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
12 kN0.6 m1.4 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 12 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 12 kNAD = 0.6 mAB = 2 mAC = 0.6 m
FCD = kN
2.Easy
12 kN5 m1.2 m1.2 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 12 kN acts on leg AC at the point K, 1.875 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 5 mhorizontal distance A to K = 1.875 m
By = kN
3.Medium
4 kN2.4 m0.8 m2.8 m0.72 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 3.6 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.72 m (horizontally) from A. Find the tension T in the tie.

P = 4 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 0.8 mhorizontal distance A to K = 0.72 m
T = kN
4.Medium
5 kN2 m0.5 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 5 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 5 kNAD = 2 mAB = 2.5 mAC = 1.5 m
A = kN
5.Hard
w = 1.5 kN/m8 kN0.5 m1 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 1.5 kN/m over its full length and a point load of 8 kN at its free end B. Find the force FCD in the strut.

w = 1.5 kN/mP = 8 kNAD = 0.5 mAB = 1.5 mAC = 0.5 m
FCD = kN
6.Hard
F = ?4000 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 4000 N at the slider C? Neglect friction and weights.

Q = 4000 NAB = BC = 200 mmh = 15 mm
F = N

Answer key

  1. 1. FCD = 56.57 kN
  2. 2. By = 4.5 kN
  3. 3. T = 0.5143 kN
  4. 4. A = 8.427 kN
  5. 5. FCD = 38.71 kN
  6. 6. F = 601.7 N

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