Subido por Edwin Conde

# Chapter 7

Anuncio
```7 Solutions 44918
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•7–1. Determine the internal normal force and shear
force, and the bending moment in the beam at points C and
D. Assume the support at B is a roller. Point C is located just
to the right of the 8-kip load.
8 kip
40 kip ⭈ ft
A
C
8 ft
545
D
8 ft
B
8 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–2. Determine the shear force and moment at points C
and D.
500 lb
300 lb
200 lb
B
A
C
6 ft
546
4 ft
E
D
4 ft
6 ft
2 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–3. Determine the internal normal force, shear force, and
moment at point C in the simply supported beam. Point C is
located just to the right of the 1500-lb – ft couple moment.
500 lb/ft
B
A
C
6 ft
547
1500 lb ft
6 ft
30
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–4. Determine the internal normal force, shear force,
and moment at points E and F in the beam.
C
A
E
D
45
F
B
300 N/m
1.5 m
548
1.5 m
1.5 m
1.5 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–5. Determine the internal normal force, shear force,
and moment at point C.
0.2 m
400 N
1m
A
B
C
1.5 m
3m
549
2m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–6. Determine the internal normal force, shear force, and
moment at point C in the simply supported beam.
4 kN/m
A
B
C
3m
550
3m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–7. Determine the internal normal force, shear force, and
moment at point C in the cantilever beam.
w0
A
L
––
2
551
B
C
L
––
2
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*7–8. Determine the internal normal force, shear force,
and moment at points C and D in the simply supported
beam. Point D is located just to the left of the 5-kN force.
5 kN
3 kN/m
A
B
C
1.5 m
552
1.5 m
D
3m
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•7–9. The bolt shank is subjected to a tension of 80 lb.
Determine the internal normal force, shear force, and
moment at point C.
C
90
A
553
6 in.
B
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–10. Determine the internal normal force, shear force,
and moment at point C in the double-overhang beam.
3 kN/m
A
1.5 m
554
B
C
1.5 m
1.5 m
1.5 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–11. Determine the internal normal force, shear force,
and moment at points C and D in the simply supported
beam. Point D is located just to the left of the 10-kN
10 kN
6 kN/m
A
B
D
C
1.5 m
555
1.5 m
1.5 m
1.5 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–12. Determine the internal normal force, shear force,
and moment in the beam at points C and D. Point D is just
to the right of the 5-kip load.
5 kip
0.5 kip/ft
A
6 ft
556
B
D
C
6 ft
6 ft
6 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–13. Determine the internal normal force, shear force,
and moment at point D of the two-member frame.
250 N/m
B
A
D
2m
1.5 m
C
E
4m
557
300 N/m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–14. Determine the internal normal force, shear force,
and moment at point E of the two-member frame.
250 N/m
B
A
D
2m
1.5 m
C
E
4m
558
300 N/m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–15. Determine the internal normal force, shear force,
and moment acting at point C and at point D, which is
located just to the right of the roller support at B.
300 lb/ft
200 lb/ft
200 lb/ft
D
F
E
A
4 ft
4 ft
C
B
4 ft
*7–16. Determine the internal normal force, shear force,
and moment in the cantilever beam at point B.
6 kip/ft
B
A
3 ft
559
12 ft
4 ft
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•7–17. Determine the ratio of a&gt;b for which the shear force
will be zero at the midpoint C of the double-overhang beam.
w0
C
A
a
560
C
b/2
B
B
b/2
a
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–18. Determine the internal normal force, shear force,
and moment at points D and E in the overhang beam. Point
D is located just to the left of the roller support at B, where
the couple moment acts.
2 kN/m
6 kN m
C
A
D
3m
B
E
1.5 m
1.5 m
3
5
4
5 kN
561
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–19. Determine the distance a in terms of the beam’s
length L between the symmetrically placed supports A
and B so that the internal moment at the center of the
beam is zero.
w0
w0
A
B
a
––
2
a
––
2
L
562
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–20. Determine the internal normal force, shear force,
and moment at points D and E in the compound beam.
Point E is located just to the left of the 10-kN concentrated
load. Assume the support at A is fixed and the connection at
B is a pin.
10 kN
2 kN/m
B
C
A
1.5 m
563
D
1.5 m
E
1.5 m
1.5 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–21. Determine the internal normal force, shear force,
and moment at points F and G in the compound beam. Point
F is located just to the right of the 500-lb force, while point G
is located just to the right of the 600-lb force.
