A simply supported beam of 9 m span carries a point load of 30 kN at 2 m from the left end of the support. It also carries a UDL of 12 kN/m over 4 m span from the right support. What is the value of shear force at 5 m from the left support?

Calculation:

Given

Span of beam (L) = 9 m

Shear force (V) =? (5 m from left support) 

∑ F_y = 0

R_A + R_B = 30 + 12 × 4 

RA + RB = 78 kN .................... (1)

∑ M_B = 0

R_A × 9 - 30 × 7 -12 × 4 × 2 = 0

R_A = 34 kN

Shear force at A (V_A) = R_A = 34 kN (constant up to 2 m)

Shear force at C (V_c) = R_A - 30 = 34 - 30 = 4 kN (constant up to point D)

Shear force at D (V_D) = 34 - 30 = 4 kN

Shear force at D (V_D) = 4 kN

Shear force at 5 m from left support is 4 kN. Hence option (1) is the correct answer.