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
2 kN2.4 m1.5 m2.5 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, 4 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 2 kN acts at C. Find the tension T in the tie DE.

P = 2 kNAB = 2.4 mheight of C = 4 mheight of DE = 1.5 m
T = kN
2.Easy
15 kN4 m2 m2.5 m1.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4 m apart. A vertical load of 15 kN acts on leg AC at the point K, 1.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 15 kNAB = 4 mhorizontal distance A to K = 1.5 m
By = kN
3.Medium
5 kN5 m4 m3 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 4 m above the ground and 3 m to the right of A. A vertical load of 5 kN acts on member AB at K, 1.2 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 5 mH = 4 mhorizontal distance A to B = 3 mhorizontal distance A to K = 1.2 m
FBC = kN
4.Medium
6 kN6 m1.2 m2.8 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 4 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 6 kN acts on leg AC at K, 2.25 m (horizontally) from A. Find the tension T in the tie.

P = 6 kNAB = 6 mheight of C = 4 mheight of DE = 1.2 mhorizontal distance A to K = 2.25 m
T = kN
5.Hard
5 kN2 m0.8 m1.2 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, 2 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 5 kN to the right acts at C. Find the tension T in the tie.

P = 5 kNAB = 2 mheight of C = 2 mheight of DE = 0.8 m
T = kN
6.Hard
15 kN8 kN3 m2 m0.9 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 2 m high and 0.9 m to the right of A. Member AB carries a vertical load of 15 kN at K, 0.225 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 15 kNQ = 8 kNL = 3 mH = 2 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.225 m
Ax = kN

Answer key

  1. 1. T = 0.48 kN
  2. 2. By = 5.625 kN
  3. 3. FBC = 1.342 kN
  4. 4. T = 2.411 kN
  5. 5. T = 4.167 kN
  6. 6. Ax = 1.219 kN

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