The reaction and bending moments at point A of the cantilever beam are:

 

Concept:

In the 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:

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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 the 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)