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
15 kN3 m0.8 m1.6 m0.9 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3 m apart. A vertical load of 15 kN acts on leg AC at the point K, 0.9 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 15 kNAB = 3 mhorizontal distance A to K = 0.9 m
By = kN
2.Easy
O40 N40 NQ80 mm25 mm

The handles of a pair of pliers are squeezed with 40 N each, 80 mm from the pin O, and the jaws grip a wire 25 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 40 Na = 80 mmb = 25 mm
FO = N
3.Medium
OAB150 NQ200 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 150 N at A (200 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 150 NOA = 200 mmOB = 150 mm
FO = N
4.Medium
12 kN6 m4 m0.9 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 6 m apart, and B is 4 m above the ground and 0.9 m to the right of A. A vertical load of 12 kN acts on member AB at K, 0.36 m (horizontally) from A. Find the force FBC in member BC.

P = 12 kNL = 6 mH = 4 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.36 m
FBC = kN
5.Hard
8 kN0.5 kN3 m2.5 mABC

A uniform horizontal boom AB of weight 0.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2.5 m above A. A load of 8 kN hangs at B. Find the tension T in the cable.

W = 8 kNWb = 0.5 kNAB = 3 mAC = 2.5 m
T = kN
6.Hard
15 kN1.5 kN2.5 m1.5 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, 1.5 m above A. A load of 15 kN hangs at B. Find the tension T in the cable.

W = 15 kNWb = 1.5 kNAB = 2.5 mAC = 1.5 m
T = kN

Answer key

  1. 1. By = 4.5 kN
  2. 2. FO = 168 N
  3. 3. FO = 250 N
  4. 4. FBC = 1.167 kN
  5. 5. T = 12.89 kN
  6. 6. T = 30.61 kN

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