500 lb
2 ft
2 ft
600 lb
A
F
B
D
C
1.5 ft
E
G
2 ft
564
2 ft
2 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–22. The stacker crane supports a 1.5-Mg boat with the
center of mass at G. Determine the internal normal force,
shear force, and moment at point D in the girder. The trolley
is free to roll along the girder rail and is located at the
position shown. Only vertical reactions occur at A and B.
2m
1m1m
5m
A
B
C
7.5 m
D
2m
3.5 m
G
565
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–23. Determine the internal normal force, shear force,
and moment at points D and E in the two members.
0.75 m
1m
B
D
60 N
0.75 m
A
60
30
2m
566
E
C
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–24. Determine the internal normal force, shear force,
and moment at points F and E in the frame. The crate
weighs 300 lb.
1.5 ft
1.5 ft
1.5 ft
1.5 ft
0.4 ft
A
4 ft
B
567
F
C
E
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–25. Determine the internal normal force, shear force,
and moment at points D and E of the frame which supports
the 200-lb crate. Neglect the size of the smooth peg at C.
4.5 ft
C
4 ft
E
2 ft
B
1.5 ft
D
1.5 ft
568
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–26. The beam has a weight w per unit length. Determine
the internal normal force, shear force, and moment at point
C due to its weight.
B
L
––
2
L
––
2
C
u
A
569
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–27. Determine the internal normal force, shear force,
and moment acting at point C. The cooling unit has a total
mass of 225 kg with a center of mass at G.
F
D
30
30
E
0.2 m
3m
3m
G
570
B
C
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–28. The jack AB is used to straighten the bent beam
DE using the arrangement shown. If the axial compressive
force in the jack is 5000 lb, determine the internal moment
developed at point C of the top beam. Neglect the weight of
the beams.
2 ft
10 ft
2 ft
10 ft
C
B
A
D
E
571
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–29. Solve Prob. 7–28 assuming that each beam has a
uniform weight of 150 lb&gt;ft.
2 ft
10 ft
2 ft
10 ft
C
B
A
D
E
572
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–30. The jib crane supports a load of 750 lb from the
trolley which rides on the top of the jib. Determine the
internal normal force, shear force, and moment in the jib at
point C when the trolley is at the position shown. The crane
members are pinned together at B, E and F and supported
1 ft
3 ft
5 ft
3 ft
1 ft
1 ft
2 ft
H
B C
G
F
D
E
3 ft
750 lb
A
573
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–31. The jib crane supports a load of 750 lb from the
trolley which rides on the top of the jib. Determine
the internal normal force, shear force, and moment in the
column at point D when the trolley is at the position shown.
The crane members are pinned together at B, E and F and
supported by a short link BH.
1 ft
3 ft
5 ft
3 ft
1 ft
1 ft
2 ft
H
B C
G
F
D
E
3 ft
750 lb
A
574
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–32. Determine the internal normal force, shear force,
and moment acting at points B and C on the curved rod.
C
B
2 ft
45
30
5
3
4
500 lb
575
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–33. Determine the internal normal force, shear force,
and moment at point D which is located just to the right of
the 50-N force.
50 N
50 N
D
50 N
50 N
B
30
A
576
30
30 30
30
600 mm
C
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
at point C in the pipe assembly. Neglect the weight of the
pipe. The load is F1 = 5-24i -10k6 lb, F2 = 5-80i6 lb,
and M = 5 -30k6 lb # ft.
F1
B
M
3 ft
A
C
y
F2
x
1.5 ft
2 ft
z
at a section passing through point C in the pipe assembly.
Neglect the weight of the pipe. Take F1 = 5350j - 400k6 lb
and F2 = 5150i - 300k6 lb.
F2
C
x
1.5 ft
2 ft
y
F1
3 ft
577
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
a section passing through point C in the pipe assembly. Neglect
the weight of the pipe. Take F1 = 5-80i + 200j - 300k6 lb
and F2 = 5250i - 150j - 200k6 lb.
F2
C
x
1.5 ft
2 ft
y
F1
3 ft
578
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
•7–37. The shaft is supported by a thrust bearing at A and
a journal bearing at B. Determine the x, y, z components of
A
750 N
0.2 m
0.5 m
600 N
C
x
1m
900 N
1m
750 N
1m
579
0.2 m
B
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
in the rod at point D. There are journal bearings at A, B,
and C. Take F = 57i - 12j - 5k6 kN.
