Advanced Simulation for Thermal Stress Assessment

1. Introduction

Architecture is an ever-evolving field of study, like a chameleon that changes its skin with the trends of the changing world. Architects and engineers have managed to keep up with these trends using curtain wall systems. The versatility of curtain wall systems allows for a wide range of materials to fit comfortably within its framing members and as a result, it allows the architects to push past the traditional monotone facade of a building (Murray 2009). One of the most popular and attractive materials used within curtain wall systems is glass, thanks to its unique and variegated properties. Architectural glass provides transparency for natural lighting, thermal insulation, sound isolation, as well as a variety of looks through the use of tints, frits, screen prints, and even from its composition itself (the type of heat treatment or substrate used on the glass) (Chowdhury 2007). Not to mention its mechanical strength and resistance to chemical agents, qualities that give glass the praise it deserves (Galuppi et al. 2023; Hinfi et al. 2022). In the last 10 years, due to more stringent building codes to meet energy reduction goals, local energy guidelines and regulations require curtain wall applications to introduce highly insulated spandrels and shadowbox to limit head losses in winter or complex exterior solar shading and glass treatment to reduce unwanted solar heat gains (Xie, Y. et all, 2023; Jackson et al. 2020; Sozer 2010). All these measures have a direct impact on glass thermal stress risk as they increase heat build-up, create uneven temperature distributions or shadow patterns (Galuppi et al. 2021; Hinfi et al. 2022; Polakova et al. 2018).

During its service life, the glazing undergoes thousands of cycles of external climatic conditions: air temperature variations, wind speed, sky conditions and solar radiation. Even small-scale environmental conditions such as neighbouring buildings, external shading elements, internal blinds and opaque back-panels, all of which have an impact on the temperature distribution on the glass (Anastasiou 2016).

In the presence of a large temperature difference across the glass pane (at a given instant) mechanical stresses are generated by the differential thermal expansion of the glass mass. Although glass can withstand high values of compression stress, tension stress can easily cause the glass to break, particularly at its edges, where defects and imperfections tend to concentrate due to the cutting process, grinding and manipulation of the glass panes (Foraboschi 2017).

As a result, curtain wall configurations that include glazing can be at risk for thermally induced fractures also known as thermal shock or thermal breakage. Thermal breakage occurs when a glass pane experiences a large temperature gradient across its surface, in essence a large portion of the glass pane exhibits considerably higher temperature than the remainder, inducing high-tension levels along the edges (Fronsoe et al 2018).

For example, when the building has a large overhang feature that casts a shadow on the glass in the early afternoon, the shaded area of the glass remains cool from the morning hours and the non-shaded area begins to warm up from the rays of the sun. These climatic and geometric conditions could cause the glass pane to break (Galuppi et al. 2023). With this said, it does not mean that we can never have a glazing close to an overhang feature, there are many variables that need to be taken into account in order to determine if there is risk for thermally induced fractures, such as but not limited to:

• Location of the building
• Orientation of the building
• Type of heat treatment on the glass panes
• Type of architectural features on the building
• Colours of framing members and panels
• Presence of shadow boxes (material build up behind the glazing to conceal ceiling or floor)

During the early design stages of a curtain wall facade, it is important to assess the potential risk of thermal breakage. The earlier it is determined, the more time available to discuss and modify the system in order to eliminate the risk. Failure to complete a thermal stress assessment can undermine people's safety and could result in large monetary losses. Requiring the facade contractor to acquire and secure replacement glass, site personnel to remove the broken glass and install glass replacements, and potential damage to the facade contractor’s company image, providing a difficult financial environment to obtain new projects.

