Thermal stesses

By : Chandresh Suthar ,
Govind Tade ,
Manav Sonani..

1. Gandhinagar Institute of Technology Group member name & enrollment no. :- Chandresh Suthar 140120119229 Subject : Mechanics of Solid(2130003) Topic : Thermal Stress & Strain Branch:Mechanical BatchC-3

2. Flow of the Presentation :- Introduction of thermal stress and strain Thermal Stresses in Bars of Tapering Section Thermal Stress in Bars of Varying section Temperature stresses in composite bars

3. FIG. 2-19 Block of material subjected to an increase in temperature Thermal effects Changes in temperature produce expansion or contraction of materials and result in thermal strains and thermal stresses For most structural materials, thermal strain ε T is proportional to the temperature change Δ T : ε T = α ( Δ T) When a sign convention is needed for thermal strains, we usually assume that expansion is positive and contraction is negative coefficient of thermal expansion

4. FIG. 2-20 Increase in length of a prismatic bar due to a uniform increase in temperature (Eq. 2-16) Suppose we have a bar subjected to an axial load. We will then have: ε = σ / E Also suppose that we have an identical bar subjected to a temperature change Δ T. We will then have: ε T = α ( Δ T) Equating the above two strains we will get: σ = E α ( Δ T) We now have a relation between axial stress and change in temperature Thermal Stress

5. FIG. 2-19 Block of material subjected to an increase in temperature Assume that the material is homogeneous and isotropic and that the temperature increase ΔT is uniform throughout the block. We can calculate the increase in any dimension of the block by multiplying the original dimension by the thermal strain. δ T = ε T L = α (ΔT) L Temperature – Displacement relation

6. Thermal Strain

7. Thermal Stresses In Bars of Tapering Section:- Taken circular bar uniformly tapering which has: l = length of bar = Dia of bigger end of bar = Dia of smaller end of bar t = change in temperature = coefficient of thermal expansion.   l A B    

8. Derive the equation of thermal stress for tapering section ; Due to contraction Compressive force P acted when temperature will be rise ; Due to expansion when temperature will be rise that time; Here no change in length in equation (1) & (2), so , = 𝑙.𝛼.𝑡  P Max. stress =   𝛿𝑙=𝑙.𝛼.𝑡 (2) (1)  

9. Thermal Stress in Bars of Varying section From Hooke’s Law: From the definition of strain: Equating and solving for the deformation, With variations in loading, cross-section or material properties,

10. Example Determine the deformation of the steel rod shown under the given loads. SOLUTION: Divide the rod into components at the load application points. Apply a free-body analysis on each component to determine the internal force Evaluate the total of the component deflections.

11. SOLUTION: Divide the rod into three components: Apply free-body analysis to each component to determine internal forces, Evaluate total deflection,

12. Temperature stresses in composite bars

13. Temperature Stresses Contd.

14. Thank you