Concept explainers
The truss shown consists of six members and is supported by a short link at A. two short links at B, and a ball and socket at D. Determine the force in each of the members for the given loading.
The force in each of the members of the truss for the given loading.
Answer to Problem 6.35P
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,
Write the equilibrium equations taking the moments about
Here,
Write the equation for
Here,
Put the above equation in equation (II).
The
Here,
Write the expression for
Put the above equation in equation (III).
Put equation (I) in the above equation.
Substitute
The
Here,
Write the expression for
Put the above equation in equation (IV).
Put equation (I) in the above equation.
Write the expression for the reaction at the point B.
Here
Substitute
Consider the free-body joint C. The free-body diagram of joint C 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
Put the above equation in equation (XI).
Substitute
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.
Here,
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
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