Deformation Analysis and Optimization of Steel-Tube-Columns Combined-with-Bailey-Beams Doorway Support

Abstract

As a commonly used support system in highway bridge construction, the deformation of steel-tube-columns-combined-with-Bailey-beams doorway supports is often an indicator for safety and quality control. In this paper, through finite element simulation and theoretical derivation, the main form of deformation of each part of the combined doorway is analyzed, by using the rigid body function of ANSYS. The study shows that when bearing vertical load, the deformation of the combined doorway is mainly caused by the deflection of the Bailey beams; when bearing transverse horizontal load, the deformation of the combined doorway is mainly caused by the rotation of the foundation; when bearing longitudinal horizontal load, the deformation of the combined doorway is mainly caused by the offset bending of the Bailey beams out of the plane. When several loads are applied to the combined doorway at the same time, the deformation in the linear phase follows the superposition principle, and the geometric nonlinearity has little effect on the overall deformation of the structure. The structural deformation caused by different types of loads can be calculated separately, and then the structural deformation under composite load can be calculated by linear superposition, using geometric relationships. The safety and deformation resistance of steel-tube-columns-combined-with-Bailey-beams doorway supports can be effectively improved by choosing reinforced Bailey beams, increasing the width of the foundation, and setting lateral supports between the Bailey beams.

1. Introduction

Old urban bridges exist worldwide [1,2], and these old bridges are often accompanied by various risks of possible collapse [3,4]. As urbanization progresses, these old urban bridges often need to be demolished [5]. During the construction of such urban transportation renewal projects, existing roads are often crossed. Therefore, large-span doorway supports are often used, to ensure the safety of the existing roads and the construction process [6,7,8]. In this type of construction, various types of supports are used [9,10], and the combination of steel pipe columns and Bailey beams is a commonly used doorway construction program. Originally a military product, Bailey beams are increasingly used in civil applications, due to their high assembly and excellent stress performance [11,12,13]. Deformation is often a critical index by which to examine the safety and quality of such combined doorway supports, and the unreasonable design of brackets often leads to more severe engineering accidents [14].

Scholars worldwide have also researched the main bodies of old bridges and the supports used in the demolition process [15,16]. Wang [16] combined finite element analysis, theoretical calculations, and actual measurements, to study the relevant parameters affecting the demolition construction process of large-span continuous rigid bridges, as well as a reasonable construction safety assessment method. Stephan [17] used ultrasonic detection technology, the location of wire breaks in pre-stressed reinforcement in old bridges was detected and localized before the demolition of the old bridges, and the suitability of Schmidt hammer impacts as an acoustic reference source was validated. Xie [18] used finite element analysis to simulate the impact of impact drilling on undemolished bridges, and the results showed that impact drilling causes settlement and lateral displacement of adjacent frame bridges. Pan [19] utilized ABAQUS to analyze the steel support system and steel pipe piles during bridge construction, to verify the safety of the construction plan. Jelena [20] described methods of rebuilding and reinforcing bridges damaged due to flooding. Gao [21] analyzed the bridge and the steel pipe support in the process of bridge jacking technology, and verified the feasibility and safety of bridge jacking technology.

Algorithms are also an important method often used in construction engineering [22,23]. Fu [24] used the hierarchical analysis method to analyze the multi-source data in the bridge demolition process, so as to successfully ensure the safety of the bridge during the demolition construction process. Using field test data, Jiang [25] validated a neural network and surface damage evaluation method for hollow-slab girders, and investigated the lateral connectivity and durability of concrete hollow-slab bridges. Alireza [26] proposed a novel unsupervised meta-learning method for long-term SHM with extensive data and profound environmental effects. The results demonstrated that this method succeeds in mitigating severe environmental effects and accurately detecting damage. Giglioni [27] proposed a self-encoder-based damage detection technique in the context of unsupervised learning, to support practical engineering applications. Boonkanit [28] developed a decision support system to find the most suitable solution for construction waste after the demolishing of concrete structures.

