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
12 kN6 m0.6 m1.9 m1.8 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 6 m apart. A vertical load of 12 kN acts on leg AC at the point K, 1.8 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 6 mhorizontal distance A to K = 1.8 m
By = kN
2.Easy
3 kN1.2 m1.3 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 m below A. A load of 3 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 3 kNAD = 1.2 mAB = 2.5 mAC = 1.2 m
FCD = kN
3.Medium
4 kN3 m3 m1.35 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 3 m above the ground and 1.35 m to the right of A. A vertical load of 4 kN acts on member AB at K, 0.675 m (horizontally) from A. Find the force FBC in member BC.

P = 4 kNL = 3 mH = 3 mhorizontal distance A to B = 1.35 mhorizontal distance A to K = 0.675 m
FBC = kN
4.Medium
OAB300 NQ150 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 300 N at A (150 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction FO.

F = 300 NOA = 150 mmOB = 80 mm
FO = N
5.Hard
15 kN3.2 m0.8 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart. The legs meet at the pin C, 2.4 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 15 kN to the right acts at C. Find the tension T in the tie.

P = 15 kNAB = 3.2 mheight of C = 2.4 mheight of DE = 0.8 m
T = kN
6.Hard
15 kN4 m0.8 m3.2 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, 4 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 15 kN to the right acts at C. Find the tension T in the tie.

P = 15 kNAB = 4 mheight of C = 4 mheight of DE = 0.8 m
T = kN

Answer key

  1. 1. By = 3.6 kN
  2. 2. FCD = 8.839 kN
  3. 3. FBC = 1.027 kN
  4. 4. FO = 637.5 N
  5. 5. T = 11.25 kN
  6. 6. T = 9.375 kN

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