The thermal stress analysis (TSA), more generally called thermal shock risk assessment, is addressed unevenly by standards, glass producers, universities and industry expertise across the world. In design practices, standards and codes are typically referenced, such as the French standard (NF DTU 39 P3, Polakova et al. 2018), and ASTM E2431 (ASTM E2431). However, these recommendations are somewhat outdated, offering simplified rules and specifications that often conflict with each other when calculating thermally induced stresses. Furthermore, there is a lack of standardized procedures regarding the type of analysis (stationary or transient), time frame, and thermal parameters involved. While commercial software exists for this purpose, they are often “black-boxes”, lacking documentation on the underlying assumptions. Additionally, general-purpose thermal software coupled with linear stress calculation based on the French standard equations, may not capture the full complexity of the problem often overlooking the conduction phenomena between regions of the panel, thus inducing an overestimation of the thermal and stress gradients.

Although these standards and methodologies are in place there are still limitations to this approach, proving to be too conservative and failing to optimise the curtain wall system. The design of glass panes under transient or semi-transient climatic loads, specifically solar radiation and environmental temperatures are often overlooked despite being a key aspect of glass thermal behaviour. (Polakova et al. 2018; Schwind et al. 2022)

The objective of this paper is to evidence gaps in current assumptions and approximations of existing analytical/numerical calculation methods and to present a novel finite elements (FE) based approach aiming to provide a more realistic assessment of temperature and stress distributions across glass lites due to climatic conditions.

2. Proposed Methodology

Considering the current standards lack of uniformly-defined procedures, which often carry simplified assumptions that lead to over-conservative results, this paper presents an advanced simulation workflow to accurately assess the temperature and stress distribution in glass lites for complex curtain wall applications. To start with, the location and orientation of the building must be evaluated in order to appropriately extract the required climatic data used to define the boundary conditions. Secondly, a typical 2D steady-state heat-transfer analysis is completed to set as a comparative baseline for the proposed methodology. Thirdly, a simplified 2D transient simulation considering a typical year's weather data is assessed to identify the high risk boundary conditions within that year in terms of orientation and specific time/days of the year. Once the critical environmental conditions are defined, a custom 3D thermoelastic model is used for assessing thermal stresses in each monolithic glass panel of an insulated glazing unit under transient conditions. This model accounts for environmental factors such as time-varying external/internal temperatures and radiation from the sun, sky vault, shadow effects and incorporates heat conduction between regions at varying temperatures. In a further stage of the approach, the temperatures are applied to a finite element model in order to assess the state of stress derived by the temperature distribution. Because of the large number of input temperature data to the finite element model, the pre-processing and post-processing from the commercial FEM code (Strand®) is undertaken through a tool automating the procedure by means of the Strand® Application Programming Interface (API). This combined thermal-mechanical analysis allows for a more accurate temporal and spatial assessment of the temperature and stress distribution on each glass lite compared to the current linear approaches.

Fig. 1: Simulation Workflow. In grey the steps for comparison with typical simulation workflow

2.1 2D Steady State thermal analysis

In current practice, based on guidelines and standards, facade consultants, facade contractors and glass manufacturers often implement one-dimensional or two-dimensional steady state thermal simulations to assess the temperature distribution across the glass panes.

Understanding the behavior of the glazing alone, 1D simulations, without taking into consideration the surrounding facade components, can lead to incorrect assessments of thermal break risk. In order to provide a more precise assessment, 2D simulations have the ability to capture in more detail the actual behavior of the facade system considering heat flow through glazing and framing systems. Two-dimensional steady-state heat-transfer FE analyses using Physibel BISCO are carried out on this paper to compare typical delta temperatures and induced mechanical stress against the proposed simulation methodology.

The approach used for the 2D steady state analysis, according to industry practice and French Standard involves the creation of two models recreating the conditions shown in figure 2. The initial model assumes the full effects from the sun and the supplementary model limits the sun’s radiation to 10% across the part or entirety of the model to simulate a partly shaded condition. The delta temperature for each lite is calculated by taking the highest temperature reading from the full radiation model and the lowest temperature reading from the 10% radiation model. This calculation approach could be defined as representative of absolute worst case conditions, however, it is the typical approach used by glass manufacturers when analyzing thermal stress and maximum temperature.

