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 kN1.6 m0.9 m0.8 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.8 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 = 1.6 mAB = 2.5 mAC = 0.8 m
FCD = kN
2.Easy
O80 N80 NQ150 mm25 mm

The handles of a pair of pliers are squeezed with 80 N each, 150 mm from the pin O, and the jaws grip a wire 25 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 150 mmb = 25 mm
FO = N
3.Medium
10 kN3 m0.8 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 2.4 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 10 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 3 mheight of C = 2.4 mheight of DE = 0.8 m
C = kN
4.Medium
4 kN3.2 m1.5 m3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart. The legs meet at the pin C, 4.5 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 = 3.2 mheight of C = 4.5 mheight of DE = 1.5 m
C = kN
5.Hard
15 kN2 kN2.5 m1.5 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, 1.5 m above A. A load of 15 kN hangs at B. Find the tension T in the cable.

W = 15 kNWb = 2 kNAB = 2.5 mAC = 1.5 m
T = kN
6.Hard
6 kN3.2 m1.2 m2.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart. The legs meet at the pin C, 4 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 6 kN to the right acts at C. Find the tension T in the tie.

P = 6 kNAB = 3.2 mheight of C = 4 mheight of DE = 1.2 m
T = kN

Answer key

  1. 1. FCD = 27.95 kN
  2. 2. FO = 560 N
  3. 3. C = 6.854 kN
  4. 4. C = 2.267 kN
  5. 5. T = 31.1 kN
  6. 6. T = 4.286 kN

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