a)Remove the semi-circular void from the composite area.The x-coordinate of the centroid of the composite area is _____ in.b)Remove the semi-circular void from the composite area.The y-coordinate of the centroid of the composite area is _____ in.c)Remove the semi-circular void and the rectangular void from the composite area.The x-coordinate of the centroid of the composite area is _____ in.d)Remove the semi-circular void and the rectangular void from the composite area.The y-coordinate of the centroid of the composite area is _____ in. function of y and z does not affect X.256 Chapter 5 Distributed ForcesSAMPLE PROBLEM 5/6Locate the centroid of the shaded area.12"4"Solution. The composite area is divided into the four elementary shapesshown in the lower figure. The centroid locations of all these shapes may be ob-tained from Table D/3. Note that the areas of the "holes" (parts 3 and 4) aretaken as negative in the following table:4"3"2"Solutiontaken as ay that thThe n35"-ements shA2" 2"yAin 3xAPARTin.2in.in.in.3112072060030planation.1410/34201003-14.1411.273-84.8-184-8124-96-322ТОTALS127.9959650For Partmass is orThe area counterparts to Eqs. 5/7 are now applied and yield3[x-]ΣΑΤATes becoX= 959127.9ΣΑ= 7.50 in.Ans.EAyY =ΣΑ650Y =127.9= 5.08 in.They- aneiant by ithe formAns.SAMPLE PROBLEM 5/7PARTApproximate the x-coordinate of the volume centroid of a body whose lengthis 1 m and whose cross-sectional area varies with x as shown in the figure.6.4Solution. The body is divided into five sections. For each section, the averagearea, volume, and centroid location are determined and entered in the followingtable:1TOTALS0.0.20.41.0Aav0.6x, mVolume V0.8INTERVALmm3Vx0-0.230.2-0.40.60.14.50.900.0600.4-0.65.20.31.040.2700.6-0.85.20.50.8-1.01.040.5204.50.70.900.7280.9ТОТALS0.8104.482.388X =EVIX =4.48Helpful Hint2.388EV= 0.533 m%3DAns.1 Note that the shape of the body as athe borninor2611.A, m218 E

Answered: Image /qna-images/answer/a4a9f0e0-a3a0-478e-b01f-ba058316a604.jpg

SAMPLE PROBLEM 5/6 12" Locate the centroid of the shaded area. 4" Solution. The composite area is divided into the four elementary shapes shown in the lower figure. The centroid locations of all these shapes may be ob- tained from Table D/3. Note that the areas of the "holes" (parts 3 and 4) are taken as negative in the following table: 4" 3" 12" 5" 2" yA in 3 xA PART in.? in. in. in.3 ont 1 120 6. 720 600 100 -18 30 14 10/3 420 -14.14 1.273 -84.8 4 -8 12 4 -96 -32 ТОТTALS 127.9 959 650 The area counterparts to Eqs. 5/7 are now applied and yield 3 EAx X = 959 = 7.50 in. 127.9 X = blov Ans. ΣΑ ΣΑ 650 Y = ΣΑ Y = 127.9 = 5.08 in. Ans. SAMPLE PROBLEM 5/7 Anprovimato the r cOordinate of the volume centroid of a body whogo longth

SAMPLE PROBLEM 5/6 12" Locate the centroid of the shaded area. 4" Solution. The composite area is divided into the four elementary shapes shown in the lower figure. The centroid locations of all these shapes may be ob- tained from Table D/3. Note that the areas of the "holes" (parts 3 and 4) are taken as negative in the following table: 4" 3" 12" 5" 2" yA in 3 xA PART in.? in. in. in.3 ont 1 120 6. 720 600 100 -18 30 14 10/3 420 -14.14 1.273 -84.8 4 -8 12 4 -96 -32 ТОТTALS 127.9 959 650 The area counterparts to Eqs. 5/7 are now applied and yield 3 EAx X = 959 = 7.50 in. 127.9 X = blov Ans. ΣΑ ΣΑ 650 Y = ΣΑ Y = 127.9 = 5.08 in. Ans. SAMPLE PROBLEM 5/7 Anprovimato the r cOordinate of the volume centroid of a body whogo longth

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.43P

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