EP4524340A1 - The system and method to anchor flexible structural strips - Google Patents

Abstract

The invention presents a novel anchorage system tailored for precise mechanical testing of fiber-reinforced plastic flat strips used as tension members. The device is pivotal in structural engineering, aiding the design, materials characterizing, and assessing durable structures, employing such tension members. Unlike existing solutions that exhibit stress concentrations, the innovative design ensures uniform load transmission by utilizing a curved disc with a unique curvature profile and a micro-slipping phenomenon based on friction. This eliminates the stress peaks and enhances the accuracy of mechanical testing. Comprising two main components, the device securely fastens and stabilizes the flexible strip, enabling controlled tension application. The invention's practical installation and internal clamping system further enhance its functionality. In industries like aerospace, automotive, and construction, where fiber-reinforced plastics are increasingly employed, this anchorage system plays a crucial role in ensuring the reliability and effectiveness of tension members in complex structures.

Description

TECHNICAL FIELD
• The invention relates to structural and materials engineering fields and can fabricate and characterize structural composites, which employ flat flexible strips. Specifically, it discloses an anchoring system for flexible components made from reinforced plastics subjected to tension-the friction nature of the anchorage allows for minimizing the stress concentration at the outer gripping edge.
• Within the broader engineering context, the invention finds a crucial role in structural engineering. It significantly contributes to designing, analyzing, and assessing safe and robust structures incorporating fiber-reinforced plastic tension members. The device's ability to accurately apply tensile forces to these materials without introducing artificial stress points aligns seamlessly with the demands of modern structural engineering. This innovative approach ensures that tension members' behavior can be thoroughly understood and optimized for real-world applications.
• Industries such as aerospace, automotive, construction, and manufacturing stand to benefit from this invention's advancements in structural engineering. As these sectors increasingly adopt fiber-reinforced plastic materials to enhance performance and durability, the anchorage system is a critical tool for verifying the reliability and effectiveness of tension members within complex structural systems.
BACKGROUND
• Tensioned elements made of composite materials, particularly fiber-reinforced plastic (FRP) composites, offer numerous advantages, including corrosion resistance, high tensile strength, lightweight nature, flexibility, and cost-effectiveness. These attributes make them highly desirable for various applications due to their availability in customizable lengths and low installation costs.
• The transmission of external loads to tensioned composite elements presents a significant challenge in their practical application and testing. To address this challenge, anchorages known as grips or gripping devices are utilized. These grips facilitate load transmission through the tensioned composite by inducing shear stresses on the material's surface. These stresses can arise due to micro-slipping of the composite strip within the anchorage system, generating frictional shear stresses.
• For effective load transmission, various anchoring techniques have been explored. The use of carbon fiber-reinforced polymers (CFRP) has gained attention in recent research, highlighted by the following studies:
• Mohee, F. M., Al-Mayah, A., & Plumtree, A. (2017). Development of a novel prestressing anchor for CFRP plates: Experimental investigations. Composite Structures, 176, 20-32.
• You, Y. C., Choi, K. S., & Kim, J. (2012). An experimental investigation on flexural behavior of RC beams strengthened with prestressed CFRP strips using a durable anchorage system. Composites Part B: Engineering, 43(8), 3026-3036.
• Correia, L., Teixeira, T., Michels, J., Almeida, J. A., & Sena-Cruz, J. (2015). Flexural behaviour of RC slabs strengthened with prestressed CFRP strips using different anchorage systems. Composites Part B: Engineering, 81, 158-170.
• Hosseini, A., Ghafoori, E., Motavalli, M., Nussbaumer, A., & Zhao, X. L. (2017). Mode I fatigue crack arrest in tensile steel members using prestressed CFRP plates. Composite Structures, 178, 119-134.
• Michels, J., Martinelli, E., Czaderski, C., & Motavalli, M. (2014). Prestressed CFRP strips with gradient anchorage for structural concrete retrofitting: Experiments and numerical modeling. Polymers, 6(1), 114-131.
• Hosseini, A., Ghafoori, E., Motavalli, M., Nussbaumer, A., Zhao, X. L., & Koller, R. (2018). Prestressed unbonded reinforcement system with multiple CFRP plates for fatigue strengthening of steel members. Polymers, 10(3), 264.
