Beam support reactions worksheet with answers

Free printable Beam support reactions worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
P = 50 kN, 60°ABAx​ = ?1 m7 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 1 m from A, inclined at 60° to the horizontal. Find the magnitude of the horizontal reaction Ax at the pin A.

L = 8 mP = 50 kN at 1 mθ = 60°
Ax = kN
2.Easy
M₀ = 25 kN·mABRB​ = ?2 m3 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 25 kN·m applied at 2 m from A. Find the vertical reaction RB, taking upward as positive.

L = 5 mM₀ = 25 kN·m (clockwise) at 2 m
RB = kN
3.Medium
P = 20 kNM = 25 kN·mABRB​ = ?2 m1 m2 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 2 m from A and a counter-clockwise couple M at 3 m from A. Find the vertical reaction RB, taking upward as positive.

L = 5 mP = 20 kN at 2 mM = 25 kN·m (counter-clockwise) at 3 m
RB = kN
4.Medium
P1​ = 20 kNP2​ = 40 kNABRA​ = ?RB​2.5 m0.5 m3 m

The simply supported beam has a pin at A and a roller at B. Find the vertical support reaction RA.

L = 6 mP1 = 20 kN at 2.5 mP2 = 40 kN at 3 m
RA = kN
5.Hard
w0​ = 8 kN/mP = 50 kNABMA​ = ?1.5 m3.5 m

The cantilever beam is fixed to the wall at A. It carries a linearly varying load that is zero at the wall and rises to 8 kN/m at the free end B, plus a point load P at 1.5 m from the wall. Find the magnitude of the reaction moment MA at the wall.

L = 5 mw0 = 8 kN/mP = 50 kN at 1.5 m
MA = kN·m
6.Hard
P = 30 kNQ = 65 kNADCMA​ = ?1.5 m1.5 m1 m2 m

A compound beam is fixed to the wall at A, has an internal hinge at C (3 m from A) and rests on a roller at D (6 m from A). It carries a point load P at 4 m from A and a point load Q at 1.5 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 6 mP = 30 kN at 4 mQ = 65 kN at 1.5 m
MA = kN·m

Answer key

  1. 1. Ax = 25 kN
  2. 2. RB = 5 kN
  3. 3. RB = 3 kN
  4. 4. RA = 31.67 kN
  5. 5. MA = 141.7 kN·m
  6. 6. MA = 157.5 kN·m

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