Apparatus, systems and methods for improved vertical structural supports

Abstract

Disclosed herein are various methods, systems, and devices relating to vertical structural supports, including acute Z-shaped piers and further including vertical structural features that provide additional structural support for various types of piers.

Claims

1. A vertical support structure comprising: (a) an elongate central strut; (b) a first flange coupled to a first side of the elongate central strut, wherein a first angle between the first flange and the elongate central strut is acute; (c) a second flange coupled to a second side of the elongate central strut, wherein a second angle between the second flange and the elongate central strut is acute; and (d) a shear center disposed at a geographical center of mass of the vertical support structure, wherein a lateral load is applied to the vertical support structure in the same direction of as a principle neutral axis, wherein the principal neutral axis is aligned with the shear center and the principal neutral axis being aligned with the direction of the lateral load.

2. The vertical support structure of claim 1, further comprising a first angled end segment extending from the first flange.

3. The vertical support structure of claim 2, further comprising a second angled end segment extending from the second flange.

4. The vertical support structure of claim 1, wherein the vertical support structure has a cross-sectional shape that is substantially Z-shaped.

5. The vertical support structure of claim 1, further comprising at least one rib defined in the elongate central strut.

6. The vertical support structure of claim 5, further comprising two ribs defined in the elongate central strut, the two ribs disposed between substantially straight sections of the elongate central strut.

7. A support structure comprising: (a) a central strut comprising at least one rib; (b) a first flange coupled at a first acute angle to a first side of the central strut; (c) a second flange coupled at a second acute angle to a second side of the central strut; and (d) a neutral axis disposed at a centerpoint of a mass of the support structure.

8. The support structure of claim 7, wherein the central strut, the first flange, and second flange form a Z-shaped cross-section.

9. The support structure of claim 7, wherein deflection only occurs in a direction of an applied lateral load.

10. The support structure of claim 7, wherein the central strut comprises a substantially straight portion interrupted by the at least one rib.

11. The support structure of claim 7, further comprising at least one attachment feature defined in the first flange.

12. The support structure of claim 11, wherein the at least one attachment feature comprises at least one opening.

13. A support structure comprising: (a) a central strut; (b) a first flange coupled at a first acute angle to a first side of the central strut; (c) a second flange coupled at a second acute angle to a second side of the central strut; and (d) a neutral axis disposed at a cross-sectional centerpoint of a mass of the support structure and oriented in an identical direction as an expected lateral load.

14. The support structure of claim 13, wherein the support structure comprises first and second ribs defined within the central strut.

15. The support structure of claim 14, wherein the first rib extends outward from the first side of the central strut and the second rib extends outward from the second side of the central strut.

16. The support structure of claim 13, wherein the central strut, the first flange, and second flange form a substantially Z-shaped cross-section.

17. The support structure of claim 13, further comprising at least one attachment feature defined in the first flange.

18. The support structure of claim 13, further comprising at least one rib defined in the first flange.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A depicts a perspective view of a field of known solar arrays.

(2) FIG. 1B is a perspective view of known wide flange beams supporting solar array panels.

(3) FIG. 1C is a perspective view of multiple known piers firmly positioned in the ground according to a known process prior to placement of multiple solar arrays.

(4) FIG. 1D is a top view of a known wide flange beam.

(5) FIG. 1E is a top view of a known 90-degree Z-shaped structure.

(6) FIG. 1F is a top view of a known C-shaped structure.

(7) FIG. 2 is a top view of an acute angled Z-shaped support structure, according to one embodiment.

(8) FIG. 3A is a perspective view of an acute angled Z-shaped support structure with ribs, according to one embodiment.

(9) FIG. 3B is a top view of the acute angled Z-shaped support structure of FIG. 3A, according to one embodiment.

(10) FIG. 3C is a side view of the acute angled Z-shaped support structure of FIG. 3A, according to one embodiment.

(11) FIG. 4A is a perspective view of another acute angled Z-shaped support structure with ribs, according to a further embodiment.

(12) FIG. 4B is a side view of the acute angled Z-shaped support structure of FIG. 4A, according to one embodiment.

(13) FIG. 5A is a perspective view of a C-shaped support structure, according to one embodiment.

(14) FIG. 5B is a top view of the C-shaped support structure of FIG. 5A, according to one embodiment.

(15) FIG. 5C is a side view of the C-shaped support structure of FIG. 5A, according to one embodiment.

(16) FIG. 6A is a line graph depicting the projected elastic buckling caused by lateral loading of one embodiment of the acute Z-shaped pier according to the software analysis described in the Example, according to one embodiment.

