Chap 5 (Beams and Cables)

p


6

|


 

Ô
Ô Forces in Beams and ables



|ector Mechanics for Engineers: Ôtatics p 



 
                 
    
             !
 "  # #    


   $     %   &
% 

  %   &
'

     %  

7- 2

|ector Mechanics for Engineers: Ôtatics   -   
 
(
) * 
  +
   
   

  * 
   ( 


,     

 - 
 
   (

  
À
   -#
  .

 #  #   *( 


,   
 ,  -    
(


    

 )   /  

  #
 
# 
   
 
     
,  
  


  /  +     (

  
  #  
 
 



   

7- 3

|ector Mechanics for Engineers: Ôtatics     

- 
 

(/÷    0    
    - 
  0, 

   00 / ÷  - 
÷   0 /    
     

  - 
  0, 

 /   
  

0 / /  ÷ - " 
 /  
  00 
(/  (  

 
 7- 4

|ector Mechanics for Engineers: Ôtatics Ô   1213) - %
 
   
  
   - %
÷

   
  
0, 
 /  
( 
    0 
 


'
 

  ·   ÷

 ·   


- %

'
  /  
0, 

 
  
     0  
 

 


7- 5

|ector Mechanics for Engineers: Ôtatics Ô   1213) - %
 
   
   % 
   /) 
Õ 4)  $44



ë 


$5 

Õ4

Õ 544 a

Œ Õ 4 )  $44 3
544 3
Œ Õ 4 r

Õ 4)

Œ

Õ ë44



r Õ 4

7- 6

|ector Mechanics for Engineers: Ôtatics Ô   %  /) î Õ 4)  $44 3

ë 
 Œ $  Õ 4

 Œ Õ ë44 3

 $44 3  
 Œ $  Õ 4  îr
 r Õ 4 r Õ 4)

 Œ Õ 44 3



 Õ 4 )

% ÷  /) ÷ Õ 4)

r 6  Õ 4

r Õ 4

r Õ 4 )

 r  ÷r Õ 4

÷r Õ 4

Œ Õ 4 )

 ÷Œ
 Œ
ë44 3 Õ 4 ÷ Œ Õ 544 3

# r Õ 4 )

 r
 r Õ 4

r Õ 4 7- 7

|ector Mechanics for Engineers: Ôtatics Ô   - %
÷

  
   
0, 
/  
 % /÷)  Õ 4)  544 3  
 Õ 4 r

 Õ ë4 a å 

Õ 4)

 544 a  $6 Õ 4

Õ  $$ a

Œ Õ 4 )  |
544 a  $6 Õ 4

| Õ 76 3

7- 8

|ector Mechanics for Engineers: Ôtatics Ô   - %

'
  / 


0, 


  
  % /) 6 Õ 4)

44 a   r

Õ 4)

Œ

Õ 4)


 Õ4

 44 a  | Õ 4

 Õ 544 a å  Õ4

| Õ 44 a

7- 9

|ector Mechanics for Engineers: Ôtatics |     Ô  -  /

   
 


    
,  
  
  
 -    8

 

    À
À 
   
 
 -   À  
(/


) * 
         
     *  


/ 
 
 

 


      


7- 10

|ector Mechanics for Engineers: Ôtatics |     Ô 

-    

  
(  (
 


 - ! 
 
  
 


  , , 
 9 ( 1
( #
 





 

 7- 11

|ector Mechanics for Engineers: Ôtatics Ô       - & 

   
    
 
     8

 

  

    - '
  
 
 


 (   / - %
 
  (/    ÷   
 # 
,  
  /  
    (  - 0  
 # 
  |  |

7- 12

|ector Mechanics for Engineers: Ôtatics Ô      

-  
       
      

 - '
  
 



 - %
 
   ÷# | Õ
   Õ
r  - %
 
    # | Õ     Õ
  r  -    8

  

   #    


(    
 
,       7- 13

|ector Mechanics for Engineers: Ôtatics Ô  ! 1213) -  9 
   /#  
 
 
 

