This invention relates in general to a rapidly-deployable lightweight tubular arch load resisting system capable of resisting loads both in the vertical and horizontal directions, useful for the rapid construction of buried arched bridges, tunnels, underground storage facilities, hangers, or bunkers, which minimizes the need for heavy construction equipment at the site.
In the past, there have been several types of technologies that have been used in order to construct short and medium span buried arch bridges, as well as some underground storage facilities and tunnels. These structures are typically covered with a soil overburden which receives traffic or other loading.
One technology includes the use of precast concrete structures which are made in one location and then shipped to the construction site. While the precast concrete structures are made skillfully and meet the construction requirements, the use of precast concrete structures adds greatly to the cost since it is expensive to ship and then install the precast concrete structures. While the precast concrete structures are somewhat quick to install, the precast concrete structures are very heavy and require heavy equipment at the site.
Another technology includes the use of cast-in-place concrete structures which are formed at the construction site and then lifted into place by cranes or the like. This cast-in-place technology provides the benefit of not having to ship the structures. On the other hand, the use of cast-in-place is also expensive and time consuming since an on-site concrete plane must be first constructed at the construction site. The cast-in place concrete structures require time-intensive and very expensive erection and removal of formwork, placement of reinforcing bars, and long construction lead times.
Yet another technology includes the use of pipe metallic structures. Metallic pipe structures have reduced life spans due to corrosion. Another drawback is that pipe metallic structures are limited to short spans and light loads.
Each of these existing construction method technologies has significant disadvantages that are overcome by the present invention. In addition to the need for heavy equipment for construction at the site in order to construct and then erect most bridges today, a major drawback that is common to these existing construction technologies is that, while metallic and steel reinforced concrete are widely used and accepted in the construction of many structures, the reinforced concrete structures are susceptible to deterioration. Over time, particularly in northern climates, numerous freeze-thaw cycles and the use of de-icing chemical accelerate corrosion and material degradation. The exposure of the steel reinforced concrete structures to conditions such as water, road salt and the like, and the freezing and thawing thereof, can cause cracks to form in the structures. These cracks, in turn, cause reinforcing steel to corrode and expand, causing further cracking, thereby allowing air and more water to enter the structure, thereby weakening and damaging the structure.
In one aspect, the present invention relates to a lightweight load resisting system having a network of generally arched hollow tubular main support members which minimize the requirement for heavy construction equipment at the site. In one aspect, the present invention includes a network of arched tubular support members that are juxtaposed to each other.
In another aspect, the present invention includes a network of spaced apart arched tubular support members that are operatively held together. In yet another aspect, both the juxtaposed and spaced apart networks can include flat or corrugated vertical and lateral force resisting members positioned on and attached to the support members.
In yet another aspect, the present invention relates to a load resisting system where the tubular main support members are site-filled with a flowable material such as grout, sand, concrete or the like in order to provide additional strength and stiffness to the load resisting system.
In a particular aspect, the present invention relates to a network load resisting system comprising a plurality of tubular support members for supporting a vertical overburden. In certain embodiments, the load resisting system is especially useful for supporting a soil overburden, such as in a roadway, bridge or underground storage facility, or vehicular loading such as in a bridge.
In certain embodiments, each tubular support member has an opening near a top portion of the tubular support member such that the tubular support members are capable of being site-filled with non-shrink or expansive concrete, nonshrink or expansive grout, or sand via the openings near the top of tubular support members.
The tubular support members are connected in a transverse direction using substantially horizontal rods fitted through transverse holes spaced along the length of each tubular support member.
In certain embodiments, the tubular support members comprise a plurality of longitudinal, substantially parallel, at least partially hollow structural members operatively connected by at least one connector member.
The tubular support members are operatively connected to at least one or more lateral force resisting members. The lateral force resisting members are generally positioned in a direction perpendicular to the tubular support members. The lateral force resisting members are capable of transferring vertical loads to the tubular support members and providing lateral load capacity to the load resisting system. In certain embodiments, the lateral force resisting members comprise corrugated sheets, where the sheet corrugations run in a direction perpendicular to the vertical plane of the tubular support members.
Various objects and advantages of this invention will become apparent to those skilled in the art from the following detailed description of the preferred embodiment, when read in light of the accompanying drawings.
