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
4 kN0.8 m0.7 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 m below A. A load of 4 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 4 kNAD = 0.8 mAB = 1.5 mAC = 1.2 m
FCD = kN
2.Easy
12 kN4 m1 m1 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 12 kN acts on leg AC at the point K, 0.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 4 mhorizontal distance A to K = 0.5 m
By = kN
3.Medium
8 kN2.4 m1.2 m3.3 m0.6 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 4.5 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 8 kN acts on leg AC at K, 0.6 m (horizontally) from A. Find the tension T in the tie.

P = 8 kNAB = 2.4 mheight of C = 4.5 mheight of DE = 1.2 mhorizontal distance A to K = 0.6 m
T = kN
4.Medium
2 kN4.8 m1.5 m3 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, 4.5 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 2 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 2 kNAB = 4.8 mheight of C = 4.5 mheight of DE = 1.5 m
C = kN
5.Hard
4 kN2.4 m1.5 m3 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, 4.5 m high, and are tied by the horizontal bar DE at 1.5 m. A horizontal force of 4 kN to the right acts at C. Find the tension T in the tie.

P = 4 kNAB = 2.4 mheight of C = 4.5 mheight of DE = 1.5 m
T = kN
6.Hard
10 kN2 kN5 m2 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 m above A. A load of 10 kN hangs at B. Find the tension T in the cable.

W = 10 kNWb = 2 kNAB = 5 mAC = 2 m
T = kN

Answer key

  1. 1. FCD = 9.014 kN
  2. 2. By = 1.5 kN
  3. 3. T = 0.7273 kN
  4. 4. C = 1.281 kN
  5. 5. T = 3 kN
  6. 6. T = 29.62 kN

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