Digitized by Kansas Correctional Industries

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For a structure to remain serviceable, crack widths must be small enough to be acceptable from an aesthetic point of view, small enough to avoid waterproofing problems and small enough to prevent the ingress of water that may lead to corrosion of the reinforcement. Crack control is therefore an important aspect of the design of reinforced concrete structures at the serviceability limit state. Despite its importance, code methods for crack control have been developed, in the main, from laboratory observations of the instantaneous behaviour of reinforced concrete members under load and fail to account adequately for the time-dependent development of cracking. In this study numerical models have been developed to investigate timedependent cracking of reinforced concrete structures. Two approaches were adopted to simulate cracking in reinforced concrete members. The first approach is the distributed cracking approach. In this approach, steel reinforcement is smeared through the concrete elements and bond-slip between steel and concrete is accounted for indirectly by including the tension stiffening effect. The second approach is the localized cracking approach, in which concrete fracture models are used in conjunction with bond-slip interface elements to model stress transfer between concrete and steel. Creep of concrete has been incorporated into the models by adopting the principle of superposition and the time-dependent development of shrinkage strain of concrete is modelled using an approximating function. Both creep and shrinkage were treated as inelastic pre-strains and applied to the discretized structure as equivalent nodal forces. Apart from material non-linearity, non-linearity arising from large deformation was also accounted for using the updated Lagrangian formulation. The numerical models were used to simulate a series of laboratory tests for verification purposes. The models were assessed critically by comparing the numerical results with the test data and the numerical results are shown to have good correlations with the test results. In addition, a comparison was undertaken among the numerical models and the pros and cons of each model were evaluated. A series of controlled parametric numerical experiments was devised and carried out using one of the numerical models. Various parameters were identified and investigated in the parametric study. The effects of the parameters were thoroughly examined and the interactions between the parameters were discussed in detail.

Due to the relatively low tensile strength of concrete, cracks are inevitable in reinforced concrete structures. Therefore, studying the cracking behaviour of reinforced concrete elements and controlling the width of cracks are necessary objectives both in research and in design. The introduction of higher strength reinforcing steel has exacerbated the problem of crack control. Using higher strength steel, means less steel is required for a given structure to satisfy the strength requirements. The stiffness after cracking is reduced and wider crack widths will occur under normal service loads. Unserviceable cracking may encourage corrosion in the reinforcement and surface deterioration, and may lead to long term problems with durability. Indeed excessive cracking results in a huge annual cost to the construction industry because it is the most common cause of damage in concrete structures. In this study cracking caused by both shrinkage and external loads in reinforced concrete members is examined experimentally and analytically. The mechanisms associated with cracking and the factors affecting the time-varying width and spacing of both direct tension cracks due to restrained shrinkage deformation and flexural cracks due to the combined effects of constant sustained service loads and shrinkage are examined. Laboratory tests on eight fully restrained slab specimens were conducted for up to 150 days to measure the effects of drying shrinkage on the time-dependent development of direct tension cracks due to restrained deformation. The effect of varying the quantity, diameter, and spacing of reinforcing steel bars was studied. In addition, an analytical model previously developed without experimental verification by Gilbert (1992) to study shrinkage cracking was modified and recalibrated. A second series of tests on twenty four prismatic, singly reinforced concrete beams and slabs subjected to monotonically increasing loads or to constant sustained service loads for up to 400 days, were also conducted. The effects of steel area, steel stress, bar diameter, bar spacing, concrete cover and shrinkage were measured and quantified. An analytical model is presented to simulate instantaneous and time-dependent flexural cracking. The tension chord model (Marti et al, 1998) is modified and used in the proposed model to simulate the tension zone of a flexural member and the time-dependent effects of creep and shrinkage are included. The analytical predictions of crack width and crack spacing are in reasonably good agreement with the experimental observations.

Thesis (M.S.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains x, 131 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 114-117).

