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
O150 N150 NQ150 mm40 mm

The handles of a pair of pliers are squeezed with 150 N each, 150 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 = 150 Na = 150 mmb = 40 mm
FO = N
2.Easy
15 kN1.2 m1.3 m1 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1 m below A. A load of 15 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 15 kNAD = 1.2 mAB = 2.5 mAC = 1 m
FCD = kN
3.Medium
15 kN6 m0.8 m1.7 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, 2.5 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 = 2.5 mheight of DE = 0.8 m
C = kN
4.Medium
4 kN4.8 m1.2 m1.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart. The legs meet at the pin C, 3 m high, and the horizontal tie DE is 1.2 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 = 4.8 mheight of C = 3 mheight of DE = 1.2 m
C = kN
5.Hard
4 kN1 kN6 m4 mABC

A uniform horizontal boom AB of weight 1 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 = 1 kNAB = 6 mAC = 4 m
T = kN
6.Hard
10 kN6 kN5 m2.5 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 2.5 m high and 1.5 m to the right of A. Member AB carries a vertical load of 10 kN at K, 0.375 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 10 kNQ = 6 kNL = 5 mH = 2.5 mhorizontal distance A to B = 1.5 mhorizontal distance A to K = 0.375 m
Ax = kN

Answer key

  1. 1. FO = 712.5 N
  2. 2. FCD = 48.81 kN
  3. 3. C = 15.21 kN
  4. 4. C = 3.333 kN
  5. 5. T = 8.112 kN
  6. 6. Ax = 0.75 kN

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