Fig. 2: Left - Representation of typical simulation approach in 2D steady state thermal modelling (REF), Right - 2D thermal model

Additional level of conservatism and uncertainty in typical steady state thermal stress assessment is linked to the boundary conditions selected as the governing case. Usual approach relies on the designer analyzing the climate file for the project location and determining worst case climate conditions based on experience and/or 1D checks without absolute certainty that the selected air temperature and radiation will translate into actual worst thermal stress across the glass pane. In the 2D steady-state analysis carried out for this paper the boundary conditions are listed in the table below.

Table 1: Boundary conditions for the 2D Steady State Analysis

After simulating the temperature distribution across the glass panes and identifying the max delta temperature,, the maximum stress on the glass is calculated According to NF P78-201-1_A1:,

σth ＜σadm (1)
σth = Kth * E * 𝛼 * ΔT (2)

Where,
Kth = Kf * Ko (3)

Where,
Kf: frame heat capacity
Ko: external shadow on the glass
Kth: thermal stress coefficient
= 0.8 for frame systems with low heat capacity, no shades
= 0.9 for frame systems with low heat capacity, with shades
= 1.0 for frame systems with mean heat capacity, with shades
= 1.1 for frame systems with high heat capacity, with shades
E: glass Young’s Modulus (70000 MPa)
𝛼: glass thermal dilation coefficient (9*10-6)

2.2 2D Transient thermal analysis

The first step in the proposed methodology requires the completion of a 2D transient thermal simulation for the typical horizontal and vertical sections of the facade system. Geometric, material properties and environmental hourly data (air temperature, global and diffuse solar radiation, wind speed) are imported in Physibel Bistra. The Bistra software employs advanced finite element analysis (FEA) and detailed solar processor, to model the dynamic thermal behaviour of building elements subjected to varying environmental conditions. 2D detailed transient analyses carried out in software like Bistra allow to take into account for hourly variation of temperature and incident solar radiation, actual sun position, shadows cast on the glazing by exterior building features (like fins, projections, solar shading), solar angular dependent properties of glazing and thermal inertia of the facade system. All characteristics that play an important role to accurately determine the magnitude and temperature distribution in facade systems that are often missed in traditional 2D steady state or simplified 1D transient models.

Fig. 3: Left - Glass solar reflection angular behavior, Right - 2D thermal model with solar calculator

The main objective of the hourly yearly transient simulation, proposed in the paper, is to determine the environmental conditions, orientations and time of year that lead to the highest temperature differential across each individual glass lite in the facade assembly and subsequent risk of thermal stress breakage as shown in section 4.1, figure 6 and 7. Selected environmental conditions and timeframes across the year are then used in detailed 3D transient thermal analysis.

In addition, the hourly delta temperature calculated with this set of simulations can still be used to calculate the linear maximum stress according to the formulas presented in section 2.3. For the purpose of this paper, the stresses calculated with a linear formula are used for comparison between steady-state results and detailed stress distribution as result of 3D transient analysis as shown in section 4.1 and 4.2.

2.3 3D Transient thermal analysis

The results of 2D transient analysis, presented in the previous section are fed to detailed 3D transient thermal models to generate accurate temperature distributions across each individual glass lite. Once detailed 3D geometry is created thermal and optical properties of the facade system can be set up in Physibel Voltra. Physibel Voltra, similarly to Bistra, is a finite element analysis (FEA) with detailed simulation of radiation based on view factors and stable calculation of non-linear radiation problems. Crucial step in the simulation workflow is the creation of a calculation grid/mesh. For thermal stress analysis it is recommended to create a uniform grid between 25-50 mm size in the plane of the glass with refinement across the edges, and three sections across the thickness of the glass (two surface and midpoint). Dynamic thermal behavior 3D transient models allow to fully capture the thermal behavior of the system like heat build-up in shadowboxes, heat flow through vertical and horizontal framing members, and are able to generate detailed temperature distribution maps that can be exported and analyzed by structural mechanical software.