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It has been demonstrated that transverse reinforcement not only provides the strength and stiffness for reinforced concrete (RC) members through direct resistance to external force demands, but also helps confine the inner core concrete. The confinement effect can lead to improved overall structural performance by delaying the onset of concrete fracture and allowing more inelastic energy dissipation through an increase in both strength and deformability of RC members. The objective of this research was to evaluate the effect of confinement due to the transverse reinforcement on enhancing the shear performance of RC members. A new constitutive model of RC members was proposed by extending the Modified Compression Field Theory (MCFT) to incorporate the effect of confinement due to transverse reinforcement by adjusting the peak stress and peak strain of confined concrete in compression. The peak stress of confined concrete was determined from the five-parameter failure surface for concrete developed by Willam and Warnke (1974). The peak strain adjustment was carried out using a relationship proposed by Mander et al. (1988). The proposed analytical model was compared with results from an experimental program on sixteen RC bent caps with varied longitudinal and transverse reinforcement details. Two-dimensional Finite Element Modeling (FEM) using the proposed constitutive model was conducted to numerically simulate the RC bent cap response. Results showed that the proposed analytical model yielded good results on the prediction of the strength but significantly overestimated the post-cracking stiffness of the RC bent cap specimens. The results also indicated that the confinement effect led to enhanced overall performance by increasing both the strength and deformability of the RC bent caps. Two potential causes of the discrepancy in the underestimation of the RC bent cap deformations, namely the effects of concrete shrinkage and interfacial bond-slip between the concrete and main flexural reinforcement in the bent caps, were discussed. Parametric studies showed that the tension-stiffening in the proposed constitutive models to implicitly take into account the bond-slip between the concrete and main flexural reinforcement was the major cause of the overestimation of the post-cracking stiffness of RC bent caps. The explicit use of bond-link elements with modified local bond stress-slip laws to simulate the slip between the concrete and main flexural reinforcement led to good predictions of both strength and deformation.

Gravity load designed (GLD) reinforced concrete (RC) buildings represent a common type of construction in the Mid-America Region. These buildings have limited lateral resistance and are susceptible to story mechanisms during earthquake loading. Fragility estimates are developed to assess the seismic vulnerability of GLD RC buildings in the Mid-America Region. Fragility is defined as the conditional probability of reaching or exceeding a performance level for a given earthquake intensity measure. Five sample buildings of various story heights (1, 2, 3, 6, and 10 stories) are used to represent generic RC frame buildings of 1 to 10 stories tall. A Bayesian methodology is used to develop probabilistic demand models to predict the maximum inter story drift given the spectral acceleration at the fundamental period of the building. The unknown parameters of the demand models are estimated using the simulated response data obtained from nonlinear time history analyses of the structural models for a suite of synthetic ground motions, developed for Memphis, Tennessee. Seismic structural capacity values are selected corresponding to the performance levels or damage states as specified in FEMA-356 and as computed by nonlinear pushover analyses. For the sample buildings, fragility estimates are developed using the predicted drift demands and structural capacity values. Confidence bounds are developed to represent the epistemic uncertainty inherent in the fragility estimates. In addition, bivariate fragility estimates, formulated as a function of spectral acceleration and the fundamental building period, are developed from the fragility estimates of the individual buildings. The bivariate fragilities can be used to quantify the seismic vulnerability of GLD RC frame buildings of 1 to 10 stories. Using the Bayesian approach, a framework is developed to update the analytical fragility estimates using observed damage data or experimental test data. As an illustration of the updating framework, the analytical bivariate fragility estimates for the sample buildings in the Mid-America Region are updated using the damage data obtained from 1994 Northridge, California earthquake. Furthermore, to investigate and demonstrate the increase in seismic performance of the GLD RC frame buildings, the columns of the 2 and 3 story buildings are retrofitted by column strengthening. Fragility estimates developed for the retrofitted buildings show the effectiveness of the retrofit technique by the improved seismic performance of GLD RC frame buildings.

Thesis (Ph. D.)--West Virginia University, 2009. / Title from document title page. Document formatted into pages; contains xii, 153 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 129-136).

Thesis (M.S. in civil engineering)--Washington State University, December 2009. / Title from PDF title page (viewed on Dec. 28, 2009). "Department of Civil and Environmental Engineering." Includes bibliographical references (p. 51).