However, there is no design standard for this type of doorway support, and the analysis of the settlement of this type of combined doorway is also relatively lacking. Therefore, to ensure construction safety and quality, the design is often conservative. Using such structures, often targeted, low turnover, conservative design will cause much material waste, increasing construction costs. At present, most of the studies on the deformation of steel-tube-columns-combined-with Bailey-beams doorway supports are only simple vertical deformation calculations, with less analysis of the horizontal and vertical horizontal load, and they do not analyze the main reasons leading to the deformation of the doorway [29,30,31]. Therefore, there is no accurate reference basis for the design optimization of the doorway, and empirical design is mainly used. In regard to the algorithm class optimization for first-line designers, the threshold is higher, and not applicable to daily design work. Therefore, for the current design of the combined doorway support, it is necessary to clarify the influence of each part of the combined doorway support on the overall deformation of the structure, to facilitate targeted deformation control and cost control. It is also necessary to comprehensively consider the loads in different directions, so that the design of the combined doorway is more in line with the actual use of the process.

Relying on an urban renewal project spanning an existing roadway, this study analyzed the deformation of a steel-tube-columns-combined-with Bailey-beams doorway support, by combining finite element analysis and theoretical calculation. The steel-tube-columns-combined-with-Bailey-beams doorway support was divided into three parts, i.e., transition beams–Bailey beams, steel tube columns, and foundation–ground. By utilizing the rigid body function in ANSYS software (https://www.ansys.com/), different parts of the combined doorway support were set as rigid bodies in an innovative way, to investigate the influence of the non-rigid body parts on the deformation of the combined doorway, and to clarify the primary forms of deformation of each part of the combined doorway support. Based on the deformation characteristics of each part, a simple calculation model of each part of the combined doorway support is proposed, which is convenient for designers to use. Unlike most of the previous studies, which only focused on vertical loads, this study also considered the deformation effects on the structure in the horizontal direction, which are often common wind loads in the construction process. The effects of loads in different directions on the deformation of the structure were analyzed, and the deformation patterns of the combined doorway support were compared when the three different loads acted separately and when they acted together.

The conclusions of this paper can provide a reference for designers in the design of combined doorway support and targeted control of the deformation of the combined doorway in different directions, so that the design is more economical and reasonable, which is of great significance in promoting urban renewal. A simplified calculation model of each part of the combined doorway is proposed, making this paper’s conclusions more operable for designers. The three possible types of loads in construction were considered comprehensively, so that the design of the combined doorway support is more in line with the actual working conditions and has a high degree of universality.

2. Materials and Methods

2.1. Project Overview

The project on which this study was based was located in Zhengzhou, China, and the specific works included the demolition and new construction of old overpasses in the city. Due to the inefficiency and congestion of the old bridges, the existing routes needed to be remodeled. Once the construction was completed, the original semi-interchange status could be changed to a full interchange, improving traffic congestion and access efficiency. In this urban interchange renewal project, there was a construction section spanning the lower existing roadway with a span of about 8m, which required the construction of a new bridge over the existing highway. The lower road was an important transportation route for the city, so traffic could not be interrupted during construction. To ensure that the traffic on the lower existing road was not affected, it was necessary to use a support to protect the lower passing vehicles and routes. The support was required to have a large span and high resistance to deformation, and it needed to be erected quickly, so a steel-tube-columns-combined-with-Bailey-beams doorway support was used.

The steel-tube-columns-combined-with-Bailey-beams doorway support consisted of transition beams, Bailey beams, load-bearing beams, tubular steel columns, and a foundation. The soil under the foundation was simply leveled and compacted. The size of the doorway support is shown in Figure 1 and Figure 2, with units in mm.

2.2. Finite Element Modeling

2.2.1. Sections and Material Properties

The main material of this doorway support was Q235 steel, with a yield strength of 235 N/mm${}^2$. There were typical material nonlinear characteristics, and considering the nonlinearity of the material could make the finite element simulation more accurate [32]. The steel used the biso intrinsic model [33,34], and the model equation was

$$\sigma =\left\{\begin{array}{cccc}& E\epsilon ,\hfill & \hfill & \epsilon ⩽{\epsilon }_s\hfill \\ & {\sigma }_s+E_1(\epsilon -{\epsilon }_s),\hfill & \hfill & \epsilon >{\epsilon }_s,\hfill \end{array}\right.$$

(1)

where $\sigma$ was the material stress, $\epsilon$ was the material strain, E was the material-elastic modulus, ${\epsilon }_s$ was the material strain at the material yield point, and $E_1$ was the material-strain-hardening modulus.

