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
12 kN5 m1.5 m3 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, 4.5 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 12 kN acts at C. Find the tension T in the tie DE.

P = 12 kNAB = 5 mheight of C = 4.5 mheight of DE = 1.5 m
T = kN
2.Easy
2 kN3 m0.8 m1.2 m0.375 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3 m apart. A vertical load of 2 kN acts on leg AC at the point K, 0.375 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 2 kNAB = 3 mhorizontal distance A to K = 0.375 m
By = kN
3.Medium
2 kN6 m0.8 m3.2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 6 m apart. The legs meet at the pin C, 4 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 2 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 2 kNAB = 6 mheight of C = 4 mheight of DE = 0.8 m
C = kN
4.Medium
4 kN4.8 m1.5 m1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart. The legs meet at the pin C, 2.5 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 = 4.8 mheight of C = 2.5 mheight of DE = 1.5 m
C = kN
5.Hard
F = ?3000 N20 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 20 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 3000 N at the slider C? Neglect friction and weights.

Q = 3000 NAB = BC = 120 mmh = 20 mm
F = N
6.Hard
10 kN1.5 kN2 m2 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2 m above A. A load of 10 kN hangs at B. Find the tension T in the cable.

W = 10 kNWb = 1.5 kNAB = 2 mAC = 2 m
T = kN

Answer key

  1. 1. T = 5 kN
  2. 2. By = 0.25 kN
  3. 3. C = 1.371 kN
  4. 4. C = 5.2 kN
  5. 5. F = 1014 N
  6. 6. T = 15.2 kN

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