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
15 kN4.8 m0.8 m1.2 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 m high, and are tied together by the horizontal bar DE at a height of 0.8 m. A load of 15 kN acts at C. Find the tension T in the tie DE.

P = 15 kNAB = 4.8 mheight of C = 2 mheight of DE = 0.8 m
T = kN
2.Easy
O100 N100 NQ80 mm15 mm

The handles of a pair of pliers are squeezed with 100 N each, 80 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 = 100 Na = 80 mmb = 15 mm
FO = N
3.Medium
200 NQ = ?12°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 12° with the line AC. A downward force of 200 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 200 Nθ = 12°
Q = N
4.Medium
12 kN3 m2.5 m0.45 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 above the ground and 0.45 m to the right of A. A vertical load of 12 kN acts on member AB at K, 0.1125 m (horizontally) from A. Find the force FBC in member BC.

P = 12 kNL = 3 mH = 2.5 mhorizontal distance A to B = 0.45 mhorizontal distance A to K = 0.1125 m
FBC = kN
5.Hard
2 kN5 m0.6 m1.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 2.4 m high, and are tied by the horizontal bar DE at 0.6 m. A horizontal force of 2 kN to the right acts at C. Find the tension T in the tie.

P = 2 kNAB = 5 mheight of C = 2.4 mheight of DE = 0.6 m
T = kN
6.Hard
10 kN10 kN3 m3 m1.35 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 3 m high and 1.35 m to the right of A. Member AB carries a vertical load of 10 kN at K, 0.81 m (horizontally) from A, and a horizontal load of 10 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 10 kNQ = 10 kNL = 3 mH = 3 mhorizontal distance A to B = 1.35 mhorizontal distance A to K = 0.81 m
Ax = kN

Answer key

  1. 1. T = 15 kN
  2. 2. FO = 633.3 N
  3. 3. Q = 470.5 N
  4. 4. FBC = 0.6428 kN
  5. 5. T = 1.333 kN
  6. 6. Ax = 3.015 kN

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