A simple concrete ground was set up at the bottom of the steel tube column; the material was C25, the yield strength was 16.7 N/mm${}^2$, and the concrete adopted a linear elastic principal structure. To eliminate the influence of boundary conditions, the ground $L\times W\times H$ dimensions were 13 m × 2.55 m × 1 m. In addition to the Bailey beams webs using BEAM units, all the other structures used SOLID units, and the dimensions and material properties of each part of the doorway support are shown in

Table 1. Material properties table.

Name	Section Type	Material	Modulus of Elasticity (N/mm${}^2$)	Poisson’s Ratio	Density (kg/m${}^3$)
Transition beams	12 I-beams	Q235	2.0 × 10${}^5$	0.3	7850
Bailey beams	321 Bailey beams	Q235	2.0 × 10${}^5$	0.3	7850
Load-bearing beams	40a I-beams	Q235	2.0 × 10${}^5$	0.3	7850
Tubular steel columns	$\varphi$273 mm × 8 mm	Q235	2.0 × 10${}^5$	0.3	7850
Foundation	-	C25	2.8 × 10${}^4$	0.2	2300
Ground	-	loess	1.07 × 10${}^1$	0.35	1800

.

2.2.2. Loads and Boundary Conditions

Combined with the situation in the actual project, the doorway support was subjected to two kinds of loads, i.e., top vertical load and horizontal load, of which the horizontal load was divided into longitudinal load and transverse load. The combined doorway support was in the elastic stage when working, and its deformation was small, compared to the overall size, so it was assumed that it met the principle of elastic superposition in the elastic stage. The vertical and horizontal loads are discussed separately. The loading surface was the top surface of the transition beams, as shown in Figure 3. In Figure 3, one beam is taken to indicate the load direction, and the actual load in each direction is spread on the top surface of the transition beams. The load size was able to cause plastic deformation of the doorway in this study. After the trial calculation, the size of the vertical load was 1 MPa, the size of the transverse horizontal load was 0.008 MPa, and the size of the longitudinal horizontal load was 0.035 MPa.

To ensure that all potentially affected soils were included in the computational model, ground soils about five times the size of the foundation were taken for modeling, and the boundary conditions were fixed for the bottom ground soils, except for the top surface. The overall finite element model is shown in Figure 3.

2.2.3. Analytical Methods

To study the degree of contribution of different parts to the overall deformation of the structure, combined with the deformation characteristics of the gantry, the deformation of the steel-tube-columns-combined-with-Bailey-beams doorway support was divided into three parts, to be analyzed, i.e., transition beams–Bailey beams, tubular steel columns, and foundation–ground. Using the rigid body function in ANSYS software, different parts were set as rigid bodies, to study the effect of the deformation of each part on the overall deformation of the structure. For example, when analyzing the contribution of the tubular steel columns to the overall deformation of the structure, the transition beams–Bailey beams and the foundation-ground were set as a rigid body, and the tubular steel columns for the elastomer, and, according to this method, the influence of each part’s deformation on the structure’s overall deformation was obtained.

3. Results

3.1. Deformation under Vertical Loading

According to the analysis of the finite element results, the structure was under vertical load, the maximum displacement of the structure occurred at the center position of the top surface (the location is shown in Figure 4), the direction was vertically downward, and it was stipulated that the displacement was vertically downward in the negative direction.

The load-displacement curves are shown in Figure 5 and Figure 6, where the curves were taken from the load-displacement curves at the location of the maximum displacement of the structure. Figure 5 shows the load-displacement curves obtained from the analysis, according to the method described in Section 2.2.3. Figure 6 is a comparison of the superposition of the load-displacement curves of the various parts of Figure 4 to that of the structure under the full elastic body.

As can be seen from Figure 5 and Figure 6, the maximum displacement value of the overall structure in the linear elastic phase under the vertical load was 15.8 mm, and the maximum displacement of the structure was mainly caused by the deflection of the transition beams–Bailey beams. The maximum value of the contribution of the transition beams–Bailey beams to the overall deformation in the linear elastic phase was 9.9 mm, accounting for 63% of the overall deformation, followed by the deformation of the foundation–ground. The axial compression of the steel tube column had little effect on the maximum displacement of the structure. It can be seen from Figure 5 that the structural displacement deformation was nonlinear and, in the linear elastic deformation stage, the maximum displacement of the structure satisfied the linear superposition. The deformation of the transition beams–Bailey beams and foundation–ground are shown in Figure 7. To make the observation more obvious, the deformation diagram in this paper expands the display effect by ten times.

