Question

Draw Shear force and bending moment diagram for below problem with marking values

of shear force and bending moment at supports and midpoint of beam.
pl answer it ​

Answer 1

Answer:

There are two possible ways to do it:

You divide your beam into imaginary sections and introduce x variables which are used to calculate bending moment from forces acting in each section multiplied by the distance expressed with x variable for specific section. The same can be done for shear forces. This way you can find the values of bending moment (and shear force) at the beginning and at the end of your imaginary section and. Next you mark these values on diagram and connect them knowing some general rules (when M diagram is parabolic, when linear and when constant/zero).

You skip tedious calculations of M and T values at both ends of each cross-section and use more clever way to draw these diagrams. What do you need for that ? Only this formula:

T(x)=dM(x)dxT(x)=dM(x)dx

and some general rules.

What this equation tells us is, among others, that in order to get bending moment values we have to integrate (reverse of derivative used to calculate shear force from bending moment) bending moments. And. since integration is basically the same as calculating the area under function curve, if we already have shear force diagram drawn, we can just calculate area of each part of it for different sections and use these values to draw bending moment diagrams.

When it comes to general rules, there are few (mostly obtained from aforementioned equation):

if there’s an applied concentrated vertical force or reaction acting on the beam, then shear force diagram will jump in its place about its value

if there’s a bending moment applied then moment diagram will jump in its place about its value

if T is constant then M is linear function

if T is linear function then M is parabolic

if T is second order parabolic (in case of trapezoidal distributed load) then M is third order parabolic