|
Now the value of the
bending moment at x = 0 is zero.
Since dM/dx =
V(x)
the slope of the moment diagram is + P/2 from 0 ≤ x ≤ L/2 and ˗ P/2 from
L/2 ≤ x ≤ L. Also the
area under the shear diagram from 0 ≤
x ≤ L/2,
M(x) = ʃ V(x) dx, equals (P/2)(L/2) = PL/4.
Hence the bending moment
distribution along the beam from 0 ≤ x ≤ L/2
increases linearly from 0 to PL/4 at which time the slope of the moment
becomes ˗ P/2 and the bending
moment decreases linearly from PL/4 to zero
at x = L.
Note: The bending moment is zero at both ends of the beam. This result is in agreement (provides a
check) with the boundary conditions for a pin at A and a roller at C. Pin supports cannot carry a moment. |
