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
20 kN4.8 m1 m2 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 together by the horizontal bar DE at a height of 1 m. A load of 20 kN acts at C. Find the tension T in the tie DE.

P = 20 kNAB = 4.8 mheight of C = 3 mheight of DE = 1 m
T = kN
2.Easy
5 kN0.8 m1.6 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 5 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 5 kNAD = 0.8 mAB = 2.4 mAC = 0.6 m
FCD = kN
3.Medium
10 kN2 m1.8 m2.7 m0.6 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 1.8 m above the ground. A vertical load of 10 kN acts on leg AC at K, 0.6 m (horizontally) from A. Find the tension T in the tie.

P = 10 kNAB = 2 mheight of C = 4.5 mheight of DE = 1.8 mhorizontal distance A to K = 0.6 m
T = kN
4.Medium
8 kN6 m1.5 m2.5 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 4 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 8 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the tension T in the tie.

P = 8 kNAB = 6 mheight of C = 4 mheight of DE = 1.5 mhorizontal distance A to K = 1.8 m
T = kN
5.Hard
4 kN3 kN2.5 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 4 kN hangs at B. Find the tension T in the cable.

W = 4 kNWb = 3 kNAB = 2.5 mAC = 1 m
T = kN
6.Hard
12 kN1 kN2.5 m1.5 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 1.5 m above A. A load of 12 kN hangs at B. Find the magnitude of the pin reaction A.

W = 12 kNWb = 1 kNAB = 2.5 mAC = 1.5 m
A = kN

Answer key

  1. 1. T = 12 kN
  2. 2. FCD = 25 kN
  3. 3. T = 1.111 kN
  4. 4. T = 2.88 kN
  5. 5. T = 14.81 kN
  6. 6. A = 20.84 kN

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