Question

A Circular metal column is to support a load of 500 Tonne and it must not compress more than 0.1mm. The modulus of elasticity is 210 GPa. the column is 2m long. Calculate the cross sectional area of and the diameter.​

Answer 1

Answer: idk

Step-by-step explanation:

A Circular metal column is to support a load of 500 Tonne and it must not compress more than 0.1mm. The modulus of elasticity is 210 GPa. the column

Answer 2

Given,

Load, $\[P = 500\,tonne\]$

Compression, $\[\Delta l = 0.1mm\]$

Modulus of elasticity, $\[E = 210GPa.\]$

Length, $\[L = 2m\]$

Solution,

Know that, $\[1\,ton = 1000kg\]$

Calculate the cross-sectional area of the column.

Consider the area is A.

$\[\Delta l = \frac{{P.L}}{{A.E}}\]$

$\[ \Rightarrow A = \frac{{P.L}}{{\Delta l.E}}\]$

$\[ \Rightarrow A = \frac{{500 \times 1000 \times 9.81 \times 2}}{{0.1 \times {{10}^{ - 3}} \times 210 \times {{10}^9}}}\]$

$\[ \Rightarrow A = \frac{{{{10}^6} \times 9.81}}{{21 \times {{10}^6}}}\]$

$\[ \Rightarrow A = \frac{{9.81}}{{21}}\]$

$\[ \Rightarrow A = 0.4671{m^2}\]$

Calculate the diameter of the column.

Consider the diameter is d.

$\[\begin{array}{l}\frac{\pi }{4}{d^2} = 0.4671\\ \Rightarrow {d^2} = 0.4671 \times \frac{4}{\pi }\\ \Rightarrow d = 0.77122m\\ \Rightarrow d = 77.122cm\end{array}\]$

Hence the diameter is $\[77.122cm\]$.