A uniform distrubuted load (UDL) is a distributed load which has a constant value such as 1kN/m. Simple point forces do not always provide an accurate enough way to determine the stresses in an object such as a beam so more complex theoretical loads must be used in our analysis.
A cantilever beam subjected to U.D.L, draw S.F and B.M diagram.
Here the cantilever beam is subjected to a uniformly distributed load whose intensity is given w / length.
Consider any cross-section XX which is at a distance of x from the free end. If we just take the resultant of all the forces on the left of the X-section, then
S.Fxx = -Wx for all values of ‘x'. ---------- (1)
S.Fxx = 0
S.Fxx at x=1 = -Wl
So if we just plot the equation No. (1), then it will give a straight line relation. Bending Moment at X-X is obtained by treating the load to the left of X-X as a concentrated load of the same value acting through the centre of gravity.
Therefore, the bending moment at any cross-section X-X is
The above equation is a quadratic in x, when B.M is plotted against x this will produces a parabolic variation.
The extreme values of this would be at x = 0 and x = l
Hence S.F and B.M diagram can be plotted as follows: