When is shear force changes its sign, bending moment in a beam will be eir maximum positive or maximum negative. This is because of sign convention adopted.

Calculation:

ΣF_y = 0,

R_A + R_B = 10 × 6 = 60 kN

Taking moment about point A, 

ΣM = 0

R_B × 10 - 10 × 6 × 3 = 0

R_B = 18 kN 

Shear Force diagram started from left side of m as per load. For point loads draw vertical lines and under UDL draw slope lines.

The support reaction is normal to axis of beam. It facilitates vertical support. It helps beam to overcome temperature stresses effectively. It is similar to simple support.

Concept:

In Cantilever beam at support, we have a horizontal reaction, vertical reaction and moment.

From force and moment balancing we can find reactions and moment at A

 $\sum F_h=0$, $\sum F_v=0$, $\sum M_A=0$

Calculation:

Given:

?

R_Av = Vertical reaction at A, R_Ah = Horizontal reaction at A, M_A = Moment at A

$\sum F_v=0$  

R_Av - 10 - 5 - 15 = 0

RAv - 30 = 0 ⇒ RAv = 30 kN 

$\sum M_A=0$ ⇒ M_A + (10 × 1) + (5 × 3) + (15 × 6) = 0

MA + 115 = 0 ⇒ MA = -115 kNm

Additional Information

Shear force and Bending moment Diagram of given cantilever beam :

Shear force (S.F)

• Shear force at D = 15 kN
• Shear force at C = 15 + 5 = 20 kN
• Shear force at B = 15 + 5 + 10 = 30 kN

Bending moment

• Bending moment at D = 0 kNm
• Bending moment at C = - (15 × 3) = - 45 kNm or 45 kNm (CW)
• Bending moment at B = - (15 × 5) - (5 × 2) = - 85 kNm or 85 kNm (CW)
• Bending moment at A = - (15 × 6) - (5 × 3) - (10 × 1) = - 115 kNm or 115 kNm (CW)

At support B, BM is zero. The beam undergoes maximum BM at fixed end.
By joining base line, free end and maximum BM point. We obtain a right angled triangle.

A beam which is fixed at one end and free at or end is called cantilever beam. In this case, some support or than existing ones may be provided in order to avoid excessive deflection or to reduce amount of bending moment, additional support is known as a prop. The beam is known as a propped cantilever beam.

The positive bending moment in a section is considered because it causes convexity downwards. Such bending moment is called a sagging bending moment or positive bending moment.

Shear Force diagram is a graphical representation of shear force plotted as ordinate on baseline representing axis of Beam.

In determination of shear force and bending moment diagrams it is clear that shear force changes its sign when bending moment in a beam is maximum and shear force in a beam subjected to pure positive bending will be zero as neutralizing effect comes under.