' (
     
    
     

( 

-  0, 

 / 


 /  

   
     
 
 -  
 


7- 14

|ector Mechanics for Engineers: Ôtatics Ô  ! 1213) -  9 
   /# 
  
 
  -  0, 

 /  
 



  
     
 
  Œ Õ 4 )  4 93  | Õ 4 | Õ 4 93  Õ 4)

4 9a 4 


 Õ 4

 Õ 4

  # | Õ  4 
| Õ ë 93 |$ Õ ë 93

  Õ  4


 Õ 4 93 å   $ Õ
5 93 å 

| Õ $ 93

  Õ
5 93 å 

|ë Õ $ 93

 ë Õ 4 93 å  7- 15

|ector Mechanics for Engineers: Ôtatics Ô  ! -  
 
 3


   

,  
(  

       
,      

7- 16

|ector Mechanics for Engineers: Ôtatics Ô  " 1213) -  9 
  /#  
 
 
÷  - '
 0, 

 /   
 
 
 
(
 


÷##  ' (
     
    
 ÷ 

  $4 . +
   , 
 #÷
# 
$44      
 

-  
 


7- 17

|ector Mechanics for Engineers: Ôtatics Ô  " 1213) -  9 
   /# 
  
 
÷  ÷ Õ 4) î Œ      $54  ë    $44     Õ 4  Œ Õ ë  î Õ 4)

$54  ë 


$44  4    ÷    Õ 4 ÷ Õ  

r Õ 4 )

r Õ 4

- 3
)$44   
     $44  ë44 /  
 7- 18

|ector Mechanics for Engineers: Ôtatics Ô  " -

, 
0, 

 /  
 
 
 
(
  
÷##  "
)  Œ Õ 4 )   $4 r  | Õ 4 | Õ   $4 r  Õ 4 )



  r  $4 r  r
 Õ 4

 Õ  r  4 r 


) Œ Õ 4 )

  $54  | Õ 4 | Õ  

 Õ 4)

  r
$54r  ë
 Õ 4

 Õ 554
 r   å   7- 19

|ector Mechanics for Engineers: Ôtatics Ô  " -

, 
0, 

 / 


 
 
 
(
  
÷# #  
) Œ Õ 4 )

  $54  $44  | Õ 4 | Õ  ë 

 Õ 4)   r
$54r  ë  ë44
$44r  5
 Õ 4

 Õ #ë54  ë r   å  

7- 20

|ector Mechanics for Engineers: Ôtatics Ô  " -  
 
 "
) | Õ   $4 r  Õ  r  4 r 


) | Õ    Õ 554
 r   å  


) | Õ  ë   Õ #ë54  ë r   å  

7- 21

|ector Mechanics for Engineers: Ôtatics   
 #Ô #     - !
 
(      ) |  |
|  Dr Õ 4 | | Õ D Õ  r  r  4 r r

|   | Õ   D r Õ      , r

- !
 
(      
)




   |r
r

r Õ4 

  Õ  |   r Õ | Õ  r r 4 r r 4



r

     Õ  | r Õ      , r 7- 22

|ector Mechanics for Engineers: Ôtatics   
 #Ô #     - ! 
 
 
#

 ÷ Õ  Õ

 

-  ,# r

|  | ÷ Õ   D r Õ  Dr 4

| Õ | ÷  Dr Õ

D

   Dr Õ D  r    

- 
,# r

   ÷ Õ | r 4 r

D

   Õ  D  r  r Õ  r  r    4    +



D Õ 5



 Õ Õ 
 4  |   r  7- 23

|ector Mechanics for Engineers: Ôtatics Ô  $ 1213) -  9 
   /#
   
 
 
 - 
(  

    
  
#     | r Õ D Õ 4 



' (
     / 
   
      ( 

- &
    
(   #


 , 
      - 
(  

    
   r Õ | Õ 

 
#   

(     
 
  0 
     ,
(  
 - &
      , 
 
(   #
  
         7- 24

|ector Mechanics for Engineers: Ôtatics Ô  $ 1213) -  9 
   /# 
  
 
 