(17) FIG. 6B is a graphical depiction—and related data—of the projected elastic buckling caused by lateral loading of one embodiment of the acute Z-shaped pier according to the software analysis described in the Example, according to one embodiment.

(18) FIG. 6C is a graphical depiction—and related data—of the projected elastic buckling caused by lateral loading of one embodiment of the acute Z-shaped pier according to the software analysis described in the Example, according to one embodiment.

(19) FIG. 6D is a graphical depiction—and related data—of the projected elastic buckling caused by lateral loading of one embodiment of the acute Z-shaped pier according to the software analysis described in the Example, according to one embodiment.

(20) FIG. 7A is a line graph depicting the lateral deflection of the test piers at 5 feet embedment in the Example, according to one embodiment.

(21) FIG. 7B is a line graph depicting the lateral deflection of the test piers at 5.5 feet embedment in the Example, according to one embodiment.

(22) FIG. 7C is a line graph depicting the lateral deflection of the test piers at 5 feet embedment in the Example, according to one embodiment.

(23) FIG. 8A is a line graph depicting the lateral deflection of Pier 1 in the load testing of the Example, according to one embodiment.

(24) FIG. 8B is a line graph depicting the lateral deflection of Pier 2 in the load testing of the Example, according to one embodiment.

(25) FIG. 8C is a line graph depicting the lateral deflection of Pier 3 in the load testing of the Example, according to one embodiment.

(26) FIG. 8D is a line graph depicting the lateral deflection of Pier 4 in the load testing of the Example, according to one embodiment.

(27) FIG. 8E is a line graph depicting the lateral deflection of Pier 5 in the load testing of the Example, according to one embodiment.

(28) FIG. 8F is a line graph depicting the lateral deflection of Pier 6 in the load testing of the Example, according to one embodiment.

(29) FIG. 8G is a line graph depicting the lateral deflection of Pier 7 in the load testing of the Example, according to one embodiment.

(30) FIG. 8H is a line graph depicting the lateral deflection of Pier 8 in the load testing of the Example, according to one embodiment.

(31) FIG. 8I is a line graph depicting the lateral deflection of Pier 9 in the load testing of the Example, according to one embodiment.

(32) FIG. 8J is a line graph depicting the lateral deflection of Pier 10 in the load testing of the Example, according to one embodiment.

(33) FIG. 8K is a line graph depicting the lateral deflection of Pier 11 in the load testing of the Example, according to one embodiment.

(34) FIG. 8L is a line graph depicting the lateral deflection of Pier 12 in the load testing of the Example, according to one embodiment.

DETAILED DESCRIPTION

(35) The various embodiments disclosed or contemplated herein relate to improved support beam embodiments. Further embodiments relate to roll form support beams. The various support structure embodiments can be used in a number of implementations, including in the solar industry.

(36) Amongst various processes for forming a structural shape, roll forming provides flexibility such that it allows the engineer to use her/his creativity to generate the perfect shape for the specific application it is designed for. In use, roll forming takes slit coil known as band and cold form the shape through a progressive set of specially designed rollers to achieve the shape desired.

(37) The various support structure embodiments disclosed herein provide an optimized shape that can achieve the 3 measurements for a solar pier (discussed below) yet reduce the amount of material used in comparison to a standard wide flange beam (such as the beam 10 as depicted in FIG. 1D), thus reducing the cost while improving the stability of the support structure. As such, certain of the embodiments disclosed or contemplated herein utilize certain shapes that can meet or exceed the advantages of the industry accepted wide flange beam shape as a solar array pier.

(38) As discussed above, in the solar industry, large fields with tens or hundreds of acres of solar arrays are becoming commonplace, as is shown generally at 1 in FIG. 1A. As a result of the increasing demand to keep the cost of electricity down, it is important to optimize the cost of installing these arrays 1.

(39) The various implementations of the vertical support structures 20 disclosed or contemplated herein offer an economical and improved replacement for the known wide flange beam of FIG. 1D and other known vertical support structures having different cross-sectional shapes or configurations, as discussed in further detail below. In certain implementations, these improved piers 20 have an acute angled (also referred to herein as “acute”) “Z” shape, as best shown in the various embodiments depicted in FIGS. 2-4B, which are discussed in further detail below. Alternatively, the piers can have ribs that provide additional structural stability and other benefits to any of the vertical support structures, including an acute Z-shaped pier, a C-shaped configuration, as best shown in FIGS. 5A-5C, or any other known shape or configuration. The ribs are also discussed in further detail below. In a further alternative, it is understood that the vertical support structure can be any known structure for supporting one or more solar panels in an array that can meet the three requirements for a solar pier, as discussed below.

