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 kNABRA​RB​ = ?2 m8 m

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

L = 10 mP = 50 kN at 2 m
RB = kN
2.Easy
P = 55 kN, 40°ABRA​ = ?7 m1 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 7 m from A, inclined at 40° to the horizontal. Find the vertical support reaction RA.

L = 8 mP = 55 kN at 7 mθ = 40°
RA = kN
3.Medium
P1​ = 45 kNP2​ = 10 kNABRA​ = ?RB​1 m5 m4 m

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

L = 10 mP1 = 45 kN at 1 mP2 = 10 kN at 6 m
RA = kN
4.Medium
w0​ = 10 kN/mP = 65 kNABRB​ = ?1 m9 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. A point load P also acts at 1 m from A. Find the vertical support reaction RB.

L = 10 mw0 = 10 kN/mP = 65 kN at 1 m
RB = kN
5.Hard
w = 8 kN/mP = 70 kNABCRA​ = ?2 m4 m2 m2 m

The beam has a pin at A and a roller at B, 8 m from A, and overhangs B to the free end C. It carries a point load P at 2 m from A and a uniformly distributed load w from 6 m to the free end at 10 m. Find the vertical reaction RA, taking upward as positive.

AB = 8 mAC = 10 mP = 70 kN at 2 mw = 8 kN/m from 6 to 10 m
RA = kN
6.Hard
P = 35 kNADCMA​ = ?5 m2 m3 m

A compound beam is fixed to the wall at A, has an internal hinge at C (5 m from A) and rests on a roller at D (10 m from A). It carries a point load P at 7 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 5 mAD = 10 mP = 35 kN at 7 m
MA = kN·m

Answer key

  1. 1. RB = 10 kN
  2. 2. RA = 4.419 kN
  3. 3. RA = 44.5 kN
  4. 4. RB = 23.17 kN
  5. 5. RA = 52.5 kN
  6. 6. MA = 105 kN·m

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