Concept explainers
(a)
The distance a from the ends of the beam to the points where the cables should be attached if the maximum absolute value of the bending moment in the beam AB is the smallest.
(a)
Answer to Problem 7.61P
The distance a from the ends of the beam to the points where the cables should be attached if the maximum absolute value of the bending moment in the beam AB is the smallest is
Explanation of Solution
Refer Figure 1.
Write an expression to calculate the counter clockwise moment at point A.
Here,
Write an expression to calculate the counter clockwise moment at point A.
Here,
Write an expression to calculate the counter clockwise moment at point A.
Here,
Conclusion:
Refer Figure 1:
Calculate the moment about point A.
Here,
Rearrange the equation to calculate the D.
Substitute
Refer Figure 2.
Calculate the moment about point C.
Rearrange the equation to calculate the
Substitute
Refer Figure 2.
Calculate the moment about point D.
Rearrange the equation to calculate the
Substitute
The magnitude of the maximum moment is equal to the magnitude of the minimum moment.
Substitute (I) and (II) in above equation to find a.
Rearrange the equation to find a.
Thus, the distance a from the ends of the beam to the points where the cables should be attached if the maximum absolute value of the bending moment in the beam AB is the smallest is
(b)
The value of
(b)
Answer to Problem 7.61P
The value of
Explanation of Solution
Refer Figure 4.
The magnitude of the maximum moment is equal to the magnitude of the minimum moment.
Conclusion:
Substitute
Thus, the value of
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Chapter 7 Solutions
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