How to account for thermal expansion?

Daily Dose 042 | Mechanics of Materials

How to account for thermal expansion?

Thermal expansion.

If we are not accounting for it in all of our engineering designs we are introducing a potentially catastrophic flaw.

Failing to account for the tendency of matter to change its shape, area, and volume in response to a change in temperature, then we are –

Welp, we are screwed, and we are screwing the public.

We are sure to see a problem in this vicinity on the FE Exam – we can afford to mess this one up y’all.

In this video, we dive into an FE Exam Practice Problem in the subject of MECHANICS OF MATERIALS, showing you how to quickly and efficiently account for THERMAL EXPANSION.

Key Definition

What is THERMAL EXPANSION?

As a solid material experiences an increase in temperature, the volume of the structure is ultimately impacted by increasing.

This happens because when the material is at standard conditions, the molecules are located in close proximity to one another which contributes to the defined shape of the structure.

As temperature increases, the molecules begin to vibrate at a more rapid speed and push away from one another.

This increased separation between the individual atoms causes the solid to expand…increasing the volume of the structure.

The Process

So how can we account for thermal expansion?

Accounting for thermal expansion in an engineering design problem typically involves the following steps:

• Understand the Material Properties

As you read through the problem statement, identify the material’s coefficient of thermal expansion. This value represents how much a material expands or contracts when subjected to a temperature change. The coefficient of thermal expansion is usually given in units of length per unit temperature.

• Determine the Temperature Range

Identify the temperature range over which the expansion or contraction needs to be considered. This range should include the initial and final temperatures of the system.

• Calculate the Thermal Expansion

Calculate the thermal expansion (or contraction) of the material using the formula found on page 131 of the NCEES FE Reference Handbook:

δ_t = αL(T – T₀)

Where:

• δ_t is the change in length or dimension due to thermal expansion or contraction
• α is the coefficient of thermal expansion
• L is the initial length or dimension of the material
• T is the Final Temperature
• T₀ is the Initial Temperature

This formula assumes that the material expands or contracts uniformly.

• Consider Constraints and Boundary Conditions

Take into account any constraints or boundary conditions that may affect the thermal expansion. For example, if the material is restrained from expanding in a certain direction, the resulting stress can cause deformation or structural issues.

• Evaluate Structural Integrity

Assess the impact of thermal expansion on the structural integrity of the system. Consider factors such as the material’s strength, the presence of joints or connections, and any potential stress concentrations.

• Design Compensating Mechanisms

If necessary, design compensating mechanisms to accommodate thermal expansion and prevent damage or failure. These mechanisms can include expansion joints, flexible connections, or other features that allow for controlled movement.

• Verify and Test

Validate your calculations and design assumptions through testing and analysis. Conduct experiments or simulations to observe the actual behavior of the system under thermal expansion conditions and verify that it meets the desired performance criteria.

Check out the video and see how we can go about solving this type of problem in the most efficient manner.

We are here to help.

As always, with Love, Prepineer

Video Review

[VIDEO] How to account for thermal expansion?