Across flat dimension of hexagonal face is 20√3 mm. What is the minimum diameter of road required to machine the hexagon?

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ISRO VSSC Technician-B (Fitter) Official Paper (Held On: 14 July 2021)
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  1. 20 mm
  2. 40 mm
  3. 35 mm
  4. 30 mm

Answer (Detailed Solution Below)

Option 2 : 40 mm
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Detailed Solution

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Concept:

Hexagonal nut:

  • The upper corners of this nut are rounded-off or chamfered.
  • The chamfering is generally conical.
  • The angle of chamfer is 30° or 45° with the base of the nut.
  • Due to chamfering, an arc is formed on each vertical face, and a circle is formed on the top surface of the nut.
  • The dimensions of the hexagonal nut cannot be expressed exactly in terms of the nominal diameter of the bolt.
  • For elementary work, the following approximately standard dimensions may be adopted
  • If D = the nominal diameter of the bolt, then:
    • Thickness of the nut, T = D
    • Width across flats, W = 1.5D + 3 mm
    • Angle of chamfer = 30°
    • Radius of chamfer arc, R = 1.4D (approx.)
  • Very often, and especially when a nut is shown in one view only, the following rough rule dimensions are used:
    • Thickness of the nut, T = D
    • Distance across diagonally opposite corners = 2D
    • Angle of chamfer = 30°
    • Radius of chamfer arc, R = 1.5D

Calculation:

Given:

Across flat dimension of the hexagonal face is 20√3 mm

∵ Width across flats, W = 1.5D + 3 mm

⇒ 1.5D + 3 = 20√3

⇒ D = 21 mm

∴ The nominal diameter of the bolt = 21 mm

∵ Distance across diagonally opposite corners = 2D = 2 × 21 = 42 mm

The minimum diameter of the road required to machine the hexagon will be 40 mm (the nearest value amongst the given options)

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