Structural visualization analysis applied to the preservation of architectural heritage: the case of stilted houses in southwest Hubei, China

Abstract

Wooden buildings represent a unique aspect of China’s architectural heritage. However, over time, these buildings have suffered varying degrees of structural damage, particularly those located in China’s mountainous regions. Frequent natural disasters and inconvenient transportation further exacerbate the vulnerability of these structures. This study focuses on the typical wooden stilt houses found in the Wuling Mountain area of southwest Hubei. The different forms of columns and beams, as well as the overall structural symmetry of the stilt houses, were classified into five common structural types. Precise digital models were established via real photos and collected dimensional data, and these five models were evaluated for static, buckling, utilization, and ultimate limit states. The results indicate that: (1) overall symmetrical structures perform better than asymmetrical ones; (2) structures where all columns are grounded and act as support columns exhibit the best overall mechanical performance; and (3) transverse-tie beams(chuanfang) primarily serve a connecting role rather than a load-bearing role, thus an excess of transverse-tie beams(chuanfang) can reduce the stability of the building structure. Based on the analysis results, targeted protective measures and recommendations were proposed and verified through structural evaluations. These initiatives provide new methods and insights for the protection of architectural heritage.

Introduction

A nation’s cultural and architectural heritage is considered its most valuable, unique, finite, and irreplaceable asset, symbolizing its wealth and historical standing [1]. Wooden buildings, as the foundation of traditional Chinese architecture, not only preserve the country’s rich cultural legacy but also showcase the skillful use of wood and the superb craftsmanship of traditional artisans. These buildings reflect the high level of wisdom and technological advancements of ancient Chinese society [2]. Wooden buildings in China constitute a significant part of the world’s cultural heritage, as ancient craftsmen have continuously improved their building systems to adapt to environmental and temporal changes.

Wooden buildings that have survived natural disasters and conflicts provide crucial insights into the economic, social, and cultural context of the past [3, 4]. Without timely restoration and protection, these wooden buildings may eventually vanish from our history [5, 6]. This situation is particularly true for traditional residential buildings, which do not share the same cultural significance as famous wooden buildings such as the Forbidden City, Foguang Temple Hall, and Yingxian Wooden Pagoda. Consequently, the resources and efforts dedicated to their preservation are insufficient [7]. Additionally, the vast number of traditional houses, combined with their widespread distribution, makes it impractical to develop comprehensive conservation plans for each structure. Therefore, research on traditional residential buildings is essential for establishing a universal protection system.

Several scholars have researched the materials and construction techniques of these buildings, providing theoretical recommendations for their preservation. For example, Chen Wei from Southeast University studied the use of wood in traditional Chinese wooden buildings and discussed the four stages of wood selection, felling, removal, and erection, thereby offering opportunities for historical restoration work [2, 8]. Liu Cuilin classified and characterized roof rafter structures in the Jiangsu and Zhejiang regions, providing references for the restoration of historical buildings [9]. Li Zhen conducted a comprehensive study on the wooden structures in the Jiangnan region, focusing on their systematization, significance, and principles of historical evolution, and highlighted the construction differences with those of northern official-style buildings. He also provided valuable theoretical guidance for the future preservation of southern wooden structures [10]. Lv Yingqi and Li Zhen carried out in-depth research on pole-and-foot methods, architectural forms, and construction techniques in central Fujian [11] and demonstrated that different regions have distinct building technologies, architectural frameworks, and material usage methods. Zhang Lianggao from Huazhong University of Science and Technology researched the Tujia architecture in southwest Hubei, including various structural types such as stilted houses [12] and ganlan buildings [13]. Through field investigations and interactions with Tujia master carpenters, Chen Siliang compiled and meticulously examined the construction techniques and technical characteristics of the Tujia stilted house trusses in the Xianfeng area of western Hubei [14], making it easier to understand the basic characteristics of southern truss methods. However, current analysis techniques for the precise preservation and restoration of historical buildings are still limited to two-dimensional documents and drawings [15]. Therefore, the use of advanced structural analysis methods and powerful modeling tools available today to create 3D models of these wooden structures and execute a structural analysis is crucial [16].

