2=29: The block is deformed into the position shown by the dashed

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© 2008 by 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.

2=29: The block is deformed into the position shown by

the dashed lines. Determine the shear strain at corners C and£».

15 mmL_ r

-—1--

110 mm

85 mm

100 mm

100 mm

Gtomttiy :

8 = 90"+Jin"' ( ^\ 97.84° « 1.70759 rad

0=jr-1.70759" 1.43401 rid

Shtar Strain :

X It it It

</£,)„ = J - J - J - l <

D

HO(I>">

tQO mm

*&~4. f\n icsi was pcnurnrcu on a sieei speiauicil ~~~ ~ having an original diameter of 0.503 in. and gauge length of Load (Kip)

2.00 in. The data is listed in the table. Plot the stress-strain diagram and determine approximately the modulus of ®^ elasticity, the yield stress, the ultimate stress, and the rupture _j ^ stress. Use a scale of 1 in. = 20 ksi and 1 in. — 0.05 in./in. 8.00

Redraw the elastic region, using the same stress scale but a 11.00

strain scale of I in. = 0.001 in./in. 11.80

11.80

12.00

16.60

&(**<•') 20.00

21.50

19.50

tU>-

Elongation (in.)

0

0.0005

0.0015

0.0025

0.0035

0.0050

0.0080

0.0200

0.0400

0.1000

0.2800

0.4000

0.4600

f __^

y^-- — o^ -

J

2i^L£2t

Bf

L = 2.00 in.

to-

40-

zo-

O

/ o(ksi) e(in./in.)

1 jj « 0 0

a^ 7.55 0.00025

f*V*()*rfrtt - fS fis't 23.15 0.00075

7 40^6 0.00125

/ 4j 55.36 0.0017S

/ £> w

><» - — — = 32.0(l(r)lui Am 5938 00025

/ ' 5938 0.0040

/ 60.39 0.010

/ 83J4 0.020

/ 100.65 0.050

/ ^ /-- . 108.20 0.140

1 f~ "*"! Ttr _,-. ^

tS

J

«13

93W

820

O

° ao o-eou O'Oot. O-0*3 0-00^ 0-fOS

76

Ji-23. The beam is supported by a pin at C and an A-36

steel guy wire AB. If the wire has a diameter of 0.2 in., determine how much it stretches when a distributed load of

w = 100 Ib/ft acts on the pipe. The material remains elastic.

+ZMc = ft F

M

sn30f(lO) - 0.1<10)(5) m O.

F a

= 1.0 kip

a * Ee; 31.83 « 29(10

3

)£«;

0.0010981 in./in.

120

0.0010981<-^-—) = 0.152 in.

oos 30°

84

© 2008 by 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.

•$-39. The rigid pipe is supported by a pin at C and an

A-36 guy wire AB, If the wire has a diameter of 0.2 in., determine the load P if the end B is displaced 0.10 in. to the right. E st

= 29(10

3

) ksi.

Gtemetry :

:

2ll dm 0.05968°

96

a = 90° + 0.05968" = 90.05968°

AC = 96 lan 30" =55.4256 in

96

AB-.

cos 30°

: 110.8513 in

AB' = /962 + S5.4256

2

-2(96)(55.4256)cos 90.05968°

= 110.9012 in.

Normal Stress and Strain :

AB'-AB

AB

110.9012-110.8513

' 110.8513

= 0.4510(10'') in./in.

Applying Hooke's law

, = 29.0( 10

3

) 0.4510( 10'

5

) = 13.08 ksi

Thus.

041 =

= 410.85 Ib

Equation of Equilibrium :

410.85sin30

e

(8)-/'(8)=0

P*=205lb AIM

&H

r

44. The A-36 steel column is used to support the symmetric loads from the two floors of a building. Determine the vertical displacement of its top, A, if PI = 40 kip,

P

2

= 62 kip, and the column has a cross-sectional area of

23.4 in

2

.

12ft

12ft

Internal Forets : As shown on FBD (a) and (b)

Displacement .-

c _ y ^ _ -80.0(121(12) (-204)(I2)(12)

'

=

^ AE ~ 23.4(2<>.OHIO>) 23.4(29.0)(10')

= - 0.0603 in. Ans

Negative sign indicates thai end A moves toward end C.

4o nip +O kip

I cfc;

95

© 2008 by 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.

4"3S. The column is constructed from high-strength con-

crete and four A-36 steel reinforcing rods. If it is subjected to an axial force of 800 kN, determine the required diameter of each rod so that one-fourth of the load is carried by the steel and three-fourths by the concrete. E st

= 200 GPa,

E c

= 25 GPa.

Equilibrium : Require P

a

= -(800) = 200 kN and

4

/>„„

= ^

4

Compatibility :

S

con =

S n

(0..3

2

-/l tt

)(25.0)(IO») A

M

(200)(10»)

0.09P

SI

0.09( 200)

8(600)+ 200

d- 0.03385m = 33.9mm Ans

The assembly has the diameters and material make-up indicated. If it fits securely between its fixed supports when the temperature is TI = 70°F, determine the average normal stress in each material when the temperature reaches TI = 110°F.

2014-T6 Aluminum 304 Stainless

- C 86100 Bronze steel

J_

D

IF. =0;

= 277.69 kip a,, « - '— = 2.46 ksi Ana

377 fiQ

0

M

= - — as 22.1 ksi AIM

137

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