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.

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1.Easy
5 kN6 m1.2 m2.8 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 are tied together by the horizontal bar DE at a height of 1.2 m. A load of 5 kN acts at C. Find the tension T in the tie DE.

P = 5 kNAB = 6 mheight of C = 4 mheight of DE = 1.2 m
T = kN
2.Easy
O40 N40 NQ = ?80 mm35 mm

A hand squeezes the handles of a pair of pliers with 40 N each, 80 mm from the pin O. The jaws grip a bolt 35 mm from the pin. Find the gripping force Q on the bolt.

F = 40 Na = 80 mmb = 35 mm
Q = N
3.Medium
20 kN3 m2 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 m above the ground and 1.8 m to the right of A. A vertical load of 20 kN acts on member AB at K, 0.72 m (horizontally) from A. Find the force FBC in member BC.

P = 20 kNL = 3 mH = 2 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.72 m
FBC = kN
4.Medium
12 kN5 m1.5 m1 m1 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 5 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 12 kN acts on leg AC at K, 1 m (horizontally) from A. Find the tension T in the tie.

P = 12 kNAB = 5 mheight of C = 2.5 mheight of DE = 1.5 mhorizontal distance A to K = 1 m
T = kN
5.Hard
4 kN2 m0.6 m1.4 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 2 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 2 mheight of C = 2 mheight of DE = 0.6 mhorizontal distance A to K = 0.75 m
C = kN
6.Hard
F = ?5000 N12 mmABC

A toggle press has two equal links AB and BC, each 200 mm long between pins. The joint B sits 12 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 5000 N at the slider C? Neglect friction and weights.

Q = 5000 NAB = BC = 200 mmh = 12 mm
F = N

Answer key

  1. 1. T = 2.679 kN
  2. 2. Q = 91.43 N
  3. 3. FBC = 5.598 kN
  4. 4. T = 6 kN
  5. 5. C = 1.843 kN
  6. 6. F = 601.1 N

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