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
OAB120 NQ = ?300 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 120 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 120 NOA = 300 mmOB = 80 mm
Q = N
2.Easy
OAB250 NQ = ?250 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 250 N acts at A, 250 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 250 NOA = 250 mmOB = 120 mm
Q = N
3.Medium
OAB100 NQ300 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 100 N at A (300 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 100 NOA = 300 mmOB = 150 mm
FO = N
4.Medium
6 kN3 m3 m0.45 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 3 m above the ground and 0.45 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.3375 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 3 mH = 3 mhorizontal distance A to B = 0.45 mhorizontal distance A to K = 0.3375 m
FBC = kN
5.Hard
6 kN1.5 kN6 m1 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, 1 m above A. A load of 6 kN hangs at B. Find the tension T in the cable.

W = 6 kNWb = 1.5 kNAB = 6 mAC = 1 m
T = kN
6.Hard
w = 2.5 kN/m6 kN2 m0.5 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 6 kN at its free end B. Find the force FCD in the strut.

w = 2.5 kN/mP = 6 kNAD = 2 mAB = 2.5 mAC = 0.5 m
FCD = kN

Answer key

  1. 1. Q = 450 N
  2. 2. Q = 520.8 N
  3. 3. FO = 223.6 N
  4. 4. FBC = 0.8859 kN
  5. 5. T = 41.06 kN
  6. 6. FCD = 47.03 kN

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