(40) Various known cross-sectional shapes have been used in a variety of solar and/or non-solar industrial applications, including the known wide flange beam 10 (as best shown in FIG. 1D), the known 90-degree Z shape pier 14 (as best shown in FIG. 1E), and the known C-shaped pier 16 (as best shown in FIG. 1E). The known wide flange beam 10 is currently the most commonly used pier for solar panel support, because, as shown in FIG. 1D, the shear center S of the beam 10 is located in the geographical center of the mass of the pier 10, and the principal neutral axis of the beam 10 (as represented by arrow E) is aligned to the direction that the lateral load will be applied (as shown by arrow A). These two characteristics (the location of the shear center S at the geographical center and the principal neutral axis E being aligned with the direction of the lateral load (as shown by arrow A) are advantageous, because they prevent the pier 10 from twisting when a lateral load is applied in the direction shown by arrow A (as best shown in FIGS. 1B and 1E).

(41) In contrast, neither of the traditional 90-degree Z shape pier 14 of FIG. 1E or the known C-shaped pier 16 of FIG. 1F have both of these characteristics and thus are more prone to structural failures in the face of lateral loads. More specifically, the principal neutral axis E of the “traditional” Z shaped structure 14 as shown in FIG. 1E is rotated at an angle relative to the direction of the lateral load as represented with arrow A. This causes the known pier 14 to deflect out of the plane of loading when the lateral load is applied (as represented by arrow A), which can cause failure twisting or other mechanical failure of the pier 14. In contrast, the known C-shaped pier 16 has a shear center S that is located outside of the cross-sectional structure of the pier 16 and thus nowhere near the geographical center of the mass of the pier 16. This characteristic results in the pier 16 being subject to mechanical failure when a lateral load is applied as shown by arrow A.

(42) One vertical support structure that addresses these shortcomings is the acute angled Z shape vertical support structure 20 depicted in FIG. 2, according to one implementation. More specifically, the pier 20 has a cross-sectional shape that is modified from the typical 90-degree Z shape (of FIG. 1E) such that the angles D between the central support piece or strut (also known as a “web”) 22 and the outer walls or wings (also known as “flanges”) 24 are acute (less than 90 degrees), resulting in one embodiment in the cross-section configuration depicted in FIG. 2. Each of the flanges 24 also has an angled end segment 26, which is also referred to as a “tail” or “appendage.” In this embodiment and other embodiments herein, the end segments 26 add additional structural support to the pier 20 and provide additional resistance to lateral loading. In these acute Z shaped piers 20, according to one embodiment, as best shown in FIG. 2, much like the wide flange beam 10, the principal neutral axis represented by arrow E is aligned to the direction that the lateral load will be applied (as best shown by arrow A in FIG. 2) and the shear center S of the pier 20 is located in the geographical center of the mass of the pier 20.

(43) These implementations eliminate the out of plane deflection failures that can occur in the known 90-degree Z shape pier 14 of FIG. 1E and the C-shaped pier 16 of FIG. 1F. That is, in contrast to the known pier cross-sectional shapes discussed above, when the acute Z shape pier 20 is loaded laterally (as is shown by the arrow A in FIG. 2), the deflection only occurs in the direction of the lateral load, which reduces or eliminates the out-of-plane deflection failures. Further, in these implementations, the acute Z shape pier 20 meets or exceeds the performance of the wide flange beam in all three measurements discussed above. In further embodiments in which the acute Z shape pier 20 is formed using a roll forming process, the resulting pier 20 can have significantly less weight in comparison to a known wide flange beam by optimizing the material thickness and flange lengths to maximize the weight savings when compared to the wide flange beam.

(44) Another acute Z-shaped pier 30 embodiment is depicted in FIGS. 3A-3C, in which the pier 30 has a web 32, flanges 34, angled end segments 35, and angles F between the web 32 and the flanges 34 that are acute. In addition, in this implementation, the web 32 has structural support features (also referred to herein as “ribs”) 36 defined or otherwise formed in the web 32 that extend along the entire length of the web 32. The ribs 36 can serve a variety of purposes, including, for example, providing increased structural support to the pier 30 and thereby increasing the driving ability of the pier 30.

