Maximum height of a uniform vertical column

AI Thread Summary
The maximum height of a uniform vertical column that can support itself without breaking is determined by the material's density and its limit of durability, which is independent of the cross-sectional area. For steel with a density of 7.8 x 10^3 kg/m³, the height can be calculated using the formula l = σ/(g*ρ), where σ is the material's maximal stress. Similarly, for granite with a density of 2.7 x 10^3 kg/m³, the same formula applies. To find the limit of durability for a material, one must refer to its maximal stress values, which can vary based on specific material properties. Understanding these calculations is crucial for engineering applications involving vertical columns.
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There is a maximum height of a uniform vertical column made of any material that can support itself without breaking, and it is independent of the cross-sectional area.

(a) Calculate this height for steel (density 7.8 103 kg/m3).

(b) Calculate this height for granite (density 2.7 103 kg/m3).
 
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You have to know limit of durability of material
M*g=σ*s
M=ρ*l*S
g*l*ρ=σ
l=σ/(g*ρ), where ρ=density, σ=limit of durability (maximal stress), S=Area
 
How do I find the limit durability of material?
 
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