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
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
2.Easy
OAB400 NQ = ?300 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 400 NOA = 300 mmOB = 150 mm
Q = N
3.Medium
15 kN2.4 m1.2 m1.3 m0.3 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.3 m (horizontally) from A. Find the tension T in the tie.

P = 15 kNAB = 2.4 mheight of C = 2.5 mheight of DE = 1.2 mhorizontal distance A to K = 0.3 m
T = kN
4.Medium
OAB80 NQ200 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (200 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 200 mmOB = 80 mm
FO = N
5.Hard
w = 4 kN/m4 kN2 m1.6 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 4 kN/m over its full length and a point load of 4 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 4 kNAD = 2 mAB = 3.6 mAC = 0.5 m
FCD = kN
6.Hard
F = ?5000 N15 mmABC

A toggle press has two equal links AB and BC, each 200 mm long between pins. The joint B sits 15 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 5000 N at the slider C? Neglect friction and weights.

Q = 5000 NAB = BC = 200 mmh = 15 mm
F = N

Answer key

  1. 1. Q = 520.8 N
  2. 2. Q = 800 N
  3. 3. T = 1.731 kN
  4. 4. FO = 215.4 N
  5. 5. FCD = 83.12 kN
  6. 6. F = 752.1 N

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