This invention overcomes many difficulties with existing construction method technologies for constructing buried concrete and metallic arch structures. The present invention is especially useful for construction of such applications as, for example, short-span buried bridges, underground storage facilities, and tunnel structures where the use of lightweight components speeds construction and reduces the requirements for heavy equipment at the construction site.
Thus, in one aspect, this invention relates to a load resisting system having a network of generally arched or bent-shaped tubular support members substantially oriented in a vertical plane for supporting live or dead loads, generally shown in the figures herein as L. It is to be understood that the load L can be, for example, a soil overburden that exerts a force on the load resisting system of the present invention.
In one aspect, the present invention relates to a rapidly-erectable lightweight load resisting system for the construction of buried arched bridges, tunnels or underground bunkers. The rapidly-erectable lightweight load resisting system has a plurality of lightweight arched tubular support members which are formed of a fiber reinforced polymer material and are substantially oriented in a vertical plane such that the tubular support members collectively form the vertical load resisting system. The lightweight tubular support members are connected by at least one or more lateral force resisting members. The lateral force resisting members are positioned in a direction perpendicular to the vertical plane of the tubular support members. The lateral force resisting members are capable of transferring vertical loads to the tubular support members and of providing lateral-load capacity to the load resisting system. The tubular support members have one or more holes near the top, or crown, of the tubular support member which allows the tubular support member to be filled with an expansive grout, expansive polymer, nonshrink concrete, or sand material to provide additional strength or stiffness. Among the key features of the present inventive lightweight system are its transportability, its durability, and its ability to be rapidly erected with minimal equipment needed at the construction site.
In certain other aspects, the support members are operatively connected to at least one or more lateral force resisting members which are generally positioned in a direction perpendicular to a vertical plane defined by the tubular support members such that the lateral force resisting members function to transfer the loads to the tubular support members and to provide lateral load, or racking, strength to the load resisting system.
Referring now to the drawings, there is illustrated in
In one aspect, as shown in
In certain embodiments, the load resisting system includes a plurality of cross extending rods 51, such as dowels, rebar or fiberglass. Each rod 51 is positioned to extend through radially extending openings 52 in the tubular support members 50a, 50b, 50c, 50d, and 50e. In certain embodiments, a nut can be coaxially positioned adjacent outermost openings 52 in the network of tubular support members 50a, 50b, 50c, 50d, and 50e. In one embodiment, the longitudinal tubular support members 50a, 50b, 50c, 50d, and 50e are placed parallel to traffic in a bridge end use application. Each rod 51 can be positioned at a distance 54 from an adjacent 51, as shown in
In certain embodiments, each tubular support member 50a, 50b, 50c, 50d, and 50e includes at least one opening 52 through which the tubular support members 50a, 50b, 50c, 50d, and 50e may be filled with a reinforcing material 57 at the construction site in order to provide additional strength and stiffness to the structural members 50a, 50b, 50c, 50d, and 50e.
In another embodiment, as shown in
In certain embodiments, the load resisting system includes plurality of lateral force resisting members 62a, 62b, 62c, etc. which are in a spaced-apart configuration on an outer surface of the spaced apart tubular support members 60a, 60b and 60c. In certain embodiments, the first lateral force resisting member 62a is positioned at a distance 64 from the second force resisting member 62b. Each lateral force resisting member 62a, 62b and 62c has a preferred width 63 such that each lateral force resisting member 62a, 62b and 62c can be easily positioned on the network of tubular support members 60a-60c. The force resisting members 62a, 62b and 62c are secured to the tubular support members 60a-60c by a plurality of suitable fasteners 65. The network of the tubular support members 60a, 60b and 60c and the lateral force resisting members 62a etc. collectively form a main load resisting system which receives a load such as a soil overburden to form a roadway or a bridge or an underground storage facility.
