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
OAB100 NQ = ?180 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 100 N acts at A, 180 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 100 NOA = 180 mmOB = 60 mm
Q = N
2.Easy
8 kN6 m2 m2.5 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, 4.5 m high, and are tied together by the horizontal bar DE at a height of 2 m. A load of 8 kN acts at C. Find the tension T in the tie DE.

P = 8 kNAB = 6 mheight of C = 4.5 mheight of DE = 2 m
T = kN
3.Medium
20 kN5 m2 m2 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 4 m high and the horizontal tie DE 2 m above the ground. A vertical load of 20 kN acts on leg AC at K, 1.875 m (horizontally) from A. Find the tension T in the tie.

P = 20 kNAB = 5 mheight of C = 4 mheight of DE = 2 mhorizontal distance A to K = 1.875 m
T = kN
4.Medium
6 kN2.4 m0.8 m2.8 m0.6 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 6 kN acts on leg AC at K, 0.6 m (horizontally) from A. Find the tension T in the tie.

P = 6 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 0.8 mhorizontal distance A to K = 0.6 m
T = kN
5.Hard
2 kN2.4 m1.2 m1.8 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, 3 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 2 kN to the right acts at C. Find the tension T in the tie.

P = 2 kNAB = 2.4 mheight of C = 3 mheight of DE = 1.2 m
T = kN
6.Hard
2 kN3.2 m2 m2.5 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, 4.5 m high, and are tied by the horizontal bar DE at 2 m. A horizontal force of 2 kN to the right acts at C. Find the tension T in the tie.

P = 2 kNAB = 3.2 mheight of C = 4.5 mheight of DE = 2 m
T = kN

Answer key

  1. 1. Q = 300 N
  2. 2. T = 4.8 kN
  3. 3. T = 9.375 kN
  4. 4. T = 0.6429 kN
  5. 5. T = 1.667 kN
  6. 6. T = 1.8 kN

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