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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
P = 20 kNABRA​ = ?RB​3 m1 m

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

L = 4 mP = 20 kN at 3 m
RA = kN
2.Easy
P = 15 kN, 60°ABRA​ = ?0.5 m3.5 m

The simply supported beam has a pin at A and a roller at B. A point load P acts at 0.5 m from A, inclined at 60° to the horizontal. Find the vertical support reaction RA.

L = 4 mP = 15 kN at 0.5 mθ = 60°
RA = kN
3.Medium
P1​ = 30 kNP2​ = 55 kNABRA​RB​ = ?2 m0.5 m1.5 m

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

L = 4 mP1 = 30 kN at 2 mP2 = 55 kN at 2.5 m
RB = kN
4.Medium
P1​ = 50 kNP2​ = 65 kNABCRA​ = ?4 m1 m3 m

The beam has a pin at A and a roller at B, 5 m from A, and overhangs B to the free end C. Find the vertical reaction RA, taking upward as positive.

AB = 5 mAC = 8 mP1 = 50 kN at 4 mP2 = 65 kN at 8 m
RA = kN
5.Hard
w = 4 kN/mP = 55 kNQ = 70 kNADCMA​ = ?2 m1 m6 m1 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 9 m from A, a uniformly distributed load w on the whole part CD and a point load Q at 2 m from A. Find the magnitude of the reaction moment MA at the wall.

AC = 3 mAD = 10 mP = 55 kN at 9 mw = 4 kN/m from 3 to 10 mQ = 70 kN at 2 m
MA = kN·m
6.Hard
w = 2 kN/mP = 65 kNABCRB​ = ?1.5 m0.5 m0.5 m1.5 m

The beam has a pin at A and a roller at B, 2.5 m from A, and overhangs B to the free end C. It carries a point load P at 1.5 m from A and a uniformly distributed load w from 2 m to the free end at 4 m. Find the vertical reaction RB, taking upward as positive.

AB = 2.5 mAC = 4 mP = 65 kN at 1.5 mw = 2 kN/m from 2 to 4 m
RB = kN

Answer key

  1. 1. RA = 5 kN
  2. 2. RA = 11.37 kN
  3. 3. RB = 49.38 kN
  4. 4. RA = −29 kN
  5. 5. MA = 205.6 kN·m
  6. 6. RB = 43.8 kN

Full step-by-step solutions: practise this topic on examproblems.com.