66. If two loads are applied to a cantilever beam as shown inX 1sthe accompanying drawing, the bending moment at 0 dueto the loads is a,X, + a,X2.olgniz s no 2oloirav loX loro X, vanoinsivsb bincombarcbusfrom thea. Suppose that X, and X, are independent rv's withmeans 10 and 20 kN, respectively, and standard devi-odi ations 2 and 4 kN, respectively. If a, = 1 m and25ulev na, = 2 m, what is the expected bending moment andbiabaete what is the standard deviation of the bendingi 1edW moment?b. If X, and X, are normally distributed, what is theprobability that the bending moment will exceed75 kN-m?dmC. Suppose the positions of the two loads are randomvariables. Denoting them by A, and A,, assume thatthese variables have means of 1 m and 2 m, respec-с.tively, that each has a standard deviation of 0.1, andthat 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 ofthe bending moment?e. If the situation is as described in part (a) except thatCorr(X, X,) = .5 (so that the two loads are not inde-pendent), what is the variance of the bending%3Dmoment?

Given information: Given that the random variables X1 and X2 are independent random variables with…

Answered: If two loads are applied to a…

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.

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.CT: Test

Problem 11CT: aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _

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Question

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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