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:
·
Between
W = intensity of load;
V = shear force;
M = bending
moment
W = dv/dx = d^{2}M/dx^{2}
·
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 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 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
Simply supported beam subjected to moment in its span
Simply supported beam subjected to moments at both the ends
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