0.75 m
C
3 kN m
A
F
D
B
E
0.5 m
x
0.2 m
0.2 m 0.6 m
0.5 m
y
580
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
in the rod at point E. Take F = 57i - 12j - 5k6 kN.
0.75 m
C
3 kN m
A
F
D
B
E
0.5 m
x
0.2 m
0.2 m 0.6 m
0.5 m
y
581
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
P
*7–40. Draw the shear and moment diagrams for the
beam (a) in terms of the parameters shown; (b) set
P = 800 lb, a = 5 ft, L = 12 ft.
a
a
L
582
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9 kN
•7–41. Draw the shear and moment diagrams for the
simply supported beam.
A
B
4m
583
2m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
584
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–42. Draw the shear and moment diagrams for the beam
ABCDE. All pulleys have a radius of 1 ft. Neglect the weight
of the beam and pulley arrangement. The load weighs 500 lb.
2 ft
8 ft
2 ft
3 ft
B
C
D
2 ft
A
E
2 ft
3 ft
585
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–43. Draw the shear and moment diagrams for the
cantilever beam.
2 kN/m
A
6 kN m
2m
586
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–44. Draw the shear and moment diagrams for the
beam (a) in terms of the parameters shown; (b) set
M0 = 500 N # m, L = 8 m.
M0
A
B
L/2
587
L/2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–45. If L = 9 m, the beam will fail when the maximum
shear force is Vmax = 5 kN or the maximum bending
moment is Mmax = 22 kN # m. Determine the largest couple
moment M0 the beam will support.
M0
A
B
L/2
588
L/2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–46. Draw the shear and moment diagrams for the
simply supported beam.
w0
A
B
L
––
2
589
L
––
2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
590
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–47. Draw the shear and moment diagrams for the
simply supported beam.
300 N/m
300 N m
A
B
4m
591
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
592
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–48. Draw the shear and moment diagrams for the
overhang beam.
8 kN/m
C
A
B
4m
593
2m
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•7–49.
beam.
Draw the shear and moment diagrams for the
2 kN/m
50 kN m
A
5m
594
C
B
5m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–50.
Draw the shear and moment diagrams for the beam.
250 lb/ft
A
150 lb ft
595
B
20 ft
150 lb ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–51.
Draw the shear and moment diagrams for the beam.
1.5 kN/m
B
A
3m
596
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–52. Draw the shear and moment diagrams for the
simply supported beam.
150 lb/ft
300 lb ft
A
B
12 ft
597
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
598
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–53. Draw the shear and moment diagrams for the beam.
30 lb/ft
180 lb ft
A
B
9 ft
599
C
4.5 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–54. If L = 18 ft, the beam will fail when the maximum
shear force is Vmax = 800 lb, or the maximum moment is
Mmax = 1200 lb # ft. Determine the largest intensity w of
w
A
B
L
600
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–55.
Draw the shear and moment diagrams for the beam.
4 kip/ft
A
12 ft
601
12 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–56. Draw the shear and moment diagrams for the
cantilevered beam.
300 lb
200 lb/ft
A
6 ft
602
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
603
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–57. Draw the shear and moment diagrams for the
overhang beam.
4 kN/m
A
B
3m
604
3m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2w0
7–58. Determine the largest intensity w0 of the distributed
load that the beam can support if the beam can withstand a
maximum shear force of Vmax = 1200 lb and a maximum
bending moment of Mmax = 600 lb # ft.
w0
A
B
6 ft
605
6 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
606
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–59. Determine the largest intensity w0 of the distributed
load that the beam can support if the beam can withstand a
maximum bending moment of Mmax = 20 kN # m and a
maximum shear force of Vmax = 80 kN.
w0
A
C
B
4.5 m
607
1.5 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
608
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–60. Determine the placement a of the roller support B
so that the maximum moment within the span AB is
equivalent to the moment at the support B.
w0
A
B
a
L
609
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1/27/09
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Page 610
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
500 lb/ft
•7–61. The compound beam is fix supported at A, pin
connected at B and supported by a roller at C. Draw the
shear and moment diagrams for the beam.
3 ft
610
C
B
A
6 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 611
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
611
7 Solutions 44918
1/27/09
10:39 AM
Page 612
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–62. The frustum of the cone is cantilevered from point
A. If the cone is made from a material having a specific
weight of g, determine the internal shear force and moment
in the cone as a function of x.
