Notations and units:
= Deflection,
= Slope,
= Modulus of elasticity/youngs modulus,
= Area moment of inertia
Units of the notations are in SI units.
1) CANTILEVER BEAM
Cantilever beam with point load at free end:
At fixed end : Maximum bending moment = PL
Cantilever beam with uniformly distributed load:
At free end :
At free end :
Maximum bending moment = at fixed end
Cantilever beam with one point load acting in between the ends:
At free end :
Cantilever beam with moment acting at the free end:
At free end :
At free end :
2) SIMPLY SUPPORTED BEAM
Simply supported beam with point load at centre:
at centre
Maximum bending moment = at centre
Simply supported beam with uniformly distributed load:
at centre
Maximum bending moment =
Simply supported beam with only point load:
At point load :
Maximum bending moment =
Simply supported beam with two moments at each end:
At centre :
Simply supported beam with moment at centre:
Maximum bending moment =
2) FIXED BEAM
Fixed beam with point load at centre:
At point load :
Fixed beam with uniformly distributed load:
Fixed beam with only point load:
At point load :