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 kN2.4 m1.5 m2.1 m0.72 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2.4 m apart. A vertical load of 15 kN acts on leg AC at the point K, 0.72 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 15 kNAB = 2.4 mhorizontal distance A to K = 0.72 m
By = kN
2.Easy
O60 N60 NQ100 mm40 mm

The handles of a pair of pliers are squeezed with 60 N each, 100 mm from the pin O, and the jaws grip a wire 40 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 60 Na = 100 mmb = 40 mm
FO = N
3.Medium
OAB80 NQ150 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (150 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 150 mmOB = 150 mm
FO = N
4.Medium
6 kN4 m0.8 m1.7 m1 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 6 kN acts on leg AC at K, 1 m (horizontally) from A. Find the tension T in the tie.

P = 6 kNAB = 4 mheight of C = 2.5 mheight of DE = 0.8 mhorizontal distance A to K = 1 m
T = kN
5.Hard
6 kN4.8 m0.8 m1.2 m1.44 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart, with its apex pin C 2 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 6 kN acts on leg AC at K, 1.44 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 4.8 mheight of C = 2 mheight of DE = 0.8 mhorizontal distance A to K = 1.44 m
C = kN
6.Hard
10 kN2 kN3 m1.5 mABC

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

W = 10 kNWb = 2 kNAB = 3 mAC = 1.5 m
A = kN

Answer key

  1. 1. By = 4.5 kN
  2. 2. FO = 210 N
  3. 3. FO = 113.1 N
  4. 4. T = 1.765 kN
  5. 5. C = 4.025 kN
  6. 6. A = 22.02 kN

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