Academics from all over the world have achieved incredible feats in their thorough examination and preservation of architectural history by implementing cutting-edge technologies. The development of building conservation technology was greatly facilitated, for example, by Juan Moyano and colleagues’ experiments with digital twin technology and their creation of geometric digital models of structures using 3D reconstruction technology. With this strategy, they could monitor and collect building construction data over time. Accurate analyses and a comprehensive understanding of the evolution of architecture have been made possible by changes in environmental elements and other environmental factors [17]. Sara Gonizzi Barsanti and her colleagues presented a way to use 3D real models to perform a finite element analysis (FEA) on cultural heritage buildings. This strategy simplifies and improves the data’s usefulness by rearranging the forms. This work proposes the use of a retopology approach to generate simpler models that can be used to develop novel FEA software package processing strategies. A thorough examination of three case studies also demonstrated the value of this approach for precisely modeling and reproducing the mechanical behavior of damaged cultural materials [18]. To help identify which model parameters are most likely to harm the heritage building model, Rosario Ceravolo and colleagues adopted a global sensitivity analysis of architectural heritage structures [19]. This analysis is useful for both heritage building identification and structural repair. Domenico Giaccone and colleagues performed a structural investigation on five columns that were different in many ways. They examined the columns’ static, buckling, modal, and dynamic response spectra. On the basis of these results, they developed useful ways to protect historic buildings [16]. Using a range of factors, WanFang et al. investigated the effects of the soil-structure interaction (SSI) on the seismic response of self-contained mid-rise structures in hilly regions. It has been discovered that altering the SSI effect parameter can improve a structure’s safety and reliability by more closely simulating its behavior during earthquakes [20]. This is accomplished by comparing three models that do not consider the SSI effect but do, consider the traditional SSI effect, and the changing parameter SSI effect. These studies provide novel concepts and approaches to the real-world protection of historical buildings.

This study aims to provide new perspectives for research on Chinese wooden buildings and similar architectural heritage through complex structural analysis techniques. Furthermore, this study aims to assist the government and other relevant organizations in developing more targeted protection plans to support the efficient and long-term preservation of these historical sites. Thus through detailed descriptions and comparative analyses, this study aims to achieve the following two objectives: (1)conduct an assessment of the advantages and disadvantages of various structural configurations within a single building type and select the structure that exhibits superior mechanical performance. (2) develop protection methods and renovation strategies for stilted houses and similar wooden structures on the basis of the results of structural analysis.

Materials and methods

Analysis of the case study

This study focuses on traditional stilted houses that are found in southwest Hubei, China. Geographically, this area is sandwiched between the fruitful Jianghan Plain and the Central Sichuan Plain, and as such, it is the hub of “the Bashu” and “Jingchu cultures.” Because of its uniqueness, this location offers a special cultural background for the evolution of architectural styles [21, 22]. As a result, the peculiar stilted architectural designs that local traditional households have created by combining features of Southwest and Central Plains architecture are of major study value [23, 24]. Because of its location in the Wuling Mountains, southwest Hubei has a topography marked by significant topographical changes and altitude-dependent climate fluctuations [15]. This complex geographic location has resulted in a multitude of structural configurations for stilted houses.

The specific research locations cover 80 villages within the eight county-level administrative districts of Enshi Tujia and Miao Autonomous Prefecture in Hubei Province. After careful selection, seven well-preserved and more representative village clusters were chosen for in-depth study. These clusters are: Pengjiazhai Village in Shadaogou Town, Xuan’en County; Erguanzhai Village in Jiaba Town, Enshi City; Zhuangfangba Village in Tangya Town, Xianfeng County; Baiyanshui Village in Jingyang Town, Jianshi County; Shemihou Village in Baifusi Town, Laifeng County; Nashui Town in Liangwu Township, Lichuan City; and Daxi Village in Rongmei Town, Hefeng County. Among them, the most renowned is Pengjiazhai, which is a key national cultural relic protection unit in China, well-preserved and provides abundant resources for our academic research.

Through a visual analysis of structural stress, this study is able to identify structural concerns effectively and provide a comprehensive assessment of the advantages and disadvantages of various building structural forms using visual analysis of structural stress. The Wuling Mountain region, an area in which natural disasters are frequent, contains structures supported by stilts. As the structures are widely scattered, it is challenging to preserve the architectural history [15]. Thus, in this study, all structural types of stilted houses are categorized and assessed via structural stress analysis. Strong visual analysis identifies the most illogical types of building structures and recommends suitable precautions, providing a fresh method for preserving and repairing classic homes. The research locations are shown in Fig. 1.

Fig. 1

Research locations

Finite element model of stilted houses

All of the structural models of the stilted houses in the study were derived from field surveys. Field research was conducted to identify the types and sizes of wood used in construction, and the various structural forms of the stilted buildings were recorded. Every virtual model is created via Rhino [25].

