Question

A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure. 

The vertical reaction at support X (in kN, in integer) is \(\underline{\hspace{1cm}}\)

Hint:

For a propped cantilever beam, use the equilibrium equations to solve for reactions at supports.

Answer 1

Correct Answer: 30

Step 1: Vertical force equilibrium

Let the vertical reaction at support X be R_A

Let the vertical reaction at support Y be R_C

Total uniformly distributed load on the beam:

= 10 × 4 = 40 kN

Applying equilibrium of vertical forces:

ΣF_y = 0

R_A + R_C = 40    ...(1)

Step 2: Moment equilibrium about the internal hinge

Take moments about the internal hinge point B, considering the right portion of the beam.

Load on segment BY:

UDL = 10 kN/m over 2 m

Equivalent point load = 10 × 2 = 20 kN

This load acts at the midpoint of BY, i.e. 1 m from hinge B.

Taking moments about B:

R_C × 2 = 20 × 1

R_C = 10 kN

Step 3: Calculation of reaction at X

Substitute R_C = 10 kN into equation (1):

R_A + 10 = 40

R_A = 30 kN

Final Answer:

The vertical reaction at support X = 30 kN