Contents

###### Daily Dose 031 | Mechanics of Materials

#### How can you solve for the reaction force from thermal expansion?

Why would knowing the reaction force from thermal expansion be important to us as engineers?

Properly accounting for thermal effects in our engineering designs is important to ensure safe, efficient and reliable systems in practice.

If we fail to do so, the consequences could be determinantal.

From bridges collapsing to airplane turbines exploding, understanding how to properly account for thermal changes in our designs should be a top priority.

At Prepineer, we believe it’s important *for all engineers* to be well versed in thermal expansion, and so does the NCEES as you will see on the FE Exam.

In this video, we dive into an FE Exam Practice Problem from the subject MECHANICS OF MATERIALS, specifically revolving around 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 is better known as THERMAL EXPANSION.

This happens because when material is at standard conditions, the molecules are located in close proximity to one another…this 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

## How can you solve for the reaction force from thermal expansion faster?

In the world of engineering, understanding how materials behave under different conditions is crucial.

One aspect we must account for is that of thermal expansion — which is the way materials expand or contract when exposed to temperature changes.

Thermal expansion has practical implications for the design and analysis of everything from bridges to spacecraft.

In situations where structures are constrained, thermal expansion can lead to significant forces, known as reaction forces. These forces must be carefully considered to ensure structural integrity and reliability.

But how do we determine the magnitude of these forces?

The process involves a blend of material science, physics, and mechanics of materials principles.

The following is a systematic approach to unraveling the forces at play due to thermal expansion, providing you with the tools to tackle this FE Exam problem type with confidence:

**Step 1: Understand Thermal Expansion**Recognize that thermal expansion occurs when a material changes in dimension (length, area, or volume) as a result of temperature change. This expansion can induce forces in structures that are constrained.

**Step 2: Identify the Material and Structure**Determine the material of the object and the type of structure it is part of. Different materials have different coefficients of thermal expansion, which affect how much they expand or contract with temperature changes.

**Step 3: Gather Necessary Information**Collect all relevant information: the coefficient of thermal expansion (α), the original length of the structure (L

_{0}), the temperature change (ΔT), and any constraints that prevent free expansion.**Step 4: Calculate the Expansion**Calculate the expected thermal expansion or contraction using the formula ΔL = αL

_{0}ΔT, where ΔL is the change in length.**Step 5: Analyze the Constraints**Examine how the structure is constrained. A structure that is not free to expand or contract will develop internal stresses and reaction forces at the supports or constraints.

**Step 6: Apply Static Equilibrium**For a structure in static equilibrium, the sum of the forces and moments must be zero. Use static equilibrium equations to relate the reaction forces to the thermal stresses caused by the restrained expansion or contraction.

**Step 7: Calculate the Reaction Force**Use the formula F = EA (ΔL/L

_{0}) to calculate the reaction force, where E is the modulus of elasticity of the material, A is the cross-sectional area, and ΔL is the change in length from Step 4. This formula assumes that the material is linearly elastic and that the deformation is within the elastic limit.**Step 8: Consider Additional Factors**Take into account any additional factors that might affect the reaction force, such as temperature gradients within the material, the presence of multiple materials with different expansion coefficients, and non-linear material properties.

Following these steps will help you solve for the reaction force from thermal expansion quick, efficiently and with a lot less stress.

And with all that, check out the video and see how to solve for the reaction force from thermal expansion.

As always, we are here to help, Prepineer