Question

Stainless steel rod has a gap of 0.0371 mm between its end and a rigid wall. The modulus of elasticity E = 210 GPa. The coefficient of thermal expansion α= 10 ×10⁻⁶ mm / mm⋅°C. The diameter of the rod is 13 mm.

When the temperature is raised to 140 °C, the magnitude of the stress (MPa) in the rod is _____.

Answer 1

The value of stress in the rod is 220.9 MPa

Step-by-step explanation:

As the data is not complete, a similar question is found online and the missing data is used from that question. Similar question is attached herewith.

From the given data

The allowed total strain is given as
`\delta_a=0.0371 mm`

The length of the rod is missing in this data which in the additional data is l=290 mm

The Modulus of Elasticity is given as E=210 GPa

The coefficient of thermal expansion is given as α= 10 ×10⁻⁶ mm / mm⋅°C.

The initial temperature is room temperature which is given as T1=22C

The final temperature is given as T2=140 C

The strain due to stress is given as

`\delta_s=(\sigma l)/(E)`

`\delta_s=(\sigma (0.290))/(210* 10^9)\\\delta_s=1.38095\sigma * 10^(-12)`

Now the thermal strain is given as

`\delta_c=l\alpha \Delta T\\\delta_c=0.290* 10 * 10^(-6)(T_2-T_1)\\\delta_c=0.290* 10 * 10^(-6)(140-22)\\\delta_c=0.0003422`

So now the equation of the allowed strain is given as

`\delta_a=\delta_s+\delta_c\\0.0371* 10^(-3)=1.38095\sigma * 10^(-12)+0.0003422\\(1.38095)/(10^(12))\sigma+0.0003422=(0.0371)/(1000)\\\sigma=-(10^(12)* \:0.0003051)/(1.38095)\\\sigma=-220934863.68 Pa\\\sigma=-220.9 MPa`

The negative sign indicate that the stress is compressive.

The value of stress in the rod is 220.9 MPa