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
O200 N200 NQ100 mm25 mm

The handles of a pair of pliers are squeezed with 200 N each, 100 mm from the pin O, and the jaws grip a wire 25 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 200 Na = 100 mmb = 25 mm
FO = N
2.Easy
O200 N200 NQ100 mm18 mm

The handles of a pair of pliers are squeezed with 200 N each, 100 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 = 200 Na = 100 mmb = 18 mm
FO = N
3.Medium
OAB150 NQ300 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 150 N at A (300 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 150 NOA = 300 mmOB = 100 mm
FO = N
4.Medium
12 kN0.8 m1.2 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 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 = 0.8 mAB = 2 mAC = 0.5 m
A = kN
5.Hard
6 kN10 kN8 m2 m1.2 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 2 m high and 1.2 m to the right of A. Member AB carries a vertical load of 6 kN at K, 0.3 m (horizontally) from A, and a horizontal load of 10 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 6 kNQ = 10 kNL = 8 mH = 2 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.3 m
Ax = kN
6.Hard
w = 3 kN/m5 kN0.6 m0.9 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 3 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 = 3 kN/mP = 5 kNAD = 0.6 mAB = 1.5 mAC = 0.5 m
FCD = kN

Answer key

  1. 1. FO = 1000 N
  2. 2. FO = 1311 N
  3. 3. FO = 474.3 N
  4. 4. A = 51.26 kN
  5. 5. Ax = 0.735 kN
  6. 6. FCD = 28.31 kN

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