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The truss shown consists of six members and is supported by a ball and socket at B, a short link at C, and two short links at D. Determine the force in each of the members for P= (−2184 N)j and Q = 0.
The force in each of the members of the truss for
Answer to Problem 6.36P
The force in member AC is
Explanation of Solution
The free-body diagram of the entire truss is shown in figure 1.
Refer to figure 1 and use symmetry.
Here,
The
Here,
Write the expression for
Put the above equation in equation (II).
Put equation (I) in the above equation.
The
Here,
Write the expression for
Here,
Put the above equation in equation (III).
Write the equilibrium equations taking the moments about the point C in the
Here,
Write the equation for
Put the above equation in equation (IV).
Write the expression for the reaction at the point B.
Here
Substitute
Consider the free-body joint A. The free-body diagram of joint A is shown in figure 2.
Refer to figure (2) and write the expression for the forces.
Here,
Write the expression for
Find the magnitude of
Substitute
Write the expression for
Here,
Substitute
Write the expression for
Here,
Substitute
The net force must be equal to zero.
Here,
Write the expression for
Put the above equation in equation (IX).
Put equations (VI), (VII) and (VIII) in the above equation.
Equate the coefficient of
Equate the coefficient of
Equate the coefficient of
Multiply equation (XI) by
Put equation (XIII) in equation (XI).
Substitute
Put the above equation in equation (XIII).
Consider the free-body joint B. The free-body diagram of joint B is shown in figure 3.
Refer to figure (3) and write the expression for the forces.
Substitute
Write the expression for
Here,
Substitute
Write the expression for
Here,
Write the expression for
Put the above equation in equation (IX).
Put equations (XIV), (XV) and (XVI) in the above equation.
Substitute
Equate the coefficient of
Equate the coefficient of
Substitute
From symmetry,
Here,
Substitute
Conclusion:
Thus, the force in member AC is
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Chapter 6 Solutions
Vector Mechanics for Engineers: Statics
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