In another aspect, as shown in
In another aspect, as shown in
In another aspect, as shown in
In another aspect, as shown in
In another aspect, as shown in
In one aspect of the present invention, the tubular support members are made of a fiber-reinforced polymer (FRP) composite matrix. The FRP matrix may comprise a thermosetting resin, including but not limited to, at least one of epoxies, vinyl esters, polyesters, phenolics, or urethanes. The FRP matrix may also comprise a thermoplastic resin including, but not limited to, at least one of polypropylenes, polyethylenes, PVCs, or acrylics. The FRP reinforcement may comprise, but not be limited to fiberglass, carbon fiber, aramid fibers or a combination of one or more of these types of fibers. Fiber reinforced polymer composite tubular support members may be manufactured using a variety of processes, including but not limited to resin infusion (Vacuum-Assisted Resin Transfer Molding) or filament winding over a curved mold, or other suitable methods. The fiber forms may be, but are not limited to, stitched, woven or braided fabrics. The wall thickness and the diameter of each tubular support member are such that the tubular support members support the self-weight of the load resisting system and the weight of the material infill. For example, when concrete is used, the composite tubular support member/concrete section is designed to carry the soil overburden and any additional gravity dead or live loading.
In certain aspects, the reinforcing material infill can comprise at least one of non-shrink or expansive wet concrete, nonshrink or expansive grout, and/or sand.
In yet another aspect, the tubular support members can be covered with a flexible fabric, such as a geomembrane or other suitable geotextile. The load resisting system is then backfilled with a suitable material, such as sand, soil, or the like.
In other aspect, the lateral force resisting members are fastened to the tubular support members via screws or other suitable fasteners. The lateral force resisting members and fasteners together function to transfer the loads to the tubular support members and provide lateral load, or racking, strength to the load resisting system of the present invention. In certain embodiments, the lateral force resisting members comprise a flexible flat or corrugated sheet including but not limited to corrugated metal sheets, FRP, extruded PVC, polycarbonate, and wood-plastic composite. In certain embodiments, the sheet corrugations of the lateral force resisting members run in the direction perpendicular to the tubular support members.
In yet another aspect, the present invention relates to a method for building a load resisting system such as a bridge or tunnel which includes erecting longitudinal, substantially parallel, at least partially curved hollow tubular support members where each tubular support members forms an arch substantially oriented in a plane. As the tubular support members are being erected, the tubular support members are temporarily braced and spaced at a prescribed distance from one another. Starting at the low end of the tubular support members, the tubular support members are at least partially covered with a plurality of lateral force resisting members. In certain embodiments, the lateral force resisting members are corrugated sheets which are positioned such that the sheet corrugations run in the direction perpendicular to the tubular support members. The lateral force resisting members are operatively connected to the tubular support members via screws or other fasteners. In certain embodiments, the tubular support members are substantially filled with a suitable reinforcing material via at least one opening near the crown of the tubular support members. Also, in certain embodiments, vibration can be applied to the tubular support members to facilitate proper and complete filling of the tubular support members. Suitable construction supports such as wingwalls and the like are then attached to the load resisting system, and, as may be necessary, and the load resisting system is backfilled with soil to a required depth and paved.
In yet another aspect, the present invention relates to a method for building a load resisting system such as a bridge or tunnel which comprises first assembling a plurality of short arch segments into longer curved hollow tubular support members, then continuing with the method as described above.
In one example, the arch tubes of this invention are designed, by illustrating the design of 15 ft (4.6 m), 7 in. (178 mm) concrete-filled FRP arch tube, under the following conditions:
Local wall buckling is also checked.
1. Check FRP Arch Tubes under Weight of Wet Concrete
The FRP arch tube is modeled using a structural analysis computer program while applying a vertical uniformly distributed load equivalent to the weight of wet concrete along the length of the structure. The arch may be meshed with straight beam elements. The boundary conditions may be taken as pin supports. The area, 1.398 in2 (9.0 cm2), moment of inertia, 8.717 in4 (363 cm4), and the modulus of elasticity, 1.795×106 psi (13.3 GPa) were taken as that for an FRP hollow tube having a thickness of 0.088 in. (2.23 mm) and a radius of 7 in.
Ashell=2·π·r·t (1)
Ishell=2·π·r3·t (2)
The elastic modulus of the tube is calculated by transforming the elastic property of the lamina in the material principle axis, found in Table 1, to principle laminate axis.
