Assignment 11 - Homework 11 from Mechanics of Materials 7th Edition PDF

Preview

Summary

Homework 11 from Mechanics of Materials 7th Edition...

Description

PROBLEM 4.100

y b 3 in.

6 kips

A short wooden post supports a 6-kip axial load as shown. Determine the stress at point A when (a) b 0, (b) b 1.5 in., (c) b 3 in.

C

A

z

x

SOLUTION A I S P

(a )

(b)

b

0

V



b

V

(c)

M P A



6 28.27

P M  A S

b

3 in.

V



S (3)2

S

S

r4

28.27 in2

(3) 4 63.62 in 4 4 4 I 63.62 21.206 in3 c 3 M Pb 6 kips

0

1.5 in. M



S r2

M

P M  A S

0.212 ksi

(6)(1.5)





212 psi W

V

637 psi W

9 kip  in.

6 9  28.27 21.206

(6)(3)

V

0.637 ksi

18 kip  in.

6 18  28.27 21.206

1.061 ksi

V

1061 psi W

PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 550

PROBLEM 4.102

y

30 mm

60 mm

A short 120 × 180-mm column supports the three axial loads shown. Knowing that section ABD is sufficiently far from the loads to remain plane, determine the stress at (a) corner A, (b) corner B.

30 kN 20 kN 100 kN C z

x

A

D 90 mm 90 mm

B

120 mm

SOLUTION

M

(0.120 m)(0.180 m) 21.6 u 10 3 m2 1 (0.120 m)(0.180 m)2 6.48 u 104 m 2 6 (30 kN)(0.03 m)  (100 kN)(0.06 m)  5.10 kN  m

VA



A

S

(a)

P



A

M S

150 u 10 3 N 5.10 u 10 3 N  m  2 3 21.6 u 10 m 6.48 u 104 m3

VA (b)

VB



P A



M S

3

0.926 MPa W

3

150 u 10 N 5.10 u 10 N  m  2 3 21.6 u 10 m 6.48 u 104 m3

VB

14.81 MPa W

PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 552

PROBLEM 4.107

P'

a d a

P

A milling operation was used to remove a portion of a solid bar of square cross section. Knowing that a 30 mm, d 20 mm, and V all 60 MPa, determine the magnitude P of the largest forces that can be safely applied at the centers of the ends of the bar.

SOLUTION A e

V V Data:

ad ,

I

1 3 ad , 12

c

a d  2 2 P Mc P 6 Ped   A I ad ad 3 P 3 P ( a  d) KP  ad ad 2

K

20 mm

0.020 m

30 mm

K

1 (3)(0.010)  (0.030)(0.020) (0.030)(0.020)2

P

V K

60 u 106 4.1667 u 103

1 3( a  d)  ad ad 2

where

a

0.030 m

d

1 d 2

14.40 u 103 N

4.1667 u 103 m 2

P

14.40 kN W

PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 557

y R " 125 mm C

P " 4 kN

PROBLEM 4.149

E !

In Prob. 4.148, determine (a) the value of θ for which the stress at D reaches it largest value, (b) the corresponding values of the stress at A, B, C, and D.

x

z

A

D

PROBLEM 4.148 A rigid circular plate of 125-mm radius is attached to a solid 150 u 200-mm rectangular post, with the center of the plate directly above the center of the post. If a 4-kN force P is applied at E with T 30q, determine (a) the stress at point A, (b) the stress at point B, (c) the point where the neutral axis intersects line ABD.

B 200 mm 150 mm

SOLUTION 4 u 103 N

PR

Mx

 PR sinT

500sin T

Iz xD A 

dV D dT

(b)

VA



30 u 103 mm2

(200)(150)

dV dT

with z

0

Rz cosT Rx sinT ½  P ® 0  D  D ¾ Ix IZ ¯ ¿

sin T cosT

I zz D I xx D

tan T



sin T

0.8,

P M x z A M z xA   A Ix Iz



zD , x

30 u 10 3 m2

xD

0



(100 u 106 )(75 u 103 ) (56.25 u10 6)(100 u10 3)

cosT

4 u 10 3 3

30 u 10



6

56.25 u 10

VD

( 0.13333  0.53333  0.300) u 106 Pa



100 u 10 6

6

0.100 u 10 Pa

VA

700 kPa W

VB

100 kPa W

VC

6

 0.967 u 106 Pa

53.1q W

(500)(0.6)(100 u 10 3 )

0.700 u 106 Pa

( 0.13333  0.53333  0.300) u 10 Pa ( 0.13333  0  0) u 10 Pa

T

(500)(0.8)(75 u 10 3)

6

VC

4 3

0.6

( 0.13333  0.53333  0.300) u 106 Pa

VB

500 cos T

Rx cosT ½  1 Rz sin T P ®   ¾ A I Iz ¿ ¯ x

P Mxz M zx   A Ix Iz

For V to be a maximum,

500 N  m

 PR cos T

Mx

1 3 6 4 6 4 (200)(150) 56.25 u 10 mm 56.25 u 10 m 2 1 3 6 4 6 4 (150)(200) 100 u 10 mm 100 u 10 m 2 zD  75 mm 100 mm

Ix

V

(4 u 10 3)(125 u 10 3)

P

(a)

VD

133.3 kPa W 967 kPa W

PROPRIETARY MATERIAL. Copyright © 2015 McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 607...