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 kN5 m1 m2 m1.875 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 5 m apart. A vertical load of 6 kN acts on leg AC at the point K, 1.875 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 6 kNAB = 5 mhorizontal distance A to K = 1.875 m
By = kN
2.Easy
4 kN2 m1.5 m1 m0.25 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 4 kN acts on leg AC at the point K, 0.25 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 4 kNAB = 2 mhorizontal distance A to K = 0.25 m
By = kN
3.Medium
OAB50 NQ150 mm75 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 50 N at A (150 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction FO.

F = 50 NOA = 150 mmOB = 75 mm
FO = N
4.Medium
6 kN1.6 m2 m1 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 m below A. A load of 6 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 6 kNAD = 1.6 mAB = 3.6 mAC = 1 m
A = kN
5.Hard
F = ?1500 N20 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 20 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1500 N at the slider C? Neglect friction and weights.

Q = 1500 NAB = BC = 150 mmh = 20 mm
F = N
6.Hard
6 kN1.5 kN2 m3 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, 3 m above A. A load of 6 kN hangs at B. Find the tension T in the cable.

W = 6 kNWb = 1.5 kNAB = 2 mAC = 3 m
T = kN

Answer key

  1. 1. By = 2.25 kN
  2. 2. By = 0.5 kN
  3. 3. FO = 111.8 N
  4. 4. A = 22.87 kN
  5. 5. F = 403.6 N
  6. 6. T = 8.112 kN

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