0132183137_ism.06 solutions
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Transcript of 0132183137_ism.06 solutions
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364
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
61. Determine the area and the centroid of the area.(x, y) y
1 m
1 m
y2 x3
x
-
365
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
62. Determine the area and the centroid of the area.(x, y) y
x
3 ft
3 ft y x3
19
-
366
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
63. Locate the centroid of the area.x y
x
2 ft
x1/2 2x5/3y
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367
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*64. Locate the centroid of the area.y y
x
2 ft
x1/2 2x5/3y
-
368
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
65. Determine the area and the centroid of the area.(x, y) y
x
a
b
xy c2
-
369
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
66. Determine the area and the centroid of the area.(x, y) y
x
a
h y x2 ha2
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370
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
67. Locate the centroid ( , ) of the area.yx y
x2 m
1 m
y 1 x214
-
371
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 in.
2 in.
y 1
0.5 in.
0.5 in.
x
*68. Locate the centroid of the area.x
69. Locate the centroid of the area.y y
x
2 in.
2 in.
y 1
0.5 in.
0.5 in.
x
-
372
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
9 ft
3 ft
y 9 x2
610. Locate the centroid ( , ) of the area.yx
-
373
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
611. Determine the area and the centroid of thearea.
(x, y) y
x
y
y x
3 ft
3 ft
x39
-
374
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*612. Locate the centroid of the area.x y
x1 m
y x2
1 m
y2 x
613. Locate the centroid of the area.y y
x1 m
y x2
1 m
y2 x
-
375
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
614. Locate the center of mass of the circular coneformed by revolving the shaded area about the y axis. Thedensity at any point in the cone is defined by ,where is a constant.r0
r = (r0 >h)y
y
y
x
z
h
a
z y aah
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376
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
615. Locate the centroid of the homogeneous solidformed by revolving the shaded area about the y axis.
y
y
x
z
y2 (z a)2 a2
a
-
377
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*616. Locate the centroid of the solid.z
y
z
x
a
z a1
a a y( )2
-
378
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
617. Locate the centroid of the homogeneous solidformed by revolving the shaded area about the y axis.
y z
y
x
z2 y3116
2 m
4 m
-
379
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
618. Locate the centroid of the homogeneous solidfrustum of the paraboloid formed by revolving the shadedarea about the z axis.
z
a
z (a2 y2)ha2
h2
h2
z
x
y
-
380
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
619. Locate the centroid of the cross-sectional area ofthe concrete beam.
y
x
y
3 in.
6 in.
3 in.
27 in.
3 in.
12 in. 12 in.
-
381
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*620. Locate the centroid of the cross-sectional area ofthe built-up beam.
y y
x
6 in.1 in.
1 in.
1 in.1 in.
3 in.3 in.
6 in.
-
382
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
622. Locate the distance to the centroid of themembers cross-sectional area.
y
x
y
0.5 in.
6 in.
0.5 in.
1.5 in.
1 in.
3 in. 3 in.
621. Locate the centroid of the channels cross-sectional area.
y
2 in.
4 in.
2 in.12 in.
2 in.
C
y
-
383
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
623. Locate the centroid of the cross-sectional area ofthe built-up beam.
y y
x
1.5 in.
1.5 in.
11.5 in.
1.5 in.
3.5 in.
4in. 1.5 in.4 in.
-
384
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*624. The gravity wall is made of concrete. Determine thelocation ( , ) of the center of mass G for the wall.yx
y
1.2 m
x
_x
_y
0.6 m 0.6 m2.4 m
3 mG
0.4 m
-
385
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
625. Locate the centroid of the cross-sectional area ofthe built-up beam.
y y
x
450 mm
150 mm150 mm
200 mm
20 mm
20 mm
-
386
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
626. Locate the centroid of the cross-sectional area ofthe built-up beam.
y
200 mm
20 mm50 mm
150 mm
y
x
200 mm
300 mm
10 mm
20 mm 20 mm
10 mm
-
387
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
627. Locate the center of mass for the compressorassembly.The locations of the centers of mass of the variouscomponents and their masses are indicated and tabulated inthe figure.What are the vertical reactions at blocks A and Bneeded to support the platform?