 ÷ Õ 4) $
 49 ë
 9 $
 9 5
Õ 4

 Õ ë9  Œ Õ4 ) ÷ Œ  49  9
ë9  9 Õ 4 ÷ Œ Õ 59

- 
(  

    
 
# | r Õ  D Õ 4    

 - &
    
(   #
   , 
      7- 25

|ector Mechanics for Engineers: Ôtatics Ô  $ - 
(  

    
   r Õ | Õ 

 
#   

(     
 
  0 
   
  ,
(  
     ÷ Õ
45

  Õ
459 å 


     Õ ë

  Õ
79 å 


     Õ $4   Õ $59 å 
    Õ
$5  Õ 4

- &
      , 
 
(   #
  
        

7- 26

|ector Mechanics for Engineers: Ôtatics p % p  

- %       

  
       #
 

    #  
 (  #( 
( #
 -    #

) *  

,
     ,  ,
    # * (
      # *     + ## 

     

# * 
   
(  

,

   

 
(  - & 

     ## ,
 
 
÷
 

 
 7- 27

|ector Mechanics for Engineers: Ôtatics p % p  

- % 
   /     
÷   
9 ( /
( 
   
0
  
 -  9 (   , , 
 0
 0   
 

 
 
 
  - "
 0
  
    0 
    ÷ 

 


 
  
   9 (  
  0
     Õ 4 - 

   #   Õ 4    Œ  r Õ 4#

Œ Õ 4 r #  Œ

-
r Õ
 M Õ ÷r Õ 

7- 28

|ector Mechanics for Engineers: Ôtatics p %     

-      

  ) *         , * 
   
  
  


, - % /
   +
    (


, 
    :
?
% 

 ?
 - 
  )    Õ 4

   Õ 

 4 -
:
 
?   ,   - 
  
?  0 
  
   (

 -     
 (

  +
÷   Õ 4
 


 Õ

7- 29

|ector Mechanics for Engineers: Ôtatics p - %     
   #:


 

  ## 
    

    - &
       (


  
 ,   Õ Dr # 
 
     
 
   r     Õ 4
 r
 Õ 4 -  
 
# r  Õ 4) r  4 Œ Õ 4   Dr  ŒÕ 
4        , 7- 30

|ector Mechanics for Engineers: Ôtatics Ô   1213) - '
  
  

 ÷   
 
(0
  
9 
   /   
 
 #  
9   
 ÷  /    
 
   ÷ 

,
 

  

 
 
  
 (
 
 
# 
 ·
 ,
 
  # ·
 +   +
   
  

- % 
 ,
     ÷  /    
  # 
  ,
    ÷  /  -

, 
 +    +
  (   7- 31

|ector Mechanics for Engineers: Ôtatics Ô   1213) - '
 
( 
  

÷   
 
(0
 
9 
    /    
 
 #  Õ 4) 4 ÷r  ë4 ÷Œ
$4ë
4
$ Õ 4 4 ÷r  ë4 ÷Œ
ëë4 Õ 4


9   
 ÷   /   
 
  Õ 4 )   ÷r  4 ÷ Œ
4ë Õ 4

 ,  
 # ÷r Õ 59 ÷Œ Õ 9 7- 32

|ector Mechanics for Engineers: Ôtatics Ô   - % 
 ,
    ÷  /   
  Õ 4)

Œ  5  4 Õ 4 Œ î Õ ë¦


  # 
 ,
     ÷  /  Õ 4)  Œ  5  $
ë
 Õ 4

Œ  Õ 5 


7- 33

|ector Mechanics for Engineers: Ôtatics Ô   -

, 
 +    +
  (  
 Õ

$6 

 Õ $ $

 + Õ

59  

 + Õ $59

7- 34

|ector Mechanics for Engineers: Ôtatics

?


7- 35