If two loads are applied to a cantilever beam as shown in the accompanying drawing, the...
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If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is a₁X₁ + a₂X₂. X₁ mit O 0 a1 X₂ ↓ 92 a. Suppose that X₁ and X₂ are independent rv's with means 2 and 4 kips, respectively, and standard devia- tions .5 and 1.0 kip, respectively. If a₁ = 5 ft and a = 10 ft, what is the expected bending moment and what is the standard deviation of the bending moment? b. If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? c. Suppose the positions of the two loads are random variables. Denoting them by A₁ and A₂, assume that these variables have means of 5 and 10 ft, respec- tively, that each has a standard deviation of .5, and that all A's and X's are independent of one another. What is the expected moment now? d. For the situation of part (c), what is the variance of the bending moment? e. If the situation is as described in part (a) except that Corr(X₁, X₂) = .5 (so that the two loads are not inde- pendent), what is the variance of the bending moment? If two loads are applied to a cantilever beam as shown in the accompanying drawing, the bending moment at 0 due to the loads is a₁X₁ + a₂X₂. X₁ mit O 0 a1 X₂ ↓ 92 a. Suppose that X₁ and X₂ are independent rv's with means 2 and 4 kips, respectively, and standard devia- tions .5 and 1.0 kip, respectively. If a₁ = 5 ft and a = 10 ft, what is the expected bending moment and what is the standard deviation of the bending moment? b. If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 75 kip-ft? c. Suppose the positions of the two loads are random variables. Denoting them by A₁ and A₂, assume that these variables have means of 5 and 10 ft, respec- tively, that each has a standard deviation of .5, and that all A's and X's are independent of one another. What is the expected moment now? d. For the situation of part (c), what is the variance of the bending moment? e. If the situation is as described in part (a) except that Corr(X₁, X₂) = .5 (so that the two loads are not inde- pendent), what is the variance of the bending moment?
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Related Book For
Shigleys Mechanical Engineering Design
ISBN: 978-1121345317
9th edition
Authors: Richard G. Budynas, J. Keith Nisbett
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