AN ABSTRACT OF THE THESIS OF Saurav Shrestha, for the Masters of Science degree in CIVIL ENGINEERING, presented on November 22, 2016, at Southern Illinois University Carbondale. TITLE: VERIFICATION OF SHEAR LAG IN LONGITUDINALLY WELDED TENSION MEMBERS. MAJOR PROFESSOR: Dr. J. Kent Hsiao, Ph.D., P.E. (CA), S.E. (UT) Tension members are used broadly as bracing members in buildings and truss. When double channels or double tees are welded to a gusset plate, stresses are distributed non-uniformly in connected members since only a part of its cross-section is connected. Shear lag factor describes this phenomenon. The main objective of this study is to verify shear lag factor of tension steel members with welded connections using the finite element computer analysis and the current design Specification for Structural Steel Buildings (AISC 2010). The provision for calculating shear lag factor, U, is given by AISC Specification as 1-x ̅/L for angles, tees, channels and wide flange tension members. Weld size and length of the weld are the main parameters studied here. The current AISC design provision over-estimates the design tensile strength of double channel shapes. While, for WT Shapes it under-estimates one. The increase in weld size and decrease in weld length shows slight change in shear lag factor. Comparison is also made with the equation proposed by Fortney and Thornton (2012). The equation under-estimates the design tensile strength of both sections.

<p>U radu su izvedene diferencijalne jednačine tankozidnog kompozitnog štapa proizvoljnog poprečnog preseka, primenom principa virtualnih pomeranja, a polazeći od funkcije deplanacije koju je predložio A. Prokić, za tankozidne štapove homogenog poprečnog preseka. Ona omogućava jedinstvenu analizu tankozidnih štapova otvorenog i zatvorenog poprečnog preseka, pretpostavka o zanemarenju klizanja u srednjoj površi štapa nije<br />neophodna, pa se smičući naponi određuju direktno iz odgovarajućih deformacija. Raspodela normalnih napona nije više određena sektorskom koordinatom već parametrima pomeranja čvornih tačaka, i u opštem slučaju je promenljiva od preseka do preseka, što omogućuje registrovanje i analizu shear lag uticaja, koji se klasičnom teorijom tankozidnih nosača ne može opisati. Kao što je poznato, shear lag uticaj predstavlja neravnomernu<br />raspodelu normalnih napona u pojasevima, s tim što se maksimalna vrednost javlja na mestu spoja pojasa sa rebrima, i u opštem slučaju je veća od vrednosti napona koja se dobija klasičnom teorijom savijanja štapova zasnovanoj na Bernoullijevoj hipotezi. To je posebno izraženo kod štapova napregnutih na savijanje kod kojih dolazi do značajne deplanacije poprečnog preseka.<br />Dobijeni sistem diferencijalnih jednačina se ne može rešiti u zatvorenom obliku te se pristupilo numeričkoj metodi, odnosno primeni metode konačnih elemenata. Definisana su dva tipa elementa sa različitim polaznim pretpostavkama. Prvi tip elementa zasnovan je na teoriji Timoshenka, odnosno uticaj transverzalnih sila na deformaciju se uzima u obzir. Drugi tip elementa zanemaruje uticaj transverzalnih sila na deformaciju, odnosno usvaja se pretpostavka da poprečni preseci i nakon deformacije ostaju ravni i upravni<br />na srednju liniju štapa. Kao dokaz tačnosti prethodno izvedenih teorijskih razmatranja urađen je niz primera pomoću programa napisanog u programskom jeziku C.</p> / <p>Differential equations of thin-walled composite beams of arbitrary cross section were<br />derived, using the principle of virtual displacements and starting from function of deplanation suggested by A. Prokic, for thin-walled beams of homogeneous cross section. It enables unique analysis thin-walled beams of open and closed cross section, assumption of neglecting shear strain in the middle surface is not necessary and shear stresses can be calculated directly from the strains. Distribution of longitudinal stresses is not defined by warping function, but parameters of longitudinal displacement, and in general case it is variable of section to section, that enables registering and analysis of shear lag, which classical theory of thin-walled beams is unable to reflect. As it is known, shear lag effect presents a non-uniform distribution of normal stresses in the flanges, maximal values are on the connection of flange and web, in general case it is larger from the value of stress obtained by classical theory of beams based on the Bernoulli hypothesis. It is especially<br />expressed at beams subjected to bending where deplanation of cross section is significant. Derived system of differential equations can not be solved in closed form solution and it was accessed to numerical method, respectively on the finite element method. Two types of element with different starting settings were defined. First type of element is based on the theory of Timoshenko, apropos the influence of transversal forces on deformation were taken into account. The second type of element neglects influence of transversal forces on deformation, concerning assumption that cross section remain plane and orthogonal on the middle line is adopted. A number of numerical examples are calculated by a computer program written in program language C as a proof of accuracy of previously derived theoretical reviews.</p>

