Shear force on cantilever beam is the sum of vertical forces acting on a particular section of a beam. While bending moment is the algebraic sum of moments about the centroidal axis of any selected section of all the loads acting up to the section.

Example:

Draw shear force and bending moment diagrams of the cantilever beam carrying point loads. As shown in figure;

##### Solution

**Shear Force**

To draw a shear force diagram. First find value of shear force between varying loads.

Let start from left side.

Shear force Between point **D** and **C**

S.F (D-C) = -100 kg.

Shear force value increases gradually as we move towards fixed end.

Shear force Between Point **C** and **B**

S.F (C-B) = -(100 + 200 ) = -300 kg.

Now one can see, shear force between point C and B is the sum of point loads acting up to that point.

Shear force Between Point **B** and **A**

S.F (B – A) = -(100 + 200 +300 ) = – 600 kg.

One can see shear force between B and A is the sum of all point loads acting on it. This shows shear force is maximum at fixed end and minimum at free end of cantilever beam.

**Shear Force Diagram**

**Bending Moment**

Bending moment at point D = B.M (D) = 0

Bending moment at point C = B.M (C) = -(100×1) = -100 kg.m

Bending moment at point B = B.M (B) = – (100×2 +200×1)

B.M (B) = -400 kg.m

Bending moment at point A = B.M (A) = (100×3 + 200×2 + 300×1)

Total Moment at point A = B.M (A) = -1000 kg.m

This shows that maximum bending will be at fixed end. Point loads from free end transfer their bending strength towards fixed end. At the end it acts as a sum of all bending moments.

**Bending Moment Diagram**