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
10 kN0.75 m1.75 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 10 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 10 kNAD = 0.75 mAB = 2.5 mAC = 0.5 m
FCD = kN
2.Easy
O50 N50 NQ = ?80 mm18 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 18 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 80 mmb = 18 mm
Q = N
3.Medium
8 kN6 m2 m2.5 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, 4.5 m high, and the horizontal tie DE is 2 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 6 mheight of C = 4.5 mheight of DE = 2 m
C = kN
4.Medium
100 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 100 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 100 Nθ = 12°
Q = N
5.Hard
F = ?4000 N12 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 12 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 4000 N at the slider C? Neglect friction and weights.

Q = 4000 NAB = BC = 120 mmh = 12 mm
F = N
6.Hard
F = ?1500 N30 mmABC

A toggle press has two equal links AB and BC, each 100 mm long between pins. The joint B sits 30 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1500 N at the slider C? Neglect friction and weights.

Q = 1500 NAB = BC = 100 mmh = 30 mm
F = N

Answer key

  1. 1. FCD = 60.09 kN
  2. 2. Q = 222.2 N
  3. 3. C = 6.248 kN
  4. 4. Q = 235.2 N
  5. 5. F = 804 N
  6. 6. F = 943.5 N

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