• CFRP materials, known for their strength and flexibility, have been employed in applications ranging from reinforcing old structures with cracks to enhancing concrete constructions using pre-stretched CFRP bands. Current techniques often involve anchoring CFRP elements with metal plates, achieving the desired reinforcement effects. However, existing methods primarily focus on single or parallel CFRP bands, and the anchoring systems might not provide uniformly distributed stress.
• The distribution of shear stresses during load transmission presents a challenge, resulting in stress concentration at the entry point of the anchorage system. This stress concentration has exceeded the average stress within the tensioned strip, leading to premature failure near the anchorage entry point. Achieving uniformly distributed stress across the tensioned strip is essential for determining its maximum load-carrying capacity and preventing premature failure.
• Existing patents have proposed solutions to mitigate shear stress concentration. The patent application US2007221894A suggests inserting compliant interlayers between steel wedges and tensioned strips to reduce stiffness and frictional shear stresses. However, selecting appropriate interlayer materials that combine compliance with sufficient bearing resistance and shear strength remains challenging. Furthermore, manufacturing complexities and reusability issues hinder the practicality of these interlayers.
• In recent developments, the patent application WO2018072589A1 introduces an automated control system for pre-tensioning bundled steel strands, enhancing efficiency and reducing labor costs. It incorporates a pre-tensioning device, an integrated tensioning device, and a control center, allowing synchronized tensioning of multiple steel strands. The system's integration minimizes the need for multiple pumping stations and control centers, enabling simultaneous pre-tensioning and integrated tensioning of pre-stressed strands.
• The patent LT6275B introduces fastening equipment for producing and testing tensile composite elements. It features symmetrical anchorage joints embracing reinforcement bars of structural components. Plates serve as permanent formwork, while tension devices measure deformation. Despite its merits, this invention primarily focuses on internal bars and ties within composite elements.
• Another way to reduce the stress concentration at the anchor's entry is using wedge-shaped grips made of materials with variable stiffness, which increases in the direction away from the entry point. This way was described in the patent US5713169B , entitled "Anchorage device for high-performance fiber composite cables". A cone element made of material with a minimum stiffness is located at the entry in the anchor, followed by another cone element of material with higher stiffness, and so on. This results in the flattening of the shear stress peak.
• However, selecting materials, manufacturing the cone elements, and assembling the anchorage are labor-consuming. Moreover, the reliability of the compliant materials under high stress needs to be improved. Finally, by applying this method, the shear stress peak at the entry in the anchor may be reduced but could not be avoided.
• An anchorage system of variable rigidity is proposed in the patent application US2004216403A entitled "The anchor for a strip-type tension member". The main idea is to divide clamping plates into segments connected by bridges of varying rigidity; the farther the part from the entry point, the higher the bridge's rigidity.
• However, the construction is challenging to manufacture and assemble, whereas it only reduces the shear stress peak but only permits it partially.
• Thus, the existing solutions to the problem of load transmission on a tensioned high-strength CFRP strip partially solve this problem. They lead to an inevitable decrease in shear stress concentration, but the shear stress peak on the surface of the tensioned strip does not disappear completely. The character of shear stress distribution along a tensioned strip remains essentially the same - with maximum stress at the entry point in the anchorage system followed by their decrease farther away from the entry. Hence, the stress concentration at the entrance in anchorage, while decreased, remains. Moreover, applying adhesive or compliant interlayers in the anchorage system practically excludes the possibility of re-use the anchorage parts in immediate contact with the surface of the tensioned element.
• Therefore, there is a need for a simple anchorage system with no shear stress peak at the entry point.
SUMMARY OF THE INVENTION
• The anchorage system of the present invention addresses the challenge of transmitting tensile loads to flexible strips made of composite materials. It utilizes a spiral surface on a flat disc to accommodate the flexible strip, gradually increasing shear stress along its surface through friction. The device eliminates stress concentration at the entry point, enhancing load transmission. Made from materials like fiber-reinforced plastic (FRP) or carbon fiber-reinforced plastic (CFRP), the device is particularly effective with anisotropic materials like CFRP.
• Existing solutions partially reduce stress concentrations on tensioned strips, but stress peaks at entry points remain. This new anchorage system eliminates stress peaks, enhancing load transmission. Its innovative design overcomes challenges associated with shear stress concentration, ensuring more accurate mechanical testing of tension members.
