Failure Behavior of Aluminum Solar Panel Mounting Structures Subjected to Uplift Pressure: Effects of Foundation Defects

Abstract

This study investigates the failure behavior of aluminum solar panel mounting structures subjected to uplift pressure, with particular focus on conditions not typically considered in conventional design, specifically, foundation defects. To clarify critical failure modes and evaluate potential countermeasures, full-scale pressure loading tests were conducted. The results showed that when even a single column base was unanchored, structural failure occurred at approximately half the design wind pressure. Although reinforcement measures—such as the installation of uplift-resistant braces—increased the failure pressure to 1.5 times the design value, they also introduced the risk of undesirable failure modes, including panel detachment. Additionally, four-point bending tests of failed members and joints, combined with structural analysis of the frame, demonstrated that once the ultimate strength of each component is known, the likely failure location within the structure can be reasonably predicted. To prevent panel blow-off and progressive failure of column bases and piles, specific design considerations are proposed based on both experimental observations and numerical simulations. In particular, avoiding local buckling in members parallel to the short side of the panels is critical. Furthermore, a safety factor of approximately two should be applied to column bases and pile foundations to ensure structural integrity under unforeseen foundation conditions.

1. Introduction

1.1. Expansion of Photovoltaic Power Generation and Introduction of Mounting Structure Design Guidelines in Japan

Amid the rapid changes in the global environment, the development and utilization of renewable energy sources have been accelerating worldwide. In Japan, the Fukushima Daiichi nuclear disaster triggered by the Great East Japan Earthquake in 2011 [1] sparked a surge in public support for renewable energy. This societal momentum, coupled with the introduction of the Feed-in Tariff (FIT) scheme by the Agency for Natural Resources and Energy in July 2012, led to a tenfold increase in solar power generation over the past decade. As a result, solar power has overtaken hydropower in terms of electricity generation [2]. Globally, Japan is among the leading countries in PV adoption, ranking first among major countries in terms of installed capacity per unit land area [3].

However, this rapid expansion preceded the establishment of proper structural design and construction standards for PV module mounting structures. Consequently, numerous cases of structural damage have been reported [4,5,6,7]. Among the various causes of PV system failures in Japan, wind-induced damage during typhoons has been the most frequently observed [4,5]. Although the widespread adoption of solar power has advanced rapidly in Japan, repeated structural failures—especially following the shift to low-cost mounting systems without sufficient technical oversight—pose a significant risk to its stable and sustainable deployment. Continued damage incidents could undermine public confidence and hinder further expansion of photovoltaic energy [6,8].

In response to these challenges, Japan’s Ministry of Economy, Trade and Industry (METI) has led efforts to establish technical standards for PV power generation facilities. As part of this initiative, design guidelines for PV systems have been developed by organizations such as the Japan Association for Wind Engineering and the New Energy and Industrial Technology Development Organization (NEDO). These guidelines [9,10] comprehensively cover site-specific requirements, including ground investigations, load estimation methods, and structural design procedures for mounting structures, including their foundations. Each section is accompanied by relevant technical documentation to support the recommended practices [11]. NEDO also provides structural design examples of steel and aluminum PV mounting structures on their website [12,13]. The reference [14] can also be cited as a source that summarizes key considerations and design methods for the structural design of PV mounting systems. Furthermore, dedicated design guidelines have also been established for PV installations on sloped terrain [15]. These provide specific considerations for ground conditions and introduce wind load calculation formulas that take topographical effects into account. Today, it can be concluded that a reliable structural design methodology for ensuring the safety of the ground-mounted PV systems is being established in Japan.

1.2. Purpose of the Study: Evaluating the Wind Resistance Performance of Solar Panel Mounting Structures with Foundation Deficiencies

Although comprehensive design guidelines for solar panel mounting structures have been established, it is not easy to ensure that all structures installed across large-scale PV power plant sites are constructed under the ideal conditions assumed in the design phase. Screw piles are widely adopted as foundations for PV systems due to their reputed resistance to uplift forces. However, reference [15] reports cases of foundation failure—specifically, pile pull-out leading to structural collapse—under wind conditions where the recorded wind speeds were lower than the design wind speeds. As shown in Reference [16], some studies present improvement strategies by evaluating the pull-out resistance of support piles used in photovoltaic mounting structures installed in desert environments, and proposing methods for selecting appropriate pile types. However, it remains highly questionable whether comprehensive geotechnical investigations and appropriate construction management can be conducted across an entire large-scale solar power plant to ensure that the expected pile bearing capacity is fully achieved. In addition, according to the technical documentation [11], pile pull-out resistance can be significantly reduced by construction defects such as inclined driving or idle rotation. Additional factors such as sloped terrain and surface erosion caused by rainwater runoff further compromise foundation performance [17,18].

To date, both in Japan and internationally, most related studies have primarily focused on the wind loads acting on the solar panels themselves, while only a limited number have examined the stress distribution within mounting structures under wind loading [19,20,21]. Moreover, few studies have investigated the actual failure mechanisms of these structures. Since solar panel mounting structures are typically designed to remain elastic under design-level loads, they often employ minimal structural redundancy. Therefore, in the event of unforeseen conditions such as foundation defects, their wind resistance performance is highly likely to degrade significantly from the intended design capacity.

This study primarily focuses on elucidating the failure behavior of solar panel mounting structures and evaluating their structural safety margin against uplift wind loads, particularly under unanticipated conditions not considered during the design phase, such as foundation defects. Specifically, full-scale mounting structures are subjected to upward pressure to simulate uplift wind forces, and the progression of damage and failure modes is experimentally observed in order to identify the structural components or joints that are particularly prone to losing redundancy under foundation defects (Section 2). Subsequently, component-level experiments are conducted to evaluate the strength of the structural elements identified as weaknesses, and potential countermeasures are proposed to mitigate the reduction in wind resistance under unexpected conditions; their effectiveness is also evaluated (Section 3). In addition, all test results are reviewed to extract insights for preventing critical failure modes, including the blow-off of solar panels and the chain failure of the foundation, which may lead to the collapse of the entire mounting structure. Finally, supplemental numerical analyses are conducted on multi-span mounting systems to quantify the extent of performance degradation due to foundation defects. Based on these findings, design strategies are proposed to ensure both safety and cost-effectiveness in the structural design of solar panel mounting systems (Section 4). It should be noted that, as this study aims to elucidate the physical failure behavior of solar panel mounting systems, the term “solar panel mounting structures” hereafter refers to the structural system, including the mounting frame and the attached solar panels.

2. Uplift Pressure Resistance Performance of a Solar Panel Mounting Structure with Foundation Defects Evaluated by Pressure Loading Tests

2.1. Test Setup of Full-Scale Pressure Loading Tests

2.1.1. Solar Panel Mounting Structure Specimen

Figure 1 shows the test specimen of the solar panel mounting structure used in the pressure loading test. Figure 1a illustrates the structural configuration of the mounting structure, while Figure 1b shows the specimen after the installation of 20 solar panels. Figure 2 illustrates (a) the north-south frame (west-side elevation view) and (b) the panel arrangement of the solar panel mounting frame. The mounting structure consists of three braced column-beam frames arranged in a span of 3.4 m (labeled as Frames 1, 2, and 3 from west to east in the figure), with five rails arranged in the east-west direction on top. Given that the span of north-south frames is typically in the range of 2.5 to 3.5 m, the present specimen, with a span of 3.4 m, is considered relatively large. The solar panels are fixed to the rails in a 4-row × 5-column configuration. Each solar panel has dimensions of approximately 1 m × 1.6 m and weighs 20 kg. The total weight of the frame, including the solar panels, is approximately 5000 N. The solar panel surface measures 8.25 m × 4.25 m, with a total area of approximately 35 m². As shown in Figure 2b, each solar panel is fixed to the rails at four points using two panel fixing clamps per long side. Notably, the short sides of adjacent solar panels are not fixed to each other. The solar panel surface is inclined at an angle of 20 degrees. Hereafter, the inclination direction of the specimen is defined as the north-south direction, indicating the orientation of the test specimen.

The major components of the frame are made of aluminum. The mounting structure was produced by a Chinese manufacturer, and the manufacturer states its material strength is equivalent to that of high-strength aluminum alloy AL6005-T5 [22]. The design pressure (uplift pressure) for the mounting structure is P_d = 1333 Pa. The design pressure was calculated based on the design guidelines [9,23], assuming a reference wind speed of 34 m/s, considering an urban suburban area (surface roughness category III [23]) and a panel tilt angle on the wind pressure coefficient.

