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
10 kN2.4 m1 m3 m0.48 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2.4 m apart. A vertical load of 10 kN acts on leg AC at the point K, 0.48 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 10 kNAB = 2.4 mhorizontal distance A to K = 0.48 m
By = kN
2.Easy
4 kN4 m1.8 m2.2 m1.2 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4 m apart. A vertical load of 4 kN acts on leg AC at the point K, 1.2 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 4 kNAB = 4 mhorizontal distance A to K = 1.2 m
By = kN
3.Medium
10 kN6 m0.6 m1.8 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 2.4 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 10 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the tension T in the tie.

P = 10 kNAB = 6 mheight of C = 2.4 mheight of DE = 0.6 mhorizontal distance A to K = 1.8 m
T = kN
4.Medium
OAB50 NQ200 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 50 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 = 50 NOA = 200 mmOB = 150 mm
FO = N
5.Hard
2 kN0.5 kN2 m1.5 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, 1.5 m above A. A load of 2 kN hangs at B. Find the tension T in the cable.

W = 2 kNWb = 0.5 kNAB = 2 mAC = 1.5 m
T = kN
6.Hard
15 kN4 kN6 m2 m1.8 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 2 m high and 1.8 m to the right of A. Member AB carries a vertical load of 15 kN at K, 0.72 m (horizontally) from A, and a horizontal load of 4 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 15 kNQ = 4 kNL = 6 mH = 2 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.72 m
Ax = kN

Answer key

  1. 1. By = 2 kN
  2. 2. By = 1.2 kN
  3. 3. T = 5 kN
  4. 4. FO = 83.33 N
  5. 5. T = 3.75 kN
  6. 6. Ax = 2.58 kN

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