the result obtained is 67.38°. A free-body diagram of joint A is considered, and all unknown forces are resolved into their respective components.

The vertical force equilibrium condition can then be used to calculate the force acting on member CA, which is equal to 173.08 N.

Equation 1

Similarly, the horizontal force equilibrium condition can be used to find the force FAB as 161.54 N.

Equation 2

Free-body diagrams of joints B and C are considered, and the vertical and horizontal force equilibrium conditions are applied to calculate the unknown forces FBD , FCD , and FEC. The resulting values for FBD , FCD , and FEC are 161.53 N, 173.08 N and 207.70 N, respectively.

Free-body diagrams of joints D and E are finally considered, and the vertical and horizontal force equilibrium conditions are applied. This gives the values of FED and FDF as 138.46 N and 265.39 N, respectively.


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Truss Structure Method Of Joints Force Analysis Joint A Member AC Member AB Angle Free-body Diagram Vertical Force Equilibrium Horizontal Force Equilibrium Member CA Member AB Joint B Joint C Member BD Member CD Member EC Joint D Joint E Member ED Member DF

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