Calculate the support reactions for the structures shown bel

Calculate the support reactions for the structures shown below. ANS: a) V_A = 20 kN; H_A = -10 kN; M_A = 150 kN.m b) H_A = -2 kN; V_A = 1.71 kN; V_B = 1.29 kN

Solution

a) Let the sign convention be normal cartesian and anticlock is taken positive

Let F₁=14.1 kN and F₂=-10

Along Y-axis

Fy = -F₁sin45 - F₂ = -14.1/1.41 - 10 = -20kN

Since, V_a= -Fy (Normal Force is opposite to net Force)

V_a=20kN (Ans)

Similarly along X-axis

H_a = -F₁cos45 = -14.1/1.41 =-10kN (Note the negative sign is because the reaction is opposite to net force)

Calculating Moment about A

M_a = F₁sin45*x₁ + F₂*x₂ (Anti-clockwise is positive)

Ma= (14.1/1.41)*5 + 10*10 =50+100 = 150kN.m (Ans)