Unit 2 / Practice Drills
Unit 2 Practice Drills
Equilibrium
Beam reactions, free-body diagrams, and classic contact problems. This is the safest high-ROI unit.
Simply Supported Beam Reactions
5 drills. Start from the top. Attempt each problem before revealing any steps.
These problems are drawn from the SPPU FE Engineering Mechanics paper families. The procedure is identical across all five. Own it here and you will not drop marks on beam reactions in the exam.
How to use these drills
Attempt the problem on paper first. Then reveal Step 1. Check your work. Continue step by step. If your answer matches at each step, move on. If it does not, stop at that step and find your error before continuing.
Unit 2 Practice Drills
Drill 1 - UDL over full span with a point load
Problem
A simply supported beam AB has a span of 8 m. It carries a uniformly distributed load of 10 kN/m over its entire length and a point load of 20 kN acting vertically downward at 3 m from A. Find the support reactions at A and B.
Figure 1A
Beam with full-span UDL and point load
Step 1 - Convert the UDL to an equivalent point load.
Total UDL load = w × L = 10 × 8 = 80 kN.
This acts at the midpoint of the beam = 4 m from A.
Check: you should have two loads now: 80 kN at 4 m from A, and 20 kN at 3 m from A.
Step 2 - Take moments about A to find RB.
ΣMA = 0 (anticlockwise positive):
RB × 8 − 80 × 4 − 20 × 3 = 0
RB × 8 = 320 + 60 = 380
RB = 47.5 kN ↑
Step 3 - Apply ΣFy = 0 to find RA.
RA + RB = total downward load
RA + 47.5 = 80 + 20 = 100
RA = 52.5 kN ↑
Step 4 - Check.
RA + RB = 52.5 + 47.5 = 100 kN, which matches the total downward load.
Worked Diagram Hidden
Reveal worked diagram
Open this only after you have attempted the setup yourself.
Worked Diagram Hidden
Reveal worked diagram
Open this only after you have attempted the setup yourself.
Figure 1B
Converted FBD for the moment equation
The UDL is replaced by an equivalent 80 kN point load acting at the midpoint of the loaded 8 m span.
Where students lose marks on this type
The UDL resultant acts at the midpoint of the loaded length, not automatically the midpoint of the beam. Here the UDL covers the full 8 m so it acts at 4 m from A. If the UDL covered only 6 m from A, the resultant would act at 3 m from A, not 4 m.
The remaining beam-reaction families stay premium
Free access includes the first full drill. The partial UDL, applied couple, UVL, mixed-loading, and inclined-load beam drills unlock with the premium pass.
What the premium set completes
The premium drills complete these beam-reaction families:
- UDL over full span
- UVL over full span
- Mixed loading with a couple
- A close repeat-family beam variant
- An inclined load
These are the five problem families that cover beam-reaction questions in SPPU FE Engineering Mechanics papers. If you can solve all five without hesitation, you will not drop marks on Unit 2 beam reactions.