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 kN1 m1 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 = 1 mAB = 2 mAC = 0.6 m
FCD = kN
2.Easy
O100 N100 NQ = ?140 mm20 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 140 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 = 140 mmb = 20 mm
Q = N
3.Medium
250 NQ = ?30°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 30° with the line AC. A downward force of 250 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 250 Nθ = 30°
Q = N
4.Medium
12 kN8 m4 m4.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 4 m above the ground and 4.8 m to the right of A. A vertical load of 12 kN acts on member AB at K, 1.92 m (horizontally) from A. Find the force FBC in member BC.

P = 12 kNL = 8 mH = 4 mhorizontal distance A to B = 4.8 mhorizontal distance A to K = 1.92 m
FBC = kN
5.Hard
4 kN3.2 m0.6 m1.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 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 4 kN to the right acts at C. Find the tension T in the tie.

P = 4 kNAB = 3.2 mheight of C = 2.4 mheight of DE = 0.6 m
T = kN
6.Hard
12 kN6 m1.2 m0.8 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, 2 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 12 kN to the right acts at C. Find the tension T in the tie.

P = 12 kNAB = 6 mheight of C = 2 mheight of DE = 1.2 m
T = kN

Answer key

  1. 1. FCD = 11.66 kN
  2. 2. Q = 700 N
  3. 3. Q = 216.5 N
  4. 4. FBC = 3.688 kN
  5. 5. T = 2.667 kN
  6. 6. T = 15 kN

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