Overhanging beam: shear force and bending moment calculation

Calculate the shear force and bending moment values due to the imposed loading on the overhanging beam of Figure 1. 

The free-body-diagram is shown in Figure 2. The beam’s reactions are calculated as:

ΣF_x = 0 -> A_x = 0

ΣΜ_Α = 0 -> Β_Yx6 - 30x10 -5x4x4 = 0-> Β_Y =63.33kN

ΣF_Y = 0 -> A_Υ + B_Υ = 5x4 + 30 -> A_y =-13.33kN

Calculations of shear force

Shear force is calculated in both sides (left and right) of each point.

F_A-right = -13.33kN

F_C = -13.33kN

F_B-left = -13.33 – 5x4 = - 33.33kN

F_B-right = -13.33 – 5x4 + 63.33 = +30kN

F_D-left = +30kN

Calculations of bending moment

Bending moment is calculated as follow (same left and right):

M = 0

M = –13.33x2 = -26.66kNm

M = –13.33x6 – 5x4x2 = –80 –40 = –120kNm

M = 0

Shear force and bending moment plots

The following Figure 3 presents the plots of shear force and bending moment. 

Some interesting points should be outlined:

1. The maximum bending moment will occur at the point where shear force changes sign. Point B is such a point.

2. The bending moment sign does not change, hence there is no point of contra-flexure. The bending moment diagram is a straight line from point A to C, a parabolic curve from C to B and a straight line from B to D.