Problem 5-3

Draw the free-body diagram of the beam supported at A by a fixed support and at B by a roller.Explain the significance of each force on the diagram.

Given:

w 40lbft

=

a 3 ft=

b 4 ft=

θ 30 deg=

Solution:

Ax, Ay, MA effect of wall on beam.

NB force of roller on beam.

wa2

resultant force of distributed load on beam.

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.

Problem 5-2

Draw the free-body diagram of the hand punch, which is pinned at A and bears down on thesmooth surface at B.

Given:

F 8 lb=

a 1.5 ft=

b 0.2 ft=

c 2 ft=

Solution:

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.

Problem 5-26

Determine the reactions at the roller A and pin B.

Given:

M 800 lb ft= c 3 ft=

F 390 lb= d 5=

a 8 ft= e 12=

b 4 ft= θ 30 deg=

Solution:

Guesses RA 1 lb= Bx 1 lb= By 1 lb=

Given

RA sin θ( ) Bx+d

e2 d2+

⎛⎜⎝

⎞⎟⎠F− 0=

RA cos θ( ) By+e

e2 d2+

⎛⎜⎝

⎞⎟⎠F− 0=

M RA cos θ( ) a b+( )− Bx c+ 0=

RA

Bx

By

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

Find RA Bx, By,( )= RA 105.1 lb=Bx

By

⎛⎜⎝

⎞⎟⎠

97.4

269⎛⎜⎝

⎞⎟⎠

lb=

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.

Problem 5-8

Draw the free-body diagram of the automobile, which is being towed at constant velocity up theincline using the cable at C.The automobile has a mass M and center of mass at G. The tires arefree to roll. Explain the significance of each force on the diagram.

Units Used:

Mg 103 kg=

Given:

M 5 Mg= d 1.50 m=

a 0.3 m= e 0.6 m=

b 0.75 m= θ1 20 deg=

c 1 m= θ2 30 deg=

g 9.81m

s2=

Solution:

NA, NB force of road on car.F force of cable on car.Mg force of gravity on car.

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.

Problem 5-20

Determine the reactions at the supports.

Given:

w 250lbft

=

a 6 ft=

b 6 ft=

c 6 ft=

Solution:

Guesses

Ax 1 lb= Ay 1 lb= By 1 lb=

Given

Ax 0= Ay By+ w a b+( )−12

wc− 0=

waa2⎛⎜⎝⎞⎟⎠

wbb2⎛⎜⎝⎞⎟⎠

−12

wc bc3

+⎛⎜⎝

⎞⎟⎠

− By b+ 0=

Ax

Ay

By

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

Find Ax Ay, By,( )=

Ax

Ay

By

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

0

2750

1000

⎛⎜⎜⎝

⎞⎟⎟⎠

lb=

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.

Problem 5-27

The platform assembly has weight W1 and center of gravity at G1. If it is intended to support amaximum load W2 placed at point G2,,determine the smallest counterweight W that should beplaced at B in order to prevent the platform from tipping over.

Given:

W1 250 lb=

W2 400 lb=

a 1 ft=

b 6 ft=

c 1 ft=

d 8 ft=

e 6 ft=

f 2 ft=

Solution:

When tipping occurs, Rc = 0

ΣMD = 0; W2− f W1 c+ WB b c+( )+ 0=

WBW2 f W1 c−

b c+=

WB 78.6 lb=

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.

Problem 5-28

The articulated crane boom has a weight W and mass center at G. If it supports a load L ,determine the force acting at the pin A and the compression in the hydraulic cylinder BC whenthe boom is in the position shown.

Units Used:

kip 103 lb=

Given:

W 125 lb=

L 600 lb=

a 4 ft=

b 1 ft=

c 1 ft=

d 8 ft=

θ 40 deg=

Solution:

Guesses Ax 1 lb= Ay 1 lb= FB 1 lb=

Given Ax− FB cos θ( )+ 0= Ay− FB sin θ( )+ W− L− 0=

FB cos θ( )b FB sin θ( )c+ W a− L d c+( )− 0=

Ax

Ay

FB

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

Find Ax Ay, FB,( )= FB 4.19 kip=Ax

Ay

⎛⎜⎝

⎞⎟⎠

3.208

1.967⎛⎜⎝

⎞⎟⎠

kip=

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.

Problem 5-40

Soil pressure acting on the concrete retaining wall is represented as a loading w per foot lengthof wall. If concrete has a specific weight γ per foot length, determine the magnitudes of the soildistribution, w1 and w2, and the frictional force F for equilibrium.

Units Used:

kip 103 lb=

Given:

γ 150lb

ft2=

w 200lbft

=

a 2 ft=

b 12 ft=

c 6 ft=

Solution:

Initial Guesses:

w1 1lbft

= w2 1lbft

= F 1 lb=

Given

γ− a bc a−

2b+⎛⎜

⎝⎞⎟⎠

w1 c+w2 w1−

2⎛⎜⎝

⎞⎟⎠c+ 0=

γ a ba2

⎛⎜⎝

⎞⎟⎠

12

γ c a−( ) b ac a−

3+⎛⎜

⎝⎞⎟⎠

+ w1 cc2

⎛⎜⎝

⎞⎟⎠

−12

w2 w1−( ) cc3

⎛⎜⎝

⎞⎟⎠

−12

w bb3

⎛⎜⎝

⎞⎟⎠

+ 0=

F12

w b− 0=

w1

w2

F

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

Find w1 w2, F,( )=w1

w2

⎛⎜⎝

⎞⎟⎠

1

1.4⎛⎜⎝

⎞⎟⎠

kipft

= F 1.2 kip=

© 2007 R. C. Hibbeler. Published by Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may

be reproduced, in any form or by any means, without permission in writing from the publisher.

For the exclusive use of adopters of the Hibbeler series of books.