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 kN1.5 m2.5 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 4 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 4 kNAD = 1.5 mAB = 4 mAC = 0.5 m
FCD = kN
2.Easy
12 kN6 m1.2 m1.3 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, 2.5 m high, and are tied together by the horizontal bar DE at a height of 1.2 m. A load of 12 kN acts at C. Find the tension T in the tie DE.

P = 12 kNAB = 6 mheight of C = 2.5 mheight of DE = 1.2 m
T = kN
3.Medium
2 kN2.4 m1.2 m1.3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 2.5 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 2 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 2 kNAB = 2.4 mheight of C = 2.5 mheight of DE = 1.2 m
C = kN
4.Medium
4 kN0.5 m1 m1 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 m below A. A load of 4 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 4 kNAD = 0.5 mAB = 1.5 mAC = 1 m
A = kN
5.Hard
8 kN2 kN2.5 m1 mABC

A uniform horizontal boom AB of weight 2 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 1 m above A. A load of 8 kN hangs at B. Find the magnitude of the pin reaction A.

W = 8 kNWb = 2 kNAB = 2.5 mAC = 1 m
A = kN
6.Hard
8 kN1.5 kN6 m3 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 3 m above A. A load of 8 kN hangs at B. Find the magnitude of the pin reaction A.

W = 8 kNWb = 1.5 kNAB = 6 mAC = 3 m
A = kN

Answer key

  1. 1. FCD = 33.73 kN
  2. 2. T = 13.85 kN
  3. 3. C = 1.361 kN
  4. 4. A = 10 kN
  5. 5. A = 22.52 kN
  6. 6. A = 17.52 kN

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