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 kN4 m1.2 m1.8 m0.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4 m apart. A vertical load of 6 kN acts on leg AC at the point K, 0.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 6 kNAB = 4 mhorizontal distance A to K = 0.5 m
By = kN
2.Easy
O150 N150 NQ = ?110 mm20 mm

A hand squeezes the handles of a pair of pliers with 150 N each, 110 mm from the pin O. The jaws grip a bolt 20 mm from the pin. Find the gripping force Q on the bolt.

F = 150 Na = 110 mmb = 20 mm
Q = N
3.Medium
15 kN6 m0.8 m2.2 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, 3 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 15 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 6 mheight of C = 3 mheight of DE = 0.8 m
C = kN
4.Medium
4 kN4 m1.5 m2.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 4 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 4 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 4 mheight of C = 4 mheight of DE = 1.5 m
C = kN
5.Hard
4 kN8 kN5 m4 m1.5 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 4 m high and 1.5 m to the right of A. Member AB carries a vertical load of 4 kN at K, 1.125 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 = 4 kNQ = 8 kNL = 5 mH = 4 mhorizontal distance A to B = 1.5 mhorizontal distance A to K = 1.125 m
Ax = kN
6.Hard
4 kN3 kN3 m4 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 4 m above A. A load of 4 kN hangs at B. Find the tension T in the cable.

W = 4 kNWb = 3 kNAB = 3 mAC = 4 m
T = kN

Answer key

  1. 1. By = 0.75 kN
  2. 2. Q = 825 N
  3. 3. C = 12.68 kN
  4. 4. C = 2.561 kN
  5. 5. Ax = 1.613 kN
  6. 6. T = 6.875 kN

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