What is Shear Force and bending Moment

 

                                                      Shear Force and bending Moment

Shear force: Resistance to keep beam in equilibrium against external transverse loads. Shear force at any section is equal to the sum of transverse loads either to the right-hand side or left-hand sight of the section.

Bending moment:  Bending moment at any section is equal to sum of moments either to the right-hand side or left-hand side of the section.

Shear force diagram (SFD): A graphical representation of vertical (or) transverse forces along the length of a beam.

Sign convention for shear force and bending moment at a section:

 

Relation Between Intensity of Loading, Shear Force and Bending Moment:

·         Between W = intensity of load;

                                V = shear force;

                                M = bending moment

                           W = dv/dx = d2M/dx2

·         Slope of shear force diagram is intensity of load.

·         Rate of change of shear force is intensity of load

                          V = dam/dx

·         Slope of bending moment diagram is shear force.

·         Rate of change of bending moment is shear force.

·         Maximum magnitude of bending moment occurs at a point where shear force changes its sign.

S. No

Type of loading

Variation of S.F.

Variation of B.M

 

  1

 

Point load

Rectangle/ Uniform/ Horizontal Straight line

Rectangular/ inclined straight line/ linear

 

  2

 

       Udl

Rectangular/ inclined straight line/ linear

 

    Square        Parabola

  

  3

     uvl or

Triangular

Square parabola

Cubic parabola

  4

parabolic

Cubic parabola

Fourth degree parabola

 

  5

Bending Couple

No shear variation

A vertical step at the point of application

 Cantilever beam subjected to point load

Cantilever beam subjected to UDL 

Cantilever beam subjected to UVL of maximum intensity at fixed end and zero at free end



Simply supported beam subjected to point load

 

Simply supported beam subjected to UDL


Simply subjected beam subjected to UVL

 
 

Cantilever beam subjected to UVL of zero intensity at fixed end and maximum intensity at free end

 

Cantilever beam subjected to end moment

 

Cantilever beam subjected to two moments

 

 Simply supported beam subjected to moment at one end

 

Simply supported beam subjected to moment in its span


 Simply supported beam subjected to moments at both the ends

 


 

 

 

 

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