DESCRIPTION OF DRAWINGS
• The following pictures are provided and referenced hereafter to understand the frictional fixture principle of a flexible FRP strip and appreciate its applications. Figures are given as examples only and in no way should limit the scope of the invention. The invention is explained in the drawings, wherein:
• FIG. 1 depicts a schematic of the spiral anchorage device of a flexible flat strip;
• FIG. 2 depicts a schematic of load components acting on an elementary arc segment;
• FIG. 3 shows a theoretical application example of equipment fixing CFRP flexible strips of the pedestrian stress-ribbon bridge prototype;
• FIG. 4 shows laboratory application examples ensuring different traction coefficients χ of spiral surfaces manufactured from PLA using 3D printing technology and tested as anchors for CFRP strip: a) χ = 10; b) χ = 20.
DETAILED DESCRIPTION
• The present invention relates to a novel anchorage system S, as shown in Fig. 1, encompassing:
1. 1. Spiral friction support;
2. 2. A pair of plates to fix the support 1 and connect the system S to permanent support at point 6;
3. 3. Bolts;
4. 4. Internal clamps to pre-fix the flexible strip 5 while activating the frictional force;
5. 5. The flexible strip;
6. 6. A hole for fixing; remarkably, the hole aligns with the tensile load entrance vector P and ensures system S rotation by following the dynamic loading effects;
7. 7. A possible layered structure of the spiral support 1. The various materials, e.g., plastic, steel, and concrete, and a combination thereof in different layers 7 are applicable for constructing the spiral support 1;
8. 8. A slope of the spiral surface of the support 1 in contact with the flexible strip 5;
9. 9. The zero-curvature entrance point of the flexible strip 5 to the anchorage system S;
10. 10. The axial load P application line.
• The anchorage system of the present invention is characterized in that it efficiently transmits tensile loads onto flexible ribbon strips (5), thereby revolutionizing the manipulation of tension members constructed from fiber-reinforced plastic (FRP) flat strips. The invention presents a new anchorage system and outlines a method for applying force to these tension members. The invention's core is a two-part anchorage system S that interacts effectively with flexible strips 5. The first part features a carefully contoured spiral friction support 1 with a curved surface accommodating the flexible strip 5. This curvature has a unique characteristic: the curvature value is zero when the flexible strip 5 initially contacts the support 1. This design establishes an innovative interaction between the anchorage system S and the flexible strip 5, enhancing its functional efficiency.
• The gripping process relies on frictional forces generated between the tensioned flexible strip 5 and the curved surface of the support 1. This interaction results in micro-slippage across the curved surface, enabling the effective transmission of the applied load to the flexible strip 5. The device's architecture leverages friction to effectively transfer tensioning forces from the flexible strip 5, creating an efficient load transmission mechanism.
• The second part of the device complements the first by securely fastening the end of the flexible strip 5 emerging from a defined exit point. The second part envelops the first one, providing a seamless integration that improves the gripping process and stabilizes the flexible strip 5 during tension application.
• Practicality is a crucial consideration in this invention, evident in the straightforward installation process. Two side plates 2 facilitate load transfer from a testing machine's power drive to the support 1. Bolts 3 fix the disk, ensuring stability during operation. Internal clamps 4 enhance the gripping process by clamping the inner end of the flexible strip 5 before applying tension force P, adding control to the mechanism. A strategically positioned hole 6 is an anchor point acting as a hinge aligning the contact surface of the support 1 at the entrance point 9 with the load P application line 10 because of dynamic loading effects and enhancing reliability in practical applications.
• Beyond its components, the invention's significance lies in its ability to manipulate tension flexural strips 5. The reliance on frictional forces and careful design result in the anchorage system S that addresses challenges in tension member manipulation.
• Analytical model of the anchorage system S. The analytical model constitutes the simplified assumptions of constant friction coefficient, absolute rigidity of the support disc 1, and inextensible material of the flexural strip 5. Figure 2 sketches the distribution of the corresponding load components. In this scheme, point O determines the center of the planar curve; point O₁ defines the circle of curvature drawn at point L, in which radius ρ describes the curvature radius at L.
• The rate of the increase of the angle dθ for the segment length ds determines the curvature at L (Fig. 2): $$\kappa =\frac{1}{\rho }=\frac{\mathit{d\theta }}{\mathit{ds}}.$$

