A steel rod of 20 mm diameter is used as a tie member in the roof bracing system and may be subjected to possible reversal of stress due to wind load. What is the maximum permissible length of the member?

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SSC JE CE Previous Year Paper 9 (Held On: 23 Sept 2019 Morning)
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  1. 1750 mm
  2. 2000 mm
  3. 3000 mm
  4. 2500 mm

Answer (Detailed Solution Below)

Option 1 : 1750 mm
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As per IS 800:2007, The maximum slenderness ratio for a member normally acting as a tie in a roof truss or a bracing system but subjected to possible reversal of stresses resulting from the action of wind or earthquake forces will be 350.

Slenderness ratio “λ” is given by:

\({\rm{\lambda }} = \frac{{{{\rm{l}}_{{\rm{eff}}}}}}{{{{\rm{r}}_{{\rm{min}}}}}}\)

Where,

rmin = minimum radius of gyration of the member, and ℓeff = effective length of the member

\({{\rm{r}}_{{\rm{min}}}} = \sqrt {\frac{{\rm{I}}}{{\rm{A}}}} = \sqrt {\frac{{\frac{{\rm{\pi }}}{{64}}{{\rm{D}}^4}}}{{\frac{{\rm{\pi }}}{4}{{\rm{D}}^2}}}} = \frac{{\rm{D}}}{4} = \frac{{20}}{4} = 5{\rm{\;mm}}\)

Where,

A = Area of the member and I = Moment of the inertia of the member about its center of gravity

λ = 350

∴ ℓeff = 350 x 5 = 1750 mm
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