The structural investigation was conducted via the finite element method, which is widely used in studies on architectural history. Specifically, a finite element analysis (FEA) was performed in this study via the Karamba3D [26] and Beaver [27] plug-ins for the Grasshopper [28] platform. These methods allow for accurate structural behavior simulations. The Grasshopper’s parametric design environment can fully incorporate the finite element calculation program Karamba3D, thereby enabling interactive mode usage. The structure is subjected to conventional stress analysis via Karamba 3D, which specifies the structural frame’s load and support locations, as well as the cross-sectional shape and dimension of each piece of wood in the stilted houses. Bearver, a plug-in device, specializes in the structural analysis of wood structures. Karamba 3D has been completely integrated. Compared with other structural analysis tools, the Beaver plug-in accurately and completely identifies wood materials, accounting for variables such as transverse-tie considerations, span length, and other structural analysis tools. A number of significant indicators, including buckling length and service level, improve the accuracy of the structural analysis of wooden buildings. In this study, the Beaver plug-in is primarily used to examine the state of timber structures.

Structural assessment of the selected building element

Finally, through static analysis, buckling analysis, utilization analysis, and ultimate limit state (ULS) analysis, the five models were compared from multiple perspectives. In the context of extreme loading, the term “ULS” refers to the ultimate state of the structure, typically when it is exposed to very high loads or extreme environments. The study results were used to examine the advantages and disadvantages of the five structural models and the processes leading to the development of different structural forms. The recommendations for heritage conservation strategies provide new insights into preservation efforts.

Static analysis is used to determine the response of structures under static loads. Static loads are constant loads that do not change over time, such as dead loads, live loads, and the weight of permanent equipment. The primary objective of static analysis is to calculate the internal forces and deformations under these loads, to assess whether the structure meets strength and stiffness requirements, thereby ensuring its safety and reliability under normal operating conditions. The displacement-load relationship is given by:

$$\begin{aligned} {[}K]\{d\}=\{F\} \end{aligned}$$

(1)

where [K] is the stiffness matrix, {d} is the nodal displacement vector, and {F} is the external force vector.

Buckling analysis is used to evaluate the stability of structures under compressive loads. Buckling refers to the lateral instability that occurs in slender components, such as columns, when they reach a critical load. The purpose of buckling analysis is to determine the critical buckling load, which is the minimum load at which a component begins to buckle. Through buckling analysis, it is possible to predict the locations and modes of potential buckling in a structure, allowing for the design and implementation of reinforcement measures to prevent instability failure. The characteristic equation is as follows:

$$\begin{aligned} {[}K]\{d\}=\lambda [kg]\{d\} \end{aligned}$$

(2)

where $\lambda$ represents the critical buckling load factor, [K] is the linear stiffness matrix, and [kg] is the geometric stiffness matrix.

Utilization analysis is used to evaluate the stress conditions of structural components under design loads. Utilization is defined as the ratio of the actual stress or strain experienced by a component to its allowable stress or strain, usually expressed as a percentage:

$$\begin{aligned} {Utilization} = \frac{\text {Actual stress}}{\text {Allowable stress}} \times 100\% \end{aligned}$$

(3)

The purpose of utilization analysis is to determine the working state of each component and assess whether it is operating within safe limits.

Ultimate limit state (ULS) analysis is used to evaluate the safety of structures under ultimate conditions. The ultimate state refers to the condition where a structure or component reaches its limits in terms of strength, deformation, or stability under design loads. The primary goal of ULS analysis is to determine the load-bearing capacity of a structure under extreme conditions, ensuring that the structure remains sufficiently safe and reliable even in the most adverse scenarios. The formula for ULS is expressed as:

$$\begin{aligned} R \ge S \end{aligned}$$

(4)

where R represents the resistance or load-bearing capacity of the structure, and S represents the applied design load.

Among the four types of analysis, static analysis, buckling analysis, and utilization analysis each applied a 1 KN horizontal force and a 1 KN vertical force, in addition to considering the self-weight of the structure. In the ULS analysis, a vertical force was continuously added until the model reached its ultimate load-bearing state. The flowchart of the study is shown below (Fig. 2).

