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
6 kN2 m1.2 m0.8 m0.4 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 6 kN acts on leg AC at the point K, 0.4 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 6 kNAB = 2 mhorizontal distance A to K = 0.4 m
By = kN
2.Easy
OAB250 NQ = ?100 mm50 mm

The bell crank shown turns about the pin O. A vertical force of 250 N acts at A, 100 mm from O, and is balanced by a horizontal force Q at B, 50 mm above O. Find Q.

F = 250 NOA = 100 mmOB = 50 mm
Q = N
3.Medium
15 kN2.4 m1 m2.6 m0.9 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 1 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.9 m (horizontally) from A. Find the tension T in the tie.

P = 15 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 1 mhorizontal distance A to K = 0.9 m
T = kN
4.Medium
15 kN5 m1 m3.5 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 4.5 m high and the horizontal tie DE 1 m above the ground. A vertical load of 15 kN acts on leg AC at K, 1 m (horizontally) from A. Find the tension T in the tie.

P = 15 kNAB = 5 mheight of C = 4.5 mheight of DE = 1 mhorizontal distance A to K = 1 m
T = kN
5.Hard
10 kN1 kN5 m3 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 3 m above A. A load of 10 kN hangs at B. Find the magnitude of the pin reaction A.

W = 10 kNWb = 1 kNAB = 5 mAC = 3 m
A = kN
6.Hard
5 kN8 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 high and 0.9 m to the right of A. Member AB carries a vertical load of 5 kN at K, 0.675 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 8 kNL = 6 mH = 4 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.675 m
Ax = kN

Answer key

  1. 1. By = 1.2 kN
  2. 2. Q = 500 N
  3. 3. T = 2.596 kN
  4. 4. T = 2.143 kN
  5. 5. A = 17.51 kN
  6. 6. Ax = 0.4828 kN

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