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 kN0.75 m1.25 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 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 = 0.75 mAB = 2 mAC = 1.2 m
FCD = kN
2.Easy
6 kN0.6 m1.4 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 the free end B. Neglect the weights. Find the force FCD in the strut.

P = 6 kNAD = 0.6 mAB = 2 mAC = 1 m
FCD = kN
3.Medium
OAB150 NQ240 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 150 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 = 150 NOA = 240 mmOB = 80 mm
FO = N
4.Medium
3 kN0.75 m1.65 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 3 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 3 kNAD = 0.75 mAB = 2.4 mAC = 0.8 m
A = kN
5.Hard
w = 1.5 kN/m5 kN2 m0.5 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 5 kN at its free end B. Find the force FCD in the strut.

w = 1.5 kN/mP = 5 kNAD = 2 mAB = 2.5 mAC = 0.5 m
FCD = kN
6.Hard
F = ?3000 N20 mmABC

A toggle press has two equal links AB and BC, each 120 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 3000 N at the slider C? Neglect friction and weights.

Q = 3000 NAB = BC = 120 mmh = 20 mm
F = N

Answer key

  1. 1. FCD = 31.45 kN
  2. 2. FCD = 23.32 kN
  3. 3. FO = 474.3 N
  4. 4. A = 11.16 kN
  5. 5. FCD = 35.43 kN
  6. 6. F = 1014 N

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