What is shear force and bending moment diagrams ?

Shear force diagrames :- Theses are the diagrams those shows the value of shear force at various sections of the members.

Bending moment diagrams :- These are the diagrams those shows the value of the bending moment at various sections of the members.

(A). CANTILEVER BEAMS :- These beams are fixed from one Ends.

(1). Cantilever beams carry W concentrated load of length l.

Considering any section X from distance x from end B.
So     S.F.  at X=S=+W
        B.M. at X=M= -Wx

at x=0 then M=0 

if x=l then M= -Wl


(2). Cantilever beam of length l having uniformaly distributed load w

S.F and B.M at any section X will be

S= wx and M= -(wx^2)/2

if x=l Then
   M= -(wl^2)/2






(3). cantilever beam of length l carry uniformly distributed load w per unit length runs in whole length and have concentrated load W at free end.




S= wx+W
M= -{(wx^2)/2 +Wx}

if x= l then

S= (wl+W)
M= -{(wl^2)/2 +Wl}



(4). Cantilever beam of length l ccarry UDL w per unit length for a distance 'a' from the free end

Here, At x=0 S= 0   and   M= 0

Now section between A and D distance x from end B

S = +wa
M= -wa{x-(a/2)}

At x=a
M= -wa{l -(a/2)}





(B). SIMPLY SUPPORTED BEAMS :-


(1). SSB have concentrated load W at mid having span length l

S.F. at C point

S = -W/2
BM = M= Wl/4

hence BM increase uniformaly

from zero at A to  Wl/4 at C then decrease to zero at B.

(2). SSB have eccentric concentrated load on the span.

assume AD=a  and DB=b
Va and Vb are vertical reaction at the ends.

Vb = Wa/l    and Va = Wb/l

So, shear force between A and D  S = Va = +Wb/l  
      shear force between D nad B  S = Vb = -Wa/l

Bending moment at section between A and D at distance x from A.

M= + (Wb/l)x  at x=0 M= 0

if x= a  M= Wab/l




(3). SSB carry UDL w per unit length over whole span.




At x=0      S = wl/2    and M=0

At  x =l    S=  -(wl/2)    and    M = 0

At l/2        S = 0   and M =  + (wl^2)/8