FE Civil / Free study sprint

Balance the beam. Check both reactions.

Find the support reactions of a simply supported beam with one point load, then check equilibrium.

Before you start: Resolve forces, use consistent units and interpret a perpendicular moment arm.

1. Try2. Understand3. Practice4. Revisit

01 / Start from memory

What would you choose?

Commit to an answer before reading the board.

One-question checkA 12 kN load acts 2 m from A on a 6 m simply supported beam. Which support carries more vertical load?

FE Civil / Statics / Rigid-body equilibrium

Balance the beam. Check both reactions.

Find the support reactions of a simply supported beam with one point load, then check equilibrium.

01Summary board

The decision path

1

Isolate the beam

Draw the applied load and both vertical support reactions. The pin also allows a horizontal reaction; with no horizontal load, it is zero.

[F1, F2]
2

Take moments about a support

Choose A as the moment center so its reaction has zero lever arm. Use one sign convention consistently.

ΣM_A = 0: R_B × L - P × a = 0
[F1, F2]
3

Balance and cross-check

Use vertical force balance for the other reaction. Check moments about B independently.

ΣF_y = 0: R_A + R_B - P = 0
[F1, F2]

Worked example / Original StudyMaps scenario

A 12 kN load, 2 m from A

A horizontal beam spans 6 m from pin A to roller B. A single 12 kN downward load acts 2 m from A. Ignore beam weight.

12 kNA (R_A)B (R_B)2 m4 m
  1. Take counterclockwise moments as positive about A.
  2. R_B × 6 - 12 × 2 = 0, so R_B = 4 kN upward.
  3. R_A + 4 - 12 = 0, so R_A = 8 kN upward.
  4. Check about B: -8 × 6 + 12 × 4 = 0 kN·m. Both balances hold.
ResultA: 8 kN up. B: 4 kN up.
Principles: [F1, F2]. Original example: StudyMaps.
StudyMaps · Planar static equilibrium, one vertical point load, pin and roller supports; beam self-weight neglected.6f54299a / 1 of 3

03 / Apply it

Your turn.

Three new problems. Explain your choice on paper, then check the reasoning.

Practice 1A 20 kN point load is at the midpoint of an 8 m simply supported beam. What is R_B? Ignore beam weight.
Practice 2A 15 kN load is 1 m from A on a 5 m simply supported beam. What is R_A? Ignore beam weight.
Practice 3For the worked 12 kN example, a solution claims A = 6 kN and B = 6 kN. Which check rejects it?

0 of 3 practice problems checked

04 / Return later

Does it still make sense tomorrow?

Bookmark this page and try the new problem without the board. This is a practice check, not an exam-readiness score.

Open the return-later problem
Unseen problemA 16 kN load acts 3 m from A on an 8 m simply supported beam. Ignore beam weight. Find R_A and R_B.

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Sources and scope

Planar static equilibrium, one vertical point load, pin and roller supports; beam self-weight neglected. A focused statics supplement; this simplified beam model is not structural design guidance.

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