x
y
1
2
34
Instrument panel
Filter system
Piping assembly
Liquid storage
Structural framework
230 kg
183 kg
120 kg
85 kg
468 kg
1
2
34
5
5
2.30 m1.80 m
3.15 m
4.83 m
3.26 m
A B
2.42 m 2.87 m1.64 m1.19m
1.20 m
3.68 m
-
388
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*628. Major floor loadings in a shop are caused by theweights of the objects shown. Each force acts through itsrespective center of gravity G. Locate the center of gravity( , ) of all these components.yx
z
y
G2
G4G3
G1
x
600 lb9 ft
7 ft
12 ft
6 ft
8 ft4 ft 3 ft
5 ft
1500 lb
450 lb
280 lb
-
389
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
629. Locate the center of mass of thehomogeneous block assembly.
(x, y, z)
y
z
x 150 mm
250 mm
200 mm
150 mm150 mm100 mm
-
390
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
630. Locate the center of mass of the assembly. Thehemisphere and the cone are made from materials havingdensities of and , respectively.4 Mg>m38 Mg>m3
z
y
z
x
100 mm 300 mm
-
391
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
631. Replace the distributed loading with an equivalentresultant force, and specify its location on the beammeasured from point A.
A
B
3 m 3 m
15 kN/m
10 kN/m
3 m
-
392
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*632. Replace the distributed loading with an equivalentresultant force, and specify its location on the beammeasured from point A.
B
A
8 kN/m
4 kN/m
3 m 3 m
-
393
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
633. Replace the distributed loading by an equivalentresultant force and specify its location, measured frompoint A.
3 m2 m
A B
800 N/m
200 N/m
634. Replace the distributed loading with an equivalentresultant force, and specify its location on the beammeasured from point A.
A B
L2
L2
w0 w0
-
394
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
635. The distribution of soil loading on the bottom ofa building slab is shown. Replace this loading by anequivalent resultant force and specify its location,measured from point O.
12 ft 9 ft
100 lb/ft50 lb/ft
300 lb/ft
O
*636. Determine the intensities and of thedistributed loading acting on the bottom of the slab so thatthis loading has an equivalent resultant force that is equalbut opposite to the resultant of the distributed loadingacting on the top of the plate.
w2w1
300 lb/ft
A B
3 ft 6 ft1.5 ft
w2
w1
-
395
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
637. Wind has blown sand over a platform such that theintensity of the load can be approximated by the function
Simplify this distributed loading to anequivalent resultant force and specify its magnitude andlocation measured from A.
w = 10.5x32 N>m.
x
w
A
10 m
500 N/m
w (0.5x3) N/m
638. Wet concrete exerts a pressure distribution alongthe wall of the form. Determine the resultant force of thisdistribution and specify the height h where the bracing strutshould be placed so that it lies through the line of action ofthe resultant force. The wall has a width of 5 m.
4 m
h
(4 ) kPap1/2z
8 kPa
z
p
-
396
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
639. Replace the distributed loading with an equivalentresultant force, and specify its location on the beammeasured from point A.
w
xA
B
4 m
8 kN/mw (4 x)212
-
397
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*640. Replace the loading by an equivalent resultantforce and couple moment at point A.