Com a crescente utilização de vigas mistas de aço e concreto em obras civis e devido à insuficiência de estudos relativos ao seu comportamento estrutural, investigações aprofundadas são necessárias para suprir as carências e aperfeiçoar o tema. Um fenômeno familiar na literatura de estruturas mistas é a distribuição não uniforme de tensões ao longo da largura da laje de concreto, denominado shear lag na literatura inglesa. Na análise e projeto de estruturas compostas, deflexões, tensões e resistência são tipicamente obtidas utilizando-se o conceito de largura efetiva, na qual o efeito shear lag é contabilizado indiretamente, substituindo a largura real da laje, por uma largura apropriadamente reduzida. Sem dispor de análises numéricas exatas para o dimensionamento prático, é necessário que códigos normativos forneçam métodos simplificados para a avaliação da largura efetiva minimizando perdas de precisão. Diante disso, no presente trabalho, procedimentos numéricos para a avaliação da largura efetiva, encontrados na literatura técnica, foram estudados e implementados ao modelo matemático em elementos finitos disponível no CEMACOM/PPGEC/UFRGS, capaz de representar com confiabilidade estruturas mistas. Comprovando-se a eficácia do modelo numérico em captar o efeito do shear lag, a resposta de uma viga mista biengastada, representando um vão intermediário de uma ponte contínua, submetida a um carregamento em longo prazo, e considerando-se os fenômenos reológicos do concreto de fluência e retração, além do comportamento não-linear devido a fissuração, é obtida e comparada à fórmulas estipuladas nas principais normas de projeto e em metodologias desenvolvidas por pesquisadores. Falhas potenciais nos códigos de projeto atuais foram evidenciadas, necessitando-se de adicionais estudos paramétricos experimentais e numéricos para a comprovação dos resultados. / With the increasing use of steel-concrete composite beams in bridges and buildings more investigations related to this topic are necessary to fill the needs and improve the subject. A familiar phenomenon in the literature of composite structures is the non-uniform distribution of stresses along the width of the concrete slab, called shear lag. In the analysis and design of composite beams, deflections, stresses, and strengths are typically obtained by utilizing the concept of effective width, in which shear lag effects are accounted for indirectly, by replacing the actual slab width by an appropriately reduced width. Without having exact numerical analysis for design, it is necessary that the design codes provide simplified methods for evaluating this effective width, minimizing losses of accuracy. In this work, numerical procedures for the evaluation of effective width, found in the specialized literature, were studied and implemented in the mathematical finite element model available in CEMACOM/PPGEC/UFRGS. This computational code is capable of representing the behavior of steel-concrete composite beams and is capable of capturing the shear lag effect. The response of a single span composite beam with fixed ends, representing an intermediate span of a continuous girder bridge, subject to long-term loading, and considering both rheological phenomena of concrete, such as creep and shrinkage, besides the non-linear behavior due to cracking, is obtained and compared to the stipulated formulas in the main code provisions and in the developed methodologies by some researchers. Potential failures in the current design codes were evidenced, requiring additional experimental and numerical parametric studies to prove the results.

Tese de mestrado integrado. Engenharia Civil (Área de Especialização de Estruturas). Faculdade de Engenharia. Universidade do Porto. 2012