From Figure 7, it can be seen that the deformation of the structure under vertical load was mainly caused by the deflection of the Bailey beams and the compression deformation of the ground. Considering the Bailey beam as a simply supported beam, the deflection of the Bailey beam was calculated, and its calculation sketch is shown in Figure 8.

In Figure 8, l is the length of the Bailey beams, a is the spacing of the transition beams, where $F=P/L$, F is the single transition beam to the Bailey beams load, P is the single transition beam subjected to the total load, N is the number of Bailey beams, and P is uniformly distributed through the transition beams to each piece of the Bailey beam and simplified to the simply supported beam. Because of the symmetry of the load, the maximum deflection of the Bailey beams occurred with the span, according to the mechanics of the materials [35]; the establishment of the coordinate system, as shown in the figure, and the relationship between the deflection curve equation and the structural moment equation is shown in Equation (2):

$$EI\omega =-\int \left[\int M\left(x\right)dx\right]dx+C_{1}x+C_2,$$

(2)

where E is the modulus of elasticity, I is the moment of inertia of the cross-section and the value of I of the Bailey beams can be taken from the literature [35], $\omega$ is the deflection of the beams, M is the bending moment borne by the beams, and $C_1$ and $C_2$ are the constants of integration, which were determined according to the boundary conditions.

Since the load of the transition beams at both ends of the beams was generally transferred directly to the Bailey beams supports, which had little effect on the deflection of the Bailey beams, only the cases where the number of transition beams was greater than two is discussed. According to the beams deflection formula and the principle of superposition on the Bailey beams, deflection in the span could be calculated as shown in Equations (3) and (4):

$$\mathsf{\Delta }=\left\{\begin{array}{ccc}& -\left[2\times \frac{F}{48EI}\sum _{n=3}^{\frac{N-1}{2}}3na·l^2-4{\left(na\right)}^3\right]+\frac{F{l}^3}{48EI}\hfill & \hfill \mathrm{If}N\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{number}\\ & -2\times \frac{F}{48EI}\sum _{n=4}^{\frac{N}{2}-1}3na·l^2-4{\left(na\right)}^3\hfill & \hfill \mathrm{If}N\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}\end{array}\right.$$

(3)

$$\mathsf{\Delta }=\left\{\begin{array}{cc}-{\displaystyle \frac{P{l}^3}{384EI}}·{\displaystyle \frac{5N^2-10N+1}{N^2-N}}\hfill & \mathrm{If}N\mathrm{is}\mathrm{an}\mathrm{odd}\mathrm{number}\hfill \\ \\ -{\displaystyle \frac{P{l}^3}{384EI}}·{\displaystyle \frac{5N^3-20N^2+20N-12}{{\left(N-1\right)}^3}}\hfill & \mathrm{If}N\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number},\hfill \end{array}\right.$$

(4)

where $\mathsf{\Delta }$ is the mid-span deflection, combined with the actual situation. Generally, P and l are determined according to the engineering situation, so the deflection of the Bailey beams can be reduced by increasing E and I. According to the literature [36,37,38,39], the I of an ordinary Bailey beam is 250,497 cm${}^4$, and a reinforced Bailey beam is 577,434 cm${}^4$, so a reinforced Bailey beam can be chosen, which can effectively improve the deformation resistance of the combined system. According to the monotonicity of the coefficients in Equations (3) and (4), the larger the number of transition beams, the smaller the deflection, which is a significant nonlinear change. When N is greater than 15, the deflection does not change much with the increase of the number of transition beams, so the actual project control of the number of transition beams is 15 or so, for the control of deflection and the construction cost control of the best results.

3.2. Deformation under Transverse Horizontal Loading

The location of the maximum displacement of the structure under transverse horizontal load is shown in Figure 9 at the extreme edge of the upper transition beams. The direction of displacement was parallel to the transverse direction of the support, and the displacement in the direction of the specified load was in the negative direction.

The load-displacement curves are shown in Figure 10 and Figure 11.

As can be seen from Figure 10, when the structure was subjected to transverse horizontal load, the deformation of the tubular steel columns and the foundation–ground part was much larger than that of the transition beams–Bailey beams, and the tubular steel columns and the foundation–ground mainly contributed the deformation. As shown in Figure 11, the maximum displacement of the structure as a whole under the transverse horizontal load was 37.2 mm. In the linear phase, the deformation of each part and the overall deformation also approximately satisfied the principle of superposition. The tubular steel columns and the foundation–ground deformations are shown in Figure 12.

