Mechanics 1 of materials hibbeler 6th Episode 3 Part 4 pot

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12-61 Determine the maximum slope and the maximum

deflection of the beam E/ is constant

Amax = ltacl = EI 2 4 SEI

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

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12-62 The rod is constructed from two shafts for which

the moment of inertia of AB is J and of BC is 2/ Determine

the maximum slope and deflection of the rod due to the

loading The modulus of elasticity is E

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

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12-63 Determine the deflection and slope at C E/ is con-

ge = Mol _ Mol 4MoL Ans

2EI 6EI 3EI

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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*12-64 The shalt supports the pulley at its end C

Determine the deflection at C and the slopes at the bearings

A and B Elis constant

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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12-65 The shaft supports the pulley at its end C Determine

its maximum deflection within region AB ET is constant

The bearings exert only vertical reactions on the shaft

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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12-66 Determine the deflection at C and the slope of the

beam at A, B, and C EJ is constant

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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12-67 The flat spring is made of A-36 steel and has a rec-

tangular cross section as shown Determine the maximum

elastic load P that can be applied What is the deflection at

8 when P reaches its maximum value? Assume that the

spring is fixed supported at A

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

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*12-68 The acrobat has a weight of 150 Ih, and suspends

himself uniformly from the center of the high bar Determine

the maximum bending stress in the pipe (bar) and its maxi-

mum deflection The pipe is made of L2 steel and has an

outer diameter of 1 in and a wall thickness of 0.125 in

3

¬— ` Ans

29(10°)(0.033556)

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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12-69 Determine the siope at C and the deflection at B E7

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

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12-70 The bar is supported by a rolier constraint at 8,

which allows vertical displacement but resists axial load and

moment If the bar is subjected to the loading shown,

determine the slope at A and the deflection at C El is

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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12-71 Determine the maximum deflection of the shaft

ET is constant The bearings exert only vertical reactions

= Pa : Co + 2) + 1gG)) a a 1 Pa a a

= 11Pa°

48E7 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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*12 72 The beam is subjected to the load P as shown

Determine the magnitude of force F that must be applied at

the end of the overhang C so that the deflection at C is zero

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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12-73 Determine the slope at B and deflection at C EJ

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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12-74 The A-36 steel shaft is subjected to the loadings

developed in the belts passing over the two pulleys If the

bearings at A and & exert only vertical reactions on the shaft,

determine the slope at A The shaft has a diameter of

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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12-7§ The A-36 steel shaft is subjected to the loadings

developed in the belts passing over the two pulleys If the

bearings at A and B exert only vertical reactions on the shaft,

determine the deflection at C The shaft has a diameter of

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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*12-76 The 25-mm-diameter A-36 steel shaft is supported

at A and B by bearings If the tension in the belt on the pul-

ley at C is 0.75 kN, determine the largest belt tension 7 on

the pulley at D so that the slope of the shaft at A or B does

not exceed 0.02 rad The bearings exert only vertical reac-

tions on the shaft

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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12-77 The 25-mm-diameter A-36 steel shaft is supported al

A and B by bearings If the tension in the belt on the pul-

ley at C is 0.75 kN, determine the largest belt tension T on

the pulley at D so that the slope of the shaft at A is zero

The bearings exert only vertical reactions on the shaft

oi, nĂ Tana

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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12-78 The beam is subjected to the loading shown

Determine the slope al B and deflection at C E/ is constant

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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12-79 If the bearings at A and B exert only vertical reac-

lions on the ’shaft, determine the slope at A and the maxi-

Amax Itapl ps a 1221 2 a] 288EI

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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*12-80 The two bars are pin connected at D Determine the

stope at A and the deflection at D E/ is constant

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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1281 A beam having a constant £/ is supported as shown

Attached to the beam at A is a pointer, free of load Both

the beam and pointer are originally horizontal when no load

is applied to the beam Determine the distance between the

end of the beam and the pointer after each has been dis-

placed by the loading shown

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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12-82 The two A-36 steel bars have a thickness of 1 in

and a width of 4 in They are designed to act as a spring for

the machine which exerts a force of 4 kip on them at 4 and

B If the supports exert only vertical forces on the bars,

determine the maximum deflection of the bottom bar

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

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12-83 Beams made of fiber-reinforced plastic may one day

replace many of those made of A-36 steel since they are onc-

fourth the weight of steel and are corrosion resistant Using

the table in Appendix B, with cajow = 22 ksi and tajiow = 12 ksi,

select the lightcst-weight steel wide-flange beam that will 5 kip

safely support the S-kip load, then compute its maximum

deflection What would be the maximum deflection of 4 € 2

this beam if it were made of a fiber-reinforced plastic with

Ep = 18(102) ksi and had the same moment of inertia as the

Amax = Ít, [tact = -(—)(10)(—-)(10) = —————— 3 ep! Gt ) EI

For the A-~36 steel 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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*12-84 Determine the slope at C and deflection at B EI

is constant

Support Reactions and Elastic Curve : As shown

Wa,

M/E! Diagram : As shown

A ef 4 Moment-Area Theorems : The slope at support A is zero The ae le

4lwa*$

= “Ee L 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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12-85 The A-36 steel shaft is used to support a rotor that

exerts a uniform load of 5 KN/m within the region CD of

the shaft Determine the slope of the shaft at the bearings

A and B.The bearings exert only vertical reactions on the

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