Com a crescente utilização de vigas mistas de aço e concreto em obras civis e devido à insuficiência de estudos relativos ao seu comportamento estrutural, investigações aprofundadas são necessárias para suprir as carências e aperfeiçoar o tema. Um fenômeno familiar na literatura de estruturas mistas é a distribuição não uniforme de tensões ao longo da largura da laje de concreto, denominado shear lag na literatura inglesa. Na análise e projeto de estruturas compostas, deflexões, tensões e resistência são tipicamente obtidas utilizando-se o conceito de largura efetiva, na qual o efeito shear lag é contabilizado indiretamente, substituindo a largura real da laje, por uma largura apropriadamente reduzida. Sem dispor de análises numéricas exatas para o dimensionamento prático, é necessário que códigos normativos forneçam métodos simplificados para a avaliação da largura efetiva minimizando perdas de precisão. Diante disso, no presente trabalho, procedimentos numéricos para a avaliação da largura efetiva, encontrados na literatura técnica, foram estudados e implementados ao modelo matemático em elementos finitos disponível no CEMACOM/PPGEC/UFRGS, capaz de representar com confiabilidade estruturas mistas. Comprovando-se a eficácia do modelo numérico em captar o efeito do shear lag, a resposta de uma viga mista biengastada, representando um vão intermediário de uma ponte contínua, submetida a um carregamento em longo prazo, e considerando-se os fenômenos reológicos do concreto de fluência e retração, além do comportamento não-linear devido a fissuração, é obtida e comparada à fórmulas estipuladas nas principais normas de projeto e em metodologias desenvolvidas por pesquisadores. Falhas potenciais nos códigos de projeto atuais foram evidenciadas, necessitando-se de adicionais estudos paramétricos experimentais e numéricos para a comprovação dos resultados. / With the increasing use of steel-concrete composite beams in bridges and buildings more investigations related to this topic are necessary to fill the needs and improve the subject. A familiar phenomenon in the literature of composite structures is the non-uniform distribution of stresses along the width of the concrete slab, called shear lag. In the analysis and design of composite beams, deflections, stresses, and strengths are typically obtained by utilizing the concept of effective width, in which shear lag effects are accounted for indirectly, by replacing the actual slab width by an appropriately reduced width. Without having exact numerical analysis for design, it is necessary that the design codes provide simplified methods for evaluating this effective width, minimizing losses of accuracy. In this work, numerical procedures for the evaluation of effective width, found in the specialized literature, were studied and implemented in the mathematical finite element model available in CEMACOM/PPGEC/UFRGS. This computational code is capable of representing the behavior of steel-concrete composite beams and is capable of capturing the shear lag effect. The response of a single span composite beam with fixed ends, representing an intermediate span of a continuous girder bridge, subject to long-term loading, and considering both rheological phenomena of concrete, such as creep and shrinkage, besides the non-linear behavior due to cracking, is obtained and compared to the stipulated formulas in the main code provisions and in the developed methodologies by some researchers. Potential failures in the current design codes were evidenced, requiring additional experimental and numerical parametric studies to prove the results.

Com a crescente utilização de vigas mistas de aço e concreto em obras civis e devido à insuficiência de estudos relativos ao seu comportamento estrutural, investigações aprofundadas são necessárias para suprir as carências e aperfeiçoar o tema. Um fenômeno familiar na literatura de estruturas mistas é a distribuição não uniforme de tensões ao longo da largura da laje de concreto, denominado shear lag na literatura inglesa. Na análise e projeto de estruturas compostas, deflexões, tensões e resistência são tipicamente obtidas utilizando-se o conceito de largura efetiva, na qual o efeito shear lag é contabilizado indiretamente, substituindo a largura real da laje, por uma largura apropriadamente reduzida. Sem dispor de análises numéricas exatas para o dimensionamento prático, é necessário que códigos normativos forneçam métodos simplificados para a avaliação da largura efetiva minimizando perdas de precisão. Diante disso, no presente trabalho, procedimentos numéricos para a avaliação da largura efetiva, encontrados na literatura técnica, foram estudados e implementados ao modelo matemático em elementos finitos disponível no CEMACOM/PPGEC/UFRGS, capaz de representar com confiabilidade estruturas mistas. Comprovando-se a eficácia do modelo numérico em captar o efeito do shear lag, a resposta de uma viga mista biengastada, representando um vão intermediário de uma ponte contínua, submetida a um carregamento em longo prazo, e considerando-se os fenômenos reológicos do concreto de fluência e retração, além do comportamento não-linear devido a fissuração, é obtida e comparada à fórmulas estipuladas nas principais normas de projeto e em metodologias desenvolvidas por pesquisadores. Falhas potenciais nos códigos de projeto atuais foram evidenciadas, necessitando-se de adicionais estudos paramétricos experimentais e numéricos para a comprovação dos resultados. / With the increasing use of steel-concrete composite beams in bridges and buildings more investigations related to this topic are necessary to fill the needs and improve the subject. A familiar phenomenon in the literature of composite structures is the non-uniform distribution of stresses along the width of the concrete slab, called shear lag. In the analysis and design of composite beams, deflections, stresses, and strengths are typically obtained by utilizing the concept of effective width, in which shear lag effects are accounted for indirectly, by replacing the actual slab width by an appropriately reduced width. Without having exact numerical analysis for design, it is necessary that the design codes provide simplified methods for evaluating this effective width, minimizing losses of accuracy. In this work, numerical procedures for the evaluation of effective width, found in the specialized literature, were studied and implemented in the mathematical finite element model available in CEMACOM/PPGEC/UFRGS. This computational code is capable of representing the behavior of steel-concrete composite beams and is capable of capturing the shear lag effect. The response of a single span composite beam with fixed ends, representing an intermediate span of a continuous girder bridge, subject to long-term loading, and considering both rheological phenomena of concrete, such as creep and shrinkage, besides the non-linear behavior due to cracking, is obtained and compared to the stipulated formulas in the main code provisions and in the developed methodologies by some researchers. Potential failures in the current design codes were evidenced, requiring additional experimental and numerical parametric studies to prove the results.

