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
OAB80 NQ = ?150 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 80 N acts at A, 150 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 80 NOA = 150 mmOB = 150 mm
Q = N
2.Easy
O60 N60 NQ110 mm40 mm

The handles of a pair of pliers are squeezed with 60 N each, 110 mm from the pin O, and the jaws grip a wire 40 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 60 Na = 110 mmb = 40 mm
FO = N
3.Medium
6 kN2.4 m1.2 m1.3 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, 2.5 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 6 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 2.4 mheight of C = 2.5 mheight of DE = 1.2 m
C = kN
4.Medium
OAB80 NQ300 mm75 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (300 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 300 mmOB = 75 mm
FO = N
5.Hard
10 kN3.2 m1 m1.4 m1.2 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 1 m above the ground. A vertical load of 10 kN acts on leg AC at K, 1.2 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 3.2 mheight of C = 2.4 mheight of DE = 1 mhorizontal distance A to K = 1.2 m
C = kN
6.Hard
w = 2 kN/m10 kN1 m1.4 m1.2 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.2 m below A). The beam carries a uniform load of 2 kN/m over its full length and a point load of 10 kN at its free end B. Find the force FCD in the strut.

w = 2 kN/mP = 10 kNAD = 1 mAB = 2.4 mAC = 1.2 m
FCD = kN

Answer key

  1. 1. Q = 80 N
  2. 2. FO = 225 N
  3. 3. C = 4.083 kN
  4. 4. FO = 329.8 N
  5. 5. C = 5.695 kN
  6. 6. FCD = 38.74 kN

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