Table 1. Component specification. (a) Rail; (b) Girder; (c) Column; and (d) NS brace.

(a)			(b)
	A 1 [mm2]	560.8		A [mm2]	645.3
	I 2 [mm4]	757,686.70		I [mm4]	658,906.90
	Ztop 3 [mm3]	15,212.20		Ztop [mm3]	14,857.80
	Zbottom 4 [mm3]	15,095.70		Zbottom [mm3]	14,433.10
	x 5 [mm]	49.2		x [mm]	44
(c)			(d)
	A [mm2]	466.7		A [mm2]	288.9
	I [mm4]	243,799.90		I [mm4]	78,610.80
	Z [mm3]	8126.7		Z [mm3]	3930.5

¹ Sectional area. ² Second moment of area. ³ Section Modulus (top edge). ⁴ Section Modulus (bottom edge). ⁵ Distance of centroid from top edge.

presents the component section details of the solar panel mounting frame. The components are extruded members made of aluminum alloy. The upper sides of the rail and girder have grooves for securing the fixing clamps. In the cross-sectional view of the column and NS (north-south) braces shown in the figure, bolts pass through the member ends in the left-right direction. Related connection details are provided in Figure 3.

Figure 3 illustrates the joint details of the solar panel mounting frame shown in Figure 1 and Figure 2. As shown in Figure 3a, the column base is fixed to the steel pile head, which is cut out from the screw pile only at the top 200 mm, using M14 bolts via a column base joint bracket. The base joint brackets are designed with slotted holes to accommodate height tolerances at the column bases during on-site installation. The components of the braced north-south frame (columns and braces) are pin-connected using a single bolt passing through the member axis and a connecting bracket (Figure 3a,b). The girders and rails are secured by fixing clamps placed in the groove on the upper part of the girder, as shown in Figure 3c. In this solar panel mounting frame, the structural system is designed to be expandable in the east-west direction by extending the length of the rail members that secure the solar panels. In the test specimen, as shown in Figure 3d, the rail members were extended by inserting a 250 mm-long insert into the hollow section of the rail and securing it with M6 screws from both sides. Since this test specimen is a two-span mounting frame, the 4 m-long rails were extended directly above the girder of Frame 2, which is located at the center of the frame (Figure 3d, left end).

As shown in Figure 1, Figure 2 and Figure 3, the solar panel mounting frame used as the test specimen can be characterized as a structure with pinned supports. The columns and braces are pin-connected at both ends and carry only axial forces, whereas the beams are designed to resist bending moments.

Figure 4 shows the configuration of the adopted solar panel. The wind pressure load guaranteed by the manufacturer for this panel (when acting on the rear side) is 2400 Pa. The panel frame is made of aluminum and is provided with holes for panel fixing clamps at four locations along each of its long sides. In this experiment, the panel was fixed at two locations on each side, as shown in the left photo of Figure 4.

2.1.2. Specimen List and Pressure Loading Test

Table 2 presents the list of test specimens for the pressure loading test of solar panel mounting structures with foundation defects. The applied pressure corresponds to the uplift pressure, which exerts a force that lifts the solar panel mounting structure. In Specimen O, all six column bases were fully anchored (Support condition A) during the test. In the anchored column base condition, the column base joint bracket is bolted to the pile head, as shown in Figure 3a. In Specimen I, strain gauges were attached to estimate the stress state of the test specimen (further explained later). Initially, the test was conducted with all column bases anchored (Support condition A) and pressurized up to P = 500 Pa, ensuring the structure remained elastic. Subsequently, to simulate a foundation defect in a simplified manner, the bolt fixation of the north column base in Frame 2 (marked with a red dotted circle in the bottom figure of Table 2) was removed (Support condition B). The test specimen was then subjected to increasing pressure until failure occurred. The north column base of Frame 2 was chosen as the foundation defect point because it experiences the largest uplift force under uplift pressure conditions. In the loading test of Specimen O, the bolts slipped in the slotted holes of the column base joint brackets. Taking this into account, in Specimen I, the slotted holes were sealed after assembling the frame to prevent the bolts from slipping.

Figure 5 shows an overview of the pressure loading test for the solar panel mounting structure. The solar panel mounting test specimen is enclosed by test chamber walls, and a vinyl air seal is used to block airflow between the pressure walls and the solar panels, preparing a sealed pressure chamber. By increasing the internal pressure of the pressure chamber, an uplift pressure is applied to the surface of the solar panels. When conducting the experiment under Support condition B, which includes a single unanchored column base, significant uplift deformation of the solar panel surface is expected. Therefore, a slack of approximately 500 mm was provided in the vinyl air seal.

Figure 6 illustrates the pressure loading plan. In Test O-A (Specimen O with Supporting condition A), in which the test was conducted until failure under all fixed support conditions, the pressure was gradually increased in 250 Pa increments. On the other hand, in the elastic test under all the base anchored conditions of Specimen I (Test I-A), the pressure was gradually increased in 100 Pa increments up to P = 500 Pa. In the failure test, the north column base of Frame 2 was released (Test I-B), and the pressure was gradually increased in 100 Pa increments up to P = 300 Pa. After that, the rotation angle θ of Frame 2 (defined in the figure) was gradually increased in 0.01 rad increments. Figure 6b also shows the arrangement of displacement transducers at the unfixed column base on the north side of Frame 2. The pressure was increased at a rate of approximately 10 Pa/s during each loading cycle, and the target pressure was held for 10 s after reaching the peak in each cycle.

Figure 6. Pressure loading plan: (a) Under Support condition A (all base anchored condition); (b) Under Support condition B (a single-unanchored-base condition).

Figure 6. Pressure loading plan: (a) Under Support condition A (all base anchored condition); (b) Under Support condition B (a single-unanchored-base condition).

Table 2. Specimen list for pressure loading test of solar panel mounting frames with foundation defects.

Specimen	Pressure Direction	Loading Type	Support Condition	Measurement Plan
O	uplift pressure	Elastic—Fracture	A
I		Elastic (up to 500 Pa)	A	Figure 7
		Elastic—Fracture	B

Supporting condition: A: All column bases anchored; B: A Single unanchored column base.

Table 2. Specimen list for pressure loading test of solar panel mounting frames with foundation defects.

Specimen	Pressure Direction	Loading Type	Support Condition	Measurement Plan
O	uplift pressure	Elastic—Fracture	A
I		Elastic (up to 500 Pa)	A	Figure 7
		Elastic—Fracture	B

Supporting condition: A: All column bases anchored; B: A Single unanchored column base.

2.1.3. Measurement Plan for the Mounting Structure

In addition to measuring the loading pressure and the uplift displacement of the column base—made unanchored to simulate foundation failure as shown in Figure 6b—strain gauges were attached to the main structural members of the solar panel mounting frame to estimate its stress state. Figure 7 shows the strain gauge attachment positions, both for Specimen I. Strain gauges were attached to the girders, columns, and braces of the north-south frame. For columns and braces, which have pin connections at their ends, strain was measured at a single cross-section of each member. On the other hand, for girders, which receive several concentrated loads from the rails, column and NS braces, strain was measured at eight cross-sections to capture the bending moment distribution. The strain gauges were attached to each structural member as shown in Figure 8b. In Specimen I, strain gauges were not attached to the rails used to fix the solar panels. This is because the rails, which are clamped together with the solar panels, resist bending moments in combination with the panels, making it difficult to estimate the internal stress distribution from a limited number of measurement points. Therefore, considering the structural configuration investigated in this study, priority was given to estimating the load transferred from each rail to the girder based on the bending moment of the girder, and the measurement plan was designed accordingly. Although the strain gauge positions on the rails are also shown in Figure 8b, these were attached during the additional experiments described in Section 3, and not in Tests I-A and I-B.

All measurements were taken at a frequency of once per second.

2.2. Test Results of the Solar Panel Mounting Structure: Comparison Between Cases with and Without Foundation Defects

2.2.1. Fracture Behavior of the Solar Panel Mounting Structure

Figure 8 illustrates the failure behavior of the solar panel mounting test specimen when subjected to uplift pressure. Figure 8a indicates the locations of failure, while Figure 8b shows the failure state in Test O-A, where all column bases were anchored (Support condition A), and Figure 8c presents the failure state in Test I-B, where a single column base was released or left unanchored to simulate foundation defects (Support condition B).

