The RFEM 6 and RSTAB 9 structural analysis programs offer powerful capabilities for simulating the thermal strain of structural components with the application of temperature loads. These programs enable you to account accurately for the effects of temperature variations, which can significantly impact the behavior of materials and structures. By simulating both uniform and non-uniform temperature changes, RFEM 6 and RSTAB 9 allow for a comprehensive analysis of the way thermal expansion or contraction can influence structural performance.
In this article, we will explore the theoretical background of thermal effects, specifically focusing on membrane and bending effects, and demonstrate how these thermal effects can be modeled and applied in RFEM 6. Using practical examples, you will see how these temperature-related deformations can be captured effectively within the software, providing valuable insights for the design and analysis of structures exposed to varying temperatures.
1. Membrane Effect (Uniform Temperature Change)
A uniform temperature change along the height of a component induces what is known as the membrane effect. This occurs when the entire component undergoes the same temperature variation across its length, without any gradient in the perpendicular direction. Under a uniform temperature change, the structural element experiences thermal expansion or contraction without bending deformation.
The membrane effect is characterized by uniform strain along the member axis, resulting in purely axial deformation (Image 1). When the temperature increases, the material expands along the axis, and when the temperature decreases, it contracts. Importantly, this effect does not generate internal moments or bending stresses, but it does create axial forces within the member if the linear expansion of the member is constrained, such as in a statically indeterminate system.
2. Bending Effect (Non-Uniform Temperature Change)
In contrast to the membrane effect, non-uniform temperature distribution along the height or thickness of the component results in bending deformation (Image 2). This happens when the temperature varies across the cross-section of the structural element, creating a temperature gradient.
When a component is subjected to a temperature gradient, the material expands differently at different points along its height or thickness. This differential expansion causes internal moments and bending stresses, which arise only in a statically indeterminate system, where the expansion is constrained. The component will attempt to bend in response to the varying temperatures at different sections of the element, with the top part of the section expanding more than the bottom part, or vice versa. Therefore, the bending effect can be understood as the structural element bending due to the thermal gradient.
3. Combined Effect: Membrane and Bending
In practice, structural components are often subjected to both uniform temperature changes (membrane effect) and temperature gradients (bending effect). The total thermal strain in the component can thus be described as a combination of these two effects:
- The membrane effect causes axial deformation (tension or compression) due to the uniform temperature change along the member axis.
- The bending effect produces flexural deformation due to the temperature gradient across the height or thickness of the component.
This combined effect leads to non-uniform deformation (Image 3), as both axial forces and bending moments are generated within the component, which occurs when the system is statically indeterminate and the expansion is constrained.
Simulation of Thermal Strains in RFEM 6
In RFEM 6, you can simulate both membrane and bending effects by applying two types of temperature loads: “Temperature” and “Temperature Change”. These can be defined easily using the “New Member Load” window, where you can select the appropriate load type from the “Load Type” drop-down menu (Images 4 and 5).
1. “Temperature” Load Type
The “Temperature” load in RFEM 6 allows you to specify the top temperature (Tt) and the bottom temperature (Tb) of the member. The temperature distribution can be:
- Uniform: When Tt=Tb, meaning the member undergoes a uniform temperature change, leading to membrane effects (no bending).
- Non-uniform: When Tt≠Tb, this creates a temperature gradient across the component, leading to both membrane and bending effects.
2. “Temperature Change” Load Type
The “Temperature Change” load allows you to define a centerline temperature (Tc) and directly specify the temperature difference ΔT between the top and bottom of the member. A positive centerline temperature means the member is warming, and a positive temperature difference implies that the top of the member is heating up more than the bottom, inducing bending.
Practical Examples
To better understand the effects of temperature loads, let’s explore several scenarios where the same cantilever beam is subjected to varying temperature conditions. In each case, we will consider how the different temperature variations can be simulated in RFEM 6 using the "Temperature" and "Temperature Change" load types. Both load types can represent the same temperature effects; the only difference is the way the input is defined. We will highlight how these variations influence the beam’s behavior, particularly in terms of bending and deformation.
1. Scenario: Heated Floor System in Building
In this scenario, a cantilever beam supports a portion of the floor system in a building, and it is exposed to a uniform temperature increase of 10°C due to the activation of an underfloor heating system. The heating system raises the temperature of the entire beam uniformly along its length, causing the beam to heat up evenly.
How to Apply this in RFEM 6:
This scenario can be simulated in RFEM 6 using the "Temperature Change" load type, where the centerline temperature (Tc) is set to 10°C, representing the uniform warming of the beam (Image 6). The temperature difference (ΔT) between the top and bottom surfaces of the beam would be zero, as the temperature increase is uniform along the beam’s length.
Alternatively, the same simulation can be performed using the "Temperature" load type, where both the top temperature (Tt) and bottom temperature (Tb) are set to 10°C (Image 7). In both cases, the result will be uniform expansion of the beam without causing any bending, as the entire beam undergoes the same thermal expansion (Image 8).
2. Scenario: Beam Exposed to Heat Source
A cantilever beam is situated in an industrial environment, where it is exposed to heat from one side of the beam. For example, during a manufacturing process, the beam may be subjected to higher temperatures (e.g., 30°C) on one side, while the opposite side of the beam remains at a lower temperature (e.g., 20°C) or is shielded from the heat.
How to Apply this in RFEM 6:
This can be simulated using the "Temperature" load type with Tt ≠ Tb (Image 9), where the top temperature (Tt) is set higher (30°C) due to the heat source, and the bottom temperature (Tb) remains lower (20°C). The temperature difference across the top and bottom of the beam creates a thermal gradient, which causes the beam to expand and bend (Image 10).
3. Scenario: Beam Exposed to Uneven Solar Radiation
A cantilever beam is in an outdoor environment, where one surface is exposed to sunlight, while the opposite surface is shaded. As a result, one surface of the beam heats up to 5°C, while the other remains at -5°C. In this case, the centerline temperature is 0°C, but a temperature gradient exists across the beam, with one surface experiencing a higher temperature than the other. The primary focus in this scenario is to capture the bending caused by the thermal gradient created by the temperature difference (ΔT) between the top and bottom surfaces of the beam, leading to bending due to differential expansion.
How to Apply this in RFEM 6:
This scenario can be simulated in RFEM 6 using the "Temperature Change" load type (Image 11), where the temperature difference (ΔT) between the top and bottom of the beam is specified (ΔT=10°C). The centerline temperature (Tc) is set to 0°C, but the temperature difference (ΔT) is non-zero, representing the thermal gradient that causes the beam to bend. Note that the "Temperature Change" load type is used, and there is no need to define specific temperatures for the top (Tt) and bottom (Tb) surfaces, as the focus is on the bending induced by the thermal gradient created by the ΔT.
Final Words
In conclusion, RFEM 6 offers a flexible approach for modeling thermal effects on structural components, allowing you to simulate both membrane and bending effects with the “Temperature” and “Temperature Change” load types. These load types enable accurate simulations of temperature variations along the length and height of a member, ensuring a thorough analysis of thermal strains.
By understanding how to effectively apply these load types, engineers can predict the behavior of structural components under thermal loads, leading to more accurate analyses and optimized designs. Whether dealing with uniform heating, localized temperature exposure, or varying conditions, RFEM 6 provides the necessary tools to manage temperature-related effects in your structures.