2.4 Temperature distribution to stress distribution

One the outputs provided by Voltra is a sequence of text files, one for each step of the dynamic transient thermal analysis. The file contains a list of temperatures, assigned to every node of the mesh grid. Combining these data with a structural plate model file, it is possible to generate a structural model of each glazing, by a finite element code and run an analysis to simulate the structural response of the system under the sequence of temperature distribution for the different steps of the thermal analysis. The approach is straightforward, but its adoption in scenarios of practical relevance is extremely time consuming and onerous, due to the extensive amount of data that must be processed and the need to reproduce in the structural model the same mesh of the thermal model: indeed, it is expected to apply the temperature inputs to the same positions of the Voltra outputs. For these reasons, in order to use the full procedure during the design phase, the authors have developed a tool, taking advantage of the Application Programming Interface (API) of the commercial finite element code Strand®. The user is required to choose a Voltra project file and the initial result file from a sequence. After making selections regarding the procedure for temperature extraction from the Voltra glass model (averaging data through thickness or utilizing surface temperature or maximum), FEA type (quasi-static or dynamic, linear or nonlinear), and desired results display (nodal stress or Gauss point stress), the tool initiates the collection of mesh data and temperature time histories. Subsequently, the corresponding structural model is automatically generated and solved by the API. This automated process enables rapid analysis of representative temperatures spanning multiple days within minutes. Upon completion of the procedure, the tool generates a chart displaying all stress time histories, extracted via API from the Strand® Analysis solution, as demonstrated in the case study.

3. Case Study

3.1 Facade and Location

The following case study is intended to demonstrate the proposed methodology for a typical curtain wall construction that consists of a vision portion and a shadowbox position with a kiss transom intermediate to separate them. The kiss transom creates a separation between the vision and opaque portion without physically splitting the glazing in two independent pieces, as shown in figure 4. This condition creates high temperature differences between the vision and insulated area of the glass, causing high risk for thermal stress. In addition, the glazing is framed around by an aluminum fin that will cast shadows across the surface of the glass, potentially increasing the delta temperature. The overall curtain wall panel measures 4850 mm x 1320mm with a shadowbox of 1250mm x 1160mm. The case study is located in San Jose, California, United States which is characterized by a mild dry climate (low exterior temperatures around 0-5°C during the winter and maximum temperatures around 30°C) with predominant clear sky conditions with radiation peaks up to 1000 W/m2.

Fig. 4: 3D Curtain wall panel: Bottom - 2D Horizontal sections, Right - 2D Vertical section

The glazing and shadowbox composition are as follows:

• Glazing: 8mm Low-iron Clearvision + 1.52mm Acoustic Clear PVB + 6mm Low-iron Clearvision with Stopray Vision 50 on #4 - 16mm Argon 90% - 6mm Low-iron Clearvision
• 99mm Unventilated air cavity
• 3mm Aluminum Sheet, RAL 9004, absorption 98% (Thermal conductivity λ= 160 W/mK)
• 76mm Mineral Wool (Thermal conductivity λ= 0.035 W/mK)

The climatic data for San Jose, CA, USA was acquired using the Global Meteorological Database Meteonorm software. The following table summarises the boundary conditions used at each step of the proposed methodology.

Table 2: Boundary conditions for case study

For the steady state calculation, a cool winter’s day with relatively high solar radiation has been defined as worse-case based on previous experience. For the 2D transient calculation, a full year was evaluated on two elevations of the building; south and west. The results from the 2D transient model determined the boundary condition for the 3D transient model. The 3D transient calculation considers the west elevation for 4 days at 30 minute time steps starting August 31st through September 3rd.

Fig. 5: Temperature and Horizontal Global radiation for San Jose, CA typical year.

