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 kN2 m0.8 m3.2 m0.4 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 8 kN acts on leg AC at the point K, 0.4 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 8 kNAB = 2 mhorizontal distance A to K = 0.4 m
By = kN
2.Easy
12 kN1.5 m1.5 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 12 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 12 kNAD = 1.5 mAB = 3 mAC = 1 m
FCD = kN
3.Medium
10 kN4 m3 m2.4 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 3 m above the ground and 2.4 m to the right of A. A vertical load of 10 kN acts on member AB at K, 0.6 m (horizontally) from A. Find the force FBC in member BC.

P = 10 kNL = 4 mH = 3 mhorizontal distance A to B = 2.4 mhorizontal distance A to K = 0.6 m
FBC = kN
4.Medium
8 kN5 m4 m0.75 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 above the ground and 0.75 m to the right of A. A vertical load of 8 kN acts on member AB at K, 0.45 m (horizontally) from A. Find the force FBC in member BC.

P = 8 kNL = 5 mH = 4 mhorizontal distance A to B = 0.75 mhorizontal distance A to K = 0.45 m
FBC = kN
5.Hard
4 kN1 kN4 m3 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, 3 m above A. A load of 4 kN hangs at B. Find the tension T in the cable.

W = 4 kNWb = 1 kNAB = 4 mAC = 3 m
T = kN
6.Hard
w = 2.5 kN/m3 kN0.6 m0.9 m0.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.5 m below A). The beam carries a uniform load of 2.5 kN/m over its full length and a point load of 3 kN at its free end B. Find the force FCD in the strut.

w = 2.5 kN/mP = 3 kNAD = 0.6 mAB = 1.5 mAC = 0.5 m
FCD = kN

Answer key

  1. 1. By = 1.6 kN
  2. 2. FCD = 43.27 kN
  3. 3. FBC = 1.7 kN
  4. 4. FBC = 1.051 kN
  5. 5. T = 7.5 kN
  6. 6. FCD = 19.04 kN

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