As seen from Figure 12, under the action of transverse horizontal load, the deformation of the doorway support was mainly caused by the lateral bending of the steel tube columns and the rotation of the foundation. From the geometrical relationship, it can be seen that the slight deformation of the corner of the foundation was amplified by the tubular steel columns, which led to a more obvious deformation of the superstructure. Hence, the rotation of the foundation had the most obvious influence on the horizontal displacement of the structure. The calculation sketch of the foundation rotation is shown in Figure 13.

In Figure 13, $l_c$ is the distance from the bottom surface of the foundation to the top surface of the combined support, ${\mathsf{\Delta }}^{\prime }$ is the horizontal displacement of the top surface of the combined support, $F^{\prime }$ is the horizontal load, $\theta$ is the foundation turning angle, q is the maximum ground reaction force, and b is the width of the foundation. The combined moment was obtained for the midpoint of the foundation surface of the ground:

$$F^{\prime }·l_c=\frac{2b}{3}·q·\frac{b}{2\times 2},$$

(5)

where q was the maximum ground reaction force provided by the deformation of the ground soil, q being related to the ground deformation. Due to the symmetrical distribution of the structure, load, and action point, the ground deformation was simplified as a linear distribution from the centerline to the outer edge of the foundation. Where the deformation of the foundation centerline position was 0, and ignoring the foundation deformation and the tensile action of the ground for the foundation, then q could be calculated by the following formula:

$$q=\frac{E^{\prime }b}{2}tan\theta ,$$

(6)

where $E^{\prime }$ was the modulus of the elasticity of the ground soil, and then Equation (5) could be written as

$$F^{\prime }{l}_c=\frac{2b}{3}·\frac{E^{\prime }b}{2}tan\theta ·\frac{b}{4}$$

(7)

$$tan\theta =\frac{12F^{\prime }{l}_{\mathrm{c}}}{E^{\prime }{b}^3}$$

(8)

$${\mathsf{\Delta }}^{\prime }=l_c·tan\theta =\frac{12F^{\prime }{l_{\mathrm{c}}}^2}{E^{\prime }{b}^3}.$$

(9)

From Equation (9), it can be seen that the lateral horizontal displacement mainly depends on the elastic modulus of the ground soil and the foundation width. The foundation width has a significant influence on the lateral horizontal displacement. Therefore, when constructing with a combined doorway support, the foundation width can be increased moderately, and the soil layer at the bottom of the doorway support can be strengthened, which can reduce the horizontal displacement of the doorway support.

3.3. Deformation under Longitudinal Horizontal Loading

The location of the maximum displacement of the structure under a longitudinal horizontal load is shown in Figure 14, with the direction parallel to the longitudinal direction of the support, which specifies the direction of load as the negative direction of displacement.

The load-displacement curves are shown in Figure 15 and Figure 16.

As shown in Figure 15 and Figure 16, the displacements of each part for the whole combined support under the action of longitudinal horizontal force were apparent, with the deformation of the transition beams–Bailey beams having the greatest influence. The deformation of a steel tube column is similar to that subjected to a horizontal transverse load, all of which are lateral bending, and the deformation of the transition beams–Bailey beams and foundation–ground are shown in Figure 17.

Analysis showed that under the action of longitudinal horizontal load, the deformation of the doorway support was mainly caused by the offset bending of the Bailey beams, the lateral bending of the steel tube column, and the buckling of the ground, and that the offset bending of the Bailey beams had the greatest influence on the deformation of the structure as a whole. The deformation of the Bailey beams could be approximated as a superposition of the out-of-plane offset and perpendicular to the deflection of the Bailey beams. Since the Bailey beams’ out-of-plane deflection and bending resistance were low, diagonal bracing could be added between the Bailey beam pieces, to reduce the deformation of the doorway support when subjected to longitudinal loading.

