Chapter 10, Problem 48P

To determine

Tabulate the relative magnitudes of modulus of elasticity of steel to aluminum alloys, copper alloys, titanium alloys, rubber, and wood.

Answer to Problem 48P

The relative magnitudes of modulus of elasticity of steel to given materials are tabulated in Table 1.

Explanation of Solution

The values of modulus of elasticity for the given materials are taken from table 10.5 in the text book.

The modulus of elasticity of steel $E_{\text{steel}}$ is 200 GPa.

Determining the average modulus of elasticity value for aluminum alloy is,

$\begin{array}{c}\text{Average =}\frac{\text{ 70+79}}{2}\\ =74.5\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{74.5}\\ =2.7\end{array}$

Determining the average modulus of elasticity value for copper alloy is,

$\begin{array}{c}\text{Average =}\frac{\text{ 110+120}}{2}\\ =115\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{115}\\ =1.74\end{array}$

Determining the average modulus of elasticity for titanium alloy is,

$\begin{array}{c}\text{Average =}\frac{\text{ 100+120}}{2}\\ =110\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{110}\\ =1.8\end{array}$

Determining the average modulus of elasticity for rubber is,

$\begin{array}{c}\text{Average =}\frac{\text{ 0}\text{.0007+0}\text{.004}}{2}\\ =0.002\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{0.002}\\ =100,000\end{array}$

Determining the average modulus of elasticity for steel is,

$\begin{array}{c}\text{Average =}\frac{\text{ 190+210}}{2}\\ =200\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{200}\\ =1\end{array}$

Determining the average modulus of elasticity for Douglas fir is,

$\begin{array}{c}\text{Average =}\frac{\text{ 11+13}}{2}\\ =12\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{12}\\ =16.7\end{array}$

Determining the average modulus of elasticity for oak is,

$\begin{array}{c}\text{Average =}\frac{\text{ 11+12}}{2}\\ =11.5\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{11.5}\\ =17.3\end{array}$

Determining the average modulus of elasticity for Southern Pine is,

$\begin{array}{c}\text{Average =}\frac{\text{ 11+14}}{2}\\ =12.5\end{array}$

$\begin{array}{l}\therefore \text{relative magnitude}\text{=}\frac{E_{\text{steel}}}{\text{average}}\\ =\frac{200}{12.5}\\ =16\end{array}$

Thus, the determined relative magnitudes of modulus of elasticity of steel to given materials are tabulated in table 1.

The Table 1 shows the material, modulus of elasticity, and the relative magnitudes of modulus of elasticity of steel.

Conclusion:

Hence, the relative magnitudes of modulus of elasticity of steel to given materials are tabulated in Table 1.