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 = 30 kNABRA​ = ?RB​4 m2 m

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

L = 6 mP = 30 kN at 4 m
RA = kN
2.Easy
M₀ = 30 kN·mABRA​ = ?4.5 m0.5 m

The simply supported beam has a pin at A and a roller at B. It carries only a clockwise couple of 30 kN·m applied at 4.5 m from A. Find the vertical reaction RA, taking upward as positive.

L = 5 mM₀ = 30 kN·m (clockwise) at 4.5 m
RA = kN
3.Medium
w0​ = 12 kN/mABRA​ = ?4 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that rises from zero at A to 12 kN/m at B. Find the vertical support reaction RA.

L = 4 mw0 = 12 kN/m
RA = kN
4.Medium
w0​ = 10 kN/mABRB​ = ?6 m

The simply supported beam (pin at A, roller at B) carries a linearly varying load that falls from 10 kN/m at A to zero at B. Find the vertical support reaction RB.

L = 6 mw0 = 10 kN/m
RB = kN
5.Hard
w = 10 kN/mP = 55 kNABRA​RB​ = ?1 m1 m6 m

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

L = 8 mP = 55 kN at 1 mw = 10 kN/m from 1 to 2 m
RB = kN
6.Hard
P = 15 kNADCMA​ = ?3 m5 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 (10 m from A). It carries a point load P at 8 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 10 mP = 15 kN at 8 m
MA = kN·m

Answer key

  1. 1. RA = 10 kN
  2. 2. RA = −6 kN
  3. 3. RA = 8 kN
  4. 4. RB = 10 kN
  5. 5. RB = 8.75 kN
  6. 6. MA = 12.86 kN·m

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