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 m1.8 m1.8 m0.75 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2 m apart. A vertical load of 2 kN acts on leg AC at the point K, 0.75 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 2 kNAB = 2 mhorizontal distance A to K = 0.75 m
By = kN
2.Easy
15 kN5 m0.8 m3.2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 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 0.8 m. A load of 15 kN acts at C. Find the tension T in the tie DE.

P = 15 kNAB = 5 mheight of C = 4 mheight of DE = 0.8 m
T = kN
3.Medium
OAB80 NQ150 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (150 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 150 mmOB = 150 mm
FO = N
4.Medium
5 kN6 m4 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 4 m above the ground and 1.8 m to the right of A. A vertical load of 5 kN acts on member AB at K, 1.08 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 6 mH = 4 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 1.08 m
FBC = kN
5.Hard
6 kN3 kN6 m3 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 3 m high and 1.8 m to the right of A. Member AB carries a vertical load of 6 kN at K, 1.35 m (horizontally) from A, and a horizontal load of 3 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 6 kNQ = 3 kNL = 6 mH = 3 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 1.35 m
Ax = kN
6.Hard
4 kN4.8 m1.2 m1.8 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 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 4 kN to the right acts at C. Find the tension T in the tie.

P = 4 kNAB = 4.8 mheight of C = 3 mheight of DE = 1.2 m
T = kN

Answer key

  1. 1. By = 0.75 kN
  2. 2. T = 5.859 kN
  3. 3. FO = 113.1 N
  4. 4. FBC = 1.305 kN
  5. 5. Ax = 0.99 kN
  6. 6. T = 3.333 kN

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