3.4. Deformation of the Structure under the Combined Action of Three Loads

In actual engineering, the combined doorway support is often subjected to the joint action of loads from several directions. In addition to gravity, the superstructure supported by the brace is often subjected to wind loads, which are transferred to the top surface of the transition beams in the form of friction. The design calculation considering multiple loads simultaneously is often complicated, so it was necessary to examine whether it was possible to calculate the structural deformation under composite loads, by calculating the deformation of a single load. The three loads were applied simultaneously to the combined doorway support, and the load-displacement curves were compared with those when the loads were applied separately. Take the load-displacement curve at the position of maximum displacement under different load types, as shown in Figure 18:

From Figure 18, it can be seen that in the linear elastic phase, the deformation of the structure in all directions under the joint action of the three loads was similar to the maximum deformation under the separate act of the loads, which was consistent with the assumption in Section 2.2. In the nonlinear stage, due to the nonlinearity of the material and the geometric nonlinearity of the structure, it often leads to the linear relationship between the part and the whole deformation being broken. However, the design of such a combined doorway support generally requires that the structure is in the linear load-bearing stage throughout the working cycle, and the design of the combined doorway supports is controlled by the deformation. Therefore, when designing this kind of combined doorway, the deformation of each part of the combined doorway support can be calculated separately, and then based on the geometric relationship, the deformation of each part is superimposed linearly, and the overall maximum deformation of the combined doorway support is finally calculated.

4. Discussion

The above results show that the deformation of each part of the steel-tube-columns-combined-with-Bailey-beams doorway support is different under different types of loads. The results are similar to those of the literature [29,30,31]. Referring to the structure of the literature, the deformations can be summarized as follows. The form of deformation is determined by each part’s force characteristics and the load type. Transition beams–Bailey beams can be regarded as typical simply supported deep beams, composed of transition beams and Bailey beams together, to form the intersecting beam system. Therefore, transition beams are sensitive to vertical and longitudinal horizontal loads. Transition beams are susceptible to vertical deflection and out-of-plane bending and, therefore, contribute more to the overall deformation in these two directions. Steel tube columns can be viewed as cantilever beams fixed at one end. This type of structure is more capable of resisting axial deformation but less capable of withstanding deformation perpendicular to the direction of the column length. Therefore, when carrying horizontal loads, steel tube columns contribute more to the deformation of the structure. The deformation of the foundation–ground is mainly caused by the deformation of the foundation, due to the significant difference between the stiffness of the foundation and the ground. The foundation is primarily sensitive to vertical compression and horizontal rotation, so it mainly leads to deformation in these two directions.

Combined with the force characteristics of each part, the theoretical calculation formula can be known, as well as the optimization means commonly used in the literature [9,13,31,36], for the deformation calculation and optimization of steel-tube-columns-combined-with-Bailey-beams doorway support, mainly from the following aspects. Optimization can be achieved by choosing reinforced Bailey beams or appropriately increasing the number of Bailey beams, setting up longitudinal support between the Bailey beams, increasing the cross-section of the steel pipe columns or setting up inter-column support between the steel pipe columns, widening the width of the foundation and treating the ground soil, to increase the stiffness, and other measures to optimize the deformation. For the daily design of the designers, the overall deformation of the linear stage can be calculated by divisional calculation and then superimposed.

In this study, only uniform constant load was considered, dynamic load during construction was not considered, and the optimization only aimed at deformation. Therefore, dynamic load, construction cost, and construction period could be considered, combined with the algorithm for further optimization study of the combined doorway support. Due to geometric nonlinearity, the deformation of the structure, when subjected to significant loads, cannot be simply superimposed linearly. Therefore, subsequent research could investigate the deformation method of the whole construction, considering the geometric nonlinearity and the critical relationship between the geometric nonlinearity and the dimensions of each part.

5. Conclusions

In this study, the deformation of a steel-tube-columns-combined-with-Bailey-beams doorway support was investigated, using finite element simulation and theoretical derivation, and the following conclusions were drawn:

• The deformation of the combined doorway support in the elastic phase satisfies the principle of superposition, which can be combined with the geometric relationship between the parts, to calculate the deformation of the combined doorway under the joint action of multiple loads;
• When subjected to vertical load, the deformation of the combined doorway is mainly caused by the deflection of the Bailey beams sheet; when subjected to transverse horizontal load, it is caused by the rotation of the foundation; and when subjected to longitudinal horizontal load, it is caused by the offset bending of the Bailey beams out of the plane;
• Selection of strengthened beams or increasing the number of transition beams can effectively reduce the vertical deformation and increase the width of the foundation, which can significantly reduce the transverse horizontal deformation; increasing the longitudinal diagonal bracing between the Bailey beams can reduce the longitudinal horizontal deformation.