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
O100 N100 NQ = ?90 mm20 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 90 mm from the pin O. The jaws grip a bolt 20 mm from the pin. Find the gripping force Q on the bolt.

F = 100 Na = 90 mmb = 20 mm
Q = N
2.Easy
O200 N200 NQ = ?90 mm35 mm

A hand squeezes the handles of a pair of pliers with 200 N each, 90 mm from the pin O. The jaws grip a bolt 35 mm from the pin. Find the gripping force Q on the bolt.

F = 200 Na = 90 mmb = 35 mm
Q = N
3.Medium
8 kN0.8 m0.7 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 m below A. A load of 8 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 8 kNAD = 0.8 mAB = 1.5 mAC = 1.2 m
A = kN
4.Medium
6 kN2 m1 m2.6 m0.4 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 1 m above the ground. A vertical load of 6 kN acts on leg AC at K, 0.4 m (horizontally) from A. Find the tension T in the tie.

P = 6 kNAB = 2 mheight of C = 3.6 mheight of DE = 1 mhorizontal distance A to K = 0.4 m
T = kN
5.Hard
6 kN2 kN5 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 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 2 kNAB = 5 mAC = 1 m
A = kN
6.Hard
5 kN2 kN5 m2 m0.75 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 m high and 0.75 m to the right of A. Member AB carries a vertical load of 5 kN at K, 0.375 m (horizontally) from A, and a horizontal load of 2 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 2 kNL = 5 mH = 2 mhorizontal distance A to B = 0.75 mhorizontal distance A to K = 0.375 m
Ax = kN

Answer key

  1. 1. Q = 450 N
  2. 2. Q = 514.3 N
  3. 3. A = 12.21 kN
  4. 4. T = 0.4615 kN
  5. 5. A = 35.01 kN
  6. 6. Ax = 0.4969 kN

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