(45) In addition, the ribs 36 ensure that the pier 30 is not categorized as a “slender member” by the American Institute of Steel Construction (“AISC”) in the AISC Steel Construction Manual Sections 16.1-14 through 16.1-18. It is understood that any pier categorized as a slender member may be subject to a decreased load capacity rating per the AISC code. The ribs 36 in this specific embodiment result in the web 32 having three straight sections with the two ribs 36 disposed between the straight sections. As such, the ribs 36 increase the width/thickness ratio of the web 32, thereby ensuring that the pier 30 is not a slender member.

(46) Alternatively, each of the structural support features 36 defined or otherwise formed in the web 32 can be any known structural feature—such as, for example, a channel, protrusion, ridge, castellation, or offset—that provides additional structural support and/or width to the pier 30. In one embodiment as shown, the web 32 has two ribs 36. Alternatively, the web 32 can have one rib, or three or more ribs.

(47) Further, in this implementation as best shown in FIGS. 3A and 3C, each of the flanges 34 have four holes 38 defined therein. According to one embodiment, the openings 38 can be used as attachment features for use in coupling the pier 30 to the load, such as, for example, solar panels. Alternatively, each flange 34 can have one, two, three, or five or more openings 38. In this specific embodiment, the openings 38 are ovals as shown. Alternatively, it is understood that a variety of sizes, shapes and configurations of openings 38 are possible.

(48) One specific example of another pier 40 according to a further embodiment in which the flanges 42 have a different configuration of openings 44 is depicted in FIGS. 4A and 4B. It is understood that the pier 40 embodiment as shown has substantially the same physical components and features as the pier 30 embodiment discussed above, except for the openings 44. In this embodiment, each of the flanges 42 have two round openings 44 as shown.

(49) Another embodiment is depicted in FIGS. 5A-5C, in which the pier 50 is a C-shaped pier 50. The pier 50 according to this implementation has a web 52, flanges 54, angled end segments 55, and ribs 56 defined or otherwise formed in the web 52 and the flanges 54 that extend along the entire length of the pier 50. Further, the flanges 54 have openings 58 defined therein as shown. In this implementation, the web 52 is attached or integral with an end of each flange 54 at a 90-degree angle to each such that the pier 50 has a C-shaped cross-section as best shown in FIG. 5B. According to one embodiment, the ribs 56 are formed or defined in the web 52 and flanges 54 such that each of the ribs 56 extend toward an interior of the pier 50 (toward the pier 50 center). In certain implementations, this configuration of the ribs 56 allows for a flat external surface of the pier 50 (with no ribs protruding therefrom), thereby allowing for the mounting or other type of attachment of other planar objects flush onto the external surface of the pier 50.

Example

(50) Lateral load testing was performed on six acute Z-shaped piers according to one embodiment of the invention disclosed herein and on six standard wide flange beam piers. This Example is a summary of the load testing and analysis of the comparative performance of the acute Z-shaped pier vs. the standard wide flange beam piers. sections.

(51) The specific characteristics of the two types of piers are set forth in Table 1.

(52) TABLE-US-00001 TABLE 1 Test Pier Properties Acute Wide Property Z-Shaped Pier.sup.(1) Flange Beam.sup.(2) Depth (in.) 8.00 5.83 Width (in.) 4.69 3.94 Moment of Inertia (in.sup.4.) 20.5 14.9 Section Modulus (in.sup.3.) 5.12 5.10 Area (in.sup.2.) 2.14 2.52 Weight (lb/ft) 7.26 8.5 Yield Strength (psi) 50 50 .sup.(1)Data evaluated from CFS Property Calculation .sup.(2)AISC Steel Construction Manual, 14.sup.th Ed.

(53) A total of twelve (12) test piers (six acute Z-shaped piers and six standard wide flange piers) were installed vertically into the ground at the test area, with embedment depths of 5, 5.5 and 6 feet (two piers of each type to each depth). The piers all had at least 5 feet of reveal above grade (length of each pier above the ground). The piers were installed in one row with the strong axis aligned parallel to the row.

(54) Pier testing was completed in substantial conformance with ASTM D3966 for lateral testing, appropriately modified for solar piers. For the lateral load tests, horizontal loads were applied to the pier at a height above ground of 5-feet, using a bearing plate that loaded the flanges equally.

(55) Deflection was measured at two locations along the exposed portion of the pier using dial gauges. Loads were applied using a chain hoist and measured with a dynamometer, reacting against construction equipment.

(56) Subsurface conditions at the test site were evaluated by observation of one test pit. The soil profile appeared to be brown sandy clay. No evidence of groundwater was observed.

