Chapter 6 Homework Solution Note All Three Cases The Right

PROBLEM 6.118 (Continued)

Member AFB:

0: 0

y

FFABP 

80

33

EE

FP

 

   

 

 

3FP E (3)

0: ( ) (3 ) 0

A

MFaBa  

8

(3)() (3)0

3

E

PEa a



 





380; 5

P

PEE E 

5

P



E



PROBLEM 6.119

Each of the frames shown consists of two L-shaped members connected by two rigid links. For each

frame, determine the reactions at the supports and indicate whether the frame is rigid.

SOLUTION

(a)

Member FBDs:

PROBLEM 6.119 (Continued)

(c)

FBD whole: FBD right:

I II

PROBLEM 6.120

Each of the frames shown consists of two L-shaped members connected by two rigid links. For each

frame, determine the reactions at the supports and indicate whether the frame is rigid.

SOLUTION

Note: In all three cases, the right member has only three forces acting, two of which are parallel. Thus,

the third force, at B, must be parallel to the link forces.

(a)

FBD whole:

PROBLEM 6.120 (Continued)

(c)

FBD whole:

PROBLEM 6.121

Each of the frames shown consists of two L-shaped members connected by two rigid links. For each

frame, determine the reactions at the supports and indicate whether the frame is rigid.

SOLUTION

(a)

Member FBDs:

I II

FBD I:

11

0: 2 0 2 ;

A

MaFaPFP   

0: 0

yy y

FAP P  A

FBD II:

22

0: 0 0

B

MaFF  

PROBLEM 6.121 (Continued)

(c)

Member FBDs:

I II

FBD I:

0: 0

y

FAP 

PA





PROBLEM 6.122

The shear shown is used to cut and trim electronic circuit board

laminates. For the position shown, determine (a) the vertical

component of the force exerted on the shearing blade at D, (b) the

reaction at C.

SOLUTION

We note that BD is a two-force member.

Free body: Member ABC: We have the components:

(400 N)sin 30 200 N

x

P

(400 N) cos 30 346.41 N

y

P

PROBLEM 6.122 (Continued)

(b) Returning to FB diagram of member ABC,

0: ( ) 0

xBDxxx

FFPC  

25

() 65

xBDxx BDx

CF P FP



PROBLEM 6.123

A 100-lb force directed vertically downward is applied to the

toggle vise at C. Knowing that link BD is 6 in. long and that

a = 4 in., determine the horizontal force exerted on block E.

SOLUTION

Free body: Entire Frame

PROBLEM 6.124

A 100-lb force directed vertically downward is applied to the

toggle vise at C. Knowing that link BD is 6 in. long and that

a = 8 in., determine the horizontal force exerted on block E.

SOLUTION

Free body: Entire Frame

PROBLEM 6.125

The control rod CE passes through a

horizontal hole in the body of the toggle

system shown. Knowing that link BD is 250

mm long, determine the force

Q

required to

hold the system in equilibrium when



 20.

SOLUTION

We note that BD is a two-force member.

Free body: Member ABC:

Dimensions in mm

PROBLEM 6.126

Solve Problem 6.125 when (a)



 0,

(b)



 6.

PROBLEM 6.125

The control rod CE passes

through a horizontal hole in the body of the

toggle system shown. Knowing that link BD

is 250 mm long, determine the force

Q

required to hold the system in equilibrium

when



 20.

SOLUTION

We note that BD is a two-force member.

(a)

0:





Free body: Member ABC

Since

35 mm

250 mm, sin ; 8.048

250 mm

BD





0: (100 N)(350 mm) sin (200 mm) 0

CBD

MF



  

PROBLEM 6.126 (Continued)

0: ( sin )198.90 ( cos )20.906 (100 N)348.08 0

CBD BD

MF F



   

[198.90sin 3.232 20.906cos3.232 ] 34808

1084.8 N

BD

F

  



PROBLEM 6.127

The press shown is used to emboss a small seal at E.

Knowing that P  250 N, determine (a) the vertical

component of the force exerted on the seal, (b) the reaction

at A.

SOLUTION

FBD Stamp

D

:

0: cos 20 0, cos 20

yBD BD

FEF EF    

FBD

ABC

:

PROBLEM 6.128

The press shown is used to emboss a small seal at E.

Knowing that the vertical component of the force exerted on

the seal must be 900 N, determine (a) the required vertical

force

P

, (b) the corresponding reaction at A.

SOLUTION

FBD Stamp

D

:

0: 900 N cos 20 0, 957.76 N

yBDBD

FFFC   

(a)

FBD

ABC

:

PROBLEM 6.129

The pin at B is attached to member ABC and can slide freely along the

slot cut in the fixed plate. Neglecting the effect of friction, determine

the couple

M

required to hold the system in equilibrium when

30 .





SOLUTION

Free body: Member ABC:

0: (25 lb)(13.856 in.) (3 in.) 0

C

MB  

115.47 lbB

0: 25 lb 0

yy

FC   

PROBLEM 6.130

The pin at B is attached to member ABC and can slide freely along the

slot cut in the fixed plate. Neglecting the effect of friction, determine

the couple

M

required to hold the system in equilibrium when

60 .





SOLUTION

Free body: Member ABC:

0: (25 lb)(8 in.) (5.196 in.) 0

C

MB  

38.49 lbB

0: 38.49 lb 0

xx

FC  

PROBLEM 6.131

Arm ABC is connected by pins to a collar at B and to crank CD at

C. Neglecting the effect of friction, determine the couple

M

required to hold the system in equilibrium when

0.





SOLUTION

Free body: Member ABC

0: 240 N 0

xx

FC  

240 N

x

C

PROBLEM 6.132

Arm ABC is connected by pins to a collar at B and to crank CD at

C. Neglecting the effect of friction, determine the couple

M

required to hold the system in equilibrium when

90 .





SOLUTION

Free body: Member ABC

0: 0

xx

FC 

0: (160 mm) (240 N)(90 mm) 0

By

MC  