2 r0
A
r0
L
612
x
7 Solutions 44918
1/27/09
10:39 AM
Page 613
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
7–63. Express the internal shear and moment components
acting in the rod as a function of y, where 0 … y … 4 ft.
4 lb/ft
x
y
4 ft
2 ft
y
613
7 Solutions 44918
1/27/09
10:39 AM
Page 614
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–64. Determine the normal force, shear force, and
moment in the curved rod as a function of u.
w
r
u
614
7 Solutions 44918
1/27/09
10:39 AM
Page 615
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–65. The shaft is supported by a smooth thrust bearing
at A and a smooth journal bearing at B. Draw the shear and
moment diagrams for the shaft.
600 lb
400 lb
300 lb
A
B
2 ft
615
2 ft
2 ft
2 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 616
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–66. Draw the shear and moment diagrams for the
double overhang beam.
10 kN
5 kN
5 kN
A
2m
616
B
2m
2m
2m
7 Solutions 44918
1/27/09
10:39 AM
Page 617
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–67. Draw the shear and moment diagrams for the
overhang beam.
18 kN
6 kN
A
B
2m
617
2m
2m
M = 10 kN m
7 Solutions 44918
1/27/09
10:39 AM
Page 618
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–68. Draw the shear and moment diagrams for the
simply supported beam.
4 kN
M 2 kN m
A
B
2m
618
2m
2m
7 Solutions 44918
1/27/09
10:39 AM
Page 619
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–69. Draw the shear and moment diagrams for the
simply supported beam.
10 kN
10 kN
15 kN m
A
B
2m
619
2m
2m
7 Solutions 44918
1/27/09
10:39 AM
Page 620
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–70. Draw the shear and moment diagrams for the beam.
The support at A offers no resistance to vertical load.
P
P
A
B
L
––
3
620
L
––
3
L
––
3
7 Solutions 44918
1/27/09
10:39 AM
Page 621
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–71. Draw the shear and moment diagrams for the lathe
shaft if it is subjected to the loads shown. The bearing at A is
a journal bearing, and B is a thrust bearing.
60 N 80 N 100 N
A
50 mm
621
40 N 50 N
50 N
40 N
50 mm
200 mm
B
50 mm
200 mm
100 mm 50 mm
7 Solutions 44918
1/27/09
10:39 AM
Page 622
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–72. Draw the shear and moment diagrams for the beam.
10 kN
3 kN/m
B
A
6m
•7–73. Draw the shear and moment diagrams for the
shaft. The support at A is a thrust bearing and at B it is a
journal bearing.
4 kN
2 kN/m
A
B
0.8 m
622
0.2 m
7 Solutions 44918
1/27/09
10:39 AM
Page 623
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–74.
Draw the shear and moment diagrams for the beam.
8 kN
8 kN
15 kN/m
20 kN m
A
B
1m
0.75 m
0.25 m
623
C
D
1m
1m
7 Solutions 44918
1/27/09
10:39 AM
Page 624
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–75. The shaft is supported by a smooth thrust bearing at
A and a smooth journal bearing at B. Draw the shear and
moment diagrams for the shaft.
500 N
300 N/m
A
B
1.5 m
624
1.5 m
7 Solutions 44918
1/27/09
10:39 AM
Page 625
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–76. Draw the shear and moment diagrams for the beam.
10 kN
2 kN/m
A
B
5m
•7–77. Draw the shear and moment diagrams for the
shaft. The support at A is a journal bearing and at B it is a
thrust bearing.
3m
100 lb/ft
200 lb
B 300 lb ft
A
1 ft
625
2m
4 ft
1 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 626
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–78. The beam consists of two segments pin connected at
B. Draw the shear and moment diagrams for the beam.
700 lb
150 lb/ft
8 ft
626
C
B
A
4 ft
800 lb ft
6 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 627
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–79. Draw the shear and moment diagrams for the
cantilever beam.
300 lb
200 lb/ft
A
6 ft
627
7 Solutions 44918
1/27/09
10:39 AM
Page 628
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–80. Draw the shear and moment diagrams for the
simply supported beam.
10 kN
10 kN/m
A
B
3m
628
3m
7 Solutions 44918
1/27/09
10:39 AM
Page 629
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–81.
beam.
Draw the shear and moment diagrams for the
2000 lb
500 lb/ ft
A
B
9 ft
7–82.
