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
3 kN2 m0.5 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 3 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 3 kNAD = 2 mAB = 2.5 mAC = 0.6 m
FCD = kN
2.Easy
O80 N80 NQ150 mm35 mm

The handles of a pair of pliers are squeezed with 80 N each, 150 mm from the pin O, and the jaws grip a wire 35 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 150 mmb = 35 mm
FO = N
3.Medium
2 kN4.8 m1.5 m1 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, 2.5 m high, and the horizontal tie DE is 1.5 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 = 4.8 mheight of C = 2.5 mheight of DE = 1.5 m
C = kN
4.Medium
4 kN6 m1.2 m2.4 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, 3.6 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 4 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 6 mheight of C = 3.6 mheight of DE = 1.2 m
C = kN
5.Hard
5 kN8 kN3 m4 m0.9 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 4 m high and 0.9 m to the right of A. Member AB carries a vertical load of 5 kN at K, 0.675 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 8 kNL = 3 mH = 4 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.675 m
Ax = kN
6.Hard
12 kN4 kN3 m2.5 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 2.5 m high and 1.8 m to the right of A. Member AB carries a vertical load of 12 kN at K, 0.9 m (horizontally) from A, and a horizontal load of 4 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 12 kNQ = 4 kNL = 3 mH = 2.5 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.9 m
Ax = kN

Answer key

  1. 1. FCD = 13.05 kN
  2. 2. FO = 422.9 N
  3. 3. C = 2.6 kN
  4. 4. C = 3.202 kN
  5. 5. Ax = 1.809 kN
  6. 6. Ax = 0.672 kN

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