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
5 kN0.8 m1.6 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 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 = 1.5 m
FCD = kN
2.Easy
2 kN2 m2 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 2 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 2 kNAD = 2 mAB = 4 mAC = 0.5 m
FCD = kN
3.Medium
15 kN4 m1.2 m2.8 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, 4 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 15 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 4 mheight of C = 4 mheight of DE = 1.2 m
C = kN
4.Medium
12 kN2.4 m1.2 m2.4 m0.9 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 1.2 m above the ground. A vertical load of 12 kN acts on leg AC at K, 0.9 m (horizontally) from A. Find the tension T in the tie.

P = 12 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 1.2 mhorizontal distance A to K = 0.9 m
T = kN
5.Hard
6 kN3 kN2 m2.5 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, 2.5 m above A. A load of 6 kN hangs at B. Find the tension T in the cable.

W = 6 kNWb = 3 kNAB = 2 mAC = 2.5 m
T = kN
6.Hard
w = 1.5 kN/m6 kN1 m1 m1 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1 m below A). The beam carries a uniform load of 1.5 kN/m over its full length and a point load of 6 kN at its free end B. Find the force FCD in the strut.

w = 1.5 kN/mP = 6 kNAD = 1 mAB = 2 mAC = 1 m
FCD = kN

Answer key

  1. 1. FCD = 17 kN
  2. 2. FCD = 16.49 kN
  3. 3. C = 9.217 kN
  4. 4. T = 2.25 kN
  5. 5. T = 9.605 kN
  6. 6. FCD = 21.21 kN

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