Where m=cos(θ), and n=sin(θ). Once the structural analysis is conducted, a critical section is selected and the maximum developed moment is obtained. The critical section is selected based on the maximum flexural force since the axial force transferred to the shell is minimal and is sustained by hydrostatic pressure.
After the internal forces are evaluated, the capacity of the FRP shell is checked against the developed stresses. Thin laminate analysis is assumed. The composite properties are obtained using classical laminate theory for orthotropic material. Bending stresses (σb), axial stresses σa, and shear stresses σv, resulting from developed internal forces are computed using simple elastic theory as follows:
Where M, P, and V are the applied moment, axial and shear forces, respectively; c is the distance from the neutral axis to the location where the stress is compute; Ashell and Ishell are the area and moment of inertia of the FRP tube respectively; t is the thickness of the shell; and Q is the first moment of inertia.
The moment and axial stresses are superimposed. The superimposed stresses along with the shear stresses are transformed from the principle laminate axis to the principle material axis and then checked against failure using Maximum Stress Theory. Stress calculation and failure check is done along the circumference of the shell simultaneously.
The variables used in the analysis are given in Table (2), and the calculations are automated using a computer program.
The computer program developed to facilitate the numerical calculations for this application can terminate either when the first ply undergoes failure in the direction of the fiber or when the shell has been proven to be adequate to sustain the applied forces. If the shell fails to withstand the developed stresses, the computer program generates: (1) the type of failure (fiber failure, matrix failure or shear failure), (2) the ply number where failure occurred, (3) the failure location in angles with respect to a vertical axis passing through the center and the top quadrant of the cross section, (4) and finally the strength ratio defined as the ultimate strength over the applied stress; otherwise, the program would state that the arched shell design is adequate
For the current illustrative example, and using the values given in Table (3) it is found the shell can sustain the weight of the wet concrete.
2. Analysis of FRP Concrete Arch Tube Under a Concentrated Load Applied at Midspan
An iterative method is used to calculate the ultimate vertical concentrated midspan load that the FRP-concrete arch can support. The iterative method incorporates the use of two numerical computer programs: (1) a moment-curvature program to calculate the moment capacity of an FRP-concrete cross-section and (2) a structural analysis program that calculates the internal developed forces based on a given structure model and load. A brief summary of the moment-curvature output and input variables is given first. An iterative method adopted for the analysis of the FRP-concrete specimens is described in detail. A flow-chart to aid in understanding the iterative procedure is also included.
The moment-curvature model input data is shown in Table 4, and the variables are defined in Table 1.
All the values are given in English units, psi, inches, or lb. The number of layers and the number of material types are entered next. The elastic properties for each material are given in rows. The ply layup orientation, thickness and the material reference number for each ply follow. The ply layup and the materials are separated with commas. Concrete properties are given next: initial modulus, initial Poisson's ratio, unconfined strength, and strain at peak stress for unconfined concrete. The axial force, shear span, shear flag and shear constant (vk) are listed next. The shear span is defined as the distant from the support to the nearest applied load for a four point bending test, or the distant for the support to the center of the beam for a three point bending test. The shear constant (vk) is a parameter used in calculating the shear sustained by the concrete core (Vc=vk·A·√{square root over (f′c)}). ACI recommends a (vk) between 1.9 and 3.5 for psi unit. The cross-section radius is given afterwards. Lastly, the angle for the strain output is set. The angle is taken with respect to a vertical axis having the center of the cross-section as the origin. The axial hoop and shear strains are obtained as a function of the moment and shear load.
An iterative procedure is used to determine the concentrated load that could be carried by the FRP-concrete arch tube, as described next. The axial and shear force input into the moment-curvature analysis are initially assumed to be zero and the moment capacity and secant stiffness of the cross-section are generated. The neutral axis at the moment capacity is extracted from the analysis. The arch is analyzed using a commercial structural analysis program using a series of straight beam elements. The area, A, of the cross-section is taken as the sum of the transformed FRP shell, Ashell, and the uncracked concrete section, Acr.
A=Acr+Ashell (10)
Where Ashell=(2πr·t)·n (11)
and Acr=r2·(α−sin(α)·cos(α)) (12)
Where r is the radius of the circular cross-section, α is defined as
and c is the distance from the center of the cross-section to the neutral axis at moment capacity. In the same manner, the moment of inertia, I, are taken as the sum of the transformed shell inertia, Ishell and the uncracked concrete inertia, Icr.
