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
O120 N120 NQ = ?90 mm40 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 90 mm from the pin O. The jaws grip a bolt 40 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 90 mmb = 40 mm
Q = N
2.Easy
8 kN1.6 m2.4 m0.8 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.8 m below A. A load of 8 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 8 kNAD = 1.6 mAB = 4 mAC = 0.8 m
FCD = kN
3.Medium
20 kN6 m3 m2.7 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 6 m apart, and B is 3 m above the ground and 2.7 m to the right of A. A vertical load of 20 kN acts on member AB at K, 2.025 m (horizontally) from A. Find the force FBC in member BC.

P = 20 kNL = 6 mH = 3 mhorizontal distance A to B = 2.7 mhorizontal distance A to K = 2.025 m
FBC = kN
4.Medium
300 NQ = ?15°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 15° with the line AC. A downward force of 300 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 300 Nθ = 15°
Q = N
5.Hard
2 kN4 m1 m1.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 2.5 m high, and are tied by the horizontal bar DE at 1 m. A horizontal force of 2 kN to the right acts at C. Find the tension T in the tie.

P = 2 kNAB = 4 mheight of C = 2.5 mheight of DE = 1 m
T = kN
6.Hard
10 kN8 kN5 m2.5 m3 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 high and 3 m to the right of A. Member AB carries a vertical load of 10 kN at K, 1.2 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 = 10 kNQ = 8 kNL = 5 mH = 2.5 mhorizontal distance A to B = 3 mhorizontal distance A to K = 1.2 m
Ax = kN

Answer key

  1. 1. Q = 270 N
  2. 2. FCD = 44.72 kN
  3. 3. FBC = 10.03 kN
  4. 4. Q = 559.8 N
  5. 5. T = 1.667 kN
  6. 6. Ax = 2.88 kN

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