From Figure 8a,b, under the condition where all column bases were anchored (Test O-A), no significant changes were observed up to the design wind pressure P_d = 1333 Pa. At P = 1800 Pa, loosening of the fixing clamp that secure the rails to the girders was observed (O-(1)), and at P = 2000 Pa, a phenomenon was noted in which the bolts slipped within the slotted holes provided in the column base joint brackets (O-(2)). Irreversible failure occurred at P = 2600 Pa, which is twice the design wind pressure. The failure was observed at the northern column base of Frame 2, where the highest uplift force acted, causing an edge tear failure in the column base joint bracket bolted to the pile head (O-(3)). Additionally, at P = 2500 Pa, plastic deformation was observed in the rail clamp located at the center of Rail 3 (O-(4)).

From Figure 9, under the condition where the northern column base of Frame 2 was not anchored, the solar panel mounting frame exhibited significant uplift deformation at the unfixed part. At a design wind pressure of approximately half, P = 650 Pa, the frame of the solar panel directly above the unanchored column base bent (I-(1)). During depressurization from P = 775 Pa, the cover glass of the solar panel with the bent frame fractured (I-(2)). Subsequently, at P = 885 Pa, the insert at the rail extension joint of Rail 5 failed due to bearing pressure on the lower flange of the rail (I-(3)). Simultaneously, the frame of the solar panel (I-(4)) also bent. Based on this damage progression, in the case of rail extension joints as shown in Figure 3d, insufficient rotational fixation of the joint led to early rotational deformation, which seems to cause the solar panel frame directly above to bend and the cover glass to break. These findings indicate a significant reduction in wind resistance performance of the solar panel mounting structure in cases with poor foundation conditions, as well as the possibility of the extension joint of the east-west directional members being a weak point.

Figure 9 shows the progression of the uplift displacement δ_2n,z at the unanchored column base (the north column base of Frame 2) in Test I-B. From the figure, it can be observed that the stiffness obviously decreases after the uplift displacement δ_2n,z reaches approximately 100 mm around P = 500 Pa. Considering that the initial buckling of the panel frame was observed at P = 650 Pa (Figure 8c), it is inferred that rotational deformation at the extension joint may have started around P = 500 Pa.

2.2.2. Load Sharing Ratio of Uplift Forces at Each Column Base

Figure 10 shows the ratio of the uplift force acting on the six column bases to the applied load F on the solar panel surface at P = 300 Pa for both the column base anchored test (Test 1-A) and the single-base-unanchored test (Test 1-B). Here, the applied load F was calculated by multiplying the panel surface area A by the applied pressure P. Additionally, Figure 10a presents the estimated uplift force ratios for each column base, considering the governing area of the solar panel surface assigned to each column base and the panel surface inclination. From the figure, the uplift forces for the fully fixed condition can be well predicted using the estimation method shown in Figure 10a. Under the single-base-unanchored condition (Test I-B), not only did the uplift force on the unanchored column base (the north column base of Frame 2) decrease, but the uplift forces on the south column bases of Frames 1 and 3 also became nearly zero. Consequently, with one out of the six column bases experiencing uplift, the remaining three out of six column bases had to resist the uplift forces. As a result, these column bases needed to withstand nearly twice the uplift force compared to the scenario where all column bases remained intact.

2.2.3. Stress Distribution of the Solar Panel Mounting Structure

Figure 11 shows the bending moment distribution of the beams in Frames 1 and 2, as well as the upward forces from Rails 1 to 5 fixed to the girders, and the normal components of the reaction forces from the columns and braces at P = 300 Pa. The bending moment distribution was estimated using the strain values measured by the strain gauges shown in Figure 7, applying an aluminum Young’s modulus of 70,000 N/mm² [24] and the section modulus (Table 1). The forces from the rails, columns, and braces were estimated based on the variation in the shear forces calculated from the bending moment distribution and the axial forces determined from the measured strains of the columns and braces. Note that the recorded strains were induced solely by the uplift pressure, excluding the effect of self-weight. The figure also indicates the locations of the maximum and minimum (i.e., maximum negative) bending moments in Frame 2 (M_G2,max and M_G2,min) for each case.

From the figure, it can be observed that when all foundations are intact (Test I-A), the normal forces acting on the beam from the five rails F_Rj,G2—as indicated by the red arrows—are approximately distributed in a ratio of 1:2:2:2:1 from Rails 1 to 5 (Figure 11a). This indicates that each rail mainly supports panel pressure up to the midpoint between adjacent rails. In contrast, this distribution pattern is not maintained when uplift occurs in the foundation (Figure 11b Test I-B). The most notable difference between the two support conditions appears in the magnitude of the bending moment at the midspan of the beam in Frame 2. Under the all column bases anchored condition (Test I-A), the columns placed on the north and south sides provided high restraint to the girder, resulting in the maximum negative bending moment (M_G2,min) occurring at the column-girder connections. In contrast, under the single-base-unanchored condition (Test I-B), the maximum bending moment was observed at the midspan of the girder. This phenomenon is likely attributed to the uplift of the north column base of Frame 2, while the south-side braces, which have a slope almost identical to that of the beams, were ineffective in restraining the central portion of the beam. According to the figure, the reaction force at the center in Test I-B—as indicated by the black arrow—is approximately half of that in Test I-A. Regarding the maximum bending moment in the girder, it doubled in Test I-B compared to Test I-A.

Figure 12 illustrates the method for estimating the bending moment distribution in the rails to which the solar panels are fixed (M’_R). First, as shown in Figure 12, the weight of the elements above the girders, including the panels themselves, was considered as a uniformly distributed load on each rail w_g,r (indicated by the red arrows in Figure 12). Here, as depicted on the right side of Figure 12, the rails were subjected to the component of the mounting system’s self-weight in the beam’s normal direction. Subsequently, an upward uniformly distributed load, w_p,r, corresponding to the lifting pressure P, was applied. At this point, the total applied uniformly distributed load (indicated by the blue arrows) was set to be equal to the sum of the reaction forces from the rails to the girders F_Rj,Gi, as calculated from Figure 12, where i represents the girder number and j represents the rail number. The bending moment of the rail was calculated from both ends toward the center, assuming zero moment at both ends. Figure 13 shows the calculated bending moment distribution of the solar panel-mounted rails M’_R,j. The figure also indicates the locations of the maximum and minimum (i.e., maximum negative) bending moments (M’_R,max and M’_R,min) for each case. From the figure, it is estimated that under the single-base-unanchored condition (Test I-B), the bending moment at the center of Rail 5, located directly above the unanchored column base, not only reversed its direction but also increased to more than three times the magnitude compared to all column base anchored condition (Test I-A). This result indicates that if the bending moment direction is neglected, the column base uplift may cause the bending moment in the rails to increase up to three times greater than the design assumption.

From Figure 11 and Figure 13, it can be seen that the uplift of the north-side column base in Frame 2 causes a loss of reaction force in the northern braces and columns, resulting in a significantly larger bending moment at the center of Girder 2 and Rail 5 compared to the case where all column bases are fixed. Among these, in specimen I-B, the rail joint located at the center of the rail was the first to fail.

3. Enhancement of Uplift Pressure Resistance Performance of a Solar Panel Mounting Structure with Foundation Defects

Section 2 presents the results of air pressure loading tests on solar panel mounting frames, revealing that under poor foundation conditions, the stress demand on east-west members with larger spans increases significantly. As a result, the pressure at which frame failure occurs may be substantially reduced. It is economically impractical to design solar panel mounting structures to remain entirely within the elastic range under unforeseen conditions such as foundation deficiencies, which are not typically considered at the design stage. Nevertheless, it remains essential to prevent an excessive reduction in wind resistance performance. Therefore, Section 3 focuses on the rail members damaged as reported in Section 2 and investigates the ultimate bending capacity of thin-walled aluminum members, along with the bending strength of their extension joints, for which standardized evaluation and design methodologies have not yet been fully established. These capacities are evaluated through four-point bending tests. Additionally, the effectiveness of a simple countermeasure is examined through a second series of air pressure loading tests conducted on solar panel mounting structures incorporating this measure.