9 ft
Draw the shear and moment diagrams for the beam.
w0
A
B
L
629
L
7 Solutions 44918
1/27/09
10:39 AM
Page 630
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–83.
Draw the shear and moment diagrams for the beam.
8 kN/m
3m
A
3m
8 kN/m
630
7 Solutions 44918
1/27/09
10:39 AM
Page 631
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–84. Draw the shear and moment diagrams for the beam.
20 kN
40 kN/m
A
B
8m
631
3m
150 kN m
7 Solutions 44918
1/27/09
10:39 AM
Page 632
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–85. The beam will fail when the maximum moment
is Mmax = 30 kip # ft or the maximum shear is Vmax = 8 kip.
Determine the largest intensity w of the distributed load the
beam will support.
w
B
A
6 ft
632
6 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 633
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–86. Draw the shear and moment diagrams for the
compound beam.
5 kN
3 kN/m
A
B
3m
633
D
C
3m
1.5 m
1.5 m
7 Solutions 44918
1/27/09
10:39 AM
Page 634
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–87. Draw the shear and moment diagrams for the shaft.
The supports at A and B are journal bearings.
2 kN/m
B
A
300 mm
634
600 mm
450 mm
7 Solutions 44918
1/27/09
10:39 AM
Page 635
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–88. Draw the shear and moment diagrams for the beam.
5 kip/ft
15 kip ft
15 kip ft
B
A
6 ft
635
10 ft
6 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 636
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–89. Determine the tension in each segment of the
cable and the cable’s total length. Set P = 80 lb.
B
2 ft
A
5 ft
D
C
50 lb
P
3 ft
636
4 ft
3 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 637
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–90. If each cable segment can support a maximum tension
of 75 lb, determine the largest load P that can be applied.
B
2 ft
A
5 ft
D
C
50 lb
P
3 ft
637
4 ft
3 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 638
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Determine the horizontal distance xB from the force at B to
point A. Set P = 40 lb.
xB
A
5 ft
B
P
8 ft
C
2 ft
D
3 ft
638
60 lb
7 Solutions 44918
1/27/09
10:39 AM
Page 639
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Determine the magnitude of the horizontal force P so that
xB = 6 ft.
xB
A
5 ft
B
P
8 ft
C
2 ft
D
3 ft
639
60 lb
7 Solutions 44918
1/27/09
10:39 AM
Page 640
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–93. Determine the force P needed to hold the cable
in the position shown, i.e., so segment BC remains
horizontal. Also, compute the sag yB and the maximum
tension in the cable.
E
A
3m
yB
D
B
C
6 kN
4 kN
4m
640
P
6m
3m
2m
7 Solutions 44918
1/27/09
10:39 AM
Page 641
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–94. Cable ABCD supports the 10-kg lamp E and the
15-kg lamp F. Determine the maximum tension in the cable
and the sag yB of point B.
A
D
yB
2m
C
B
F
E
1m
3m
0.5 m
641
7 Solutions 44918
1/27/09
10:39 AM
Page 642
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–95. The cable supports the three loads shown. Determine
the sags yB and yD of points B and D. Take P1 = 400 lb,
P2 = 250 lb.
4 ft
E
A
yB
yD
14 ft
B
D
C
P2
P2
P1
12 ft
642
20 ft
15 ft
12 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 643
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–96. The cable supports the three loads shown.
Determine the magnitude of P1 if P2 = 300 lb and
yB = 8 ft. Also find the sag yD.
4 ft
E
A
yB
yD
14 ft
B
D
C
P2
P2
P1
12 ft
643
20 ft
15 ft
12 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 644
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
the horizontal distance xB the force at point B acts from A.
Set P = 40 lb.
xB
A
5 ft
B
P
8 ft
C
2 ft
D
5
3
4
30 lb
3 ft
the magnitude of the horizontal force P so that xB = 6 ft.
xB
A
5 ft
B
8 ft
C
2 ft
D
3
5
4
3 ft
644
30 lb
P
7 Solutions 44918
1/27/09
10:39 AM
Page 645
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–99. Determine the maximum uniform distributed
loading w0 N/m that the cable can support if it is capable of
sustaining a maximum tension of 60 kN.
60 m
7m
w0
645
7 Solutions 44918
1/27/09
10:39 AM
Page 646
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–100. The cable supports the uniform distributed load
of w0 = 600 lb&gt;ft. Determine the tension in the cable at
each support A and B.