(57) Software Analysis of Design and Strength

(58) Prior to load testing, the design properties and strength of the acute Z-shaped pier were evaluated using the software Cold-Formed Steel Design Software (CFS), which is commercially available from RSG Systems. The software evaluates the strength of cold-rolled steel sections, based on the American Iron and Steel Institute (“AISI”) “Specification for the Design of Cold-Formed Steel Structural Members” Code.

(59) The full section properties of the pier as determined by the CFS software are set forth in Table 2.

(60) TABLE-US-00002 TABLE 2 Full Section Properties Area 2.1353 in.sup.2 Wt. 0.0072599 k/ft Width  16.947 in Ix 20.461 in.sup.4 rx   3.0956 in Ixy  −0.004 in.sup.4 Sx(t) 5.1159 in.sup.3 y(t)   3.9995 in α   0.014 deg Sx(b) 5.1159 in.sup.3 y(b)   3.9995 in Height   7.9991 in Iy  2.286 in.sup.4 ry   1.0347 in xo   0.000 in Sy(1) 0.9747 in.sup.3 x(1)   2.3457 in yo   0.000 in Sy(r) 0.9747 in.sup.3 x(r)   2.3457 in jx   0.000 in Width   4.6913 in jy   0.000 in I1 20.461 in.sup.4 r1   3.0956 in I2  2.286 in.sup.4 r2   1.0347 in Ic 22.747 in.sup.4 rc   3.2639 in Cw  54.770 in.sup.6 Io 22.747 in.sup.4 ro   3.2639 in J 0.011300 in.sup.4

(61) In addition, the buckling characteristics of the acute Z-shaped pier as determined by the CFS software are set forth in FIGS. 6A-6D. More specifically, the software analyzes the properties of the pier and projects the buckling that might occur as a result of lateral loading of that pier. FIG. 6B schematically depicts the projected local buckling (with related statistics provided as well) of one embodiment of the Z-shaped pier such that one flange of the pier buckles outward. It should be noted that this specific type of physical failure did occur in the load testing of actual piers discussed below. FIG. 6C schematically depicts the projected local buckling (with related statistics) of one embodiment such that one angle of a flange buckles outward. Finally, FIG. 6D schematically depicts the projected distortional buckling (with related statistics) of one embodiment such that the entire member fails.

(62) Based on these values and considering the application of lateral load at 60-inches above grade, it was anticipated that yield of the pile could occur at horizontal loads of approximately 4,260 pounds.

(63) Lateral Pier Load Testing

(64) The results of the lateral pile load testing are presented in FIGS. 7A-8L and further in Tables ______ as set forth below. The results relating to the acute Z-shaped pier under lateral load were well predicted by the CFS Software.

(65) Table 3 below sets forth the results of the lateral load test of Pier 1, which was a standard wide flange pier driven to a depth of 6 feet. Further, FIG. 8A depicts a line graph showing the deflection of Pier 1.

(66) TABLE-US-00003 TABLE 3 Lateral Load Test - Pier 1 Pile Number: 1 Tested by: PR Ground surface Condition: Grass Pile Size: Wide Flange Beam Height of top of pile from ground surface 62 in Height of pull chain above ground surface 62 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 6 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Bottom of Pile (lbs) Reading Defection Pile Reading Defection 0 1.984 0.000 1.532 0.000 230 2.156 0.172 1.557 0.025 430 2.280 0.296 1.606 0.074 590 2.375 0.391 1.621 0.089 800 2.507 0.523 1.660 0.128 1000 2.625 0.641 1.680 0.148 1210 2.750 0.766 1.720 0.188 1410 2.873 0.889 1.745 0.213 1610 3.008 1.024 1.766 0.234 1800 3.116 1.132 1.799 0.267 2000 3.252 1.268 1.830 0.298 2200 3.358 1.374 1.861 0.329 2400 3.504 1.520 1.894 0.362 2600 3.631 1.647 1.931 0.399 2800 3.768 1.784 1.956 0.424 3000 3.911 1.927 1.988 0.456 3200 4.059 2.075 2.032 0.500 3400 4.207 2.223 2.075 0.543 ~3600 Failure

(67) Table 4 below sets forth the results of the lateral load test of Pier 2, which was an acute Z-shaped pier driven to a depth of 6 feet. Further, FIG. 8B depicts a line graph showing the deflection of Pier 2.

