Frames & machines worksheet with answers

Free printable Frames & machines 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
O80 N80 NQ150 mm15 mm

The handles of a pair of pliers are squeezed with 80 N each, 150 mm from the pin O, and the jaws grip a wire 15 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 150 mmb = 15 mm
FO = N
2.Easy
6 kN1 m0.5 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 6 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 6 kNAD = 1 mAB = 1.5 mAC = 0.5 m
FCD = kN
3.Medium
4 kN4 m2.5 m0.6 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 2.5 m above the ground and 0.6 m to the right of A. A vertical load of 4 kN acts on member AB at K, 0.36 m (horizontally) from A. Find the force FBC in member BC.

P = 4 kNL = 4 mH = 2.5 mhorizontal distance A to B = 0.6 mhorizontal distance A to K = 0.36 m
FBC = kN
4.Medium
4 kN5 m1.5 m1.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 3 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 4 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 5 mheight of C = 3 mheight of DE = 1.5 m
C = kN
5.Hard
12 kN6 kN3 m2.5 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 2.5 m high and 1.8 m to the right of A. Member AB carries a vertical load of 12 kN at K, 0.9 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 12 kNQ = 6 kNL = 3 mH = 2.5 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.9 m
Ax = kN
6.Hard
w = 3 kN/m3 kN1.5 m0.9 m1.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.5 m below A). The beam carries a uniform load of 3 kN/m over its full length and a point load of 3 kN at its free end B. Find the force FCD in the strut.

w = 3 kN/mP = 3 kNAD = 1.5 mAB = 2.4 mAC = 1.5 m
FCD = kN

Answer key

  1. 1. FO = 880 N
  2. 2. FCD = 20.12 kN
  3. 3. FBC = 0.6077 kN
  4. 4. C = 3.887 kN
  5. 5. Ax = 1.872 kN
  6. 6. FCD = 14.93 kN

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