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 = ?200 mm75 mm

The bell crank shown turns about the pin O. A vertical force of 300 N acts at A, 200 mm from O, and is balanced by a horizontal force Q at B, 75 mm above O. Find Q.

F = 300 NOA = 200 mmOB = 75 mm
Q = N
2.Easy
6 kN5 m0.8 m1.7 m1.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 5 m apart. A vertical load of 6 kN acts on leg AC at the point K, 1.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 6 kNAB = 5 mhorizontal distance A to K = 1.5 m
By = kN
3.Medium
6 kN4 m1 m1.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 2.5 m high, and the horizontal tie DE is 1 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 = 4 mheight of C = 2.5 mheight of DE = 1 m
C = kN
4.Medium
20 kN4 m3 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 3 m above the ground and 1.8 m to the right of A. A vertical load of 20 kN acts on member AB at K, 1.08 m (horizontally) from A. Find the force FBC in member BC.

P = 20 kNL = 4 mH = 3 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 1.08 m
FBC = kN
5.Hard
20 kN4 m1 m1.4 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 2.4 m high, and are tied by the horizontal bar DE at 1 m. A horizontal force of 20 kN to the right acts at C. Find the tension T in the tie.

P = 20 kNAB = 4 mheight of C = 2.4 mheight of DE = 1 m
T = kN
6.Hard
12 kN6 m1.5 m3 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 12 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 12 kNAB = 6 mheight of C = 4.5 mheight of DE = 1.5 mhorizontal distance A to K = 1.5 m
C = kN

Answer key

  1. 1. Q = 800 N
  2. 2. By = 1.8 kN
  3. 3. C = 5 kN
  4. 4. FBC = 6.696 kN
  5. 5. T = 17.14 kN
  6. 6. C = 4.243 kN

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