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
10 kN1 m1.5 m0.8 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.8 m below A. A load of 10 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 10 kNAD = 1 mAB = 2.5 mAC = 0.8 m
FCD = kN
2.Easy
5 kN1 m2 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 the free end B. Neglect the weights. Find the force FCD in the strut.

P = 5 kNAD = 1 mAB = 3 mAC = 0.75 m
FCD = kN
3.Medium
6 kN3 m3 m0.9 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 3 m above the ground and 0.9 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.36 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 3 mH = 3 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.36 m
FBC = kN
4.Medium
2 kN3.2 m0.6 m1.8 m0.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart, with its apex pin C 2.4 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 2 kN acts on leg AC at K, 0.8 m (horizontally) from A. Find the tension T in the tie.

P = 2 kNAB = 3.2 mheight of C = 2.4 mheight of DE = 0.6 mhorizontal distance A to K = 0.8 m
T = kN
5.Hard
F = ?3000 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 3000 N at the slider C? Neglect friction and weights.

Q = 3000 NAB = BC = 200 mmh = 15 mm
F = N
6.Hard
20 kN2.4 m1.5 m1.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 3 m high, and are tied by the horizontal bar DE at 1.5 m. A horizontal force of 20 kN to the right acts at C. Find the tension T in the tie.

P = 20 kNAB = 2.4 mheight of C = 3 mheight of DE = 1.5 m
T = kN

Answer key

  1. 1. FCD = 40.02 kN
  2. 2. FCD = 25 kN
  3. 3. FBC = 0.8789 kN
  4. 4. T = 0.4444 kN
  5. 5. F = 451.3 N
  6. 6. T = 20 kN

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