60
6 ft
50 lb/ft50 lb/ft
100 lb/ft
4 ft
A
B
-
398
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
641. Replace the loading by an equivalent resultantforce and couple moment acting at point B.
60
6 ft
50 lb/ft50 lb/ft
100 lb/ft
4 ft
A
B
-
399
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
642. Determine the moment of inertia of the area aboutthe axis.x
y
x
2 m
2 m
y 0.25 x3
-
400
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
643. Determine the moment of inertia of the area aboutthe axis.y
y
x
2 m
2 m
y 0.25 x3
-
401
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*644. Determine the moment of inertia of the area aboutthe axis.x
y
x
y2 x3 1 m
1 m
-
402
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
645. Determine the moment of inertia of the area aboutthe axis.y
y
x
y2 x3 1 m
1 m
-
403
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
646. Determine the moment of inertia of the area aboutthe axis.x
y
x
y2 2x
2 m
2 m
-
404
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
647. Determine the moment of inertia of the area aboutthe axis.y
y
x
y2 2x
2 m
2 m
-
405
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*648. Determine the moment of inertia of the area aboutthe axis.x
y
xO
y 2x4 2 m
1 m
-
406
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
649. Determine the moment of inertia of the area aboutthe axis.y
y
xO
y 2x4 2 m
1 m
-
407
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
650. Determine the polar moment of inertia of the areaabout the axis passing through point .Oz
y
xO
y 2x4 2 m
1 m
-
408
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
651. Determine the moment of inertia of the area aboutthe x axis.
y
x
2 in.
8 in.
y x3
*652. Determine the moment of inertia of the area aboutthe y axis.
y
x
2 in.
8 in.
y x3
-
409
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
654. Determine the moment of inertia of the area aboutthe y axis.
x
y
1 in.
2 in.
y 2 2 x 3
653. Determine the moment of inertia of the area aboutthe x axis.
x
y
1 in.
2 in.
y 2 2 x 3
-
410
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
655. Determine the moment of inertia of the area aboutthe x axis. Solve the problem in two ways, using rectangulardifferential elements: (a) having a thickness of dx, and (b) having a thickness of dy.
1 in. 1 in.
4 in.
y 4 4x2
x
y
-
411
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*656. Determine the moment of inertia of the area aboutthe y axis. Solve the problem in two ways, using rectangulardifferential elements: (a) having a thickness of dx, and (b) having a thickness of dy.
1 in. 1 in.
4 in.
y 4 4x2
x
y
-
412
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
657. Determine the moment of inertia of the triangulararea about the x axis.
y (b x)hb
y
x
b
h
658. Determine the moment of inertia of the triangulararea about the y axis.
y (b x)hb
y
x
b
h
-
413
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
659. Determine the distance to the centroid of thebeams cross-sectional area; then find the moment of inertiaabout the axis.x
y
2 in.
4 in.
1 in.1 in.
Cx
x
y
y
6 in.
-
414
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
414
*660. Determine the moment of inertia of the beamscross-sectional area about the x axis.
2 in.
4 in.
1 in.1 in.
Cx
x
y
y
6 in.
661. Determine the moment of inertia of the beamscross-sectional area about the y axis.
2 in.
4 in.
1 in.1 in.
Cx
x
y
y
6 in.
-
2 in.
4 in.
1 in.1 in.
Cx
x
y
y
6 in.
2 in.
4 in.
1 in.1 in.
Cx
x
y
y
6 in.
415
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
662. Determine the moment of inertia of the beamscross-sectional area about the axis.x
y
x
15 mm15 mm60 mm60 mm
100 mm
100 mm
50 mm
50 mm
15 mm
15 mm
-
416
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
663. Determine the moment of inertia of the beamscross-sectional area about the axis.y
y
x
15 mm15 mm60 mm60 mm
100 mm
100 mm
50 mm
50 mm
15 mm
15 mm
-
417
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
150 mm
300 mm
150 mm
100 mm
100 mm
75 mm
*664. Determine the moment of inertia of the compositearea about the axis.x
-
418
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
665. Determine the moment of inertia of the compositearea about the axis.y
y
x
150 mm
300 mm
150 mm
100 mm
100 mm
75 mm
-
419
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
666. Determine the distance to the centroid of thebeams cross-sectional area; then determine the moment ofinertia about the axis.x
y
x
xC
y
50 mm 50 mm75 mm
25 mm
25 mm
75 mm
100 mm
_y
25 mm
25 mm
100 mm
-
420
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
667. Determine the moment of inertia of the beamscross-sectional area about the y axis.
x
xC
y
50 mm 50 mm75 mm
25 mm
25 mm
75 mm
100 mm
_y
25 mm
25 mm
100 mm
*668. Locate the centroid of the composite area, thendetermine the moment of inertia of this area about thecentroidal axis.x
y y
1 in.1 in.
