b -Strength of Materials - Sp - Solution

��E�G�� F �A�E��A�� B�E��

5. �� 6 ��. ��

1. A ��

�� 0.2% �� . E �� = 10

�� 5000 ��. F��

9 � 10 ��.

�� 5 ��

��

2

�� 64,000 ��/�� .

�. 5060 �

�.

�.

0.75 ��

�. 6050 �

��

�.

0.84 ��

��:

�. 0.79 ��

δ =

��: σ �

=

�

4�

5

��

0.002� =

2

π �

64,000

4(5000)

=

2

 π  2 10  (0.006) (9 ×10 )  4 

6. A �� 2.50 � �� 0.012%

2. �� 42,000

��

��

��

��

��/��2, �� 0.75

D�� .

�� 0.625 �� ?

�. 0.1 ��

�. 63,000 ��

��

�. 68,080 ��

�.

��

�. 0.2 ��

��

��:

ε =

� = σ �π �� = (42 ,000 )(π )(0.75 )(0.625) = 61,850 �� (�)

3. ��

δ

� , 100 −4

=

δ 2.5

� = 0.3 �� (�) 3

7. D�� , � � (�� ) ��

0.00105 �/� ��

� �� 10 �� 150 ��. ��

�� 44,000 ��?

�� 3 �� . ��

6

�. 42.300 � 10 ��

�� 6,000 ��.

6

�. 41.202 � 10 ��

�. 5.8

6

43.101 � 10 ��

�. 6.4

�

��

�.

��:

7.0

��

��

=

44,000 0.00105

= 41.9048 ×10

6

��:

�� (�)

� � =

�� AE 1010 ��,

π �

16

,

� � =

π (3) 16

= 5.3 ��

3

8. F��

7/16 �� 55 ��. ��

�� D = 6 �� D = 3 ��.

�� 50 �� 2

�. 28.97 ��

�� .

��

�. 5.8

�.

�. 3.7 ��

3

3

4. �� 5/6 ��

45.45 ��

�. 51.98 ��

�

��:

�. 6.2

 � �4 − � � 4    � � =  �  16  �  π

��: �� . � π ��

50 ,000 =

0.4 ��

0.012

δ = 3×10

��

�.

��.

��:

�. 66,800 ��

τ � =

��

� = 5089 .4 � (�)

π �

�� (�) � = 0.7052

� =

9050 �

 (6)4 − (3) 4  3 � � =   = 39.76 �� 16  6  π

55(2000)

 5  7   �  16  16 

π 

9. A �� 16 �� 500 �� . ��

� = 5.12 �� 5 �� (�)

�� 2 � 4 �� 100 ��/��. F�� . 1

��:

��

�. 10,233.2 �� .

θ =

15,677.2 ��

�. 15,388.1 ��

θ =

��:

��

=

32�� 4

π � �

(

6

32 3 ×10 4

)(1400) = 0.0035205 ��

π (110) (83,000)

 180 ��   = 0.2017 �� (�)  

θ = (0.0035205 �� )  π �� 

12. D�� 1 �� 1.5 �� . �� . �. 2.25 �� . 1.5 �� .

2.0 ��

��

��: τ =

16�

=

3

π �

4

16��

(

4

4

π � � − � �

4

)

3

� � − � � = � � � 4

4

�1 = �2 =

100(16) + 500 = 1050 �� 2

� � = 1.588 ��

�� 1.75 �� (�)

�� = � � =

�=

1

�� ,

�� 3 12

� � =

13. A �� 60��

(800)(8) + (250)(8) = 5200 �� − �� = 62,400 �� − ��

2

�

�=

=

2

4 2

�� 60�� . �� 60,000 ��

= 2 ��

�� . ��

3

=

2( 4 )

= 10.67 ��

12

3

� � − (1) = � � (1.5)

1/32��

4

��

(62,400)(2) 10.67

,696.34 �� = 11

�� . ��

2

�� (�)

��, �� 3000 ��

10. ��

�� 6 �� ?

