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Chapter: Mechanical - Strength of Materials - Transverse Loading On Beams And Stresses In Beam

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Solved Answers: Transverse Loading on Beams and Stresses In Beam

Mechanical - Strength of Materials - Transverse Loading On Beams And Stresses In Beam


Problem - 1

 

Draw the shear force & bending moment diagram for given cantilever.

 


 

Problem - 2

 

Draw the shear force diagram for given cantilever.

 

 

Solution :

To fine the support reaction:

Taking moment at A                                =          -RD   6+6  4+3  2 = 0   

RD   6                                                         =       -30   

RD                                                              =       -5 KN        

Upward force                                           =          Downward force 

RA+5                                                          =       6+3  

RA                                                              =       4 KN

Shear Force Calculation:

R.H.S                                                                            

Shear force at A                                          =       4 KN

Shear force at B                                          =       4-3 = 1 KN

Shear force at C                                          =       4-3-6

                                                                   =       -5 KN        

Shear force at D                                          =       -5 KN        

L.H.S                                                                            

Shear force at D                                          =       -5 KN        

Shear force at C                                          =       6-5    = 1 KN      

Shear force at B                                          =       6+3-5         

RA                                                           =          B       =       4 KN

To find the moment                                                                         

Bending moment at A =                           0                   

Bending moment at B =                           4  2 = 8 KNm        

Bending moment at C =                           (4         4) –(3          2)     

=                                                               10 KNm

 

 

Problem - 3

 

Draw the shear force diagram for at bending moment for givern cantilever.

 

Solution :

To fine the support reaction:                               

Taking moment at A  =                            (4         –(RE  4)

                                                                 =          32 –4RE     

RE                                                            =          8 KN

RA + 8 =                                                   15       

RA                                                            =          7 KNS       

To fine Shear force:                                             

Shear force at A                                       =          7 KN

Shear force at B                                       =          7-4 = 3 KN

Shear force at C                                       =          7-4-5  = - 2KN    

Shear force at D                                       =          7-4-5-6 = -8 KN  

Shear force at E                                        =          - 8 KN       

To find bending moment                                     

Bending Moment at A =                           0         

Bending Moment at B =                           4 KNm

Bending Moment at C =                           (7         2) –(4  2)    

                                                                 =          10 KNm     

Bending Moment D   =                             (7         3) –(4  2)    

                                                                 =          8 KNm       

Bending Moment E                                  =          0       

 

 

 

Problem - 4

 

 

A Beam of Total length 8m is freely supported at a left end & at a point 6m from left end. It carries 2 points floats of 15KN & 18KN. In which one is at the free end and another is 3m from the left support. Draw the shear force and bending moment diagram. Locate the point of contraflexture.

 

Solution :

To fine the support reactions:                   

Taking moment about A,                        

(Rc                                                           6) –(18  3) –(10  8) = 0    

6 Rc                                                          =          54+120      

Rc                                                             =          174/6

Rc                                                             =          29 KN        

RA + Rc                                                   =          18+15                  

RA + 29                                                   =          33              

RA                                                           =          4 KN          

To fine Shear force:                                                      

Shear force at D                                       =          15 KN        

Shear force at C                                       =          29 KN +15 = -14 KN

Shear force at B                                       =          -14+18        = 4 KN

Shear force at A                                       =          4 KN

To find bending moment                                               

Bending Moment at D =                           0                   

Bending Moment at C =                           -(15      2)      =       - 30 KNm

Bending Moment at B =                           -(15      5)+(29         3)     

Bending Moment at A =                           -(15      8) +(29        6)-(18          3)

 

 

=                   -120-54+174

 

=                   0

 

Problem-5:

 

 

The cross section of the beam is shown is beam is cantiliver type &carries a UDL of 16KN/m. If the span of beam is 2.5m. Determine the maximum tension & Compressible stress in the beam.

 

solution:

 

Section (1) :


 




 

Problem-6:

 

 

The cast iron bracket subjected to bending has a cross section of I-shaped with unequal flanges as shown. If the compressive force on the top of the flanges is not to exceed 17mega pa. What is the bending moment of the section can take if the section is subjected to a shear force of 90KN. Draw the shear stress distribution over the depth of the section.

 

Solution:

 

Area of section     (1)     =       lb

 

=                   250  50

 











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