2 in.
3 in.
5 in.x
xy
3 in.
C
-
421
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
669. Determine the moment of inertia of the compositearea about the centroidal axis.y
y
1 in.1 in.
2 in.
3 in.
5 in.x
xy
3 in.
C
670. Determine the distance to the centroid of thebeams cross-sectional area; then find the moment of inertiaabout the axis.x
y
300 mm
100 mm
200 mm
50 mm 50 mm
y
C
x
y
x
-
422
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
671. Determine the moment of inertia of the beamscross-sectional area about the x axis.
300 mm
100 mm
200 mm
50 mm 50 mm
y
C
x
y
x
-
423
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*672. Determine the moment of inertia of the beamscross-sectional area about the y axis.
300 mm
100 mm
200 mm
50 mm 50 mm
y
C
x
y
x
-
424
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
673. Determine the moment of inertia of the beamscross-sectional area about the axis.x
y
50 mm 50 mm
15 mm115 mm
115 mm
7.5 mmx
15 mm
-
425
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
674. Determine the moment of inertia of the beamscross-sectional area about the axis.y
y
50 mm 50 mm
15 mm115 mm
115 mm
7.5 mmx
15 mm
-
426
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
675. Locate the centroid of the cross-sectional area forthe angle. Then find the moment of inertia about the centroidal axis.
xIxy
6 in.2 in.
6 in.
x 2 in.
C x
yy
x
y
*676. Locate the centroid of the cross-sectional areafor the angle. Then find the moment of inertia about the
centroidal axis.yIy
x
6 in.2 in.
6 in.
x 2 in.
C x
yy
x
y
-
427
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
677. Locate the centroid ( , ) of the area.yx y
x
3 in.1 in.
3 in.6 in.
678. Locate the centroid of the shaded area.y
x
y
a2
a2
a
aa
-
428
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*680. Determine the moment of inertia of the area aboutthe x axis.
y
4y 4 x2
1 ft
x2 ft
679. Determine the moment of inertia of the area aboutthe y axis.
y
4y 4 x2
1 ft
x2 ft
-
429
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
681. If the distribution of the ground reaction on thepipe per foot of length can be approximated as shown,determine the magnitude of the resultant force due to thisloading.
2.5 ft
50 lb/ft
25 lb/ft
w 25 (1 cos u) lb/ft
u
-
430
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
682. Determine the moment of inertia of the beamscross-sectional area about the x axis which passes throughthe centroid C.
Cx
y
d2
d2
d2
d2 60
60
683. Determine the moment of inertia of the beamscross-sectional area about the y axis which passes throughthe centroid C.
Cx
y
d2
d2
d2
d2 60
60
-
431
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*684. Determine the moment of inertia of the area aboutthe x axis. Then, using the parallel-axis theorem, find themoment of inertia about the axis that passes through thecentroid C of the area. .y = 120 mm
x
1200
200 mm
200 mm
y
x
xy
Cy x2
-
432
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
685. Determine the moment of inertia of the beamscross-sectional area with respect to the axis passingthrough the centroid C.
x
0.5 in.
0.5 in.
4 in.
2.5 in.C x
0.5 in.
_y
686. The distributed load acts on the beam as shown.Determine the magnitude of the equivalent resultant forceand specify where it acts, measured from point A. w (2x2 4x 16) lb/ft
xB
A
w
4 ft
-
433
2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
687. The distributed load acts on the beam as shown.Determine the maximum intensity . What is themagnitude of the equivalent resultant force? Specify whereit acts, measured from point B.
wmaxw (2x2 4x 16) lb/ft
xB
A
w
4 ft
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