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
4 kN6 m0.6 m1.4 m1.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 6 m apart. A vertical load of 4 kN acts on leg AC at the point K, 1.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 4 kNAB = 6 mhorizontal distance A to K = 1.5 m
By = kN
2.Easy
4 kN2 m1.2 m2.8 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, 4 m high, and are tied together by the horizontal bar DE at a height of 1.2 m. A load of 4 kN acts at C. Find the tension T in the tie DE.

P = 4 kNAB = 2 mheight of C = 4 mheight of DE = 1.2 m
T = kN
3.Medium
4 kN2 m1.5 m2.5 m0.75 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 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the tension T in the tie.

P = 4 kNAB = 2 mheight of C = 4 mheight of DE = 1.5 mhorizontal distance A to K = 0.75 m
T = kN
4.Medium
10 kN2 m1.2 m2.4 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 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 10 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the tension T in the tie.

P = 10 kNAB = 2 mheight of C = 3.6 mheight of DE = 1.2 mhorizontal distance A to K = 0.75 m
T = kN
5.Hard
w = 1 kN/m12 kN1.6 m0.4 m0.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.5 m below A). The beam carries a uniform load of 1 kN/m over its full length and a point load of 12 kN at its free end B. Find the force FCD in the strut.

w = 1 kN/mP = 12 kNAD = 1.6 mAB = 2 mAC = 0.5 m
FCD = kN
6.Hard
w = 2 kN/m2 kN0.75 m1.65 m0.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.5 m below A). The beam carries a uniform load of 2 kN/m over its full length and a point load of 2 kN at its free end B. Find the force FCD in the strut.

w = 2 kN/mP = 2 kNAD = 0.75 mAB = 2.4 mAC = 0.5 m
FCD = kN

Answer key

  1. 1. By = 1 kN
  2. 2. T = 0.7143 kN
  3. 3. T = 0.6 kN
  4. 4. T = 1.562 kN
  5. 5. FCD = 54.48 kN
  6. 6. FCD = 25.38 kN

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