Consider the following statements regarding thermal stresses: 1. If the temperature change is uniform throughout the body, the thermal strain is also uniform. 2. If thermal deformation is permitted to occur freely, no internal forces will be induced in the body, and there will be no strain and no stress. 3. If the deformation of a body is restricted, either totally or partially, internal forces will develop that oppose the thermal expansion or contraction. The stresses caused by these internal forces are known as thermal stresses. Which of the above statements are correct?
Analysis of Statement 1: Uniform Temperature Change
Statement 1 claims that a uniform temperature change throughout a body leads to uniform thermal strain. The formula for thermal strain is \epsilon_t = \alpha \Delta T$, where \alpha$ is the coefficient of thermal expansion (a material property) and \Delta T$ is the change in temperature. If \Delta T$ is uniform across the body, then \epsilon_t$ will also be uniform. Therefore, Statement 1 is correct.
Analysis of Statement 2: Free Thermal Deformation
Statement 2 suggests that if thermal deformation is allowed freely, there will be no strain and no stress. When a body is free to deform thermally, it undergoes thermal strain (\epsilon_t = \alpha \Delta T$). However, because there are no constraints preventing this expansion or contraction, no internal forces are generated to resist the deformation. This means there is no thermal stress. The statement incorrectly claims "no strain"; thermal strain *does* occur, but it does not result in stress. Therefore, Statement 2 is incorrect.
Analysis of Statement 3: Restricted Deformation
Statement 3 explains that if a body's deformation is restricted (partially or fully) during a temperature change, internal forces arise, causing stresses known as thermal stresses. This aligns perfectly with the definition of thermal stress. When expansion or contraction is blocked, the material experiences internal forces that create stress. Hence, Statement 3 is correct.
Conclusion on Thermal Stress Statements
Based on the analysis:
- Statement 1 is correct.
- Statement 2 is incorrect.
- Statement 3 is correct.
The statements that are correct are 1 and 3.
