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
15 kN4 m1.5 m1 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, 2.5 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 15 kN acts at C. Find the tension T in the tie DE.

P = 15 kNAB = 4 mheight of C = 2.5 mheight of DE = 1.5 m
T = kN
2.Easy
2 kN4.8 m1 m1.5 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, 2.5 m high, and are tied together by the horizontal bar DE at a height of 1 m. A load of 2 kN acts at C. Find the tension T in the tie DE.

P = 2 kNAB = 4.8 mheight of C = 2.5 mheight of DE = 1 m
T = kN
3.Medium
12 kN3 m0.8 m2.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 3.6 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 12 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 12 kNAB = 3 mheight of C = 3.6 mheight of DE = 0.8 m
C = kN
4.Medium
5 kN5 m1.5 m2.5 m1.25 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 5 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 5 kN acts on leg AC at K, 1.25 m (horizontally) from A. Find the tension T in the tie.

P = 5 kNAB = 5 mheight of C = 4 mheight of DE = 1.5 mhorizontal distance A to K = 1.25 m
T = kN
5.Hard
4 kN0.5 kN2.5 m1.5 mABC

A uniform horizontal boom AB of weight 0.5 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 4 kN hangs at B. Find the magnitude of the pin reaction A.

W = 4 kNWb = 0.5 kNAB = 2.5 mAC = 1.5 m
A = kN
6.Hard
w = 3 kN/m15 kN0.75 m1.65 m0.75 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.75 m below A). The beam carries a uniform load of 3 kN/m over its full length and a point load of 15 kN at its free end B. Find the force FCD in the strut.

w = 3 kN/mP = 15 kNAD = 0.75 mAB = 2.4 mAC = 0.75 m
FCD = kN

Answer key

  1. 1. T = 15 kN
  2. 2. T = 1.6 kN
  3. 3. C = 6.807 kN
  4. 4. T = 1.25 kN
  5. 5. A = 7.088 kN
  6. 6. FCD = 84.17 kN

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