  
• The following equations define the equilibrium conditions of the elementary arc segment ds in the projections on the τ and n axes (Fig. 2): $$r:d\mathrm{<figure-callout\; id="2"\; label="P\; cos\; ds"\; filenames="imgf0001.png"\; state="\{\{state\}\}">P</figure-callout>}\mathit{cos}\frac{\mathit{ds}}{}\frac{\mathit{}}{2\rho }-d{\mathrm{F}}_f=0,d{\mathrm{F}}_f=fd\mathrm{N}$$

  

  $$n:\left(2\mathrm{P}+d\mathrm{<figure-callout\; id="2"\; label="P\; sin\; ds"\; filenames="imgf0001.png"\; state="\{\{state\}\}">P</figure-callout>}\right)\sin \frac{\mathit{ds}}{}\frac{\mathit{}}{2\rho }-d\mathrm{N=0}$$

  

  where P, N, and F _f the axial, tangential, and frictional forces acting on the arc segment ds, respectively. The solution of the above equation system defines the traction coefficient, i.e., the ratio between the axial load upcoming to and incoming from the arc segment: $$\chi =\frac{{\mathrm{P}}_{\mathit{in}}}{{\mathrm{P}}_{\mathit{out}}}=\exp \left[{\displaystyle \int {\displaystyle {\int }_{{\phi }_1}^{{\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_2}\left(\frac{1}{\rho }\right)\mathit{ds}}}\right].$$

  
• The following equations determine the differential solution of the segment length ds and the radius ρ in the polar coordinate system O _L = r(ϕ) and the corresponding traction ratio: $$\mathit{ds}=\sqrt{{\left(\mathit{<figure-callout\; id="2"\; label="dr"\; filenames="imgf0001.png"\; state="\{\{state\}\}">dr</figure-callout>}\right)}^2+{\left(\mathit{<figure-callout\; id="2"\; label="rd\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">rd\phi </figure-callout>}\right)}^2};$$

  

  $$\mathit{d\phi }=\sqrt{{\left(\mathit{<figure-callout\; id="2"\; label="dr"\; filenames="imgf0001.png"\; state="\{\{state\}\}">dr</figure-callout>}\right)}^2+r^{{\prime }^2}};$$

  

  $$\rho =\frac{{\left[{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0001.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+{\left(r\prime \right)}^2\right]}^{\frac{2}{3}}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0001.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+2{\left(r\prime \right)}^2-{\mathit{rr}}^{ʺ}};$$

  

  $$\chi =\exp \left\{\mathrm{<figure-callout\; id="2"\; label="f\; \phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">f</figure-callout>}\left[{\phi }_{}\right]\left[{}_2-{\phi }_1+{\displaystyle {\int }_{{\phi }_1}^{{\phi }_2}\frac{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="imgf0001.png"\; state="\{\{state\}\}">r</figure-callout>}}^2-\mathit{<figure-callout\; id="2"\; label="rr\; \prime \; r"\; filenames="imgf0001.png"\; state="\{\{state\}\}">rr</figure-callout>}\prime }{r^{}}\mathit{ds}}\right]\right\}.$$

  

  where r' and r'^' are the first and second derivatives of the polar radius, respectively.
• The following equations describe a spiral in polar coordinates, its radius, and the corresponding traction ratio: $$r={\mathit{A\phi }}^n;$$

  

  $$\rho ={\mathit{A\phi }}^{\left|n\right|-1}\frac{{\left[{\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\phi </figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0001.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\right]}^{\frac{2}{3}}}{{\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\phi </figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="imgf0001.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+n};$$

  

  $$\chi =\exp \left\{\mathrm{<figure-callout\; id="2"\; label="f\; \phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">f</figure-callout>}\left[{\phi }_{}\right]\left[{}_2-{\phi }_1+\left|{\tan }^{-1}\frac{{\phi }_2}{n}-{\tan }^{-1}\frac{{\phi }_1}{n}\right|\right]\right\}.$$

