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 kN4.8 m1 m3 m1.44 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 4 kN acts on leg AC at the point K, 1.44 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 4 kNAB = 4.8 mhorizontal distance A to K = 1.44 m
By = kN
2.Easy
12 kN0.75 m1.75 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 12 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 12 kNAD = 0.75 mAB = 2.5 mAC = 0.8 m
FCD = kN
3.Medium
OAB300 NQ200 mm120 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 300 N at A (200 mm from O) is balanced by a horizontal force at B (120 mm above O). Find the magnitude of the pin reaction FO.

F = 300 NOA = 200 mmOB = 120 mm
FO = N
4.Medium
5 kN8 m3 m3.6 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 3 m above the ground and 3.6 m to the right of A. A vertical load of 5 kN acts on member AB at K, 0.9 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 8 mH = 3 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 0.9 m
FBC = kN
5.Hard
w = 1 kN/m10 kN1 m0.5 m0.6 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.6 m below A). The beam carries a uniform load of 1 kN/m over its full length and a point load of 10 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 10 kNAD = 1 mAB = 1.5 mAC = 0.6 m
FCD = kN
6.Hard
w = 1.5 kN/m15 kN1.6 m0.9 m1.2 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.2 m below A). The beam carries a uniform load of 1.5 kN/m over its full length and a point load of 15 kN at its free end B. Find the force FCD in the strut.

w = 1.5 kN/mP = 15 kNAD = 1.6 mAB = 2.5 mAC = 1.2 m
FCD = kN

Answer key

  1. 1. By = 1.2 kN
  2. 2. FCD = 54.83 kN
  3. 3. FO = 583.1 N
  4. 4. FBC = 0.9985 kN
  5. 5. FCD = 31.34 kN
  6. 6. FCD = 43.95 kN

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