# Browsing by Subject "Size effect"

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Item Behavior of slender beams without stirrups: effects of load distribution and member depth(2015-12) Klein, Joseph Robert; Bayrak, Oguzhan, 1969-; Hrynyk, Trevor DShow more Though uniform loading is common in structures, the vast majority of all shear strength tests on slender reinforced concrete members without stirrups have been performed using concentrated loading. Furthermore, the uniform load tests that have been conducted typically involve members with smaller specimen depths (d) and larger reinforcement ratios (ρ) than are commonly used in practice. Previous studies usually agree that a noticeable increase in shear strength can be expected when a specimen is subjected to uniform loading as opposed to concentrated loading. Six shear tests were performed on four slender beams without stirrups at The University of Texas at Austin. Two of the specimens had approximately double the effective depth (d) as the other two. For a given depth, two concentrated load tests were carried out on either end of one specimen, and one uniform load test was carried out on the second specimen. Thus, four reinforced concrete beams were used to perform a total of four concentrated load tests and two uniform load tests, with the objective of determining the influence of load distribution as member depth (d) increases. To ensure that a direct comparison could be made between each load distribution, the ratio between maximum bending moment and maximum shear force was maintained for all tests. Additionally, to provide consistency with typical design practice, the reinforcement ratio (ρ) was selected to match that of a typical beam. The experimental results presented an influence of load distribution opposite to that of previous studies, with a range of increase in shear strength at first diagonal cracking of concentrated load tests of -16 to 50 percent, with an average increase of 18 percent, over uniform load tests. Additionally, the tests with smaller effective depths (d) saw a percent increase in shear strength of 31 to 68 percent, with an average increase of 50 percent, over tests with larger effective depths (d).Show more Item Design considerations based on size effects of anchored carbon fiber reinforced polymer (CFRP) systems(2016-05) Pudleiner, Douglas Karl; Ghannoum, Wassim M.; Jirsa, James oShow more Due to their high strength, limited architectural impact, and speed of installation, externally applied carbon fiber reinforced polymer (CFRP) materials are gaining use in infrastructure rehabilitation. To be effective, CFRP materials must be adequately anchored to develop their full capacity. Many anchorage materials and systems have been proposed for CFRP strips and laminates. CFRP spike anchors can develop the full tensile strength of CFRP strips and offer several advantages over other anchorage methods. Namely, they are easy to install, flexible, which allows them to overcome geometric complications, and resilient to environmental and corrosive factors. However, only a limited number of studies have been conducted on CFRP strips anchored using CFRP anchors. These studies identified clear size effects that influence the strength of CFRP anchors and strips. However, past research was conducted on relatively small anchor and strip systems that are on the low end of practical sizes for infrastructure retrofit and repair applications. The objectives of this study were to investigate size effects in anchored CFRP systems and provide design guidelines for CFRP anchors. Twelve tests were conducted on concrete beams reinforced in flexure with anchored CFRP strips up to 10-in. wide. The primary parameters investigated were: width of CFRP strip, number of layers of fabric in CFRP strips, number of anchors per strip width, ratio of anchor to strip cross-sections, anchor fan overlap length, and chamfer radius of the anchor hole. The full distribution of strains at the surface of the anchored CFRP strips was monitored using an optical measurement system. These measurements helped evaluate the effectiveness of various anchor details in distributing strains across strips. The experimental program confirmed the size effects uncovered in previous studies. CFRP anchors were able to fracture CFRP strips at stresses above the expected and design stresses provided by the manufacturer. However, the larger the CFRP strip area developed per anchor, the lower the stress at fracture of that strip. In addition, the anchor-hole chamfer radius was found to influence both anchor strength and the strain distribution in CFRP strips. Guidelines for designing and detailing CFRP anchors are given based on experimental results.Show more Item Solutions of Eshelby-Type Inclusion Problems and a Related Homogenization Method Based on a Simplified Strain Gradient Elasticity Theory(2011-08-08) Ma, HemeiShow more Eshelby-type inclusion problems of an infinite or a finite homogeneous isotropic elastic body containing an arbitrary-shape inclusion prescribed with an eigenstrain and an eigenstrain gradient are analytically solved. The solutions are based on a simplified strain gradient elasticity theory (SSGET) that includes one material length scale parameter in addition to two classical elastic constants. For the infinite-domain inclusion problem, the Eshelby tensor is derived in a general form by using the Green?s function in the SSGET. This Eshelby tensor captures the inclusion size effect and recovers the classical Eshelby tensor when the strain gradient effect is ignored. By applying the general form, the explicit expressions of the Eshelby tensor for the special cases of a spherical inclusion, a cylindrical inclusion of infinite length and an ellipsoidal inclusion are obtained. Also, the volume average of the new Eshelby tensor over the inclusion in each case is analytically derived. It is quantitatively shown that the new Eshelby tensor and its average can explain the inclusion size effect, unlike its counterpart based on classical elasticity. To solve the finite-domain inclusion problem, an extended Betti?s reciprocal theorem and an extended Somigliana?s identity based on the SSGET are proposed and utilized. The solution for the disturbed displacement field incorporates the boundary effect and recovers that for the infinite-domain inclusion problem. The problem of a spherical inclusion embedded concentrically in a finite spherical body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. It is demonstrated through numerical results that the newly obtained Eshelby tensor can capture the inclusion size and boundary effects, unlike existing ones. Finally, a homogenization method is developed to predict the effective elastic properties of a heterogeneous material using the SSGET. An effective elastic stiffness tensor is analytically derived for the heterogeneous material by applying the Mori-Tanaka and Eshelby?s equivalent inclusion methods. This tensor depends on the inhomogeneity size, unlike what is predicted by existing homogenization methods based on classical elasticity. Numerical results for a two-phase composite reveal that the composite becomes stiffer when the inhomogeneities get smaller.Show more Item Two higher order elasticity theories: their variational formulations and applications(2009-05-15) Park, Sung KyoonShow more Classical elasticity cannot be used to explain effects related to material microstructures due to its lack of a material length scale parameter. To mitigate this deficiency, higher order elasticity theories have been developed. Two simple higher order theories and their applications are studied in this research. One is a modified couple stress theory and the other is a simplified strain gradient theory, each of which contains only one material length scale parameter in addition to the classical elastic constants. Variational formulations are provided for these two theories by using the principle of minimum total potential energy. In both cases, the governing equations and complete boundary conditions are determined simultaneously for the first time. Also, the displacement form is explicitly derived for each theory for the first time. The modified couple stress theory is applied to solve a simple shear problem, to develop a new Bernoulli-Euler beam model, and to derive the constitutive relations for hexagonal honeycomb structures, while the simplified strain gradient theory is used to solve the pressurized thick-walled cylinder problem. All these models/solutions are obtained for the first time and supplement their counterparts in classical elasticity. Numerical results obtained from the newly developed models and derived solutions and their comparisons with their counterpart results in classical elasticity reveal that the higher order theory based models and solutions have the capacity to account for microstructural effects; their counterparts in classical elasticity do not have the same capability. Nevertheless, the former are shown to recover the latter if the microstructural effects are suppressed or ignored.Show more