Mechanics 1 of materials hibbeler 6th Episode 2 Part 3 potx

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*6-140 A 100-mm-diameter circular rod is bent into an S$

shape If it is subjected to the applied moments M =

125 N-m at its ends, determine the maximum tensile and

compressive stress developed in the rad

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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6-141 The member has an elliptical cross section If it is

subjected to a nroment of M = SON - m, determine the bend-

ing stress at points A and 8, Is the stress at point A’, which

is located on the member near the wall, the same as that at

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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6-142 The member has an elliptical cross section If the

allowable bending stress iS Osjtow = 125 MPa, determine the

maximum moment M that can be applied to the member

M = 27.9kN-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, Pearson Education, Inc., Upper Saddle River, NJ All rights reserved

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6-143 The bar has 2 thickness of 0.25 in and is made of a

material having an allowable bending stress of canow =

18 ksi Determine the maximum moment M that can be

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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*6-144 The bar has a thickness of 0.5 in and is subjected

to amoment of 60 Ib « ft Determine the maximum bending

stress in the bar

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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6-145 The bar is subjected to a moment of M = 15 N - m

Determine the maximum bending stress in the bar and

sketch, approximately, how the stress varies over the critical

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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6-146 The allowable bending stress for the bar is Cattow =

175 MPa, Determine the maximum moment M that can be

applied to the bar

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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6-147 The bar is subjected to four couple moments If it is

in equilibrium, determine the magnitudes of the largest

moments M and M’ that can be applied without exceeding

an allowabie bending stress of ơanow = 22 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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*6-148 The bar is subjected to four couple moments If

M = 180 1b - ft and M' = 70 1b - ft, determine the maximum

bending stress developed in the bar

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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6-149 Determine the maximum bending stress developed

in the bar if it is subjected to the couples shown The bar

has a thickness of 0.25 in

For the larger section :

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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6-150 Determine the length L of the center portion of the

bar so that the maximum bending stress at A, B, and C is

the same The bar has a thickness of 10 mm

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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6-151 The bar is subjected to a moment of

M = 153N-m Determine the smallest radius r of the

fillets so that an allowable bending stress of

Tallow = 120 MPa is not exceeded

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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*6-152 The bar is subjected to a moment of M=

17.5 N-m If r = 6mm determine the maximum bending

stress in the material

From Fig 6-48,

K = 1.555

Cmax = KE = 1555-00) 7 70.007)(0.04) _) =< ta6MPa Ans

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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6-153 If the radius of each notch on the plate is r = 0.5 in

determine the largest moment that can be applied The

allowable bending stress for the material is Osnow = 18 ksi

M = 180288 ib-in = 15.0 kip-ft Ans

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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6-154 The symmetric notched plate is subjected to bend-

ing If the radius of each notch is r = 0.5 in and the applied

moment is M = 10 kip ft, determine the maximum bend-

ing stress in the plate

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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@155 The simply supported notched bar is subjected to two

forces P Determine the largest magnitude of P that can be

applied without causing the material to yield The material

is A-36 steel Each notch has a radius of r = 0.125 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

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"6-156 The simply supported notched bar is subjected to

the two loads’ each having a magnitude of P= 100 tb

Determine the maximum bending stress developed in the

bar, and sketch the bending-stress distribution acting over

the cross section at the center of the bar Each natch has a

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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6-157 A bar having a width of 3 in and height of 2 in is

made of an elastic plastic materiai for which oy = 36 ksi

Determine the moment applied about the horizontal axis

that will cause half the bar to yield

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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6-158 Determine the plastic section modulus and the shape

factor for the wide-flange beam

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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6-159 The beam is made of an elastic plastic material for

which oy = 250 MPa Determine the residual stress in the

beam at its top and bottom after the plastic moment M, is

applied and then released

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

*6§-160 Determine the shape factor for the cross section

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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6-161 The H-beam is made of an elastic-plastic material

for which ay = 250 MPa Determine the residual stress

in the top and bottom of the beam after the plastic

moment M, is applied and then released

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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6-162 The rod has a circular cross section If it is made of

an elastic plastic material, determine the shape factor and

the plastic section modulus Z

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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6-163 The rod has a circular cross section If it is mace or

an elastic plastic material, determine the maximum elastic

moment and plastic moment that can be applied to the cross

section, Take r = 3 in., oy = 36 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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*6-164 The T-beam is made of an elastic-plastic material

Determine the maximum elastic moment and the plastic

moment that can be applied to the cross section o, = 36

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