  
• The given equation permits us to define the traction coefficient, i.e., the ratio between the axial load upcoming to and incoming from the curved surface on the first part of the anchorage system S.
• Optimization model. For the rectangular cross-section of the flexible strip, the following condition determines the ultimate resistance of the CFRP strip: $$\begin{array}{cc}\frac{\mathrm{P}\left(\phi \right)}{t\cdot b}+E\cdot \frac{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png"\; state="\{\{state\}\}">t</figure-callout>}}{2\cdot r\left(\phi \right)}\le f_u,& \phi \in \left[{\phi }_1;{\mathrm{<figure-callout\; id="2"\; label="\phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_2\right]\end{array}.$$

  
• Following Eqn. 12, the bending effect increases with increasing the strip thickness t and elasticity modulus E of the flexible strip 5; b is the width of the strip 5.
  The load-bearing capacity R of the internal clamps 4 determines the required traction ratio: $$\chi =\mathrm{P}/\mathrm{R}.$$

  
• The following equation accounts for the bending effect, describing the inner radius r ₁ under the assumption of P(ϕ) = R: $$r\left(\phi \right)=10\cdot \Vert \gamma \cdot \mathrm{<figure-callout\; id="2"\; label="E\; t"\; filenames="imgf0001.png"\; state="\{\{state\}\}">E</figure-callout>}\frac{t}{}\frac{}{2\cdot \left(f_u-\raisebox{1ex}{$\mathrm{P}\left(\phi \right)$}\!\left/ \!\raisebox{-1ex}{$t\cdot b$}\right.\right)}\cdot 0.1+0.5\Vert ,$$

  

  where γ is the safety factor; the norm ∥x∥ defines the rounding of the operand x to the nearest integer number. The above expression ensures rounding the required radius up to 10 mm. The internal angle ϕ ₁ depends on the assumed shape of the spiral surface of the support 1. Under the assumption of the Modified Archimedean spiral, the following equation expresses the internal angle: $${\phi }_1={\left(r_1/C\right)}^{1/n},$$

  

  where C is a coefficient (= 50 / π); n is the exponent, determining the optimization object. The following formula defines the iterative solution process because of the emergence of the unknown angle ϕ ₂ in both equation sides: $${\phi }_2={\tan }^{-1}\frac{{\phi }_1}{n}-{\tan }^{-1}\frac{{\phi }_2}{n}+\frac{\ln \chi }{f}+{\phi }_1,$$

  

  where f is the friction coefficient.
• Eqn. 14 defines the required outer radius r ₂ by assuming P(ϕ) = P, i.e., the design axial load. The following expression finalizes the optimization process, determining the exponent of the power function in Eqn. 9: $$n=\ln \left(\frac{r_2}{C}\right)/\mathrm{<figure-callout\; id="2"\; label="ln\; \phi "\; filenames="imgf0001.png"\; state="\{\{state\}\}">ln</figure-callout>}{\phi }_{}{}_2.$$

  
• Figs. 3 and 4 illustrate the application examples of the proposed anchorage system S for a pedestrian stress-ribbon bridge prototype and 3D-printed grips for materials characterization of flexible strip.

Claims (5)

1. The anchorage system (S), characterized by comprising:

   - a spiral friction support (1) with a curved surface to accommodate the flexible strip (5) and ensure a compact distribution of the flexible strip (5);

   - two plates (2) assembled by using connecting bolts (3) to prevent the out-of-the-plane movements of the flexible strip (5) and ensure the sufficient rigidity of the spiral support (1);

   - internal clamps (4) to pre-fix the flexible strip (5) to activate the frictional forces;

   - a hole (6) acting as an anchor point to ensure system (S) rotation by following the dynamic loading effects.
2. The anchorage system (S) according to claim 1, characterized in that the spiral support (1) comprises a layered structure (7) consisting of various materials, e.g., plastic, steel, concrete, or a combination thereof.
3. The anchorage system (S) according to claim 2, characterized in that the contact surface's frictional characteristics can be improved by appropriately selecting the layers (7) of the spiral support (1) and milling the contact surface with the flexible strip (5) to rehabilitate the anchor.
4. The anchorage system (S) according to claim 4, characterized in that the frictional forces and the pre-defined traction ratio χ, i.e., the ratio between the axial load upcoming to and incoming from the flexible strip (5), determines the length of the contact surface of the support (1) with the flexible strip (5).
5. A method to anchor flexible ribbon strips (5), characterized by fixing the flexible strip (5), using steadily increasing frictional forces along the contact between the flexible strip (5) and spiral support (1).

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