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
OAB250 NQ = ?300 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 250 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 250 NOA = 300 mmOB = 80 mm
Q = N
2.Easy
8 kN4.8 m1.2 m2.4 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, 3.6 m high, and are tied together by the horizontal bar DE at a height of 1.2 m. A load of 8 kN acts at C. Find the tension T in the tie DE.

P = 8 kNAB = 4.8 mheight of C = 3.6 mheight of DE = 1.2 m
T = kN
3.Medium
5 kN0.6 m1.4 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 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 = 0.6 mAB = 2 mAC = 0.6 m
A = kN
4.Medium
4 kN5 m3 m2.25 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 3 m above the ground and 2.25 m to the right of A. A vertical load of 4 kN acts on member AB at K, 1.688 m (horizontally) from A. Find the force FBC in member BC.

P = 4 kNL = 5 mH = 3 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 1.688 m
FBC = kN
5.Hard
6 kN1.5 kN5 m2.5 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, 2.5 m above A. A load of 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 1.5 kNAB = 5 mAC = 2.5 m
A = kN
6.Hard
w = 4 kN/m8 kN2 m2 m1.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.5 m below A). The beam carries a uniform load of 4 kN/m over its full length and a point load of 8 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 8 kNAD = 2 mAB = 4 mAC = 1.5 m
FCD = kN

Answer key

  1. 1. Q = 937.5 N
  2. 2. T = 4 kN
  3. 3. A = 20.34 kN
  4. 4. FBC = 1.831 kN
  5. 5. A = 13.52 kN
  6. 6. FCD = 53.33 kN

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