Example:Use Method 2 to calculate the shear and bending moment
along the beam
Strategy: Use dV/dx = w(x)to determine the slope of the shear
diagram.
The slope of the shear force, dV/dx, equals the
change in distributed loading.
UsedM/dx=V(x)to determine the slope of the moment diagram.Note:
The slope of the moment diagram equals the value of the shear
force. Also note:By integration, the area under the shear
diagram represents the change in the moment.i.e
M(x)=ʃ V(x) dx
Example:Calculate the shear and
bending moment diagram for the symmetrically loaded simply supported (pin
at A and roller at C) beam shown below.
Recall the sign conventions
for shear force and bending moment (shown below).
So atx = 0 the shear
force is + P/2 and remains constant until x = L/2 when
it drops to ˗ P/2 and remains at that value until x = L when it
returns to zero.