4. Results

4.1 2D thermal analysis results

Within this section, two types of 2D results are showcased; a typical 2D steady-state heat-transfer analysis completed to set as a comparative baseline for the proposed methodology and a simplified 2D transient simulation considering a typical year's weather data. The results of the 2D steady-state thermal analysis conducted on the vertical section of the glass assembly under full radiation and reduced radiation conditions are presented in table 3.

Table 3: Summary of Differential Temperatures for the 2D Steady State Analysis

1 _{Note that Glass Pane 1 and Glass Pane 2 are part of a laminate lite. Therefore, the temperature gradient for the laminate is considered to be the maximum temperature between Glass Pane 1 and Glass Pane 2 at full solar radiation, minus the maximum temperature between Glass Pane 1 and Glass Pane 2 at 10% radiation, considering Glass Pane 1 and Glass Pane 2 as a single lite.}

The analysis focused on assessing temperature variations across different glass panes. The temperatures recorded include the minimum and maximum temperatures observed under both full radiation and 10% radiation scenarios. Under full radiation, outer laminate lite exhibited a temperature range between 38.59°C (minimum) and 72.28°C (maximum). The temperature difference (ΔT) between maximum temperature under full radiation and minimum temperature under 10% radiation was calculated for each glass pane. For outer laminate lite, the delta temperature was determined to be 47.8°C, indicating a significant temperature differential between full and reduced radiation conditions. Glass Pane 3, constituting the inner monolithic lite, displayed a broader temperature range, with a minimum temperature of 27.45°C and a maximum temperature of 94.82°C under full radiation. The corresponding ΔT for the interior lite was calculated as 67.3°C, emphasizing the pronounced impact of radiation levels on temperature distribution within the glass assembly.

The temperature differences shown in Table 3 are then used to calculate the stress across each glass lite using the formula 2.

Outer Laminate Lite:

σth = Kth * E * 𝛼 * ΔT (2)
σth = (0.9) *(70000) * (9*10-6) * (47.8)
σth,A = 27.1 MPa

The maximum allowable stress for a laminated annealed lite with ground edges is 24.0 MPa, therefore this lite will require a heat strengthened lite with an admissible stress of 87.5 MPa.

Inner Monolithic Lite:

σth = Kth * E * 𝛼 * ΔT (2)
σth = (0.9) *(70000) * (9*10-6) * (67.3)
σth,B = 38.1 MPa

The inner monolithic lite is above the maximum allowable stress for an annealed lite and requires heat strengthened as its minimum heat treatment.

As shown, in the results generated based on steady state thermal analysis and linear stress calculation in formula 2 and 3, it is possible to notice that both inner and outer lite of the glazing layers require a heat treatment to resist thermally induced stresses.

As mentioned in section 2.1, a steady state analysis relies on the designer's ability to analyze the climate file to determine worst case climate conditions based on experience without absolute certainty that the selection translates into the actual worst thermal stress across the glass pane. To overcome this uncertainty, a 2D transient analysis allows importing environmental hourly data (air temperature, global and diffuse solar radiation, wind speed) for a full year reducing uncertainty of the boundary conditions selection and including more accurate representation of the optical and thermal behavior of the construction assembly such as shadow pattern, angular properties and thermal inertia.

The results of the 2D transient thermal analysis conducted on the vertical section of the glass assembly are presented in table 4.

Table 4: Summary of Differential Temperatures for the 2D Transient Analysis

For the outer laminate lite, glass pane 1 exhibited a temperature range between 26.25°C (minimum) and 44.35°C (maximum), while glass pane 2 recorded temperatures ranging from 27.16°C (minimum) to 48.96°C (maximum). The temperature difference (ΔT) between the maximum and minimum temperatures within the outer lite was calculated to be 23.84°C. Similarly, for the inner lite (Glass Pane 3), temperatures ranged from 27.94°C (minimum) to 73.63°C (maximum). The calculated temperature difference (ΔT) within the Inner Monolithic Lite was determined to be 45.69°C.

As per steady state analysis the temperature differences shown in Table 4 are then used to calculate the stress across each glass lite using the formula 2.

