DEFLECTION OF BEAMS

TYPES OF BEAM AND LOADING

MAX BM

SLOPE

DEFLECTION

 

CANTILEVER BEAM CARRYING A MOMENT

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

 

CANTILEVER BEAM CARRYING A POINT LOAD

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

 

CANTILEVER BEAM SUBJECTED TO UDL

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

 

CANTILEVER BEAM WITH UVL

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
SIMPLY SUPPORTED BEAM CARRYING A POINT LOAD

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

SIMPLY SUPPORTED BEAM CARRYING UDL

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