Three Bars at Different Temperatures Stress Calculator

Related Resources: calculators

Three Bars at Different Temperatures Stress Calculator

Three Bars at Different Temperatures Calculator and Equations for Stress

Stress is calculated for each bar.

Preview Three Bars at Different Temperatures Stress Calculator

Eq. 1

σ_{1} = - E_{1} α_{1} (T_{i} - T_{o}) C_{1}

Eq. 2

$σ_{2} = - E_{2} α_{2} (T_{i} - T_{o}) C_{2}$

Eq. 3

$σ_{3} = 1 / A_{3} (σ_{1} A_{1} + σ_{2} A_{2})$

Eq. 4

$C_{1} = [\frac{A_{2} E_{2} + A_{3} E_{3}}{A_{1} E_{1} + A_{2} E_{2} + A_{3} E_{3}}] [\frac{1 - A_{2} α_{2} E_{2} (T_{2} - T_{0}) + A_{3} α_{3} E_{3} (T_{3} - T_{0})}{α_{1} (T_{1} - T_{0}) (A_{2} E_{2} + A_{3} E_{3})}]$

Eq. 5

$C_{1} = [\frac{A_{1} E_{1} + A_{3} E_{3}}{A_{1} E_{1} + A_{2} E_{2} + A_{3} E_{3}}] [\frac{1 - A_{1} α_{1} E_{1} (T_{1} - T_{0}) + A_{3} α_{3} E_{3} (T_{3} - T_{0})}{α_{2} (T_{2} - T_{0}) (A_{1} E_{1} + A_{3} E_{3})}]$

Figure 1 - Three Bars at Different Temperatures

Where

E₁ = modulus of elasticity bar 1
E₂ = modulus of elasticity bar 2
E₃ = modulus of elasticity bar 3
α₁ = coefficient of thermal expansion bar 1
α₂ = coefficient of thermal expansion bar 2
α₃ = coefficient of thermal expansion bar 3
A₁ = Contact surface area bar 1
A₂ = Contact surface area bar 2
A₃ = Contact surface area bar 3
T₀ = temperature initial temperature
T₁ = temperature bar 1
T₂ = temperature bar 2
T₃ = temperature bar 3
σ₁ = Stress bar 1
σ₂ = Stress bar 2
σ₃ = Stress bar 3
C₁ = Constant
C₂ = Constant

Bell Helicopter Structural Design Manual, 1977

Pinned End Column Different Face Temperatures Calculator and Equations
Restrained Beam Different Face Temperatures Calculator and Equations
Two Bars Different Temperatures Stress Calculator and Equations
Bar Restrained With Spring Uniform Heat Applied Calculator
Bar Restrained One End and Gap on Other Formula and Calculator
Restrained Beam Thermal Expansion Force Axial Stress Calculator
Linear Thermal Expansion Equation and Calculator
Pipe Expansion Thermal Loop Equations and Calculator
Fastener Thermal Expansion Equation and Calculator
Compression Tension Stress Linear Thermal Expansion Equation and Calculator
Thermal Linear Expansion of AISI 303 Stainless Steel
Heat Loss through a Double-Pane Window Equation and Calculator A double-pane window is considered. The rate of heat transfer through the window and the inner surface temperature are to be determined.
Heat Loss through a Single-Pane Window Equation and Calculator
Heat Loss through Aluminum Framed Window Equations and Calculator
Heat Loss or Gain From Pipe Excel Spreadsheet Calculator
Heat Loss Through a Wall Equation and Calculator Determine the steady state heat loss through a single wall.
Heat Loss Through Enclosure Walls Equations and Calculator Determine required wall thickness of an enclosure for temperature control and insulation requirements. Known Design Data: Size (thickness) of insulated enclosure walls and inside and external surface temperatures