Outer Laminate Lite:

σth = Kth * E * 𝛼 * ΔT (2)
σth = (0.9) *(70000) * (9*10-6) * (23.84)
σth,A = 13.51 MPa

The maximum allowable stress for an annealed lite with clean cut edges is 20.0 MPa.

Inner Monolithic Lite:

σth = Kth * E * 𝛼 * ΔT (2)
σth = (0.9) *(70000) * (9*10-6) * (45.69)
σth,B = 25.91 MPa

The inner monolithic lite is above the maximum allowable stress of 24.0 MPa for an annealed lite with ground edges and requires heat strengthened as its minimum heat treatment.

These findings illustrate the transient thermal behavior of the glass assembly, revealing significant temperature differentials across different glass panes over time. The observed temperature stresses variation are significant compared to the two-dimensional steady state, emphasizing the importance of transient thermal analysis in capturing temporal variations and informing design considerations for glass assemblies in complex real-world applications.

In conventional assessments, the analysis often concludes at this stage. However, the proposed methodology extends beyond by employing a 2D transient model to pinpoint high-risk boundary conditions throughout the year, considering orientation and specific time/days. These crucial environmental parameters are then integrated into a 3D transient model to evaluate thermal stresses across individual monolithic glass panels. The identified worst-case boundary conditions for each glass lite are summarized in table 5.

Table 5: Worst-case boundary conditions for each lite

Since the inner lite, glass pane 3, has the largest temperature gradient, which is to be expected, given the shadow box condition being evaluated, the west orientation on day 245 at 1800 hrs is considered as the most critical boundary conditions. Figure 6 and 7 show the maximum hourly temperature difference of the outer and inner glass lite based on facade orientation. Using this visualisation is possible to identify temperature peak, duration and time of the year when high risk conditions might occur.

Fig. 6: Differential temperature for interior and exterior glass at south elevation

Fig. 7:Differential temperature for interior and exterior glass at west elevation

4.2 3D thermal analysis results

In this section, the results of the three-dimensional transient thermal analysis are presented for west orientation and the time range (from day 241 to 245) identified in the two-dimensional thermal analysis.

Day 245 @ 13:00 hrs

Day 245 @ 15:30 hrs

Day 245 @ 18:00 hrs

Fig. 8: Temperature distribution for 3D transient model, Left: Time step 245:13:00:00, Middle: Time step 245:15:30:00, Right: Time step 245:18:00:00 hrs, (Temperature range: 18.0°C - 68.0°C)

Figure 8 illustrates the temporal temperature distribution of the curtain wall panel during the afternoon hours, commencing from the solar zenith position and progressing to the sunset phase. From the three time steps selected it is possible to visualize the impact of incident solar radiation and impact of shading fin. Figure 8 on the left shows relatively cooler temperature across the assembly due to limited direct sunlight striking the surface. The figure in the middle (15:30 hrs), demonstrates the effects of the horizontal fin located at the top of the unit, with the sun at high zenith the fin's shadow is cast over the uppermost region of the glazing, resulting in a marginally lower temperature reading relative to the remainder of the glazing surface. In the right figure, it is possible to visualise the impact of low sun angle and high direct solar irradiation, with the shadowbox portion of the panel reaching much higher temperatures than the vision portion. Conditions highlighted at 15:30 and 18:00 time steps can both lead to high stress in the glass due to shadow patterns and important temperature differences. The 3D transient results are summarized in table 6.

Table 6: Summary of Differential Temperatures for the 3D Transient Analysis

For the outer laminate lite, both glass panels exhibited a similar temperature range spanning from 27.92°C to 56.12°C. The computed temperature difference (ΔT) within the outer lite was determined to be 28.20°C. As expected due to absorbed solar radiation from the shadowbox assembly, for the inner lite (glass pane 3), temperature range increases to 38.48°C with a minimum temperature of 28.84°C and a maximum of 67.32°C. Comparing 2D and 3D transient analysis results it is possible to notice that the inner maximum temperature and temperature difference are lower in the 3D results, the difference is driven by the extra heat build-up that is dissipated across the four framing members. Effect that is not captured in 2D analyses that can lead to higher thermal stress values. As per 2D steady and transient analyses the temperature differences shown in Table 6 are then used to calculate the stress across each glass lite using the formula 2.