(68) TABLE-US-00004 TABLE 4 Lateral Load Test - Pier 2 Pile Number: 2 Tested by: PR Ground surface Condition: PV Pile Lateral Pile Size: Stabilized Z Load 1 Height of top of pile from ground surface 61.75 in Height of pull chain above ground surface 61.75 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 6 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Pile Bottom of Pile (lbs) Reading Defection Reading Defection 0 1.999 0.000 0.883 0.000 280 2.109 0.110 0.921 0.038 460 2.198 0.199 0.946 0.063 600 2.286 0.287 0.970 0.087 800 2.387 0.388 0.990 0.107 990 2.472 0.473 1.015 0.132 1200 2.581 0.582 1.041 0.158 1420 2.712 0.713 1.072 0.189 1600 2.812 0.813 1.095 0.212 1590 2.848 0.849 1.120 0.237 1790 2.932 0.933 1.131 0.248 2000 3.075 1.076 1.166 0.283 2240 3.216 1.217 1.200 0.317 2400 3.331 1.332 1.235 0.352 2540 3.445 1.446 1.272 0.389 2720 3.598 1.599 1.361 0.478 2950 3.769 1.770 1.358 0.475 3150 3.988 1.989 1.431 0.548 3360 4.235 2.236 1.501 0.618 3500 4.545 2.546 1.585 0.702 ~3600 Failure, Pile Buckled

(69) Table 5 below sets forth the results of the lateral load test of Pier 3, which was a standard wide flange pier driven to a depth of 6 feet. Further, FIG. 8C depicts a line graph showing the deflection of Pier 3.

(70) TABLE-US-00005 TABLE 5 Lateral Load Test - Pier 3 Pile Number: 3 Tested by: PR Ground surface Condition: Grass Pile Size: Wide Flange Beam Height of top of pile from ground surface 61 in Height of pull chain above ground surface 61 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 6 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Pile Bottom of Pile (lbs) Reading Defection Reading Defection 0 2.432 0.000 0.969 0.000 750 2.893 0.461 1.092 0.123 1520 3.374 0.942 1.198 0.229 1840 3.594 1.162 1.248 0.279 2230 3.839 1.407 1.313 0.344 0 2.517 0.085 1.010 0.041 1510 3.449 1.017 1.229 0.260 2240 3.878 1.446 1.330 0.361 2600 4.115 1.683 1.393 0.424 3360 4.711 2.279 1.539 0.570 2990 4.562 2.130 1.524 0.555 3700 5.111 2.679 1.658 0.689 4125 Failure

(71) Table 6 below sets forth the results of the lateral load test of Pier 4, which was an acute Z-shaped pier driven to a depth of 6 feet. Further, FIG. 8D depicts a line graph showing the deflection of Pier 4.

(72) TABLE-US-00006 TABLE 6 Lateral Load Test - Pier 4 Pile Number: 4 Tested by: PR Ground surface Condition: Grass Pile Size: Stabilized Z Height of top of pile from ground surface 62 in Height of pull chain above ground surface 62 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 6 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Bottom of Pile (lbs) Reading Defection Pile Reading Defection 0 2.479 0.000 1.032 0.000 750 2.894 0.415 1.141 0.109 1480 3.282 0.803 1.250 0.218 1860 3.517 1.038 1.297 0.265 2290 3.771 1.292 1.374 0.342 0 2.630 0.151 1.081 0.049 1550 3.441 0.962 1.298 0.266 2230 3.779 1.300 1.384 0.352 2620 4.003 1.524 1.443 0.411 3320 4.586 2.107 1.623 0.591 3000 4.476 1.997 1.602 0.570 3720 4.989 2.510 1.736 0.704 4125 Failure

(73) Table 7 below sets forth the results of the lateral load test of Pier 5, which was a standard wide flange pier driven to a depth of 5.5 feet. Further, FIG. 8E depicts a line graph showing the deflection of Pier 5.

(74) TABLE-US-00007 TABLE 7 Lateral Load Test - Pier 5 Pile Number: 5 Tested by: PR Ground surface Condition: Grass Pile Size: Wide Flange Bean Height of top of pile from ground surface 61.5 in Height of pull chain above ground surface 61.5 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 6 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Pile Bottom of Pile (lbs) Reading Defection Reading Defection 0 1.614 0.000 2.718 0.000 790 2.159 0.545 2.827 0.109 1520 2.591 0.977 2.930 0.212 1870 2.804 1.190 2.977 0.259 2260 3.041 1.427 3.037 0.319 0 1.730 0.116 2.755 0.037 1890 2.681 1.067 2.990 0.272 2260 3.072 1.458 3.056 0.338 2640 3.288 1.674 3.102 0.384 3350 3.771 2.157 3.225 0.507 2990 3.648 2.034 3.219 0.501 3700 4.073 2.459 3.304 0.586 4100 4.388 2.774 3.389 0.671 0 1.870 0.256 2.806 0.088

(75) Table 8 below sets forth the results of the lateral load test of Pier 6, which was an acute Z-shaped pier driven to a depth of 5.5 feet. Further, FIG. 8F depicts a line graph showing the deflection of Pier 6.

