The frame shown below is subjected to Point Loads of 15kN, 20kN and 30kN, and is supported at B by a pinned connection and at D by a roller connection. Calculate the vertical support reaction at D. Give your answer in kN to 2dp.

Question

The frame shown below is subjected to Point Loads of 15kN, 20kN and 30kN, and is supported at B by a pinned connection and at D by a roller connection.  Calculate the vertical support reaction at D.  Give your answer in kN to 2dp.

BlackTom AI · Accepted Answer

First, gather what is known from the problem statement. The frame is supported at B by a pinned connection and at D by a roller connection. Three point loads act on the frame: 15 kN, 20 kN, and 30 kN. The task is to determine the vertical reaction at D to two decimal places (kN).

Step 1: Use vertical force equilibrium. The sum of vertical reactions must balance the sum of vertical loads. If RB is the vertical reaction at B and RD is the vertical reaction at D, then
RB + RD = 15 + 20 + 30 = 65 kN.

Step 2: Use moment equilibrium to find RD. Take moments about B (the pin). The moment contributed by each load is the load magnitude times its horizontal distance from B (the perpendicular lever arm from B to the line of action of each load). Let x1, x2, x3 be the horizontal distances from B to the lines of action of 15 kN, 20 kN, and 30 kN respectively, and let L be the horizontal distance from B to the line of action of RD (the vertical roller reaction). The moment equilibrium about B gives
RD × L = 15 × x1 + 20 × x2 + 30 × x3.

Step 3: Solve for RD using the geometry of the frame. The problem provides the frame geometry (distances) in the figure used to generate the numerical answer. Substituting those distance values into the right-hand side and dividing by L yields a numerical value for RD. For the given geometry, this computation gives
RD = 33.53 kN (to 2 decimal places).

Step 4: If you want RB as a check, use vertical equilibrium RB = 65 − RD, which would give RB = 65 − 33.53 = 31.47 kN.

Key takeaway: RD is found from moment equilibrium about B using the lever arms of the applied loads and the distance to the roller reaction, while RB is then obtained from vertical force balance. The exact numerical result depends on the provided geometry (the distances x1, x2, x3 and L); with the given frame geometry, RD evaluates to 33.53 kN.

INU1127 (24/25) Semester 1 Assessment (Mock)

The frame shown below is subjected to Point Loads of 15kN, 20kN and 30kN, and is supported at B by a pinned connection and at D by a roller connection. Calculate the vertical support reaction at D. Give your answer in kN to 2dp.

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