B
A
15 ft
10 ft
w0
25 ft
646
7 Solutions 44918
1/27/09
10:39 AM
Page 647
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–101. Determine the maximum uniform distributed
load w0 the cable can support if the maximum tension the
cable can sustain is 4000 lb.
B
A
15 ft
10 ft
w0
25 ft
647
7 Solutions 44918
1/27/09
10:39 AM
Page 648
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
the slope of the cable at point O is zero, determine the
equation of the curve y = f1x2 which defines the cable
shape OB, and the maximum tension developed in the cable.
y
A
B
8 ft
O
500 lb/ ft
15 ft
648
x
500 lb/ ft
15 ft
7 Solutions 44918
1/27/09
10:39 AM
Page 649
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–103. If cylinders C and D each weigh 900 lb, determine
the maximum sag h, and the length of the cable between the
smooth pulleys at A and B. The beam has a weight per unit
length of 100 lb&gt;ft.
12 ft
A
B
h
C
649
D
7 Solutions 44918
1/27/09
10:39 AM
Page 650
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
650
7 Solutions 44918
1/27/09
10:39 AM
Page 651
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–104. The bridge deck has a weight per unit length of
80 kN&gt;m. It is supported on each side by a cable. Determine
the tension in each cable at the piers A and B.
A
150 m
651
1000 m
B
75 m
7 Solutions 44918
1/27/09
10:39 AM
Page 652
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
652
7 Solutions 44918
1/27/09
10:39 AM
Page 653
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–105. If each of the two side cables that support the
bridge deck can sustain a maximum tension of 50 MN,
determine the allowable uniform distributed load w0 caused
by the weight of the bridge deck.
A
150 m
653
1000 m
B
75 m
7 Solutions 44918
1/27/09
10:39 AM
Page 654
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
654
7 Solutions 44918
1/27/09
10:39 AM
Page 655
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–106. If the slope of the cable at support A is 10&deg;,
determine the deflection curve y = f(x) of the cable and the
maximum tension developed in the cable.
y
40 ft
B
A
10
10 ft
x
500 lb/ft
655
7 Solutions 44918
1/27/09
10:40 AM
Page 656
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–107. If h = 5 m, determine the maximum tension
developed in the chain and its length. The chain has a mass
per unit length of 8 kg&gt;m.
50 m
A
B
h5m
656
7 Solutions 44918
1/27/09
10:40 AM
Page 657
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
657
7 Solutions 44918
1/27/09
10:40 AM
Page 658
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
150 ft
*7–108. A cable having a weight per unit length of 5 lb&gt;ft
is suspended between supports A and B. Determine the
equation of the catenary curve of the cable and the cable’s
length.
A
658
30
30
B
7 Solutions 44918
1/27/09
10:40 AM
Page 659
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
659
7 Solutions 44918
1/27/09
10:40 AM
Page 660
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–109. If the 45-m-long cable has a mass per unit length
of 5 kg&gt;m, determine the equation of the catenary curve of
the cable and the maximum tension developed in the cable.
40 m
A
660
B
7 Solutions 44918
1/27/09
10:40 AM
Page 661
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
661
7 Solutions 44918
1/27/09
10:40 AM
Page 662
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–110. Show that the deflection curve of the cable discussed
in Example 7–13 reduces to Eq. 4 in Example 7–12 when the
hyperbolic cosine function is expanded in terms of a series
and only the first two terms are retained. (The answer
indicates that the catenary may be replaced by a parabola
in the analysis of problems in which the sag is small. In this
case, the cable weight is assumed to be uniformly distributed
along the horizontal.)
662
7 Solutions 44918
1/27/09
10:40 AM
Page 663
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–111. The cable has a mass per unit length of 10 kg&gt;m.
Determine the shortest total length L of the cable that can
be suspended in equilibrium.
8m
A
663
B
7 Solutions 44918
1/27/09
10:40 AM
Page 664
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
664
7 Solutions 44918
1/27/09
10:40 AM
Page 665
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
665
7 Solutions 44918
1/27/09
10:40 AM
Page 666
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–112. The power transmission cable has a weight per
unit length of 15 lb&gt;ft. If the lowest point of the cable must
be at least 90 ft above the ground, determine the maximum
tension developed in the cable and the cable’s length
between A and B.