The modulus of elasticity is calculated by dividing the secant stiffness (EI) generated by the moment curvature analysis by I. Once the material properties are calculated, an arbitrary concentrated load is applied vertically at midspan and structural analysis is conducted. The absolute value of the maximum moment is compared with that generated by the moment curvature analysis. The arbitrary load at midspan is altered until the maximum moment developed in the arch converged to the moment capacity of the cross-section. Once this was achieved, the axial and shear force at the section of maximum moment are reentered into the moment curvature program and a new moment capacity and secant stiffness are calculated. These values are used again in the structural analysis program and a new axial and shear forces are calculated. The process is repeated several times until the change in the shear and axial forces are small enough. A flow chart illustrating the iterative method is shown in
After running the iterative method, it was found the FRP-concrete arch had a moment capacity of 40.3 ft-kip (54.6 m-kN) and a corresponding secant stiffness of 95000 ksi (655 GPa). The ultimate vertical load applied at midspan of the arch was found to be equal to 27 kips (12,272 kg).
3. FRP-Concrete Tubular Arch Buckling Analysis
The FRP arched tube is checked against global buckling under two loadings:
1. FRP arch tube under the weight of wet concrete
2. FRP concrete arch tube under a concentrated load applied at midspan.
For convenience, a computer may be used to expedite the calculations. Using virtual work for linearly elastic material, the following analysis minimizes the governing potential energy functional.
Potential Energy Equation:
Where EI is the flexural stiffness, EA is the axial stiffness, P is the critical buckling load, q(x) is the distributed load on the member, and v(x) is a set of cubic beam element shape functions, as shown in
The axial strain may be neglected and the distributed load q(x) is eliminated from the analysis. By minimizing the potential energy equation and equating it to zero, the elastic (Ke) and the geometric (Kg) stiffness matrix are deduced.
The following analysis is performed (see
(4) compute member forces (5) assemble the geometric stiffness matrix, Kg, (6) reduce Ke and Kg to remove fixed displacement, and (7) solve the generalized eigenvalue problem and compute the critical load.
For the analysis of the illustrative problem at hand, it was found that the buckling load for the FRP arch tube subjected to a uniform distributed load is 56 lb/in . . . (1,002 kg/m) while the buckling load of the FRP-concrete arch tube subjected to a concentrated load at midspan is 75 kips (34,090 kg). To calculate the critical buckling load due to the weight of wet concrete, a uniform distributed unit force is applied vertically at each node. It is found that the buckling load was 56 lb/in (1,002 kg/m), which is greater than the distributed weight of wet concrete, 46.75 lb/in. (836 kg/m), in a 3.5 in. (89 mm) radius FRP tube. Similarly, to calculate the critical buckling load for a load applied vertically at midspan, a unit force is applied at midspan. It is found that buckling load was 75 kips (34,090 kg) while the load to be carried by the FRP concrete arch tube found earlier is 27 kips (12,270 kg). Accordingly, the FRP arch tube used in this example would not be subjected to global buckling under the two load cases.
Local Wall Buckling Analysis of the FRP Hollow Tube
The last type of analysis illustrated on the FRP arch tube system is local buckling under axial compression. A set of equations using elastic shell buckling, as a simplified approximate method, are used:
Where L is the length of the cylinder, D is the cross-section diameter measure from the center of the shell thickness, t is the thickness of the shell, r is the radius of gyration, v and E is the Poisson's ratio and elastic modulus of the material, respectively, C is taken as 0.0165.
For the illustrative problem shown herein, it is found that the developed stresses resulting from the weight of wet concrete would not result in local buckling in the FRP tube. The moment, 214 lb-ft (290.2 m-N) and axial, 468 lb (212.7 kg) forces used for the buckling analysis are the maximum forces produced in the arch at any given location, respectively, which is a conservative approach.
In accordance with the provisions of the patent statutes, the principle and mode of operation of this invention have been explained and illustrated in its preferred embodiment. However, it must be understood that this invention may be practiced otherwise than as specifically explained and illustrated without departing from its spirit or scope.
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