(76) TABLE-US-00008 TABLE 8 Lateral Load Test - Pier 6 Pile Number: 6 Tested by: PR Ground surface Condition: Grass Pile Size: Stabilized Z Height of top of pile from ground surface 62 in Height of pull chain above ground surface 62 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 6 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Pile Bottom of Pile (lbs) Reading Defection Reading Defection 0 1.776 0.000 1.053 0.000 750 2.127 0.351 1.138 0.085 1520 2.505 0.729 1.238 0.185 1890 2.699 0.923 1.284 0.231 2250 2.897 1.121 1.335 0.282 0 1.929 0.153 1.123 0.070 1520 2.621 0.845 1.282 0.229 2270 2.963 1.187 1.364 0.311 2630 3.167 1.391 1.424 0.371 3250 3.624 1.848 1.557 0.504 2990 3.552 1.776 1.545 0.492 3700 4.029 2.253 1.688 0.635 4090 4.520 2.744 1.847 0.794 0 2.482 0.706 1.345 0.292

(77) Table 9 below sets forth the results of the lateral load test of Pier 7, which was a standard wide flange pier driven to a depth of 5.5 feet. Further, FIG. 8G depicts a line graph showing the deflection of Pier 7.

(78) TABLE-US-00009 TABLE 9 Lateral Load Test - Pier 7 Pile Number: 7 Tested by: PR Ground surface Condition: Grass Pile Size: Wide Flange Beam Height of top of pile from ground surface 61.25 in Height of pull chain above ground surface 61.25 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 5.5 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Pile Bottom of Pile (lbs) Reading Defection Reading Defection 0 1.626 0.000 1.427 0.000 750 2.114 0.488 1.533 0.106 1500 2.549 0.923 1.625 0.198 1880 2.775 1.149 1.681 0.254 2250 2.991 1.365 1.723 0.296 0 1.789 0.163 1.470 0.043 1500 2.627 1.001 1.653 0.226 2270 3.042 1.416 1.743 0.316 2620 3.246 1.620 1.788 0.361 3360 3.750 2.124 1.907 0.480 3010 3.612 1.986 1.891 0.464 3730 4.007 2.381 1.985 0.558 4120 4.350 2.724 2.066 0.639 0 1.986 0.360 1.540 0.113

(79) Table 10 below sets forth the results of the lateral load test of Pier 8, which was an acute Z-shaped pier driven to a depth of 5.5 feet. Further, FIG. 8H depicts a line graph showing the deflection of Pier 8.

(80) TABLE-US-00010 TABLE 10 Lateral Load Test - Pier 8 Pile Number: 8 Tested by: PR Ground surface Condition: Grass Pile Size: Stabilized Z Height of top of pile from ground surface 62.75 Height of pull chain above ground surface 62.75 Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 5.5 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Pile Bottom of Pile (lbs) Reading Defection Reading Defection 0 1.244 0.000 1.605 0.000 750 1.636 0.392 1.705 0.100 1500 1.974 0.730 1.785 0.180 1880 2.178 0.934 1.833 0.228 2260 2.396 1.152 1.901 0.296 0 1.388 0.144 1.668 0.063 1510 2.091 0.847 1.840 0.235 2270 2.440 1.196 1.914 0.309 2620 2.629 1.385 1.972 0.367 3360 3.217 1.973 2.139 0.534 2990 3.105 1.861 2.131 0.526 3700 3.582 2.338 2.263 0.658 4090 4.068 2.824 2.420 0.815 0 2.000 0.756 1.919 0.314

(81) Table 11 below sets forth the results of the lateral load test of Pier 9, which was a standard wide flange pier driven to a depth of 5 feet. Further, FIG. 8I depicts a line graph showing the deflection of Pier 9.

(82) TABLE-US-00011 TABLE 11 Lateral Load Test - Pier 9 Pile Number: 9 Tested by: PR Ground surface Condition: Grass Pile Size: Wide Flange Beam Height of top of pile from ground surface 61.5 in Height of pull chain above ground surface 61.5 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 5 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Bottom of Pile (lbs) Reading Defection Pile Reading Defection 0 2.404 0.000 1.319 0.000 740 2.840 0.436 1.411 0.092 1510 3.260 0.856 1.512 0.193 1870 3.488 1.084 1.573 0.254 2240 3.741 1.337 1.642 0.323 0 2.587 0.183 1.391 0.072 1530 3.410 1.006 1.574 0.255 2260 3.811 1.407 1.671 0.352 2620 4.107 1.703 1.750 0.431 3375 Failure

(83) Table 12 below sets forth the results of the lateral load test of Pier 10, which was an acute Z-shaped pier driven to a depth of 5 feet. Further, FIG. 8J depicts a line graph showing the deflection of Pier 10.