3.1. Four-Point Bending Tests of Rail Members and Rail Extension Joint

3.1.1. Test Setup of Four-Point Bending Tests

A four-point bending test was conducted on the rail member and its extension joints to clarify the failure characteristics and bending strength of the panel support members and their extension joints. In addition, possible improvements to the extended rail splice joint are proposed and evaluated.

Figure 14 illustrates the loading apparatus and conditions for the four-point bending test of the rail extension joint. The span between the supports was 1600 mm, and the distance between the loading points was 1000 mm. The support and loading points were pin-supported using steel rods. To prevent localized bearing pressure on the rail, rubber and metal plates were placed between the steel rods and the test specimen, ensuring that the applied force was distributed evenly.

Table 3. Specimen list of four-point bending tests.

Specimen		Bending Orientation 3	Insert Length [mm]	Number of Test Specimens
Rail (no extension joint)		Negative	NAN	1
		Positive		3 2
With extension joint	Screwed joint O (original 1)	Negative	250 mm	1
		Positive		3
	Screwed joint	Negative	400 mm	1
		Positive		3
	Bolted joint	Positive		3
	Bonded joint	Positive		2
	Bolted and boned joint	Positive		3
1 Rail extension joint used in Specimen I, as described in Section 2. 2 One out of the three specimens was excluded from further analysis due to local deformation accompanied by torsion. 3 Bending orientation is defined as follows:

presents a list of test specimens, and Figure 15 illustrates the configuration of the joint section. The specimens include a rail member (without an extension joint) and five types of specimens with extension joints. All rail extension joints are connected using an insert. The test variables are as follows:

• Screwed joint with insert lengths of 250 mm and 400 mm (Figure 15a,e)
• Bolted joint with an insert using through-bolts (Figure 15b,f)
• Bonded joint using an epoxy resin-based adhesive between the insert and the rail (Figure 15c)
• Combined joint using both epoxy adhesive and through-bolts (Figure 15d)

Since the rail member used in the test is asymmetrical in the vertical direction, the bending moment application direction was also considered as a test variable. Here, the direction of the bending moment acting on the rail extension joint of Rail 5 in Section 2 during foundation uplift, as shown in Figure 13c, is defined as positive, while the opposite direction is defined as negative.

The loading was applied as a unidirectional cyclic load of P, with its amplitude gradually increasing. The target load for each cycle of P was set to 2.0, 4.0, 6.0, 10, 15, and 20 kN, respectively.

The material of the aluminum solar panel mounting structure is AL6005-T5 [22].

Table 4. Material properties of rails.

	Young’s Modulus E [N/mm2]	Yield Stress σry [N/mm2]	Tensile Stress σru [N/mm2]
Web	61,700	238	268
Flange	60,300	235	262

summarizes the results of material tests conducted on No. 5 coupon specimens [25] cut from the web and lower flange of the rail. Here, the tensile test was conducted in accordance with [25].

3.1.2. Fracture Behavior and Flexural Strength of Extension Joint

Figure 16 shows the relationship between the bending moment M and the central displacement δ (extracting the peak value of each loading cycle). Figure 17 illustrates the failure conditions of each specimen after testing. Here, “top surface” in Figure 17 refers to the side where the solar panel is fixed.

For the rail member (without a joint), local buckling occurred directly beneath the loading points at the maximum load for both positive and negative bending (Figure 17a). In Figure 16, the yield bending strength of the rail M_R,yc, is indicated by the horizontal dashed line (the calculation method is described later). The ultimate bending strength was M_max = 3.63 kNm on the negative side and M_max = 3.55 kNm on the positive side, showing minimal difference between bending directions and 1.8 times larger than M_R,yc.

From Figure 16b,c, the bending strength of the specimens with joints did not reach the bending strength of the panel support member itself (Figure 16a). However, when compared to the yield bending strength of the rail M_r,yc, all specimens exceeded this value except for those with an insert length of 250 mm and those where the insert was bonded to the rail using adhesive. If a joint that does not fully fix the rotation, such as one using screws (Figure 15a), is adopted, an insert of at least 400 mm is required. As shown in Figure 16c, by using adhesive in combination with through bolts at the joint, the initial stiffness becomes equivalent to that of the rail alone (without the joint), and the ultimate bending strength closely approaches that of the rail.

From Figure 17, the failure modes of the test specimens can be classified into (1) bearing failure of the base material flange (black circles in Figure 16), (2) fracture of the insert (a blue square in Figure 16), and (3) local buckling of the base material (red triangles in Figure 16). Failure mode (1) occurred because the inserted insert exerted bearing pressure on the flange of the panel support member. From Figure 17b, the failure mode was similar for both negative and positive bending, while the bending strength in negative bending was 1.0 kNm higher than in positive bending. This is because the rail has an asymmetrical cross-section (as shown in Figure 15), and the top surface, where the solar panel is fixed, is less prone to bearing failure under a negative bending moment. In the specimens with the bonded joint, the adhesive layer peeled off early, preventing any significant improvement in bending strength. In the specimens with the through-bolted joint, the failure mode shifted to local buckling of the rail. In the specimens with the bonded and through-bolted joint, the insert experienced a tearing failure at the joint. This is likely due to the higher degree of fixation of the insert among all test specimens, leading to an increased load on the insert.

3.1.3. Flexural Strength Evaluation of Rails

For design purposes, the applicability of the current Japanese aluminum design standards [24] in evaluating the bending strength of members with complex shapes, such as rails, is examined. In the design of aluminum solar panel mounting systems using thin-walled plates, the consideration of local buckling is often overlooked, although it is taken into account in Reference [13]. However, as shown in Figure 17a, the ultimate strength is actually determined by local buckling, and even for the yield bending strength, it is necessary to account for the reduction in compressive strength due to local buckling. In the aluminum design standards [24], which are based on the steel structure stability design [26], the yield bending strength M_r,yc, is calculated using Equation (1). In the equation, f_c represents the compressive strength, and Z_y is the section modulus of the rail. The calculation formulas for f_c are summarized in Table 5. When local buckling is not considered, the compressive strength f_c is equal to the specified strength F, which is determined by the material type. On the other hand, when local buckling is considered, the specified strength F is reduced according to the width-to-thickness ratio b/t using the reduction factor Γ_d. Table 5 presents values for cases where both edges of the aluminum plate are supported and no welds are present. For a rail with a lower flange inner width of b = 40.5 mm and a thickness of t = 1.5 mm, the yield bending strength for positive bending moments decreases from 3.4 kNm (when local buckling is not considered) to 2.0 kNm (when local buckling is considered). Where Γ_d = 1.6, with specified strength F and Young’s modulus E, is given in Table 4.

$$M_{r,cy}=f_c{Z}_r$$

(1)

• f_c: Compressive strength
• Z_r: Sectional modulus of the rail

Table 5. Compressive strength of a thin aluminum plate.

Without Consideration of Local Buckling		With Consideration of Local Buckling (Two-Edge Supported Plate Without Weld-Induced Softening Zone [24])
$f_c=F$	(2)	(a)	${\Gamma }_d\le 1.34$	$f_c=F$	(3-1)
		(b)	${\Gamma }_d\le 1.34$	$f_c=F\left(1-0.248{\Gamma }_d\right)\times 1.5$	(3-2)
		(c)	$2.69<{\Gamma }_d$	$f_c=2.41F/{{\Gamma }_d}^2\times 1.5$	(3-3)
			$\because {\Gamma }_d={\displaystyle \frac{b}{t}}\sqrt{{\displaystyle \frac{F}{E}}}$

Table 5. Compressive strength of a thin aluminum plate.

