Concept explainers
Knowing that P = Q = 150 lb, determine (a) the distance a for which the maximum absolute value of the bending moment in beam AB is as small as possible, (b) the corresponding value of |M|max. (See the hint for Prob. 7.55.)
Fig. P7.60
7.61 Solve Prob. 7.60 assuming that P = 300 lb and Q = 150 lb.
(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.
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
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
Vector Mechanics for Engineers: Statics
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