Calculating Shear force & Bending moment

By on in ,
SHEAR FORCE
    Shear Force can be calculated by adding the vertical load that is acted at any section of beam to the right or left of the supports.


BENDING MOMENT
      Bending Moment is the algebraic sum of the moments of all the forces cutting to the right or left of the supports.

SHEAR FORCE AND BENDING MOMENT DIAGRAM
      A shear force diagram will shows the variation of the shear force along the length of the beam.

       A Bending moment diagram will shows the variation of the Bending moment along the length of the beam.

      In this section we will see about how to draw the shear force and bending moment for the given beam under different conditions. First of all we see the notations used in the formulas..
     FX   = Shear Force at X
     MX  = Bending Moment at X
     W   = Load in (N)
      L   = Length of Beam (m)
   x   = Distance of load (m)


i) POINT LOAD
    
         Shear Force at X
         FX = +W


         Bending Moment at X
         MX = -Wx
    


ii)UNIFORM DISTRIBUTED LOAD
       Shear Force at X   
       FX = +Wx
       At x=0, FX = 0
       At x=L, FX= WL


      Bending Moment at X
       MX = - Wx2∕2

iii)UNIFORMLY VARYING LOAD

   Shear Force at X
    FX =  Wx2∕2L
   At x=0, FX = 0
   At x=L, FX= W(L/2)
   
  
   Bending Moment at X 
   MX ==  - Wx3∕6L











Important formulas for calculating SF and BM are tabulated as follows:







LOADS
SHEAR FORCE
BENDING MOMENT
Formula
Diagram
Formula
Diagram

POINT LOAD

+W

-Wx



UNIFORM DISTRIBUTED LOAD

+Wx


-Wx2∕2


UNIFORMLY VARYING LOAD

 Wx2∕2L


-Wx3∕6L

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