Fig. 2

Research flowchart

Architectural characteristics and classification of stilted houses

Description of the stilted house architecture

The stilted houses are a distinct kind of column-and-tie framework(chuandou) found in southern China. They focus on detail in traditional architectural design, as well as on the caliber of traditional architectural craftsmanship. The basic structural unit is composed of central columns, straddle columns(qizhu), transverse-tie beams(chuanfang), and overhanging beams(tiaofang) that form a gable end(shanjia) [29], where every element beautifully exemplifies traditional craftsmanship. The design of the gable the produces a robust horizontal timber frame framework by carefully aligning the columns with respect to the depth of the structure and the transverse-tie beam(chuanfang) connections. The eave column and flanking column(jinzhu), which extend outward to the eaves, support the overhanging beams(tiaofang). This structural design not only significantly increases the building’s stability but also increases the interior area’s openness and adaptability to satisfy a variety of functional needs. The straddle columns(qizhu) in the gable end(shanjia) are supported by transverse-tie beams(chuanfang) to prevent them from than directly touching the ground, thus optimizing space use and evenly distributing the weight. The columns are arranged as follows from the outside to the inside: eave columns(yanzhu), huge straddle columns, flanking columns(jinzhu), second straddle columns, and central columns. Multiple gable ends(shanjia) are spaced along the building’s breadth and joined by brackets and beams, providing the building’s basic framework. This study focuses on the structural stress analysis of a single gable end(shanjia) to thoroughly evaluate its load-bearing and adaptability qualities, since each gable end has consistent dimensions and shapes, as shown in Fig. 3.

Fig. 3

Stilted house

Dimensions and materials of the stilted houses

The gable ends(shanjia) of stilted houses are built in accordance with traditional modular standards, that is, the distance between columns is typically 2 feet and 5 inches (or 0.83 m) and no more than 1.2 m, which guarantees structural stability and balance. The central floor-standing columns, which often reach a height of 19 ft (approximately 5.7 m), are the primary factor in determining the building’s overall height. These columns represent the sophisticated use of space in ancient architecture. The humid climate and undulating topography of the Wuling Mountains, in particular, cause buildings to frequently have an elevated layer that is approximately 30 cm high to respond to environmental changes. The wood used has a diameter of approximately 9 in (300 mm), emphasizing its inherent form and texture, as well as its original beauty and structural integrity, as shown in Fig. 4.

Fig. 4

Basic form and dimensions of the structure

The transverse-tie beam(chuanfang), a critical horizontal linking component, is distributed as the first, second, third, and fourth transverse-tie beams(chuanfang), with the first transverse-tie beam(chuanfang) located approximately 2.5 m above ground. To guarantee the coherence and stability of the entire construction, the higher transverse-tie beams(chuanfang) are positioned parallel to the central column. The transverse-tie beam(chuanfang) has a flat, rectangular cross-section that is 3 in (100 mm) broad and 6 in (200 mm) high, which contrasts sharply with the circular cross-sections of the columns. This design helps to more evenly distribute the weight and enhances the overall connectivity and stability of the structure, all of which contribute to the greater seismic resilience and durability of the building.

In southern China, where the temperature is good, fir is a preferred choice for traditional home construction because of its robust texture and swift growth. Fir is widely used for its excellent moisture resistance and termite resistance, particularly its ability to remain durable for “a thousand years dry, a thousand years wet, alternating dry and wet for two or three years,” demonstrating outstanding durability amidst frequent climatic changes. However, the mechanical properties of fir vary by region. For example, fir from Lushan in Sichuan is renowned for its excellent modulus of elasticity, and tensile, bending, and shear strengths, illustrating the significant impact of geographic provenance on wood performance [30].

The mechanical property data of the materials involved in this study were obtained from the material selection table provided by the Beaver plugin. This table can be downloaded from the case studies section of the Beaver website. The fir wood used for building houses in ancient times was sourced from nature and classified as softwood. Therefore, the mechanical property data I used herein are as follows.

Table 1 Mechanical property data of materials

Different forms of gable end

Although stilt houses have largely retained their traditional architectural forms throughout their development, they exhibit diverse manifestations. To gain a better understanding of the cultural and structural alterations of stilt houses, numerous researchers have attempted to classify them in a systematic manner from diverse angles. With an emphasis on the underlying reasons for stilt house adaptations to environmental changes, Jiang Zehua and colleagues have employed evolutionary techniques to investigate the beginnings and development of stilt dwellings [31]. Ma Qiuyu analyzed the notable cultural differences in the architectural forms of the Tujia and Miao communities [32] by approaching the subject from the perspective of the customs of various ethnic groups. A more thorough investigation into the classification of stilt houses was carried out in Liu Jingjing’s doctoral thesis. This study classified stilt buildings from a variety of angles, including building materials, geographic location, and architectural usage (residential or commercial). The five varieties of stilt houses presented in this article are based on structural variations, namely the dimensions and shapes of the gable ends(shanjia) of the columns and beams, as shown in Fig. 5.

Fig. 5

Classification of different structural forms

Model 1: A typical gable end arrangement in which the eave, straddle, and flanking columns(qizhu, jinzhu) are arranged symmetrically around the central column, which is supported by a lower transverse-tie beam(chuanfang) that connects them. On the base of changes in interior functioning, “transverse-tie beam(chuanfang) reduction” method is applied to the upper transverse-tie beam.

