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
M₀ = 20 kN·mABRA​ = ?4 m6 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 20 kN·m applied at 4 m from A. Find the vertical reaction RA, taking upward as positive.

L = 10 mM₀ = 20 kN·m (clockwise) at 4 m
RA = kN
2.Easy
P = 65 kNABRA​RB​ = ?2 m3 m

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

L = 5 mP = 65 kN at 2 m
RB = kN
3.Medium
P = 30 kNM = 10 kN·mABRB​ = ?1 m3 m4 m

The simply supported beam has a pin at A and a roller at B. It carries a point load P at 1 m from A and a clockwise couple M at 4 m from A. Find the vertical reaction RB, taking upward as positive.

L = 8 mP = 30 kN at 1 mM = 10 kN·m (clockwise) at 4 m
RB = kN
4.Medium
P1​ = 50 kNP2​ = 15 kNABRA​ = ?RB​1 m0.5 m2.5 m

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

L = 4 mP1 = 50 kN at 1 mP2 = 15 kN at 1.5 m
RA = kN
5.Hard
w = 10 kN/mP = 10 kNADCMA​ = ?4 m2 m4 m

A compound beam is fixed to the wall at A, has an internal hinge at C (4 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 6 m from A, a uniformly distributed load w on the whole part CD. Find the magnitude of the reaction moment MA at the wall.

AC = 4 mAD = 10 mP = 10 kN at 6 mw = 10 kN/m from 4 to 10 m
MA = kN·m
6.Hard
P = 15 kN, 50°Q = 50 kNABRA​ = ?1.5 m1 m1.5 m

The simply supported beam has a pin at A and a roller at B. A load P acts at 1.5 m from A, inclined at 50° to the horizontal, and a vertical load Q acts at 2.5 m from A. Find the magnitude of the total reaction force RA at the pin A.

L = 4 mP = 15 kN at 1.5 m, θ = 50°Q = 50 kN at 2.5 m
RA = kN

Answer key

  1. 1. RA = −2 kN
  2. 2. RB = 26 kN
  3. 3. RB = 5 kN
  4. 4. RA = 46.88 kN
  5. 5. MA = 146.7 kN·m
  6. 6. RA = 27.67 kN

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