Question
Download Solution PDFSlenderness ratio of a 5 m long column hinged at both ends and having a circular cross section with diameter 16 cm is ______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Slenderness ratio is defined as the ratio of effective length of column to the least radius of gyration.
\({\rm{\lambda }} = \frac{{{{\rm{L}}_{{\rm{eff}}}}}}{{{{\rm{r}}_{{\rm{min}}}}}} \)
where,
\({{\rm{r}}_{{\rm{min}}}} = \sqrt {\frac{{\rm{I}}}{{\rm{A}}}} \)
\({\rm{I}} = \frac{{{\rm{\pi }} \times {{\rm{D}}^4}}}{{64}} \)
\({\rm{A}} = \frac{{\rm{\pi }}}{4} \times {{\rm{D}}^2} \)
Where,
Leff = Effective length of column
rmin = Minimum radius of gyration
I = Moment of inertia of the centroidal axis.
A = Area of the cross section of the column
Calculation:
For column hinged at both ends, Leff = Length of the column itself = 5 m = 500 cm
\({{\rm{r}}_{{\rm{min}}}} = \sqrt {\frac{{{{\rm{D}}^2}}}{{16}}} = \frac{{\rm{D}}}{4} \)
D = 16 cm
rmin = 4 cm = 0.04 m
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