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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 a,X, + a,X2.

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 a,X, + a,X2.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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66. If two loads are applied to a cantilever beam as shown in X 1s the accompanying drawing, the bending moment at 0 due to the loads is a,X, + a,X2. olgniz s no 2oloirav lo X loro X, va noinsivsb bin combarc bus from the a. Suppose that X, and X, are independent rv's with means 10 and 20 kN, respectively, and standard devi- odi ations 2 and 4 kN, respectively. If a, = 1 m and 25ulev na, = 2 m, what is the expected bending moment and biabaete what is the standard deviation of the bending i 1edW moment? b. If X, and X, are normally distributed, what is the probability that the bending moment will exceed 75 kN-m? dmC. Suppose the positions of the two loads are random variables. Denoting them by A, and A,, assume that these variables have means of 1 m and 2 m, respec- с. tively, that each has a standard deviation of 0.1, 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(X, X,) = .5 (so that the two loads are not inde- pendent), what is the variance of the bending %3D moment?
Transcribed Image Text:66. If two loads are applied to a cantilever beam as shown in X 1s the accompanying drawing, the bending moment at 0 due to the loads is a,X, + a,X2. olgniz s no 2oloirav lo X loro X, va noinsivsb bin combarc bus from the a. Suppose that X, and X, are independent rv's with means 10 and 20 kN, respectively, and standard devi- odi ations 2 and 4 kN, respectively. If a, = 1 m and 25ulev na, = 2 m, what is the expected bending moment and biabaete what is the standard deviation of the bending i 1edW moment? b. If X, and X, are normally distributed, what is the probability that the bending moment will exceed 75 kN-m? dmC. Suppose the positions of the two loads are random variables. Denoting them by A, and A,, assume that these variables have means of 1 m and 2 m, respec- с. tively, that each has a standard deviation of 0.1, 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(X, X,) = .5 (so that the two loads are not inde- pendent), what is the variance of the bending %3D moment?
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