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
6 kN3 m1.8 m1.8 m1.125 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3 m apart. A vertical load of 6 kN acts on leg AC at the point K, 1.125 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 6 kNAB = 3 mhorizontal distance A to K = 1.125 m
By = kN
2.Easy
6 kN3 m1.8 m1.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 3.6 m high, and are tied together by the horizontal bar DE at a height of 1.8 m. A load of 6 kN acts at C. Find the tension T in the tie DE.

P = 6 kNAB = 3 mheight of C = 3.6 mheight of DE = 1.8 m
T = kN
3.Medium
6 kN6 m2.5 m1.8 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 2.5 m above the ground and 1.8 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.72 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 6 mH = 2.5 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.72 m
FBC = kN
4.Medium
6 kN4 m2 m0.6 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 2 m above the ground and 0.6 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.15 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 4 mH = 2 mhorizontal distance A to B = 0.6 mhorizontal distance A to K = 0.15 m
FBC = kN
5.Hard
10 kN5 m0.8 m1.7 m1.875 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 5 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 10 kN acts on leg AC at K, 1.875 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 5 mheight of C = 2.5 mheight of DE = 0.8 mhorizontal distance A to K = 1.875 m
C = kN
6.Hard
15 kN6 m0.6 m1.4 m2.25 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 2 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 15 kN acts on leg AC at K, 2.25 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 6 mheight of C = 2 mheight of DE = 0.6 mhorizontal distance A to K = 2.25 m
C = kN

Answer key

  1. 1. By = 2.25 kN
  2. 2. T = 2.5 kN
  3. 3. FBC = 1.408 kN
  4. 4. FBC = 0.4438 kN
  5. 5. C = 6.669 kN
  6. 6. C = 13.3 kN

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