Model 2: All transverse-tie beams(chuanfang) cross every column, and no “transverse-tie beam(chuanfang) reduction” is used.

Model 3: All straddle columns(qizhu) touch the ground directly, resulting in a pure floor-standing column design.

Model 4: Certain straddle columns are situated on the upper transverse-tie beams(chuanfang) rather than the lower transverse-tie beams(chuanfang), resulting in the formation of a structure composed of short straddle columns(qizhu).

Model 5: The gable end construction is asymmetrical and does not revolve around the central column.

Structural assessment

This study presents a detailed comparison of the performance of five models with respect to statics, buckling, use, and ultimate limit state (ULS).

Table 1 shows the results of the static analysis. Model 1, which represents the most common structural form in daily life, has a maximum displacement of 4.93 cm. This value serves as a benchmark for assessing the mechanical performance of the other four structural forms under static analysis. Model 2 has a maximum displacement of 6.55 cm, which is significantly greater than that of Model 1, indicating that although Model 2 has more beams than Model 1, its overall performance is inferior to Model 1. Model 3 has a maximum displacement of 3.62 cm, making it the best-performing model in the static analysis. This finding demonstrates that grounding each column provides more support points for the building, significantly enhancing structural stability. Model 4 has a maximum displacement of 6.48 cm, which is also considerably greater than the displacement of Model 1(4.93 cm). Compared with Model 1, Model 4 has shorter columns and fewer beams, making the overall structure lighter and more prone to displacement in the static analysis. Model 5 has the worst performance, with a maximum displacement of 6.90 cm. The main difference between Model 5 and the other models is its asymmetric structure, which indicates that asymmetric structures can lead to significant imbalance issues. See Fig. 6.

Additionally, under static analysis, Model 1’s maximum tensile stress and compressive stress are 0.93 $\hbox {kN/mm}^{2}$ and 2.06 $\hbox {kN/mm}^{2}$, respectively, which are used as the standard values. The maximum tensile stress and compressive stress of Model 2 are 1.07 $\hbox {kN/mm}^{2}$ and 2.45 $\hbox {kN/mm}^{2}$, respectively, with the compressive stress significantly higher than that of Model 1, indicating that the excessive number of transverse-tie beams increases the pressure on the building structure. The maximum tensile stress and compressive stress of Model 3 are 0.97 kN/mmv and 1.29 $\hbox {kN/mm}^{2}$, respectively, with the compressive stress being significantly lower than that of Model 1, indicating that the increase in support points alleviates the pressure on the structure. The maximum tensile stress and compressive stress of Model 4 are 1.07 $\hbox {kN/mm}^{2}$ and 2.10 $\hbox {kN/mm}^{2}$, respectively, which are almost the same as those of Model 1. The maximum tensile stress and compressive stress of Model 5 are 0.18 $\hbox {kN/mm}^{2}$ and 2.81 $\hbox {kN/mm}^{2}$, respectively, with the tensile stress being much lower than that of Model 1, while the compressive stress far exceeds the standard value, thus indicating that the asymmetry of the structure leads to an imbalance in the building.

Table 2 Main results of the static analysis

Fig. 6

Model displacement diagram under static analysis

Table 2 details the important outcomes of the buckling analysis. The foundation of this research is the buckling-load-factor, a metric that evaluates the structural stability of a structure by calculating the ratio of the critical load to the actual load. A factor greater than 1 indicates that the structure is robust and capable of supporting the intended load without the risk of buckling; conversely, a factor below 1 signals potential structural buckling.

According to the experimental simulations, all of the models have buckling load factors greater than 1, indicating that their structural designs allow these architectural heritage structures to withstand the test of time. However, there are significant differences in the buckling load factors among the five models. Using Model 1’s buckling load factor of 1.27 as a reference, models with factors less than 1.27 have a poorer resistance to buckling failure. As presented in the table, Model 2 has a buckling load factor of 1.09, Model 4 has a value of 1.22, and Model 5 has a value of 1.05. All three models have buckling load factors less than 1.27, with Model 2 and Model 5 being particularly close to 1, indicating a risk of instability. Model 3, however, has a buckling load factor as high as 2.22, which is consistent with the static analysis results, thus confirming that Model 3 remains the best-performing model. as illustrated in Fig. 7.

In addition to assessing the models’ resistance to buckling failure through the buckling load factors, we can also determine the direction of buckling failure from the diagrams. Models 1, 2, 3, and 4 maintain consistent overall structural alignment in the direction of buckling failure, whereas Model 5 is inconsistent in this regard, with the long side shifting more than the short side. This finding indicates that the asymmetry of the overall structure results in different resistances to buckling failure across various parts of the structure, thereby making the weaker sections highly susceptible to damage in extreme disasters.

