Mechanics 1 of materials hibbeler 6th Episode 2 Part 4 pot

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6-190 Draw the shear and moment diagrams for the shaft

if it is subjected to the vertical loadings of the belt, gear, and

flywheel The bearings at A and B exert only vertical reac-

tions on the shaft

300 mm? “(OO mm 300 mmo mam |

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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6-191 Determine the maximum bending stress in the

handle of the cable cutter at section a—a A force of 45 lb

is applied to the handles The cross-sectional area is shown

Omar = = Thi = 8.41 ksi z(0.5)(0.75) Ans

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-1 If the beam is subjected to a shear of V = 15 kN,

determine the web’s shear stress at A and B Indicate the

shear-stress components on a volume element located at

these points Set w = 125 mm Show that the neutral axis is

located at ¥ = 0.1747 m from the bottom and In, =

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-2 If the wide-flange beam is subjected to a shear of V =

30 KN, determine the maximum shear stress in the beam Set

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-3 If the wide-flange beam is subjected to a shear of V =

30 kN, determine the shear force resisted by the web of the

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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*7-4 The beam is fabricated from three steel plates, and

it is subjected to a shear force of V = 150 KN Determine

the shear stress at points A and C where the plates are

joined Show y = 0.080196m from the bottom and

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-5 The beam is fabricated from three steel plates, and

it is subjected to a shear force of V = 150 KN Determine

the shear stress at point B where the plates are joined

Show ¥ = 0.080196m from the bottom and Iy,4 =

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-6, If the T-beam is subjected to a vertical shear of

V = 10 kip, determine the maximum shear stress in the

beam Also, compute the shear-stress jump at the

flange-web junction AB Sketch the variation of the

shear-stress intensity over the entire cross section: Show

that Iy 4 = 532.04 in’

V = 10kip (1.5)(3) (14) + 6(6)(6)

3(14) + 6(6) S003") + 3(14)(3.5169 — 1.5)

(ca)y = VOp _ 104038723) _ 494 psi

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-7, If the T-beam is subjected to a vertical shear of

V = 10 kip, determine the vertical shear force resisted by

the flange Show that Iy4 = 532.04 in’

Q = (3.5769 — y)(14)( ae) = 7(3,5769" — y*) 3.57

ts 10(7)(3.5769? — y*) (532.04)(14) = 0.009398(3.5769? ~ yˆ @.36 ~y)

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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*7-8 Determine the maximum shear stress in the strut if it

is subjected to a shear force of V = 15 kN Show that In, ~

Tmax = Bmax, _ 15(10°)(0.1090544)(10 ) ~2.44 MPa It 6.6911(107°)0.1)

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-9 Determine the maximum shear force V that the strut

can support if the allowable shear stress for the material is

Tallow = 50 MPa Show that Iv, = 6.691(1075) m*

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-10 Determine the intensity of the shear stress distributed

aver the cross section of the strut if it is subjected to a shear

force of V = 12 kN Show that Iw, = 6.691(10” 5) m,

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

© 2005 R C Hibbeler Published by Pearson Prentice Hall,

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7-11 Sketch the intensity of the shear-stress distribution

acting over the beam’s cross-sectional area, and determine

the resultant shear force acting on the segment AB The

shear acting at the section is V = 35 kip Show that

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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“7-12 The strut is subjected to a vertical shear of V =

130 KN Plot the intensity of the shear-stress distribution act-

ing over the cross-sectional area, and compute the resultant

shear force developed in the vertical segment AB

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-13 The steel rod has a radius of 1.25 in If it is subjected

toa shear of V = 5kip, determine the maximum shear stress

Tt 0.610351 (a) (2.50) Spsi = 1.36ksi_ Ảng

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

© 2005 R C Hibbeler Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ All rights reserved

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7-14 Determine the largest shear force V that the mem-

ber can sustain if the allowable shear stress is Tajow = 8 Ksi

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

© 2005 R C Hibbeler Published by Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle River, NJ All rights reserved

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7-15 If the applied shear force V = 18 kip, determine

the maximum shear stress in the member

(0.5)(1) 5) + 21Q(D2) _ 1 1667 in,

1(5) + 2(1)2) l= 009 + 5(1.1667~0.5)

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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*7-16 The beam has a square cross section and is made of

wood having an allowable shear stress of tanow = 1.4 ksi If

it is subjected to a shear of V = 1.5 kip, determine the smail-

est dimension a of its sides

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-17 The wood beam has an allowable shear stress of

Tallow = 7 MPa Determine the maximum shear force V that

can be applied to the cross section

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-18 The beam is made from a polymer and is subjected to

a shear of V = 7 kip Determine the maximum shear stress

in the beam and pilot the shear-stress distribution over the

crass section Report the values of the shear stress every

0.5 in of beam depth

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

© 2005 R C Hibbeler Published by Pearson Prentice Hall,

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7-19 Plot the shear-stress distribution over the cross

section of a rod that has a radius c By what factor is the g

maximum shear stress greater than the average shear

stress acting over the cross section?

Tavg 3

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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*7-20 Develop an expression for the average vertical com-

ponent of shear stress acting on the horizontal plane through

the shaft, located a distance y from the neutral axis

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-21 A member has a cross section in the form of an equi-

lateral triangle If it is subjected to a shear force V, deter-

mine the maximum average shear stress in the member Can

the shear formula be used to predict this value? Explain

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

© 2005 R C Hibbeler Published by Pearson Prentice Hall,

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7-22 The beam is subjected to a uniform load w Determine ¬ *

the placement a of the supports so that the shear stress in J J J J | IRRNNI | ty _

the beam is as small as possible What is this stress? _ B Ta

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

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7-23 The timber beam is to be notched at its ends as shown

If it is to support the loading shown, determine the smallest

depth d of the beam at the notch if the allowable shear stress

iS Tatow = 450 psi The beam has a width of 8 in

From Mechanics of Materials, Sixth Edition by R C Hibbeler, ISBN 0-13-191345-X

© 2005 R C Hibbeler Published by Pearson Prentice Hall, 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