Integral abutment bridges are very common for short span bridges in the United State due to their less construction and maintenance cost and generally good performance. This thesis studies the first integral abutment bridge using Folded Plate Girder (FPG) Bridge System. The bridge is instrumented with a variety of gauges to capture the behavior of the bridge, and a total of two year and one month [11/2011~12/2013] of data are collected and long-term data monitoring is performed. Live load test and long term temperature effect on the bridge are studied using finite element modeling and compared with actual field data. Girder strain/stress at mid-span and quarter-span and abutment rotations were investigated. From the result, first the bridge was found to show good performance. Shear lag effect was found to be happening at the bottom flange-to-web junction of the steel girder when subjected to concentrated loading. Thermal gradient was found to be significant on the girder strain and abutment rotations.

No description available.

No description available.

The effect of thermal-cycling-induced microcracking in fiber-reinforced polymer matrix composites is studied. Specific attention is focused on microcrack density as a function of the number of thermal cycles, and the effect of microcracking on the dimensional stability of composite materials. Changes in laminate coefficient of thermal expansion (CTE) and laminate stiffness are of primary concern. Included in the study are materials containing four different Thornel fiber types: a PAN-based T50 fiber and three pitch-based fibers, P55, P75, and P120. The fiber stiffnesses range from 55 Msi to 120 Msi. The fiber CTE's range from -0.50x10⁻⁶/°F to -0.80x10⁻⁶/°F. Also included are three matrix types: Fiberite's 934 epoxy, Amoco's ERL1962 toughened epoxy, and YLA's RS3 cyanate ester. The lamination sequences of the materials considered include a cross-ply configuration, [0/90]2s, and two quasi-isotropic configurations, [0/+45/-45/90]s and [0/+45/90/-45]s. The layer thickness of the materials range from a nominal 0.001 in. to 0.005 in. In addition to the variety of materials considered, three different thermal cycling temperature ranges are considered. These temperature ranges are ±250°F, ±150°F, and ±50°F. The combination of these material and geometric parameters and temperature ranges, combined with thermal cycling to thousands of cycles, makes this one of the most comprehensive studies of thermal-cycling-induced microcracking to date. Experimental comparisons are presented by examining the effect of layer thickness, fiber type, matrix type, and thermal cycling temperature range on microcracking and its influence on the laminates. Results regarding layer thickness effects indicate that thin-layer laminates microcrack more severely than identical laminates with thick layers. For some specimens in this study, the number of microcracks in thin-layer specimens exceeds that in thick-layer specimens by more than a factor of two. Despite the higher number of microcracks in the thin-layer specimens, small changes in CTE after thousands of cycles indicate that the thin-layer specimens are relatively unaffected by the presence of these cracks compared to the thick-layer specimens. Results regarding fiber type indicate that the number of microcracks and the change in CTE after thousands of cycles in the specimens containing PAN-based fibers are less than in the specimens containing comparable stiffness pitch-based fibers. Results for specimens containing the different pitch-based fibers indicate that after thousands of cycles, the number of microcracks in the specimens does not depend on the modulus or CTE of the fiber. The change in laminate CTE does, however, depend highly on the stiffness and CTE of the fiber. Fibers with higher stiffness and more negative CTE exhibit the lowest change in laminate CTE as a result of thermal cycling. The overall CTE of these specimens is, however, more negative as a result of the more negative CTE of the fiber. Results regarding matrix type based on the ±250°F temperature range indicate that the RS3 cyanate ester resin system exhibits the greatest resistance to microcracking and the least change in CTE, particularly for cycles numbering 3000 and less. Extrapolations to higher numbers of cycles indicate, however, that the margin of increased performance is expected to decrease with additional thermal cycling. Results regarding thermal cycling temperature range depend on the matrix type considered and the layer thickness of the specimens. For the ERL1962 resin system, microcrack saturation is expected to occur in all specimens, regardless of the temperature range to which the specimens are exposed. By contrast, the RS3 resin system demonstrates a threshold effect such that cycled to less severe temperature ranges, microcracking does not occur. For the RS3 specimens with 0.005 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between between ±150°F or ±50°F. For the RS3 specimens with 0.002 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between ±50°F.. Results regarding laminate stiffness indicate negligible change in laminate stiffness due to thermal cycling for the materials and geometries considered in this investigation. The study includes X-ray examination of the specimens, showing that cracks observed at the edge of the specimens penetrate the entire width of the specimen. Glass transition temperatures of the specimens are measured, showing that resin chemistry is not altered as a result of thermal cycling. Results are also presented based on a one-dimensional shear lag analysis developed in the literature. The analysis requires material property information that is difficult to obtain experimentally. Using limited data from the present investigation, material properties associated with the analysis are modified to obtain reasonable agreement with measured microcrack densities. Based on these derived material properties, the analysis generally overpredicts the change in laminate CTE. Predicted changes in laminate stiffness show reasonable correlation with experimentally measured values. / Ph. D.