DEFLECTION OF BEAMS

DEFLECTION OF BEAMS

TYPES OF BEAM AND LOADING	MAX BM	SLOPE	DEFLECTION
Fig. 1 | CANTILEVER BEAM CARRYING A MOMENT
1. A cantilever beam subjected to a concentric moment about its free end.	M	Θ =ML/EI	𝛿=Θ. (L/2) = ML2 /2EI
Fig. 2 | CANTILEVER BEAM CARRYING A POINT LOAD
2. A cantilever beam carrying a point load at its free end.	WL	Θ=ML/2EI = WL2/2EI	𝛿=Θ.(2L/3) = WL3/3EI
Fig. 3 | CANTILEVER BEAM SUBJECTED TO UDL
3. A cantilever beam subjected to UDL (w/meter) through the spam.	WL2/2	Θ=ML/3EI = WL3/6EI	𝛿=Θ.(3L/4) =WL4/8EI
Fig. 4 | CANTILEVER BEAM WITH UVL
4. A cantilever beam subjected to UVL (w/meter) through the spam.	WL2 /6	Θ=ML/4EI =WL3 /24EI	𝛿=Θ.(4L/5) =WL4/30EI
Fig. 5 | SIMPLY SUPPORTED BEAM CARRYING A POINT LOAD
5. A simply supported beam with a point load at mid-point.	WL /4	Θ=ML/4EI =WL2/16EI	𝛿=Θ.(L/3) =WL3/48EI
Fig. 6 | SIMPLY SUPPORTED BEAM CARRYING UDL
6. A simply supported beam with a UDL (w/meter) throughout the spam.	WL2 /8	Θ=ML/3EI =WL3/24EI	𝛿=Θ.(5L/16) =5WL4/384EI