Outer Laminate Lite:

σth = Kth * E * 𝛼 * ΔT (2)
σth = (0.9) *(70000) * (9*10-6) * (28.20)
σth,A = 15.99 MPa

The theoretical thermal stress of the outer laminate lite is less than the maximum allowable stress for an annealed lite with clean cut edges (20.0 MPa).

Inner Monolithic Lite:

σth = Kth * E * 𝛼 * ΔT (2)
σth = (0.9) *(70000) * (9*10-6) * (38.48)
σth,A = 21.82 MPa

The inner monolithic lite is below the maximum allowable stress of 24.0 MPa for an annealed lite with ground edges. It is worth noting that through the implementation of refined thermal simulation, the expected stress for the outer line decrease from 47.8 MPa to 15.9 MPa and for the inner lite from 67.3 to 38.5 MPa.

4.3 Stress distribution

The temperature time history applied to each mesh of the plate shell is used to perform a sequence of linear static calculations to assess the stress distribution for each time step. Fig.9b shows the stress time histories of all the nodes of the glass, highlighting a peak of the stresses in step 182, which is also the step selected for the calculation of the probability of breakage described below. Each time step covers a 30-minute duration. The analyzed time range covers four days, but only the last day is detailed for the stress maps.

Fig. 9: Resulting Time histories of the stress over the glass surface for the test case by the tool

The three steps selected in Fig. 8 as the most relevant for the peak of the temperatures are compared in Fig. 10: the worst case scenario occurs at 18:00 of Day 245 with a peak of 8.64MPa in the surface behind the intermediate transom. The highest surface stress does not fully align with the maximum temperature. Specifically, the maximum stress of 8.77MPa occurs one time step later at 18:30, despite the peak temperature occurring at 18:00 during time step 181 on the inner glazing surface.

Day 245 @ 13:00 hrs

Day 245 @ 15:30 hrs

Day 245 @ 18:00 hrs

Fig. 10: Stress contours for the three steps selected at the previous stage

5. Conclusions

In this study, we have underscored the critical importance of conducting accurate finite element analysis (FEA) to assess thermal stresses in glass structures. By comparing the efficacy of 2D and 3D transient thermal analyses against 2D steady-state methods, we have demonstrated the significant improvements in accuracy achieved through transient simulations. Our findings unequivocally indicate that transient thermal analysis, both in 2D and 3D frameworks, offers higher precision in predicting thermal stress levels compared to traditional steady-state approaches. Specifically, our results reveal that linear stress values computed using transient analyses are substantially lower—by a margin ranging between 70% to 80%—than those derived from 2D steady-state simulations. This discrepancy underscores the limitations inherent in steady-state methodologies and underscores the necessity of adopting transient approaches for more reliable assessments of thermal stress. Furthermore, the study elucidates the contribution of finite element structural models in accounting for temperature distribution across glass structures. By incorporating the intricate interplay between thermal gradients and structural response, these models enable a comprehensive understanding of the thermal stress distribution within glass elements.

Table 7: Summary results of max delta temperature and mechanical stress

Overall, the research highlights the indispensable role of accurate thermal stress finite element analysis, particularly in the dynamic context of transient thermal simulations. These insights are instrumental in advancing our understanding of glass structural behavior and hold significant implications for optimizing the design and performance of glass-based systems.

In order to further validate the approach presented in the paper, the team is planning to start a series of experimental testing to monitor temperature profiles in different curtain wall and glazing configurations and subsequently stress distribution, exposing them to the yearly solar radiation under controlled internal temperature conditions and equipping them with a dedicated measurement systems, including thermocouples and strain gauges.