Without Consideration of Local Buckling		With Consideration of Local Buckling (Two-Edge Supported Plate Without Weld-Induced Softening Zone [24])
$f_c=F$	(2)	(a)	${\Gamma }_d\le 1.34$	$f_c=F$	(3-1)
		(b)	${\Gamma }_d\le 1.34$	$f_c=F\left(1-0.248{\Gamma }_d\right)\times 1.5$	(3-2)
		(c)	$2.69<{\Gamma }_d$	$f_c=2.41F/{{\Gamma }_d}^2\times 1.5$	(3-3)
			$\because {\Gamma }_d={\displaystyle \frac{b}{t}}\sqrt{{\displaystyle \frac{F}{E}}}$

Japanese aluminum design standards [24] do not provide a method for evaluating the ultimate bending strength considering local buckling. To evaluate the maximum bending strength of the rail obtained from the four-point bending tests (Figure 16a), the stress distribution at the ultimate state is assumed to be modeled such that, as shown on the right side of Figure 18, the stresses reach uniform values in the compressive and tensile regions, respectively. If it is assumed that both the tensile and compressive sides reach the yielding strength of the rail σ_ry given in Table 4 at the ultimate state, the interaction curve between bending moment and axial force, or M-N curve, given by Equation (4), at the ultimate strength is represented by the dashed line in Figure 18. Since the interaction curve depends on the direction of the bending moment, both negative and positive bending cases are shown in the figure. As shown in the figure, the bending strength shown by dashed lines is significantly higher than the maximum strength of the rail M_max obtained from the experiments (indicated by the red and blue plots in Figure 18). On the other hand, if it is assumed that the compressive side reaches the local buckling strength f_c (Equation (3)), the M-N curve corresponds to the solid line in Figure 18, which provides a conservative estimation of the experimentally obtained maximum strength M_max. As shown in Figure 16a and Figure 17a, the maximum bending strength and failure modes of the rail were similar for both negative and positive bending. Therefore, for the calculation of the bending strength under negative bending—where the upper side of the rail, which contains the grooves for fixing clamps, is in compression—the local buckling reduction factor Γ_d was simply estimated using the same b/t ratio as in the case of positive bending.

Based on these findings, in the elastic design method commonly adopted for the design of solar panel mounting structures, the yield stress of thin plate aluminum members should be determined using the compressive strength f_c, considering local buckling (Equation (3)).

$${\displaystyle \frac{N_r}{A_r}}+{\displaystyle \frac{M_r}{Z_{r,y}}}\le f_c$$

(4)

• A_r: Sectional area of the rail
• N_r, M_r: Axial force and bending moment acting on the rail, respectively

3.2. Test Setup of Full-Scale Pressure Loading Test with Improvement Measures

In consideration of the results presented in Section 2, a pressure loading test was conducted under the condition of foundation defects for a solar panel mounting system of the same specifications, to which simple countermeasures were applied. The test specimens and measurement plan were consistent with those used in Section 2. Figure 19 illustrates countermeasures applied to the solar panel mounting frame.

The first countermeasure was to add bracing members in the east-west direction to directly suppress the uplift of the unanchored column base, as shown in Figure 19a. The braces consist of steel rods (SS400 [27]), and in order to control the yielding load, a designated yielding section was formed at the center of each rod, referring to the standard geometry of tensile test specimens [25], as shown in the accompanying photograph. The diameter of the yielding section was set to 7 mm. This value was determined so that the design yield strength would correspond to the bearing strength of the aluminum column when the member is pin-connected using M12 bolts, as illustrated in Figure 3. This design also accounts for the fact that the connection strength is lower than the strength of the member cross-section. According to Figure 11, if the tensile force borne by the north column base of Frame 2, which is unanchored, is to be resisted by the east-west bracing, the 7 mm diameter brace with a specified yield stress of 235 N/mm² for SS 400 [26] would yield before the design wind pressure P_d = 1333 Pa is reached. Therefore, considering the nonlinear behavior of the frame after an uplift displacement of approximately 100 mm, as referenced in Figure 9, the brace was intentionally given initial slack, allowing uplift up to 100 mm before the brace becomes effective. This design was adopted based on the assumption that both the solar panel mounting structure and the added EW (east-west) braces effectively resist uplift at the unanchored column base, allowing the frame to remain elastic up to the design wind pressure P_d.

In the second countermeasure, based on the finding from Test I-B that the extension joint section of the rail located directly above the unanchored column base became a weak point, the joint method was improved, and the connection position was relocated to the center of the span (Figure 19). As for the improved joint method of the extension rail section, a combination of adhesive and bolts was adopted, as shown in Figure 15d, based on the results presented in Section 3.1. As shown in Figure 13b, the acting bending moment is reduced to two-thirds due to the relocation of the joint, while the joint strength becomes approximately doubled. As a result, the specimen fails after the rail itself reaches its bending capacity, rather than at the joint. In addition, for Specimen III, the solar panels were secured to the rail at four points on each side using mounting brackets, increased from the previous two (Figure 4).

Table 6. Specimen list for pressure loading test of solar panel mounting frames with improvement measures.

Specimen	Pressure Direction	Improvement Measure	Loading Type	Support Condition	Measurement Plan
II	uplift pressure	EW braces to resist the uplift of unanchored column bases	Elastic (up to 500 Pa)	A	Figure 7
			Elastic—Fracture	B
III		Rails with improved, extended joints	Elastic (up to 500 Pa)	A
			Elastic—Fracture	B

Supporting condition: A: All column bases anchored; B: A Single unanchored column base.

summarizes the pressure loading tests conducted on the specimens with the proposed improvements. Each specimen was first subjected to an elastic loading test up to 500 Pa under all column base anchored conditions. Subsequently, the north column base of Frame 2 was released (unanchored), and the structure was loaded until failure. The loading protocols were based on Figure 6a for Specimen II, in which uplift was suppressed using bracing, and on Figure 6b for Specimen III.

Table 7. Material properties of major components.

		Design Yield Stress σray [N/mm2]	Young’s Modulus E [N/mm2]	Yield Stress σry [N/mm2]	Tensile Stress σru [N/mm2]
Rail 1	Web	205 [24]	61,700	238	268
	Flange		60,300	235	262
Girder 1	Web		65,800	265	290
	Flange		66,900	265	287
Column 1			65,670	271	298
NS brace 1			47,000	206	228
EW brace 2 (Specimen II)		205 [28]	210,000	358	-

¹ Aluminum (AL6005-T5 [24]). ² Steel (SS400 [28]).

summarizes the material properties obtained from tensile tests on specimens cut from undamaged structural members after testing. The testing procedure was the same as that described in Table 4. As for the rails, the values are identical to those in Table 4, since the specimens were prepared at the same time as the members used in the four-point bending tests.

3.3. Test Results of the Solar Panel Mounting Structure with Improvement Measures

3.3.1. Fracture Behavior of the Solar Panel Mounting Structure

Figure 20 shows the failure behavior of the improved solar panel mounting structures with the single-base-unanchored condition when subjected to uplift pressure.

From Figure 20b, summarizing the failure behavior of Test II-B. Once the uplift at the unanchored base reached 100 mm and the braces engaged, the uplift was effectively suppressed. As a result, in Test II-B, no significant damage was observed even beyond the design pressure of 1333 Pa. At 1722 Pa, the two northern panels were suddenly blown off, and the central clamp of Rail 3 detached simultaneously. After unloading, local buckling was observed in Girder 2 near the connection with the NS braces, while no significant damage was found in the extended rail joints. In Test O-A (Figure 8b), which was conducted under conditions where all column bases were anchored, the solar panels did not blow off even when the pressure was increased to 2700 Pa. This suggests that, in Test II-B, the panel blow-off failure was likely triggered by the occurrence of local buckling in Girder 2 (II-(1)). When local buckling occurred at the center of Girder 2, the northern side of Frame 2, which was resisting uplift through the braces, consequently dropped downward. This may have caused the panel to exert an upward force on the fixing clamps on Rail 4, potentially leading to their detachment and the subsequent ejection of the two northern panels.

From Figure 20c, summarizing the failure behavior of Test III-B, in which the rail extension joint was reinforced and moved to the center of the span, the north-side center of the panel cover glass, supported by the Rail 5, failed (III-(1)) when subjected to a pressure of 1118 Pa. In addition, the central clamp of Rail 1 detached (III-(2)), and local buckling occurred on the bottom flange of Rails 3 and 5 (III-(3), (4)). Throughout the test, no damage was observed in the reinforced and relocated extension joint of the rails at the mid-span.