Table 3 Critical buckling load

Fig. 7

Buckling analysis of the model

Figure 8 visually presents the utilization analysis results. This analysis evaluates the efficiency of each structural component by comparing the ratio of normal stress to material strength. The shear and buckling effects are disregarded to concentrate on component efficiency.

We conducted a comprehensive analysis of the component consumption rates in all five models, using Model 1 as a reference, to identify any tendencies that were different from those of Model 1. Since every transverse-tie beam in Model 2 passes through every supporting column, there is a significant increase in the load on the columns. The utilization rate of the middle three columns was 122.7%, indicating that this design places more strain on the columns. Model 3, however, has superior structural stability because it achieves a homogeneous distribution of support across all columns, with a maximum use rate of only 64.6%. Model 4, which uses shorter straddle columns, not only produces greater space within the building but also maintains component usage rates similar to Model 1, demonstrating that this design maximizes space use while retaining structural integrity. Finally, the substantial discrepancies in the component utilization rates caused by Model 5’s asymmetric structure are most notably evident in the middle column, where the rate reaches 140.7%. This finding raises concerns regarding the structural integrity of the design as a whole. These comparisons show how various design strategies perform in terms of component utilization rates, offering insightful information for additional architectural structure optimization.

Fig. 8

Utilization rates of the model structural components

In Model 1, we numbered every member, and in Models 2 and 3, which added transverse-tie beams and columns, respectively, we numbered every member to better understand the effect of adding or removing members on the structural usage rates. Using Karamba3D, we determined each member’s use rates. The results are displayed in bar charts for analysis and comparison, as shown in Fig. 9. Overall, fewer transverse-tie beam members are used than column members in all models. This suggests that the main purpose of transverse-tie beams in the structural design of stilted structures is to connect things rather than to support weight.

Fig. 9

Utilization rates of the members in Models 1, 2, and 3

Using Model 1 as a reference, the highest utilization rate in Model 1 is found for Member 32, which is the bottom of the central column, with a utilization rate of 99.9%. In comparison, Model 2 increased the number of transverse-tie beams, but owing to their low utilization rates, these additional beams became a burden. This caused the utilization rate of member 36, the bottom of the central column in Model 2, to reach 122.2%, posing a risk of damage. Model 3 increased the number of ground columns, reducing the utilization rate of the bottom of the central column. The highest utilization rate shifted to the two columns near the overhanging beam, with a utilization rate of 64.6%. Although this keeps the overall structure within a very safe range, the low overall utilization rate leads to material waste.

Figure 10 shows the visual data for the ultimate limit state (ULS). The ultimate load-bearing capacity state, or ULS, is used to assess structural safety under extreme loading conditions. The use of ULS analysis in this research is beneficial for identifying structural deficiencies in the five models and generating constructive suggestions pertaining to architectural heritage conservation.

Practically speaking, this entails gradually increasing the load supplied to the structural models until the structure exceeds its limit. The five models’ ultimate load-bearing capacities are compared to describe and assess common structural difficulties and particular requirements for each construction.

Figure 10 shows a clear resemblance across the five models, that is, the load-bearing columns beneath the bottom transverse-tie beam are in a tense ultimate condition, particularly the central columns in the core area, which must support the enormous self-weight of the building above, in addition to withstanding wind loads and the intense pressure of the roof. Additionally, the mechanical interaction at the joints between transverse-tie beams and columns is extremely complicated. This means that conservation measures need to be very careful to avoid structural fatigue or cracks caused by accidents.

Using Model 1’s parameters as a reference, Models 1, 2, 4, and 5 reached their ultimate limit state under the same external loads. Model 2, owing to the additional transverse-tie beams, resulted in the central column bearing excessive loads, indicating a dangerous state in the ULS analysis. Model 3 exhibited the strongest load-bearing capacity, and was able to withstand twice the weight of the other four models. Compared with Model 1, Model 4 shortened some straddle columns and reduced the number of transverse-tie beams, thereby reducing the weight. This alleviated the pressure on the support columns, resulting in good performance in the ULS analysis. Model 5’s ultimate load-bearing state was uneven, with the structure on the left side of the central column in a very dangerous state. This was due to the extremely uneven distribution of support columns, with three support columns on the right side and only one on the left side, in addition to the central column. Therefore, when preserving this structural form, the weaker side of the structure should be reinforced.

