Probability, Statistics & Random Processes Chapter 7 Solution Manual – 2025 Parameter Estimation & Statistical Inference Solutions

CHAPTER7
g

, PROBLEMg7.1

Determinegtheginternalgforcesg(axialgforce,gshearinggforce,g
andgbendinggmoment)gatgPointgJgofgthegstructuregindicated
.

FramegandgloadinggofgProblemg6.76.



SOLUTION

FromgProblemg6.76:
Cgxg =g720gl
b

Cyg =g140glb




Fxg =g0: Fg −g720glbg=g0

Fg =g+720gl Fg=g720glb ◀
b
Fyg =g0
: V −140 lb = 0
Vg =g140glb Vg=g140.0glbg
◀
Mg −g(140glb)(8gin.)g=g0

Mg =g+1120glbggin Mg=g1120glbggin.g g
. ◀




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, PROBLEMg7.2

Determinegtheginternalgforcesg(axialgforce,gshearinggforce,gandgbendin
ggmoment)gatgPointgJgofgthegstructuregindicated.

FramegandgloadinggofgProblemg6.78.




SOLUTION

FromgProblemg6.78:
Cg=g30gl
b




Fxg =g0:g g −gFg +g120glbg=g0

Fg =g+120gl Fg=g120.0glb ◀
b

Fyg =g0:g g −gVg +g30glbg=g0
Vg=g30.0glbg
V = 30 lb ◀
M J g =g0:g g Mg +g(30glb)(4gin.)g−g(120glb)(2gin.)g=
g0


Mg=g120.0glbggin.g g
◀




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, PROBLEMg7.3

DeterminegtheginternalgforcesgatgPointgJgwheng=g90°.




SOLUTION

Reactionsg(g=g90)
MAg =g0:g g Bgyg =
0
g13g

Ag=g845g Ag=g845g
N N
5g
Fxg =g0:g g (845gN)g +gB
x
=
13
Bxg =g −325g Bgxg =g325g
FBDgBJ: N N

Fg =g0: 125gNg−gFg =g Fg=g125.0g 67.4°◀
0 N
Fg =g0: 22.6°g◀
V − 300 N = V = 300
Mg =g0: (325gN)(0.480gm)g−gMg =g0

Mg =g+156gNm
M = 156.0 Nm




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