A
300 ft
B
180 ft
90 ft
666
120 ft
7 Solutions 44918
1/27/09
10:40 AM
Page 667
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
667
7 Solutions 44918
1/27/09
10:40 AM
Page 668
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
668
7 Solutions 44918
1/27/09
10:40 AM
Page 669
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–113. If the horizontal towing force is T = 20 kN and the
chain has a mass per unit length of 15 kg&gt;m, determine the
maximum sag h. Neglect the buoyancy effect of the water
on the chain. The boats are stationary.
40 m
T
669
h
T
7 Solutions 44918
1/27/09
10:40 AM
Page 670
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–114. A 100-lb cable is attached between two points at a
distance 50 ft apart having equal elevations. If the maximum
tension developed in the cable is 75 lb, determine the length
of the cable and the sag.
670
7 Solutions 44918
1/27/09
10:40 AM
Page 671
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–115. Draw the shear and moment diagrams for beam CD.
3 ft
2 ft
10 kip
A
4 kip &middot; ft
B
D
C
2 ft
671
3 ft
2 ft
7 Solutions 44918
1/27/09
10:40 AM
Page 672
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–116. Determine the internal normal force, shear force,
and moment at points B and C of the beam.
7.5 kN
6 kN
2 kN/m
1 kN/m
C
B
A
5m
40 kN m
5m
3m
1m
672
7 Solutions 44918
1/27/09
10:40 AM
Page 673
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–117. Determine the internal normal force, shear force
and moment at points D and E of the frame.
0.25 m
0.75 m
C
0.75 m
D
1m
E
0.75 m
B
400 N/m
673
60
A
7 Solutions 44918
1/27/09
10:40 AM
Page 674
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–118. Determine the distance a between the supports in
terms of the beam’s length L so that the moment in the
symmetric beam is zero at the beam’s center.
w
a
L
674
7 Solutions 44918
1/27/09
10:40 AM
Page 675
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–119. A chain is suspended between points at the same
elevation and spaced a distance of 60 ft apart. If it has a
weight per unit length of 0.5 lb&gt;ft and the sag is 3 ft,
determine the maximum tension in the chain.
675
7 Solutions 44918
1/27/09
10:40 AM
Page 676
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–120. Draw the shear and moment diagrams for the beam.
2 kN/m
50 kN m
A
C
B
5m
5m
•7–121. Determine the internal shear and moment in
member ABC as a function of x, where the origin for x is at A.
D
A
C
B
1.5 m
3m
1.5 m
1.5 m
6 kN
676
45
7 Solutions 44918
1/27/09
10:40 AM
Page 677
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–122. The traveling crane consists of a 5-m-long beam
having a uniform mass per unit length of 20 kg/m. The chain
hoist and its supported load exert a force of 8 kN on the
beam when x = 2 m. Draw the shear and moment diagrams
for the beam. The guide wheels at the ends A and B exert
only vertical reactions on the beam. Neglect the size of the
trolley at C.
x2m
5m
A
C
B
8 kN
677
7 Solutions 44918
1/27/09
10:40 AM
Page 678
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–123. Determine the internal normal force, shear force,
and the moment as a function of 0&deg; … u … 180&deg; and
0 … y … 2 ft for the member loaded as shown.
1 ft
B
u
C
y
150 lb
2 ft
A
678
200 lb
7 Solutions 44918
1/27/09
10:40 AM
Page 679
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–124. The yacht is anchored with a chain that has a total
length of 40 m and a mass per unit length of 18 kg/m, and the
tension in the chain at A is 7 kN. Determine the length of
chain ld which is lying at the bottom of the sea. What is the
distance d? Assume that buoyancy effects of the water on
the chain are negligible. Hint: Establish the origin of the
coordinate system at B as shown in order to find the chain
length BA.
A
60
d
y
ld
s
B
679
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–125. Determine the internal normal force, shear force,
and moment at points D and E of the frame.
C
D
30
A
E
150 lb
1 ft
F
B
3 ft
8 ft
680
4 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–126. The uniform beam weighs 500 lb and is held in the
horizontal position by means of cable AB, which has a
weight of 5 lb/ft. If the slope of the cable at A is 30&deg;,
determine the length of the cable.
B
30
A
C
15 ft
681
7 Solutions 44918
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10:40 AM
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–127. The balloon is held in place using a 400-ft cord that
weighs 0.8 lb/ft and makes a 60&deg; angle with the horizontal. If
the tension in the cord at point A is 150 lb, determine the
length of the cord, l, that is lying on the ground and the
height h. Hint: Establish the coordinate system at B as
shown.
60
h
y
l
682
A
s
B
x
```