From the above, in Test II-B, the addition of EW braces to resist the uplift of the unfixed column base increased the damage pressure resistance to 1.5 times the design pressure P_d = 1333 Pa. However, it was also found that, in this structural system, local buckling of the girder led to a more critical failure mode, resulting in the blow-off of panels. In Test II-B, where the rail extension joint—identified as a weak point under the same conditions as Test I-B—was relocated away from the stress concentration area, some improvement was observed compared to Test I-B, although it still did not reach the design pressure. Furthermore, based on the results of Test I-B, the panel directly above the rail deformed together with the rail bending, without being dislodged, as observed in Test II-B. This suggests that, in terms of failure mechanisms, it is preferable for local buckling of the rail to occur prior to panel detachment. In the structural configuration of the solar panel mounting structures used in this study, the longer side of the solar panels—which is more susceptible to bending deformation—was oriented in the east-west direction. As a result, it is presumed that the damage to the solar panels, caused by the failure of the east-west rail members, remained localized. Therefore, in structural configurations where panels are more prone to being blown off, it is necessary to appropriately predict the failure mechanisms through alternative modeling approaches.

Figure 21 shows the progression of uplift displacement δ_2n,z at the unanchored column base in Tests I-B, II-B, and III-B, all conducted under the single-base-unanchored condition. From the figure, it can be observed that in Test II-B, where EW braces were added, the uplift displacement δ_2n,z initially increased in a manner similar to the tests without braces due to the initial slack designed into the bracing. However, once the displacement reached approximately 100 mm, the braces began to engage, suppressing further uplift. Contrary to the expectations at the time of design (as presented in Section 3.2), the EW braces did not yield up to the point of failure. This is likely because the yield strength of the braces (358 N/mm², as shown in Table 7) was 1.5 times higher than the design yield strength of 235 N/mm², and because the north–south frame also contributed to resisting uplift to some extent. In Test III-B, where the previously identified weak extension rail joint was reinforced and relocated, no significant reduction in stiffness was observed even after the pressure exceeded P = 500 Pa, unlike in Test I-B, where stiffness degradation was evident beyond that point.

3.3.2. Stress Distribution of the Solar Panel Mounting Structure

Figure 22 shows the bending moment distribution of Girder 2 before and after the proposed improvements, at around P = 700 Pa. This pressure level was selected to evaluate the effectiveness of the EW braces in Test II-B. The slight differences in pressure at which the bending moment distributions are shown for each specimen are due to the selection of the displacement-controlled loading cycle whose peak pressure was closest to P = 700 Pa. The figure also indicates the locations of the maximum and minimum (i.e., maximum negative) bending moments in Frame 2 (M_G2,max and M_G2,min) for each case. From the figure, it can be observed that the bending moment in the girder was largest in Test II-B, where EW braces were added. This increase is attributed to the greater reaction force from the north-side column, where the EW brace was anchored (as indicated by the black arrow in the figure). On the other hand, in Test III-B, where the rail extension joints were improved, the bending moment in the girder remained similar to that observed in Test I-B.

Figure 23 shows the bending moment distribution M’_R,j of solar panel mounted rails before and after the proposed improvements, at the same pressure as in Figure 22 (approximately P = 700 Pa). The bending moment of the solar panel mounted rail was estimated based on Figure 12, following the same procedure as in Figure 13. While the bending moment in the girder was the largest in Test II-B (as shown in Figure 22), the bending moment in the rail—identified as the failure origin in Test I-B—was successfully suppressed. In Test III-B, where the rail extension joint was relocated to the mid-span, the bending moment in Rail 5 directly above the unanchored column base increased by approximately 20% compared to Test I-B. This is likely because, at P = 700 Pa, the rail in Test III-B remained intact and continued to carry bending moment, whereas in Test I-B, the rotational stiffness at the rail extended joint had already degraded.

From Figure 22 and Figure 23, the east-west bracing installed on the north side successfully reduced the bending moment at the center of Rail 5—located directly above the uplifted column base—to one-third of its original value. However, this measure also led to an increase in the bending moment at the center of Girder 2. As a result, in Specimen II-B, the ultimate state of the mounting structure was governed by local buckling at the center of Girder 2.

3.4. Stress Demand on Solar Panel Mounting Structure Due to Foundation Defects

As shown in Section 2.2 and Section 3.3, the location of failure in members or joints that determine the ultimate state of the structure is governed by the relationship between the stress distribution within the frame and the ultimate strength of each structural component. This section summarizes the relationship between the progression of pressure-induced forces and the corresponding structural capacities of the critical members and joints, where failure was specifically observed in each specimen.

3.4.1. Yield and Ultimate Capacities of Major Structural Members and Joints

Table 8. Yielding and ultimate strength of members and joints: (a) Member; and (b) Joint.

(a)
Member	Type Of Force	Bending Orientation	Yield 2	Ultimate 2	Failure Mode
rail 1	Bending moment MR,u+	positive	2.1 (1.9)	3.2 (2.8)	Local buckling
	Bending moment MR,u−	negative	2.1 (1.9)	3.4 (3.1)
girder 1	Bending moment MG,u+	positive	1.9 (1.6)	3.2 (2.7)
	Bending moment MG,u−	negative	1.9 (1.6)	2.9 (2.4)
(b)
Joint Part		Type of Force	Bending Orientation	Ultimate	Failure Mode
column base 3		Pull-out force NBase,u	-	19.4	Edge tear failure of the base joint bracket
rial fixing clamp 4		Pull-out force NRC,u	-	11.0	Shear failure of the bottom rib
rail extended joint	Original 5 (insert length of 250 mm)	Bending moment MRJo,u+	positive	1.3	Bearing-induced flange splitting failure
		Bending moment MRJo,u−	negative	2.5
	Improved 5 (insert length of 400 mm)	Bending moment MRJi,u−	positive	3.3	Splitting failure of the insert

¹ Bending orientation follows Table 3. The yield and ultimate moment strength are determined by Equations (1) and (3), and Figure 18. ² The values outside the parentheses represent the strength calculated using the material yield strength (Table 3), while the values inside the parentheses represent the strength calculated using the design strength (Table 3). ³ The pull-out strength of the column bases in the table refers to the maximum strength obtained from pull-out tests of column bases of the same specification [11]. ⁴ The pull-out strength of the rail fixing clamp in the table refers to the maximum strength obtained from pull-out tests of the rail fixing clamp of the same specification [11]. ⁵ The bending strength of the rail extension joint is based on Figure 16.

summarizes the strengths of structural members and joints. Table 8a shows the bending capacities of the rails and girders, while (b) presents the strengths of the column base and the loosened rail clamp that failed in Test O, as well as the rail extension joint that failed in Test I-B. The member strengths were calculated based on Equations (1) and (3), whereas the joint strengths were obtained from the experimental results presented in Section 3.1 and Reference [11]. For further details, refer to the notes provided in Table 8. From Table 8a, it can be seen that the ultimate strength at which the member fails due to local buckling is approximately 1.5 times greater than the yield strength referenced in the elastic design of solar panel mounting structures. For details, refer to the notes in Table 8. The pull-out strength of the rail fixing clamp is 11 kN, whereas the pull-out force acting on the clamp at P = 700 Pa, as shown in Figure 22, is approximately 2 kN at most. Therefore, failure of the rail fixing clamp is considered unlikely.

3.4.2. Stress Demand on Solar Panel-Mounting Rails

Figure 24a shows the transition of the maximum and minimum (negative maximum) bending moments in the solar panel-mounted rails (M’_R,max, M’_R,min), estimated according to the method described in Figure 12. For Test I-A, which was conducted as an elastic test under fully anchored conditions up to P = 500 Pa, M’_R,max and M’_R,min up to the failure pressure of 2600 Pa was estimated by extrapolating the values at P = 400 and 500 Pa (shown as a thin blue line in the figure). For all cases except Test I-A, the maximum occurs at the center of Rail 5, and the minimum occurs at the center of Rail 1. The locations of M’_R,max and M’_R,min can be referenced in the bending moment distributions shown in Figure 13 and Figure 23. Figure 24b presents the progression of the bending moments borne by the rails (M_R,max, M_R,min), estimated based on the values shown in (a). M_R,max and M_R,min were calculated by multiplying the total moments in the solar panel-mounted rails (M’_R,max, M’_R,min) by the load-sharing ratio of 0.52, which was obtained through the numerical simulation in Section 4. In Figure 24b, the yield and ultimate bending moments, listed in Table 8, are shown as red dashed and solid lines, respectively. These values were calculated using Equations (1) and (3) and the material yield strength listed in Table 7. The design strengths used in actual design practice (also from Table 7) are indicated by triangles. In addition, for Specimen I-B, where the rail extension joint failed, the corresponding joint strength is indicated with a black dashed line.

