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
20 kN3.2 m1 m3 m0.64 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 3.2 m apart. A vertical load of 20 kN acts on leg AC at the point K, 0.64 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 20 kNAB = 3.2 mhorizontal distance A to K = 0.64 m
By = kN
2.Easy
15 kN6 m1 m1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 6 m apart. The legs meet at the pin C, 2 m high, and are tied together by the horizontal bar DE at a height of 1 m. A load of 15 kN acts at C. Find the tension T in the tie DE.

P = 15 kNAB = 6 mheight of C = 2 mheight of DE = 1 m
T = kN
3.Medium
10 kN1.6 m0.9 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 10 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 10 kNAD = 1.6 mAB = 2.5 mAC = 0.5 m
A = kN
4.Medium
5 kN1.2 m1.8 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 5 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 5 kNAD = 1.2 mAB = 3 mAC = 0.75 m
A = kN
5.Hard
12 kN4 m0.6 m1.9 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 by the horizontal bar DE at 0.6 m. A horizontal force of 12 kN to the right acts at C. Find the tension T in the tie.

P = 12 kNAB = 4 mheight of C = 2.5 mheight of DE = 0.6 m
T = kN
6.Hard
12 kN2 m1.5 m1.5 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 m high, and are tied by the horizontal bar DE at 1.5 m. A horizontal force of 12 kN to the right acts at C. Find the tension T in the tie.

P = 12 kNAB = 2 mheight of C = 3 mheight of DE = 1.5 m
T = kN

Answer key

  1. 1. By = 4 kN
  2. 2. T = 22.5 kN
  3. 3. A = 50.32 kN
  4. 4. A = 21.36 kN
  5. 5. T = 7.895 kN
  6. 6. T = 12 kN

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