Probability Statistics Random Processes Solution Manual Chapter 10 - Complete Solved Problems

CHAPTER10
j

, PROBLEMj10.1

Determinej thej verticalj forcej Pj thatj mustj bej appliedj atj Cj toj maint
ainjthejequilibriumjofjthejlinkage.




SOLUTION




Assumej jyA

jyCj =j2jyA

jyDj =jjyA
1j 1j
jyjEj =j jyj jD=j jy A
2 2
1j
jyjGj =jjyj jE=j jy A
2
jyA
Also j =j aj=j0.3jm
a
VirtualjWork:jWejapplyjbothjPjandjMjtojmemberjABC.
Uj =j80jyAj −jPjyCj −jMj +j60jyDj +j20jyEj −j40jyGj =j0
jjy  j1j j j1j j
80jy A −jP(2 jyjA)j−jM  A  +j60 jyjAj +j20 j jy Aj− j40 j jy Aj=j0
 a  2  2 
Mj
80j−j2Pj−j +j60j+j10j−j20j=j0
a
Mj
2Pj+j =j130jN (1)
a
NowjfromjEq.j(1)jforj Mj =j0 2Pj=j130jN Pj=j65.0jNj j ◀



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, PROBLEMj10.2

DeterminejthejhorizontaljforcejPjwhichjmustjbejappliedjatjAjsojtha
tjthejlinkagejisjinjequilibriumjforjthejpositionjshown.




SOLUTION

Assumej 
jxAj =j10j in.
j yCj =j 4j in.
j yDj =j j yCj =j 4j in.
jyDj 2j
j =j =j 
6 3
j2j j
jxjGj =j15j =j15 j j = j10j in.
3 

VirtualjWork: AssumejthatjforcejPjisjappliedjatjA.
Uj =j 0: Uj =j −jPjxAj +j 30j yCj +j 60j yDj +j 240j +j 80jxGj =j 0

j2j 
−jPj(10jjin.)j+j(30jlb)(4j in.)j+j(60jlb)(4jj)j+j(240jlbin.) 
j3j 
 

+(80jlb)(10jjin.)j=j0

−10Pj +j120j +j 240j +j160j +j800j =j 0

10Pj =j1320 Pj =j132.0j lb




Copyrightj©jMcGraw-HilljEducation.jPermissionjrequiredjforjreproductionjorjdisplay.

, PROBLEMj10.3

DeterminejthejcouplejMjthatjmustjbejappliedjtojmemberjABCjtojmaint
ainjthejequilibriumjofjthejlinkage.




SOLUTION




Assumej jyA

jyDj =jjyA
1j 1j
jyjEj =j jyj jD=j jy A
2 2
1j
jyjGj =jjyj jE=j jy A
2
jyA
Also j =j
0.3
VirtualjWork:jWejapplyjbothjPjandjMjtojmemberjABC.
Uj =j80jyAj −jPjyCj −jMj +j60jyDj +j20jyEj −j40jyGj =j0
j jy A  j1j j j1j j
80jy A −jP(2 jyjA)j−jM j  +j60 jyjAj +j20 j jy Aj− j40 j jy Aj=j0
 0.3jmj  2  2 
M
80j−j2Pj− +j60j+j10j−j20j=j0
0.3jm
M
2Pj+ =j130jN (1)
0.3jm
M
NowjfromjEq.j(1)jforj Pj=j0 =j130jN Mj=j39.0jNjjm ◀
0.3jm




Copyrightj©jMcGraw-HilljEducation.jPermissionjrequiredjforjreproductionjorjdisplay.