�� 10 ��

�. 4.7 ��

�� 100 ��/��

��

�� 1200 ��.

�.

�. 15,000

�. 9.5 ��

6.7 ��

�. 1800

��:

�.

�� :

1500

�� τ =

��:

 10  − �� (�)  + (1200)(10 ) = 17,000 ��  2 

� = (10)(100)

3

π �

3000 =

11. C��

16(60,000) 3

π �

� = 4.67 ��

� 110 �� , 1.4 ��

��

6

�� 3 � 10 ��.

δ = � θ

�� 83,000

1

2

�/�� .

32

�. 0.27

 60  θ  2 

=

θ = 0.00104 ��

�. 0.31 ��

16�

θ =

��

�. 0.24 2

��

60,000(60)

0.00104 =

π 32

4

(

� 6 ×10

6

��

�.

)

�. 5,000 ��

� = 8.75 ��

��:

��, �� 8.8 ��.

2

� � = � + �

14. C�� /�� , ��

2

�� 80 �� C.

��

��

8,000 �� 12,000 ��

�. 181,445 ��

�� :

�.

162,256 ��

��

�. 112,187 ��

�. 62,237 �� .

��: σ = α � ∆� , α = 6.6 ×10

−6

��:

6

2

� � = � + �

 9 �   = 144 �  5 �  

∆� = 80 � 

(

)

(

σ = 6.6 ×10

−6

2

)(30×10 )(144) = 28,512 ��

τ =

6

 101.325 ��   = 196,529 �� (�)  14.7 ��   

16� �

π �

16(14,422.2 )

3

π (1.5)

= 21,763 ��

(�)

6000 �� 1 � �� 60,000 �� . C�� .

�6

�� ? � �� = 11.7 � 10 �/��C.

��

�. 421 ��

�. 6810 ��

�. 303 ��

�.

��

�. 5550 ��

��

5162 ��

��:

�. 503 �� :

τ �� =

δ = α �∆� , δ = (11.7 ×10 )(400)[(40) − (− 30)] −6

δ = 0.3276 �� = 327.6 �� (�)

τ �� =

16. A 5.1 �� 677.9 ��

τ � =

�� 339 ��. ��

16� ��

=

3

π �

16� �� 3

π �

=

16(6000 ) 3

π (1.5)

16(2000)

τ �� + τ �� 2

3

π (1.5) =

= 9054 ��

= 3018 ��

9054 + 3018

2

= 6036 ��

(�)

20. A �� 1000 �� 6 ��

�� ? �. 35.14

�� 2000 �� (�� ) ��. ��

��

�� ?

�.

45.45

��

�. 65.48

�. 100 �� .

��:

σ =

2

19. �� 2000 ��

�� 30 C �� 40 C �� . ��

2

=

3

15. A �� 400 �� , ��

1

2

� � = 8000 + 12000 = 14,422.2 �� − ��

σ = 28,512 �� 

�� =

27,220 ��

�. 14,422 ��

� ��

� = 30 ×10 ��

2

2

18. �� 1.5 ��

�� 800 ��

1

2

� � = 5000 + 8000 = 9434 �� − �� (�)

��, �� 50 ��

�� =

8,000 ��

(�

+

(

2

� + �

677.9 +

32�� 3

π �

=

2

6 ��

�. 2 ��

)

��:

2

339 + 677.9

2

)

� (� + δ ) =

= 717.918 � − �

32(717 ,919 � − �� )

1 2

1000(6 + δ ) =

3

π (51 �� )

2

� δ 1 2

(2000)δ 2

(δ − 3)(δ + 2 ) = 0

σ = 55.127 �� (�)

δ = 3 �� (�)

17. �� 2��

�

�� 5000 �� 8000 �� : �. 13,000 �� 3

E�D �

b -Strength of Materials - Sp - Solution

Recommend Documents