(84) TABLE-US-00012 TABLE 12 Lateral Load Test - Pier 10 Pile Number: 10 Tested by: PR Ground surface Condition: Grass Pile Size: Stabilized Z Height of top of pile from ground surface 62.25 in Height of pull chain above ground surface 62.25 in Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 5 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Bottom of Pile (lbs) Reading Defection Pile Reading Defection 0 1.523 0.000 0.557 0.000 770 1.881 0.358 0.648 0.091 1490 2.316 0.793 0.763 0.206 1860 2.614 1.091 0.851 0.294 2230 2.994 1.471 0.973 0.416 0 1.927 0.404 0.719 0.162 1550 2.695 1.172 0.901 0.344 2260 3.162 1.639 1.031 0.474 2600 3.616 2.093 1.176 0.619 Failure

(85) Table 13 below sets forth the results of the lateral load test of Pier 11, which was a standard wide flange pier driven to a depth of 5 feet. Further, FIG. 8K depicts a line graph showing the deflection of Pier 11.

(86) TABLE-US-00013 TABLE 13 Lateral Load Test - Pier 11 Pile Number: 11 Tested by: PR Ground surface Condition: Grass Pile Size: Wide Flange Beam Height of top of pile from ground surface 60″ Height of pull chain above ground surface 60″ Height of top measurement 59.5″ Height of bottom measurement 6 in Pile Driven Depth 5 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Pile Bottom of Pile (lbs) Reading Defection Reading Defection 0 2.350 0.000 1.158 0.000 750 2.813 0.463 1.258 0.100 1480 3.268 0.918 1.358 0.200 1870 3.522 1.172 1.421 0.263 2230 3.816 1.466 1.505 0.347 0 2.547 0.197 1.232 0.074 1510 3.434 1.084 1.424 0.266 2230 3.874 1.524 1.530 0.372 2600 4.181 1.831 1.606 0.448 2970 4.591 2.241 1.743 0.585 3270 5.075 2.725 1.898 0.740 3750 Failure

(87) Table 14 below sets forth the results of the lateral load test of Pier 12, which was an acute Z-shaped pier driven to a depth of 5 feet. Further, FIG. 8L depicts a line graph showing the deflection of Pier 12.

(88) TABLE-US-00014 TABLE 14 Lateral Load Test - Pier 12 Pile Number: 12 Tested by: PR Ground surface Condition: Grass Pile Size: Stabilized Z Height of top of pile from ground surface 62.25 Height of pull chain above ground surface 62.25 Height of top measurement 60.75 in Height of bottom measurement 6 in Pile Driven Depth 5 ft STABILIZED READING LOAD Top of Pile Top of Pile Bottom of Bottom of Pile (lbs) Reading Defection Pile Reading Defection 0 1.736 0.000 1.768 0.000 750 2.317 0.581 1.958 0.190 1470 2.978 1.242 2.180 0.412 1850 3.383 1.647 2.326 0.558 2240 3.888 2.152 2.486 0.718 0 2.695 0.959 2.172 0.404 1510 3.545 1.809 2.415 0.647 2240 4.066 2.330 2.565 0.797 2570 4.563 2.827 2.738 0.970 3375 Failure

(89) Based on the load testing, the acute Z-shaped pier (called “Stabilized Z” in the tables and figures relating to the testing) has a similar or better deflection response when compared to the standard wide flange pier under lateral loading at the embedment depths of 5.5 and 6 feet. As a result, the acute Z-shaped pier may provide cost savings as a result of being lighter and slightly shorter in comparison to the standard wide flange pier while maintaining the same or better deflection response. For the piers tested at 5 feet of embedment, all four piers (both the acute Z-shaped and standard wide flange piers) exhibited excessive deflections at lower loads. It is expected that for most tracker designs, however, foundation embodiments will be greater than 5 feet, because, for typical tracker loads, there are very few sites where the soils are strong enough to resist the loads while also being soft enough to be drivable.

(90) Although the disclosure has been described with reference to preferred embodiments, persons skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the disclosed apparatus, systems and methods.