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
2 kN2 m0.8 m2.2 m0.75 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 2 kN acts on leg AC at the point K, 0.75 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 2 kNAB = 2 mhorizontal distance A to K = 0.75 m
By = kN
2.Easy
15 kN1 m1.5 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 15 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 15 kNAD = 1 mAB = 2.5 mAC = 1.5 m
FCD = kN
3.Medium
OAB100 NQ240 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 100 N at A (240 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction FO.

F = 100 NOA = 240 mmOB = 80 mm
FO = N
4.Medium
8 kN4 m1.5 m3 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 8 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the tension T in the tie.

P = 8 kNAB = 4 mheight of C = 4.5 mheight of DE = 1.5 mhorizontal distance A to K = 1.5 m
T = kN
5.Hard
F = ?2500 N10 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 10 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 2500 N at the slider C? Neglect friction and weights.

Q = 2500 NAB = BC = 120 mmh = 10 mm
F = N
6.Hard
8 kN6 m0.8 m1.6 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 2.4 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 8 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 6 mheight of C = 2.4 mheight of DE = 0.8 mhorizontal distance A to K = 1.5 m
C = kN

Answer key

  1. 1. By = 0.75 kN
  2. 2. FCD = 45.07 kN
  3. 3. FO = 316.2 N
  4. 4. T = 2 kN
  5. 5. F = 418.1 N
  6. 6. C = 4.25 kN

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