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 kN4.8 m1 m1.5 m1.44 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 4 kN acts on leg AC at the point K, 1.44 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 4 kNAB = 4.8 mhorizontal distance A to K = 1.44 m
By = kN
2.Easy
20 kN4 m1.8 m2.7 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, 4.5 m high, and are tied together by the horizontal bar DE at a height of 1.8 m. A load of 20 kN acts at C. Find the tension T in the tie DE.

P = 20 kNAB = 4 mheight of C = 4.5 mheight of DE = 1.8 m
T = kN
3.Medium
4 kN3.2 m1.2 m1.3 m0.96 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.96 m (horizontally) from A. Find the tension T in the tie.

P = 4 kNAB = 3.2 mheight of C = 2.5 mheight of DE = 1.2 mhorizontal distance A to K = 0.96 m
T = kN
4.Medium
20 kN5 m1.5 m2.1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 3.6 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 20 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 5 mheight of C = 3.6 mheight of DE = 1.5 m
C = kN
5.Hard
6 kN2 m0.8 m3.2 m0.4 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 0.8 m above the ground. A vertical load of 6 kN acts on leg AC at K, 0.4 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 2 mheight of C = 4 mheight of DE = 0.8 mhorizontal distance A to K = 0.4 m
C = kN
6.Hard
w = 3 kN/m5 kN1.6 m2.4 m1.2 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.2 m below A). The beam carries a uniform load of 3 kN/m over its full length and a point load of 5 kN at its free end B. Find the force FCD in the strut.

w = 3 kN/mP = 5 kNAD = 1.6 mAB = 4 mAC = 1.2 m
FCD = kN

Answer key

  1. 1. By = 1.2 kN
  2. 2. T = 7.407 kN
  3. 3. T = 1.477 kN
  4. 4. C = 15.55 kN
  5. 5. C = 1.257 kN
  6. 6. FCD = 45.83 kN

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