Fig. 10

Model’s ultimate limit state

Discussion and limitations

The study concludes that among all the examined models, Model 3 exhibits the highest structural performance through comprehensive static analysis, buckling analysis, utilization analysis, and ultimate limit state (ULS) analysis. However, Models 2 and 5, as well as the commonly used Model 1, show significant performance shortcomings compared with this ideal model. In practice, even though Model 3 demonstrates the best performance, it is not always adopted. This phenomenon arises from various factors, including the availability of construction materials, the comfort of space usage, and extensions to address insufficient indoor space. All these factors necessitate compromises in structural design.

In particular, the superior-performing Model 3 boasts four more support columns-nine total-than the other versions do. Although this design is physically sound, it also requires more wood to be used. The construction industry was forced to adopt a “material reduction” strategy because ancient trees that have survived for a millennium or even several millennia in China have become increasingly rare. This has resulted in a shift from Model 3 to Model 1, as well as further development of more material-efficient structures such as Model 4.

Furthermore, the dense arrangement of columns or transverse-tie beams(chuanfang) significantly impacts the practical use of the interior space. If Model 3 was applied to actual stilt houses, there would be a column every meter, severely restricting spatial efficiency. Consequently, over time, the complete column and transverse-tie beam(chuanfang) structure has been phased out in favor of more flexible structures, such as Model 1, which uses fewer transverse-tie beams(chuanfang) and support columns. The asymmetric structure of Model 5 is often designed to meet limited indoor space requirements. During construction, one side of the structure is frequently extended. Although the extended part has a limited height due to the roof’s shape, making it less comfortable to use, these auxiliary spaces can serve purposes such as storage, greatly alleviating the lack of main living space. In the absence of advanced computational tools, all architectural forms were designed to maximize the demands of daily living. While these architectural legacies may not have been the structurally optimal choice, they were undoubtedly the best options given the technical and environmental constraints of their time.

This study stresses the monitoring and prompt repair of structurally weak places to increase their longevity, on the basis of the results of the ULS analysis. This research provides a set of common problem-solving solutions for the five models, together with specific measures for each model and for structures that are already damaged or in a hazardous state. This includes removing unneeded buildings to reduce the self-weight on the basis of the findings of the utilization study, or replacing damaged structures with materials that have superior mechanical qualities or larger dimensions.

Accordingly, for Models 1, 2, 4, and 5, several common strategies and specific strategies for unique structures are proposed. Their feasibility is confirmed by comparison with the original data: Table 3 presents comprehensive data, and Fig. 11 displays the visual results:

• 1. Using wood with superior mechanical properties instead of natural fir wood;

• 2. Replacing the load-bearing columns with columns of a larger diameter;

• 3. Removing the underutilized transverse-tie beams(chuanfang) to reduce the pressure on the load-bearing columns;

• 4. Adding support columns to alleviate the pressure on the existing support columns.

Suggestions 1 and 2 are measures applicable to all of the models, whereas Suggestion 3 mainly addresses structural models with excessive transverse-tie beams, such as Model 1 and Model 2. Suggestion 4 specifically targets Model 5 by adding support columns to alleviate pressure on the weaker sections (Table 4).

Table 4 Main results of the static analysis

Fig. 11

Visualization of optimization strategies

The simulation analysis demonstrates that the application of Measure 1 exhibits significant advantages. Replacing materials with superior mechanical properties significantly reduces structural displacement and correspondingly increases the buckling load factor, indicating enhanced overall structural stability. Additionally, the increased material strength allows the structure to withstand greater tensile and compressive stresses, thereby improving the building’s resilience under extreme conditions.

Measure 2, which involves increasing the diameter of the original columns from 300 mm to 350 mm, shows significant improvement. Although its effect on reducing structural displacement is not as pronounced as that of Measure 1, it demonstrates superior performance in resisting buckling failure. The increase in material dimensions reduces the average tensile and compressive stresses borne by the structure, thereby increasing safety. However, this also results in some material waste. Therefore, in practical applications, it is crucial to carefully balance the advantages and disadvantages of implementing Measure 2.

The goal of Measure 3 is to remove excess transverse-tie beams(chuanfang). This measure was applied to Model 1 and Model 2 separately. The simulations revealed that removing the extra transverse-tie beams(chuanfang) reduced the self-weight and increased the buckling load factor, thereby increasing the resistance to buckling failure. However, removing the transverse-tie beams(chuanfang) also weakened the connections between columns, potentially leading to increased displacement. For example, the maximum displacement in Model 1 after removing the transverse-tie beams was greater than the original maximum displacement. In contrast, Model 2 yielded positive results. Therefore, thorough simulation verification is necessary before implementing Measure 3 in practical applications.

