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 kN0.75 m0.75 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 12 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 12 kNAD = 0.75 mAB = 1.5 mAC = 1.5 m
FCD = kN
2.Easy
6 kN2 m1.5 m1 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, 2.5 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 6 kN acts at C. Find the tension T in the tie DE.

P = 6 kNAB = 2 mheight of C = 2.5 mheight of DE = 1.5 m
T = kN
3.Medium
5 kN4 m1.8 m1.8 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, 3.6 m high, and the horizontal tie DE is 1.8 m above the ground. A load of 5 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 4 mheight of C = 3.6 mheight of DE = 1.8 m
C = kN
4.Medium
20 kN2.4 m1 m3 m0.48 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 4 m high and the horizontal tie DE 1 m above the ground. A vertical load of 20 kN acts on leg AC at K, 0.48 m (horizontally) from A. Find the tension T in the tie.

P = 20 kNAB = 2.4 mheight of C = 4 mheight of DE = 1 mhorizontal distance A to K = 0.48 m
T = kN
5.Hard
8 kN3 kN5 m1 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 1 m above A. A load of 8 kN hangs at B. Find the tension T in the cable.

W = 8 kNWb = 3 kNAB = 5 mAC = 1 m
T = kN
6.Hard
6 kN4 m1.8 m2.2 m1.2 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 4 m high and the horizontal tie DE 1.8 m above the ground. A vertical load of 6 kN acts on leg AC at K, 1.2 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 4 mheight of C = 4 mheight of DE = 1.8 mhorizontal distance A to K = 1.2 m
C = kN

Answer key

  1. 1. FCD = 26.83 kN
  2. 2. T = 3 kN
  3. 3. C = 3.737 kN
  4. 4. T = 1.6 kN
  5. 5. T = 48.44 kN
  6. 6. C = 2.433 kN

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