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
O40 N40 NQ120 mm15 mm

The handles of a pair of pliers are squeezed with 40 N each, 120 mm from the pin O, and the jaws grip a wire 15 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 40 Na = 120 mmb = 15 mm
FO = N
2.Easy
12 kN3 m0.8 m1.7 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, 2.5 m high, and are tied together by the horizontal bar DE at a height of 0.8 m. A load of 12 kN acts at C. Find the tension T in the tie DE.

P = 12 kNAB = 3 mheight of C = 2.5 mheight of DE = 0.8 m
T = kN
3.Medium
8 kN5 m2.5 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 2.5 m above the ground and 2.25 m to the right of A. A vertical load of 8 kN acts on member AB at K, 1.35 m (horizontally) from A. Find the force FBC in member BC.

P = 8 kNL = 5 mH = 2.5 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 1.35 m
FBC = kN
4.Medium
6 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 6 kN acts on member AB at K, 1.688 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 5 mH = 3 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 1.688 m
FBC = kN
5.Hard
w = 1.5 kN/m6 kN0.5 m1 m0.8 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.8 m below A). The beam carries a uniform load of 1.5 kN/m over its full length and a point load of 6 kN at its free end B. Find the force FCD in the strut.

w = 1.5 kN/mP = 6 kNAD = 0.5 mAB = 1.5 mAC = 0.8 m
FCD = kN
6.Hard
5 kN6 kN5 m3 m1.5 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 high and 1.5 m to the right of A. Member AB carries a vertical load of 5 kN at K, 0.9 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 6 kNL = 5 mH = 3 mhorizontal distance A to B = 1.5 mhorizontal distance A to K = 0.9 m
Ax = kN

Answer key

  1. 1. FO = 360 N
  2. 2. T = 5.294 kN
  3. 3. FBC = 3.211 kN
  4. 4. FBC = 2.747 kN
  5. 5. FCD = 25.21 kN
  6. 6. Ax = 0.75 kN

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