The rectangular column shown in the figure below carries a load P having eccentricities ‘e_{x}’ and ' e_{y} ’ along the xaxis and yaxis respectively. The stress at any point (*, y) is given by
Stress at any point
Euler’s formula for a mild steel long column hinged at both end is not valid for slenderness ratio
According to Euler's theory,
For a mild steel coumn,
σ_{y} = 300 N/mm2 and
E = 2.1 x 10^{5
∴}
Hence, when the slenderness ratio is less than this limit for mild steel columns , Euler’s formula will not be valid.
The buckling load for a column pinned at both ends is 10kN. If the ends are fixed, the buckling load changes to
For both ends pinned,
= 4 x 10 = 40kN
The radius of gyration of a rectangular section (depth d, width b) from a centroidal axis parallel to the width is
Radius of gyration,
For no tension in column of diameter D, the eccentricity of the compressive load must be less than
For no tension condition,
The Rankine constant in the formula for axial loads on column made of material of crushing strength f_{c} and modulus of elasticity E is
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