In Japan, it is generally uncommon to consider the solar panels themselves as structural components in the design process. From Figure 24a, it can be observed that the bending moment acting on the rail under the design pressure (P_d = 1333 Pa) in all bases anchored condition (indicated as “design demand” in the figure) is approximately equal to the design yield bending strength, which accounts for strength reduction due to local buckling. This indicates that the safety factor in design is nearly 1. In reality, however, since a portion of the bending moment is borne by the solar panels, the actual safety factor for the rail alone is approximately 2, as shown in Figure 24b. The figure reveals that, under the single-base-unanchored condition, the bending moment acting on the rail becomes more than three times greater than that under all base-anchored conditions (indicated by the blue line), if the direction of the moment is disregarded. However, if the rail is designed without accounting for the contribution of the solar panels—that is, based on the “design demand” indicated in Figure 24a—the stress amplification caused by foundation defects may be mitigated to approximately twice the design value due to the actual contribution of the panels. It is also noted that the estimated ultimate strengths of the rail and the rail extension joint show good agreement with the experimental results.

3.4.3. Stress Demand on Girders

Figure 25 shows the progression of the maximum and minimum bending moments in Girder 2 (M_G2,max, M_G2,min) with respect to the applied pressure for each specimen. The locations of M_G2,max and M_G2,min for each test are indicated on the right-hand side of Figure 25. For the bending moment distributions, refer to Figure 11 and Figure 22. In Figure 25, the estimated bending strengths of the rail, listed in Table 8, are also shown. From Figure 25, it can be seen that the safety factor for the girder in design is also approximately 1. The figure indicates that, compared to Test I-A (the design condition), the bending moment in the girder becomes nearly equal to that under the single-base-unanchored condition, and further increases to approximately twice the Test I-A value when braces are installed to restrain the uplift. It is also noted that, in Test II-B, the calculated bending strength of the girder at the time of local buckling was significantly lower than the measured bending moment, although on the safe side. This suggests that further investigation may be needed into the variability of material strength in the girders and the applicability of the local buckling formula (Equation (3)) for extruded aluminum members.

3.4.4. Stress Demand on Column Bases and Pile

Figure 26 shows the progression of the maximum pull-out force N_Base,max for each specimen. The column base at which the maximum pull-out force occurred is indicated on the right-hand side of the figure. Under all bases anchored conditions, the maximum pull-out force naturally occurred at the north side of Frame 2. In contrast, for specimens with the north base of Frame 2 unanchored, the pull-out forces on the south side of Frame 2 and the north side of Frame 3 tended to be of similar magnitude. The figure also shows the pull-out strength N_Base,u listed in Table 8. The figure indicates that the maximum pull-out forces N_Base,max in the specimens with the single-base unanchored condition (Tests I-B, II-B and III-B) were of similar magnitude (1.5 times that of Test I-A). In Test II-B, where east-west braces were added, it was confirmed that the tensile force acting on the column base of Frame 2 reached the pull-out strength N_Base,u, as a result of preventing failure in the rail and the rail extension joint. Although no apparent damage was observed at the corresponding column base during the experiment, it is possible that the failure propagated to the adjacent unanchored base, resulting in the uplift of all three north-side column bases, potentially representing the worst-case scenario.

4. Effect of the Number of Spans on the Wind Pressure Resistance Performance of Solar Panel Mounting Structures with Foundation Defects

Based on the investigations of wind resistance under various structural conditions in Section 2 and Section 3, it was found that unfavorable failure mechanisms, such as the blow-off of solar panels under foundation failure, can occur under certain conditions. On the other hand, for solar panel mounting structures subjected to wind uplift forces, the most critical failure mechanism to avoid is the progressive failure of foundations, which can potentially lead to the entire mounting structure being uplifted. As shown in Figure 10, when a single foundation fails, three out of the six column bases—including the failed one—cease to resist uplift forces, resulting in the remaining three foundations needing to bear 1.5 times the usual tensile force. However, this finding is derived from pressure-loading tests conducted on a two-span solar panel mounting structure—a configuration that is rarely used in practice. When extended to multi-span systems, these conditions may be alleviated.

Therefore, in this chapter, the influence of the number of spans is examined through numerical analysis. First, a numerical model replicating Specimen III from Section 3 is developed, and its simulation results are compared with those of the pressure-loading tests to validate the model. Then, the structure is extended to multiple spans, and the influence of span number on the internal forces of each member and the load distribution at the column bases is investigated.

4.1. Numerical Simulation Model

Figure 27 shows the numerical analysis model of the solar panel mounting structure, corresponding to the configurations assumed in Figure 1, Figure 2 and Figure 3. The numerical analysis was conducted using SAP2000 [29]. In the numerical analysis model, the solar panel surface was constructed on the global X–Y plane for modeling simplicity (Figure 27a). In this structure, the columns and ends of the north-south bracing members—which form the north-south frame—are connected to a joint bracket with a single bolt, allowing rotational movement at the ends. Therefore, truss elements were used for the columns and NS braces, while beam elements were used for the east-west panel supports and the north-south girders to account for bending behavior. In the figure, pins (○) at the ends of the column and bracing members indicate truss elements. The solar panels were modeled using shell elements with a 6 × 8 mesh configuration for the analysis. The panels were assumed to be thin glass plates (E = 71,600 N/mm²), with aluminum frames (E = 70,000 N/mm²) fixed around their edges following Figure 4. In the numerical analysis, the Young’s modulus of all aluminum members was uniformly set to 70,000 N/mm² [24].

For joints between components, link elements were employed. The solar panels were fixed to the rails, and the rails were fixed to the girders using fixing clamps (Figure 3c). Therefore, link elements were used to connect the respective structural elements. Since the girders and columns, as well as the girders and NS braces, are connected via joint brackets, the member axes are eccentric (Figure 3b). To account for this, link elements were also used to incorporate the eccentricity.

Table 9. Degrees of freedom of link elements modeling joints.

Joint	Panel Fixing Clamp						Rail Fixing Clamp						Girder-Column Joint						Girder-NS Brace Joint
Symbol	LL1						LL2						LL3						LS
Local axis	x	y	z	θx	θy	θz	x	y	z	θx	θy	θz	x	y	z	θx	θy	θz	x	y	z	θx	θy	θz
DOF 1	1	1	1	1	0	0	1	1	0	0	0	0	1	1	1	1	1	1	1	1	* 2	1	1	1

¹ Degree of freedom of connection modeled by a link element (Fixity: 1; freedom: 0). ² elastic stiffness of K₁ = 3000 N/mm, F₁ = 3000 N, K₂ = 1/6 K₁ (The joint stiffness and yielding force was determined through trial and error to reproduce the actual slip displacement observed in the experiment.).

summarizes the degrees of freedom for each link element. The color of each spring model in the table corresponds to the color of the link elements shown in Figure 27. Additionally, since shear slip was observed between the girders and the NS braces during the experiment, a slip-capable link element was introduced. The initial stiffness and slip initiation load for the shear slip behavior of link element LS (defined in Table 9) were determined through a trial-and-error process based on the estimated slip amount obtained from test photographs.

4.2. Comparison of Numerical and Experimental Results

Using the numerical simulation model described above, reproduction analyses were conducted for Test III-A (with all column bases anchored) and Test III-B (with the single-base-unanchored condition). In Specimen III, the rail extension joints were sufficiently secured, and therefore, these joints were not explicitly modeled in the numerical simulation. In the simulations, pressure was applied to the shell elements representing the solar panels. The self-weight of components above the girder level, including the solar panels, was applied as a uniformly distributed pressure in the gravity direction on the solar panel surface. Figure 28 compares the experimental and numerical results for Tests III-A and III-B. As shown in the figure, the numerical model described in Figure 27 and Table 9 successfully reproduces the changes in stress distribution under the partially unfixed condition.

The rails, to which solar panels were fixed using a panel fixing clamp, resist bending moments together with the solar panels. In other words, the solar panels also function as components that contribute to bending moment resistance. Specifically, a couple is generated between the solar panels and the rails (Figure 29a). Accordingly, the bending moment of a solar panel-mounted rail M’_R is the sum of the bending moment of the rail itself, M_R and the couple generated between the rail and the solar panels, M_Rc. The couple moment M_Rc was calculated by assuming that an axial force acting on the rail N_R is equal to the axial force acting on the solar panel N_P. Specifically, M_Rc was obtained by multiplying the axial force in the rail N_R, as determined through numerical simulation, by the distance between the centroid of the rail and the surface of the panel glass (78.8 mm).

