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
OAB100 NQ = ?180 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 100 N acts at A, 180 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 100 NOA = 180 mmOB = 60 mm
Q = N
2.Easy
8 kN0.5 m1 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 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 = 0.5 mAB = 1.5 mAC = 0.75 m
FCD = kN
3.Medium
10 kN1 m1 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 10 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 10 kNAD = 1 mAB = 2 mAC = 0.6 m
A = kN
4.Medium
20 kN6 m2 m3.6 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 6 m apart, and B is 2 m above the ground and 3.6 m to the right of A. A vertical load of 20 kN acts on member AB at K, 1.44 m (horizontally) from A. Find the force FBC in member BC.

P = 20 kNL = 6 mH = 2 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 1.44 m
FBC = kN
5.Hard
15 kN4 kN8 m2 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 2 m high and 3.6 m to the right of A. Member AB carries a vertical load of 15 kN at K, 0.9 m (horizontally) from A, and a horizontal load of 4 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 15 kNQ = 4 kNL = 8 mH = 2 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 0.9 m
Ax = kN
6.Hard
12 kN1 kN5 m2 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 12 kN hangs at B. Find the magnitude of the pin reaction A.

W = 12 kNWb = 1 kNAB = 5 mAC = 2 m
A = kN

Answer key

  1. 1. Q = 300 N
  2. 2. FCD = 28.84 kN
  3. 3. A = 34.8 kN
  4. 4. FBC = 7.498 kN
  5. 5. Ax = 1.913 kN
  6. 6. A = 31.25 kN

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