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 = ?120 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 300 N acts at A, 120 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 300 NOA = 120 mmOB = 150 mm
Q = N
2.Easy
10 kN6 m1.2 m1.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 6 m apart. The legs meet at the pin C, 3 m high, and are tied together by the horizontal bar DE at a height of 1.2 m. A load of 10 kN acts at C. Find the tension T in the tie DE.

P = 10 kNAB = 6 mheight of C = 3 mheight of DE = 1.2 m
T = kN
3.Medium
OAB250 NQ150 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 250 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 = 250 NOA = 150 mmOB = 80 mm
FO = N
4.Medium
4 kN3 m0.6 m1.9 m0.6 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.6 m (horizontally) from A. Find the tension T in the tie.

P = 4 kNAB = 3 mheight of C = 2.5 mheight of DE = 0.6 mhorizontal distance A to K = 0.6 m
T = kN
5.Hard
10 kN3 kN5 m2 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 10 kN hangs at B. Find the magnitude of the pin reaction A.

W = 10 kNWb = 3 kNAB = 5 mAC = 2 m
A = kN
6.Hard
6 kN3 kN5 m2 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 3 kNAB = 5 mAC = 2 m
A = kN

Answer key

  1. 1. Q = 240 N
  2. 2. T = 8.333 kN
  3. 3. FO = 531.3 N
  4. 4. T = 0.6316 kN
  5. 5. A = 28.79 kN
  6. 6. A = 18.81 kN

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