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
OAB150 NQ = ?240 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 150 N acts at A, 240 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 150 NOA = 240 mmOB = 120 mm
Q = N
2.Easy
OAB50 NQ = ?300 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 50 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 50 NOA = 300 mmOB = 60 mm
Q = N
3.Medium
8 kN8 m2.5 m1.2 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 2.5 m above the ground and 1.2 m to the right of A. A vertical load of 8 kN acts on member AB at K, 0.3 m (horizontally) from A. Find the force FBC in member BC.

P = 8 kNL = 8 mH = 2.5 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.3 m
FBC = kN
4.Medium
20 kN5 m2.5 m2.25 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 2.5 m above the ground and 2.25 m to the right of A. A vertical load of 20 kN acts on member AB at K, 0.9 m (horizontally) from A. Find the force FBC in member BC.

P = 20 kNL = 5 mH = 2.5 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 0.9 m
FBC = kN
5.Hard
w = 4 kN/m12 kN1.6 m2 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 4 kN/m over its full length and a point load of 12 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 12 kNAD = 1.6 mAB = 3.6 mAC = 1.2 m
FCD = kN
6.Hard
w = 3 kN/m12 kN1.2 m2.4 m1 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1 m below A). The beam carries a uniform load of 3 kN/m over its full length and a point load of 12 kN at its free end B. Find the force FCD in the strut.

w = 3 kN/mP = 12 kNAD = 1.2 mAB = 3.6 mAC = 1 m
FCD = kN

Answer key

  1. 1. Q = 300 N
  2. 2. Q = 250 N
  3. 3. FBC = 0.8694 kN
  4. 4. FBC = 5.352 kN
  5. 5. FCD = 72 kN
  6. 6. FCD = 81.54 kN

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