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
8 kN0.8 m1.2 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 8 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 8 kNAD = 0.8 mAB = 2 mAC = 1 m
FCD = kN
2.Easy
O80 N80 NQ = ?140 mm20 mm

A hand squeezes the handles of a pair of pliers with 80 N each, 140 mm from the pin O. The jaws grip a bolt 20 mm from the pin. Find the gripping force Q on the bolt.

F = 80 Na = 140 mmb = 20 mm
Q = N
3.Medium
5 kN4 m1.2 m0.8 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, 2 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 5 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 4 mheight of C = 2 mheight of DE = 1.2 m
C = kN
4.Medium
8 kN2.4 m1.2 m0.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 2 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 2.4 mheight of C = 2 mheight of DE = 1.2 m
C = kN
5.Hard
20 kN5 m1 m2.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 3.6 m high, and are tied by the horizontal bar DE at 1 m. A horizontal force of 20 kN to the right acts at C. Find the tension T in the tie.

P = 20 kNAB = 5 mheight of C = 3.6 mheight of DE = 1 m
T = kN
6.Hard
15 kN2 kN2 m2.5 mABC

A uniform horizontal boom AB of weight 2 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2.5 m above A. A load of 15 kN hangs at B. Find the tension T in the cable.

W = 15 kNWb = 2 kNAB = 2 mAC = 2.5 m
T = kN

Answer key

  1. 1. FCD = 25.61 kN
  2. 2. Q = 560 N
  3. 3. C = 6.731 kN
  4. 4. C = 7.211 kN
  5. 5. T = 13.85 kN
  6. 6. T = 20.49 kN

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