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
O40 N40 NQ110 mm25 mm

The handles of a pair of pliers are squeezed with 40 N each, 110 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 = 40 Na = 110 mmb = 25 mm
FO = N
2.Easy
10 kN4 m1 m3 m1 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4 m apart. A vertical load of 10 kN acts on leg AC at the point K, 1 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 10 kNAB = 4 mhorizontal distance A to K = 1 m
By = kN
3.Medium
20 kN2 m1.2 m3.3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2 m apart. The legs meet at the pin C, 4.5 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 20 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 2 mheight of C = 4.5 mheight of DE = 1.2 m
C = kN
4.Medium
OAB250 NQ150 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 250 N at A (150 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 250 NOA = 150 mmOB = 150 mm
FO = N
5.Hard
5 kN1 kN3 m3 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 3 m above A. A load of 5 kN hangs at B. Find the magnitude of the pin reaction A.

W = 5 kNWb = 1 kNAB = 3 mAC = 3 m
A = kN
6.Hard
w = 1 kN/m12 kN1.2 m2.4 m0.75 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.75 m below A). The beam carries a uniform load of 1 kN/m over its full length and a point load of 12 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 12 kNAD = 1.2 mAB = 3.6 mAC = 0.75 m
FCD = kN

Answer key

  1. 1. FO = 216 N
  2. 2. By = 2.5 kN
  3. 3. C = 10.45 kN
  4. 4. FO = 353.6 N
  5. 5. A = 5.523 kN
  6. 6. FCD = 78.11 kN

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