Chapter 9, Problem 80GP

(a)

To determine

The maximum height of the vertical column made by steel.

Answer to Problem 80GP

Maximum height of the vertical column made by steel without buckling is $\text{6}\text{.5}\times {\text{ 10}}^{\text{3}}\text{ m}$ .

Explanation of Solution

Given:

Density of steel, $\text{ρ = 7}\text{.8}\times {\text{10}}^{\text{3}}{\text{ kg/m}}^{\text{3}}$

Maximum compressive strength of steel $\text{= 500}\times {\text{10}}^{\text{6}}{\text{ N/m}}^{\text{2}}$

Formula used:

Maximum height of the steel column is determined by using the relationship of compressive strength, density and gravity.

  $\text{Compressive strength = ρ}\times \text{g}\times \text{h}$

Calculation:

Substitute the given values;

  $\begin{array}{l}{\text{h}}_{\text{max}}\text{ = }\frac{\text{Compressive strength of steel}}{\text{ρ}\times \text{g}}\\ {\text{h}}_{\text{max}}\text{ = }\frac{\text{500}\times {\text{10}}^{\text{6}}}{\text{7}\text{.8}\times {\text{10}}^{\text{3}}\times \text{9}\text{.8}}\text{ = 6}\text{.5}\times {\text{10}}^{\text{3}}\text{ m}\end{array}$

Conclusion:

Thus, maximum height of the vertical column made by steel without buckling is $\text{6}\text{.5}\times {\text{ 10}}^{\text{3}}\text{ m}$ .

(b)

To determine

The maximum height of the vertical column made by granite without buckling.

Answer to Problem 80GP

Maximum height of the vertical column made by granite without buckling is $\text{6}\text{.4 }\times {\text{10}}^{\text{3}}\text{ m}$ .

Explanation of Solution

Given:

Density of granite, $\text{ρ = 2}\text{.7}\times {\text{10}}^{\text{3}}{\text{ kg/m}}^{\text{3}}$

Maximum compressive strength of granite $\text{= 170}\times {\text{10}}^{\text{6}}{\text{ N/m}}^{\text{2}}$

Formula used:

Maximum height of the steel column is determined by using the relationship of compressive strength, density and gravity.

  $\text{Compressive strength = ρ}\times \text{g}\times \text{h}$

Calculation:

Substitute the given values;

  $\begin{array}{l}{\text{h}}_{\text{max}}\text{ = }\frac{\text{Compressive strength of granite}}{\text{ρ}\times \text{g}}\\ {\text{h}}_{\text{max}}\text{ = }\frac{\text{170}\times {\text{10}}^{\text{6}}}{\text{2}\text{.7}\times {\text{10}}^{\text{3}}\times \text{9}\text{.8}}\text{ = 6}\text{.4}\times {\text{10}}^{\text{3}}\text{ m}\end{array}$

Conclusion:

Thus, maximum height of the vertical column made by granite without buckling is $\text{6}\text{.4 }\times {\text{ 10}}^{\text{3}}\text{ m}$ .