Given an aluminum shell perfectly bonded to a steel core, what is the thermal stress in the aluminum shell when the system is heated from the unstressed state (20∘C) to 180∘C? Consider only deformations in the axial directions. Give your answer in MPa

αAl=23.6×10−6K−1

EAl=70GPa

αSteel=11.7×10−6K−1

ESteel=200GPa

Thermal stress in Al shell (in MPa):?

-48.87315Mpa

steel core, what is the thermal stress in the aluminum shell when the system is heated from the unstressed state (20∘C) to 180∘C? Consider only deformations in the axial directions. Give your answer in MPa

αAl=23.6×10−6K−1

EAl=70GPa

αSteel=11.7×10−6K−1

ESteel=200GPa

Thermal stress in Al shell (in MPa):?

To find the thermal stress in the aluminum shell, we can use the formula:

Thermal stress = E * α * ΔT

where E is the Young's modulus, α is the coefficient of thermal expansion, and ΔT is the change in temperature.

Here, we will consider the aluminum shell, so we will use the properties for aluminum.

Given:
αAl = 23.6 × 10^(-6) K^(-1) (coefficient of thermal expansion)
EAl = 70 GPa (Young's modulus)
ΔT = (180 - 20) °C = 160 °C (change in temperature)

Substituting these values into the formula, we get:

Thermal stress = (70 GPa) * (23.6 × 10^(-6) K^(-1)) * (160 °C)

Converting GPa to MPa:

Thermal stress = (70,000 MPa) * (23.6 × 10^(-6) K^(-1)) * (160 °C)

Calculating the thermal stress gives:

Thermal stress = 263.68 MPa

Therefore, the thermal stress in the aluminum shell when heated from 20∘C to 180∘C is 263.68 MPa.

To calculate the thermal stress in the aluminum shell, we need to consider the difference in thermal expansion between the aluminum shell and the steel core. We can use the formula for thermal stress:

σ = α * E * ΔT

where σ is the thermal stress, α is the coefficient of thermal expansion, E is the Young's modulus, and ΔT is the change in temperature.

Given:

αAl = 23.6 × 10^-6 K^-1 (coefficient of thermal expansion for aluminum)
EAl = 70 GPa (Young's modulus for aluminum)
αSteel = 11.7 × 10^-6 K^-1 (coefficient of thermal expansion for steel)
ESteel = 200 GPa (Young's modulus for steel)
ΔT = 180°C - 20°C = 160°C (change in temperature)

First, let's calculate the thermal strain in both materials:

εAl = αAl * ΔT
= (23.6 × 10^-6 K^-1) * (160°C)
= 3.776 × 10^-3

εSteel = αSteel * ΔT
= (11.7 × 10^-6 K^-1) * (160°C)
= 1.872 × 10^-3

Next, we can calculate the stress in each material:

σAl = EAl * εAl
= (70 GPa) * (3.776 × 10^-3)
= 265.32 MPa

σSteel = ESteel * εSteel
= (200 GPa) * (1.872 × 10^-3)
= 374.4 MPa

Since the aluminum shell and the steel core are bonded together, the thermal stress in the aluminum shell will be equal to the thermal stress in the steel core. Therefore, the thermal stress in the aluminum shell when the system is heated to 180°C is 374.4 MPa.