ASTM E2431; Standard Practice for Determining the Resistance of Single Glazed Annealed Architectural Flat Glass to Thermal Loadings. ASTM International: West Conshohocken, PA, USA, 2012.

Anastasiou, C..: Thermal Breakage of Glass: Comparison and Validation of thermal shock calculation methods. Delft University of Technology (2016)

Chowdhury H., Cortie M.B., Thermal stresses and cracking in absorptive solar glazing, Construction and Building Materials, Volume 21, Issue 2, 2007, Pages 464-468, ISSN 0950-0618, https://doi.org/10.1016/j.conbuildmat.2005.07.015.

Fronsoe, C., Krytenberg, T., Vockler, K., Swanson, J., Carbary, L., Barry, C., Hoffman, S., Torok, G., Norville, S., Blanchet, S., Silicone Spandrel Glass Coatings: Mitigating Glass Breakage Risk from Thermal and Other Stresses. Vol. 6 (2018): Challenging Glass 6

Foraboschi, P., Analytical modeling to predict thermal shock failure and maximum temperature gradients of a glass panel, Materials & Design, Volume 134, 2017, Pages 301-319, ISSN 0264-1275, https://doi.org/10.1016/j.matdes.2017.08.021.

Galuppi, L., Franco, A., Bedon, C.: Architectural Glass under Climatic Actions and Fire: Review of State of the Art, Open Problems and Future Perspectives. Buildings (2023). https://doi.org/10.3390/buildings13040939

Galuppi, L., Maffeis, M. & Royer-Carfagni, G. Enhanced engineered calculation of the temperature distribution in architectural glazing exposed to solar radiation. Glass Struct Eng 6, 425–448 (2021). https://doi.org/10.1007/s40940-021-00163-9

Honfi, D., Sjostrom, J., Bedon, C. Kozlowski, M.: Experimental and Numerical Analysis of Thermo-Mechanical Behaviour of Glass Panes Exposed to Radiant Heating. Fire (2022). https://doi.org/10.3390/fire5040124

Murray, S., Contemporary curtain wall architecture. Princeton Architectural Press, 2009.

NF DTU 39 P3; Building Works–Glazing and Mirror-Glass Works–Part 3: Calculation Memorandum for Thermal Stress [Travaux de Vitrerie-Miroiterie—Partie 3: Mémento Calculs des Contraintes Thermiques]. Association française de normalisation (AFNOR), 2006.

Jackson, JA, Saldanha, CM, Guldentops, G, Yap, JR, Abdallah, RJ, & Rentfro, SB. "Thermal Performance of Spandrel Assemblies in Glazing Systems." Building Science and the Physics of Building Enclosure Performance. Ed. Lemieux, DJ, & Keegan, J. 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959: ASTM International, 2020.

Poláková, M.; Schäfer, S.; Elstner, M. Thermal Glass Stress Analysis–Design Considerations. Challenging Glass Conference. DOAJ (DOAJ: Directory of Open Access Journals (2018). https://doi.org/10.7480/cgc.6.2193

Schwind, G.; Paschke, F.; Schneider, J. Case Studies on the Thermally Induced Stresses in Insulating Glass Units via Numerical Calculation. In Challenging Glass Conference, Proceedings of the Conference on Architectural and Structural Applications of Glass, Ghent, Belgium, (2022); CGC: Sarasota, FL, USA, (2022); Volume 8.

Sozer, H., Improving energy efficiency through the design of the building envelope, Building and Environment, Volume 45, Issue 12, 2010, Pages 2581-2593, ISSN 0360-1323, https://doi.org/10.1016/j.buildenv.2010.05.004.

Xie, Y.; Tyler, M.; Huckett, J.; Bartlett, R.; Chen, Y.; Salcido, V.; Mendon, V.; Rosenberg, M. A Review of the Evaluation of Building Energy Code Compliance in the United States. Energies 2023, 16, 5874. https://doi.org/10.3390/en16165874