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
O60 N60 NQ90 mm18 mm

The handles of a pair of pliers are squeezed with 60 N each, 90 mm from the pin O, and the jaws grip a wire 18 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 60 Na = 90 mmb = 18 mm
FO = N
2.Easy
3 kN0.75 m0.75 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 3 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 3 kNAD = 0.75 mAB = 1.5 mAC = 0.75 m
FCD = kN
3.Medium
15 kN0.6 m1.4 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 15 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 15 kNAD = 0.6 mAB = 2 mAC = 0.75 m
A = kN
4.Medium
12 kN0.5 m1 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 12 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 12 kNAD = 0.5 mAB = 1.5 mAC = 0.75 m
A = kN
5.Hard
20 kN4.8 m0.6 m1.9 m1.44 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 20 kN acts on leg AC at K, 1.44 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 4.8 mheight of C = 2.5 mheight of DE = 0.6 mhorizontal distance A to K = 1.44 m
C = kN
6.Hard
w = 2.5 kN/m3 kN1.6 m2 m1.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.5 m below A). The beam carries a uniform load of 2.5 kN/m over its full length and a point load of 3 kN at its free end B. Find the force FCD in the strut.

w = 2.5 kN/mP = 3 kNAD = 1.6 mAB = 3.6 mAC = 1.5 m
FCD = kN

Answer key

  1. 1. FO = 360 N
  2. 2. FCD = 8.485 kN
  3. 3. A = 53.15 kN
  4. 4. A = 33.94 kN
  5. 5. C = 9.666 kN
  6. 6. FCD = 24.67 kN

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