Figure 27b compares the numerical and experimental results for the bending moment of Rail 5 in Specimen III, calculated from the strain measurements (Figure 7b). The numerical results also include the total bending moment of the rail with the attached solar panels. As shown in the figure, the numerical model successfully reproduces the experimentally observed bending moment distribution of the panel support members M_R. Furthermore, the figure indicates that the bending moment at the center of Rail 5, located directly above Frame 2 and damaged in Test III-B, corresponds to only half of the estimated bending moment of the rail with the solar panel attached (Figure 23), with the ratio being 0.52 as shown in Figure 29b.

4.3. Effect of the Number of Spans on Stress Demand

Figure 30 shows the configurations of the three- and four-span models, in addition to the two-span model investigated in Section 2 and Section 3. The numerical simulation models follow the specifications given in Figure 27 and Table 9. Numerical simulations were conducted for each model under both all bases anchored and the single-base-unanchored conditions. In the single-base-unanchored condition, the unanchored column bases were set at the end column (red circles on Frame 1) and the adjacent interior column (blue circles on Frame 2), as indicated in Figure 30.

Figure 31 shows the locations and corresponding pressures at which plastic hinges were formed in the rails and girders, as identified through numerical simulation of the solar panel mounting structures. In the numerical simulation, the bending capacity at which a hinge formed was defined as the ultimate bending strength calculated using the M-N curve, defined by Equations (1), (3) and (4) with the design strength listed in Table 7. After hinge formation, the rotational stiffness was set to zero. The results indicate that increasing the number of spans beyond two raises the pressure required for hinge formation by approximately 10%. Furthermore, when the unanchored column base is located one span inward from the edge (Frame 2), the pressure at which the first hinge forms exceeds the design wind pressure P_d = 1333 Pa under multi-span conditions. In contrast, when the end column base is unanchored, plastic hinges form below the design pressure P_d, even when multiple spans are used. It was also observed that when the end column base is unanchored, hinges tend to form in the girders, which could potentially trigger the blow-off of solar panels. Therefore, in cases where foundation defects are expected at the ends, it is recommended to install braces to restrain the cantilevered girder.

Figure 32 shows the relationship between the number of spans and the maximum stress acting on the rails, girders, and column bases of the solar panel mounting frame model under P_d = 1333 Pa, assuming that the frame remains in the elastic state. The figure also includes horizontal black lines indicating the ultimate strength referenced from Table 8. From the figure, it can be seen that for the rails and girders, the induced bending moment decreases to approximately 80–90% of the value observed in the two-span case as the number of spans increases. In contrast, for the column bases, the force acting on the north-side column base of Frame 2 increases with the number of spans when the base is unanchored. This is because, in the two-span frame configuration, Frame 1 and Frame 3 were under identical boundary conditions even when the north-side column base of Frame 2 was unanchored. However, in configurations with three or more spans, the degree of fixation at Frame 3 increases relative to Frame 1, resulting in a greater share of the load being transferred to the north-side column base of Frame 3.

5. Conclusions

This study investigates the failure behavior of solar panel mounting frames through pressure loading tests on full-scale aluminum frame specimens. In particular, it focuses on failure mechanisms that become critical under conditions not assumed in design—such as foundation deficiencies—and proposes measures to mitigate excessive damage.

The main findings are summarized below by topic.

• Structural capacity of aluminum members (Section 3.1):
• From the four-point bending test described in Section 3.1, it is evident that in estimating the strength of thin-walled aluminum members used in solar panel mounting frames, the strength reduction due to local buckling must be taken into account.
• For cross-sections that can be regarded as nearly rectangular (e.g., those shown in Table 1), the ultimate bending strength at which local buckling occurs is approximately 1.5 times greater than the yield bending strength typically referenced in design (see Table 8 in Section 3.4). Therefore, even in the event of conditions not assumed in design, the structure possesses an additional safety margin of 1.5 times on top of both the design safety factor and the material-to-design strength ratio.
• Structural capacity of joints:
• For the mounting frame shown in Figure 1, Figure 2 and Figure 3 and Table 1, no significant damage was observed in the pin-connected NS braces or at the column ends even under a pressure of 2600 Pa, which is twice the design pressure.
• The east-west rail extension joint fails earlier than the base rail when a short insert is used in the joint. To prevent premature failure before the rail reaches its yield strength, it is recommended to use an insert with a length approximately four times the rail depth and to position the extension joint away from connections with other members (Section 3.1).
• Pressure resistance performance of solar panel mounting structures with foundation defects (Section 2 and Section 3):
• In the mounting frame where the primary members (rails and girders) have a design safety factor of approximately 1.0, no significant damage was observed up to twice the design wind pressure P_d under the ideal condition in which all column bases were anchored. At P = 2600 Pa, however, pull-out failure occurred at the column base.
• Under the single-base-unanchored condition modeling foundation defects, the rail extension joint became a weak point, leading to bending of the solar panel frame and failure of the rail extension joint at a pressure equal to half the design wind pressure P_d. Experimental results confirmed that the addition of east-west braces to restrain the unanchored column bases, along with reinforcement and relocation of the rail extension joint, was effective in increasing the failure pressure.
• Failure modes of solar panel mounting structures with foundation defects (Section 2 and Section 3):
• The most critical failure mode to be avoided in buildings and structures during a storm is the detachment and scattering of components, as this can lead to secondary damage. In solar panel mounting systems, the scattering of panels or any part of the frame must be prevented under all circumstances. In the structural configuration adopted for the present test specimens, it was found that local buckling of the girder could cause the solar panels to be blown off. In contrast, when local buckling occurred in the rail, the overlying solar panel only bent together with the rail and did not detach. These results suggest that the buckling of members oriented perpendicular to the short side of the solar panels may induce panel detachment.
• Stresses acting on frame members and joints under poor foundation conditions (Section 3.4 and Section 4):

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  Although the findings are based on the specific mounting frame investigated in this study, it was observed that, under the single-base-unanchored conditions, the forces acting on the rails, girders, and column bases become approximately twice as large as those under all base-anchored conditions. When foundation deficiencies are suspected, it is necessary to consider a safety factor of at least two for the column bases and foundations to prevent progressive collapse of the mounting frame.

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  Although increasing the number of spans can reduce the forces acting on structural members and column bases by approximately 10% under partially unanchored conditions, the improvement is not substantial enough to drastically alter the overall failure behavior. In particular, when uplift at end column bases and foundations is anticipated, the risk of panel blow-off and associated damage becomes significant. Therefore, proactive countermeasures are strongly recommended.

• Design considerations for solar panel mounting structures, considering potential foundation defects:
• Which component or joint of the mounting structure fails first is determined by the relationship between the stresses generated in the structure and the ultimate strength of each part. Based on (5), the stresses in the mounting structure under foundation defects can be estimated through numerical analysis, and by referring to (1) and (2) to evaluate the ultimate strength of the members and joints, the failure location can be predicted.
• Based on (3) to (5), when a member placed in the short-span direction of the solar panel fails due to local buckling, it is highly likely that such failure will cause the panel to be blown away, and therefore, such a failure mode should be avoided. Similarly, considering that a single foundation defect may affect adjacent column bases and pile foundations, a safety factor of approximately two should be provided for column bases and pile foundations to prevent progressive foundation failure and uplift of the entire mounting structure.

The above findings are based on the pressure loading tests conducted on the solar panel mounting structures with the specifications shown in Figure 1, Figure 2, Figure 3 and Figure 4 and Table 1 and Table 8. As discussed in Section 4, the stresses generated in solar panel mounting structures with low redundancy can be effectively estimated through numerical analysis. However, the ultimate strength of members and joints has thus far been evaluated only through experiments, and generalized evaluation formulas reflecting typical specifications have not yet been established. Further detailed studies are especially needed for the aluminum members and joints employed.

The present study builds upon the findings reported in References [30,31], with additional data and a newly proposed approach for addressing unexpected failures. Portions of this work were also disclosed in Reference [32] as part of a project supported by NEDO.