Measure 4 involves adding support columns, which are primarily applied to Model 5, with two different approaches. Each approach involved adding support columns at different positions in Model 5. The results indicate that adding support columns improved the structural performance, reduced the displacement and increased the resistance to buckling failure. However, the position of the support columns had a subtle effect on the improvement. According to the chart data, adding support columns closer to the central column resulted in better structural performance. Naturally, the specific structure of each stilt house will lead to variations in the improvement plans and outcomes. Therefore, it is essential to validate each plan before actual conservation and restoration work.

In real life, the aforementioned recommendations do not apply to all stilted houses. For example, Pengjiazhai in Xuan’en County, Enshi Prefecture, is designated as a key national cultural relic protection unit. The protection principles for these key cultural relics include a strict rule: “maintain the original appearance.” This rule requires that during repairs, the historical appearance and architectural style of the relic must be preserved, prohibiting any unauthorized alterations to its exterior, structure, and internal layout. Therefore, the protection of Pengjiazhai requires regular inspections and maintenance to promptly identify and repair any damage. Unless the structure is damaged by a major disaster, only Measure One can be implemented, which involves replacing the damaged parts with high-performance materials. This must be done while ensuring that the length and dimensions match the original components to maintain their original appearance.

In addition to national and key provincial cultural relic protection units, the majority of stilted houses are ordinary traditional dwellings. Although these dwellings also possess significant cultural value and require preservation, their primary function is to meet the daily needs of the residents. Therefore, preserving these stilted houses only requires maintaining their general form. In this context, Measures One, Two, Three, and Four can be applied to these traditional dwellings to cater to the ever-growing needs of the residents while enhancing the structural performance and safety of the structure. This flexible preservation strategy not only maintains the original appearance of the cultural heritage but also accommodates the practical needs of modern living.

This study carefully examined the mechanical aspects of different stilt house building configurations, how they work, their limits, and how parts are used. A number of possible solutions to these problems have also been proposed. However, it is important to be aware of and address the problems and issues that may arise from this approach. First, there is an obvious restriction in the research samples, Specifically, the study compared only five structural forms, but the architectural forms of stilt houses in actuality are far more diverse. The structural assessment results may vary due to the influence of factors such as spatial depth and the construction materials employed (in this study, for example, only fir was considered). Second, the models are highly abstract, For instance, the idealized structural models created by the Karamba3D and Beaver plugins fail to adequately represent real-world phenomena such as structural cracks, wood aging, the effects of humid environments on wood, and variations in the external load caused by the various geographic locations. As a result, these preventive recommendations are merely theoretical, while actual architectural heritage preservation necessitates in-depth research focused on particular situations. Finally, the software tools still have limitations. For example, the Beaver plugin’s ability to handle specific analyses such as ULS is not yet mature as; it cannot correctly recognize the circular sections in Karamba3D, which inevitably affects the accuracy of the research results. Nevertheless, the Beaver plugin provides great convenience for the parametric analysis of timber structures and can meticulously handle issues related to material types, span lengths, and cantilevers.

Research contributions and significance

This paper explores the application of advanced parametric structural analysis software, including Beaver and Karamba3D, in the study of architectural history. Leveraging the sophisticated features of these tools, a comprehensive digital investigation of the stilted house, a representative architectural heritage, was conducted. The analysis encompassed static analysis, buckling analysis, utilization analysis, and ultimate limit state (ULS) analysis. Through these analyses, researchers have gained an in-depth understanding of the mechanical properties of different structural forms, thereby deepening our knowledge of the structural performance of these historical buildings and providing a new perspective for the study of stilted wooden structures.

On the basis of the analysis results, this study proposes targeted protection strategies and validates their feasibility and effectiveness through structural evaluations. This approach offers new methods and tools for the preservation of traditional buildings. In previous conservation efforts, the lack of precise quantitative analysis often led to reliance on experiential methods passed down orally. These methods are not always applicable to every stilted house, and incorrect protection measures could result in adverse outcomes. The comprehensive protection process proposed in this study ensures, to the greatest extent possible, the accuracy of conservation strategies, thus significantly reducing the risk of damage to architectural heritage.

This study uses advanced parametric structural analysis software to conduct an in-depth analysis and validate protection strategies for the representative architectural heritage of stilted houses. This demonstrates the immense potential of digital technology in enhancing the accuracy and effectiveness of conservation plans. This approach not only provides new methods for the scientific preservation of traditional buildings but also offers valuable references for researchers and practitioners in related fields. We hope that this study will promote the widespread application of advanced technologies in heritage conservation, improve the scientific and sustainable aspects of preservation work, and ensure the effective protection and transmission of more cultural heritage.