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
6 kN1 m1.4 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 6 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 6 kNAD = 1 mAB = 2.4 mAC = 1.2 m
FCD = kN
2.Easy
OAB400 NQ = ?200 mm75 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 200 mm from O, and is balanced by a horizontal force Q at B, 75 mm above O. Find Q.

F = 400 NOA = 200 mmOB = 75 mm
Q = N
3.Medium
OAB150 NQ300 mm75 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 150 N at A (300 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction FO.

F = 150 NOA = 300 mmOB = 75 mm
FO = N
4.Medium
4 kN6 m2.5 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 2.5 m above the ground and 3.6 m to the right of A. A vertical load of 4 kN acts on member AB at K, 1.44 m (horizontally) from A. Find the force FBC in member BC.

P = 4 kNL = 6 mH = 2.5 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 1.44 m
FBC = kN
5.Hard
4 kN1.5 kN4 m2.5 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2.5 m above A. A load of 4 kN hangs at B. Find the tension T in the cable.

W = 4 kNWb = 1.5 kNAB = 4 mAC = 2.5 m
T = kN
6.Hard
8 kN4 kN6 m3 m1.8 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 3 m high and 1.8 m to the right of A. Member AB carries a vertical load of 8 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 = 8 kNQ = 4 kNL = 6 mH = 3 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.9 m
Ax = kN

Answer key

  1. 1. FCD = 18.74 kN
  2. 2. Q = 1067 N
  3. 3. FO = 618.5 N
  4. 4. FBC = 1.331 kN
  5. 5. T = 8.962 kN
  6. 6. Ax = 0.48 kN

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