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
4 kN4.8 m1 m1.5 m1.44 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 4 kN acts on leg AC at the point K, 1.44 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 4 kNAB = 4.8 mhorizontal distance A to K = 1.44 m
By = kN
2.Easy
5 kN2 m1.2 m2.4 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 5 kN acts on leg AC at the point K, 0.75 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 5 kNAB = 2 mhorizontal distance A to K = 0.75 m
By = kN
3.Medium
5 kN0.8 m1.6 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 5 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 5 kNAD = 0.8 mAB = 2.4 mAC = 0.75 m
A = kN
4.Medium
OAB100 NQ240 mm100 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 (100 mm above O). Find the magnitude of the pin reaction FO.

F = 100 NOA = 240 mmOB = 100 mm
FO = N
5.Hard
w = 1.5 kN/m6 kN2 m1.6 m0.6 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.6 m below A). The beam carries a uniform load of 1.5 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 = 1.5 kN/mP = 6 kNAD = 2 mAB = 3.6 mAC = 0.6 m
FCD = kN
6.Hard
F = ?2000 N25 mmABC

A toggle press has two equal links AB and BC, each 200 mm long between pins. The joint B sits 25 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 2000 N at the slider C? Neglect friction and weights.

Q = 2000 NAB = BC = 200 mmh = 25 mm
F = N

Answer key

  1. 1. By = 1.2 kN
  2. 2. By = 1.875 kN
  3. 3. A = 18.87 kN
  4. 4. FO = 260 N
  5. 5. FCD = 54.5 kN
  6. 6. F = 504 N

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