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
O50 N50 NQ = ?80 mm40 mm

A hand squeezes the handles of a pair of pliers with 50 N each, 80 mm from the pin O. The jaws grip a bolt 40 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 80 mmb = 40 mm
Q = N
2.Easy
2 kN1.5 m0.5 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 2 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 2 kNAD = 1.5 mAB = 2 mAC = 0.75 m
FCD = kN
3.Medium
150 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 150 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 150 Nθ = 15°
Q = N
4.Medium
4 kN3.2 m1 m2 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, 3 m high, and the horizontal tie DE is 1 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 = 3.2 mheight of C = 3 mheight of DE = 1 m
C = kN
5.Hard
6 kN4 m1.5 m1.5 m0.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 3 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 6 kN acts on leg AC at K, 0.5 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 4 mheight of C = 3 mheight of DE = 1.5 mhorizontal distance A to K = 0.5 m
C = kN
6.Hard
20 kN6 kN3 m3 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 3 m high and 0.9 m to the right of A. Member AB carries a vertical load of 20 kN at K, 0.225 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 20 kNQ = 6 kNL = 3 mH = 3 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.225 m
Ax = kN

Answer key

  1. 1. Q = 100 N
  2. 2. FCD = 5.963 kN
  3. 3. Q = 279.9 N
  4. 4. C = 2.561 kN
  5. 5. C = 1.25 kN
  6. 6. Ax = 0.75 kN

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