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 kN2 m1.5 m2.1 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, 3.6 m high, and are tied together by the horizontal bar DE at a height of 1.5 m. A load of 5 kN acts at C. Find the tension T in the tie DE.

P = 5 kNAB = 2 mheight of C = 3.6 mheight of DE = 1.5 m
T = kN
2.Easy
4 kN0.75 m0.75 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 4 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 4 kNAD = 0.75 mAB = 1.5 mAC = 1.5 m
FCD = kN
3.Medium
8 kN2 m1.5 m1 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, 2.5 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 2 mheight of C = 2.5 mheight of DE = 1.5 m
C = kN
4.Medium
10 kN4 m1.2 m1.8 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, 3 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 10 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 4 mheight of C = 3 mheight of DE = 1.2 m
C = kN
5.Hard
2 kN4.8 m1.2 m1.3 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4.8 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 2 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 2 kNAB = 4.8 mheight of C = 2.5 mheight of DE = 1.2 mhorizontal distance A to K = 1.8 m
C = kN
6.Hard
15 kN2 m1.8 m1.8 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 1.8 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 2 mheight of C = 3.6 mheight of DE = 1.8 mhorizontal distance A to K = 0.75 m
C = kN

Answer key

  1. 1. T = 1.19 kN
  2. 2. FCD = 8.944 kN
  3. 3. C = 5.657 kN
  4. 4. C = 7.474 kN
  5. 5. C = 1.575 kN
  6. 6. C = 6.435 kN

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