Concept explainers
Frame ABCD is supported by a ball-and-socket joint at A and by three cables. For a = 150 mm, determine the tension in each cable and the reaction at A.
Fig. P4.129 and P4.130
The tension in each cable and the reaction at
Answer to Problem 4.129P
The tension in each cable and the reaction at
Explanation of Solution
The tension in the cable
Figure 1
The position vector of the point
The position vector of the point
The position vector of the point
The position vector of the point
The vector
The tension across the cable
Here,
Substitute
The tension across the cable
Here,
Substitute
The tension across the cable
Here,
Substitute
The weight is given as,
Here,
Substitute
The force on the point is zero. This means that the sum of the moments of the force will also be zero.
Substitute the vector values and determine the cross product.
Since the force at the point is zero, the
Here,
Since the force at the point is zero, the
Here,
Since the force at the point is zero, the
Here,
Conclusion:
Equate the coefficients of
Equate the coefficients of
Equate the coefficients of
Substitute
Substitute
Substitute
From (V), (VI) and (VII), the reaction on A is given as,
Therefore, the tension in each cable and the reaction at
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Chapter 4 Solutions
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