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
OAB300 NQ = ?240 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 300 N acts at A, 240 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 300 NOA = 240 mmOB = 80 mm
Q = N
2.Easy
O50 N50 NQ120 mm40 mm

The handles of a pair of pliers are squeezed with 50 N each, 120 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 = 50 Na = 120 mmb = 40 mm
FO = N
3.Medium
OAB100 NQ120 mm60 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 100 N at A (120 mm from O) is balanced by a horizontal force at B (60 mm above O). Find the magnitude of the pin reaction FO.

F = 100 NOA = 120 mmOB = 60 mm
FO = N
4.Medium
4 kN4.8 m0.8 m2.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart. The legs meet at the pin C, 3.6 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 4 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 4.8 mheight of C = 3.6 mheight of DE = 0.8 m
C = kN
5.Hard
5 kN5 kN6 m3 m2.7 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 6 m apart, and B is 3 m high and 2.7 m to the right of A. Member AB carries a vertical load of 5 kN at K, 1.08 m (horizontally) from A, and a horizontal load of 5 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 5 kNL = 6 mH = 3 mhorizontal distance A to B = 2.7 mhorizontal distance A to K = 1.08 m
Ax = kN
6.Hard
w = 4 kN/m12 kN1.6 m0.9 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 4 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 = 4 kN/mP = 12 kNAD = 1.6 mAB = 2.5 mAC = 1.5 m
FCD = kN

Answer key

  1. 1. Q = 900 N
  2. 2. FO = 200 N
  3. 3. FO = 223.6 N
  4. 4. C = 2.634 kN
  5. 5. Ax = 1.26 kN
  6. 6. FCD = 38.84 kN

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