Formulas, tables, and graphs for trapezoidal reinforced concrete beams

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The effect of earthquakes on reinforced concrete building design

The building under consideration was the Pasadena Furniture Building, on East Colorado St., Pasadena, California. It is a modern reinforced concrete building that may be classed as a warehouse of flat-slab construction.

The patents in the introduction of reinforced concrete in Spain: "Alhondiga de Bilbao" case study

Reinforced concrete structures are introduced in Spain mainly by French influence. This happens in the late nineteenth century, following the scheme operating through proprietary systems prevailing in Europe. Systems initially have poor scientific support reaching, even early twentieth century, an impediment to the development of concrete structures, due to the lack of knowledge shown, as well as due to a series of accidents. Therefore, from the end of the first decade of the past century are enacted a series of regulations in many countries, that will change the design and calculation of reinforced concrete structure. The knowledge of the environment of the patent systems, its beginnings and the circumstances of their application allow us to understand the constraints of the early concrete structures, as presented in the Bilbao wine store (1906).

Analysis of CFRP strap-strengthened reinforced concrete beams using the modified compression field theory (MCFT)

External, prestressed carbon fiber reinforced polymer (CFRP) straps can be used to enhance the shear strength of existing reinforced concrete beams. In order to effectively design a strengthening system, a rational predictive theory is required. The current work investigates the ability of the modified compression field theory (MCFT) to predict the behavior of rectangular strap strengthened beams where the discrete CFRP strap forces are approximated as a uniform vertical stress. An unstrengthened control beam and two strengthened beams were tested to verify the predictions. The experimental results suggest that the MCFT could predict the general response of a strengthened beam with a uniform strap spacing < 0.9d. However, whereas the strengthened beams failed in shear, the MCFT predicted flexural failures. It is proposed that a different compression softening model or the inclusion of a crack width limit is required to reflect the onset of shear failures in the strengthened beams.

Precracked reinforced concrete T-Beams repaired in shear with bonded carbon Fiber-Reinforced Polymer sheets

This study investigates the structural behavior of precracked reinforced concrete (RC) T-beams strengthened in shear with externally bonded carbon fiber-reinforced polymer (CFRP) sheets. It reports on seven tests on unstrengthened and strengthened RC T-beams, identifying the influence of load history, beam depth, and percentage of longitudinal steel reinforcement on the structural behavior. The experimental results indicate that the contributions of the external CFRP sheets to the shear force capacity can be significant and depend on most of the investigated variables. This study also investigates the accuracy of the prediction of the fiber-reinforced polymer (FRP) contribution in ACI 440.2R-08, UK Concrete Society TR55, and fib Bulletin 14 design guidelines for shear strengthening. A comparison of predicted values with experimental results indicates that the guidelines can overestimate the shear contribution of the externally bonded FRP system. © 2012, American Concrete Institute.

A flexural crack model for damage detection in reinforced concrete structures

The use of changes in vibration data for damage detection of reinforced concrete structures faces many challenges that obstruct its transition from a research topic to field applications. Among these is the lack of appropriate damage models that can be deployed in the damage detection methods. In this paper, a model of a simply supported reinforced concrete beam with multiple cracks is developed to examine its use for damage detection and structural health monitoring. The cracks are simulated by a model that accounts for crack formation, propagation and closure. The beam model is studied under different dynamic excitations, including sine sweep and single excitation frequency, for various damage levels. The changes in resonant frequency with increasing loads are examined along with the nonlinear vibration characteristics. The model demonstrates that the resonant frequency reduces by about 10% at the application of 30% of the ultimate load and then drops gradually by about 25% at 70% of the ultimate load. The model also illustrates some nonlinearity in the dynamic response of damaged beams. The appearance of super-harmonics shows that the nonlinearity is higher when the damage level is about 35% and then decreases with increasing damage. The restoring force-displacement relationship predicted the reduction in the overall stiffness of the damaged beam. The model quantitatively predicts the experimental vibration behaviour of damaged RC beams and also shows the damage dependency of nonlinear vibration behaviour. © 2011 Published under licence by IOP Publishing Ltd.

Precracked reinforced concrete t-beams repaired in shear with prestressed carbon fiber-reinforced polymer straps

The results of an experimental and numerical investigation involving unstrengthened reinforced concrete (RC) T-beams and precracked RC T-beams strengthened in shear with prestressed carbon fiber-reinforced polymer (CFRP) straps are presented and discussed. The results provide insights into the influence of load history and beam depth on the structural behavior of both unstrengthened and strengthened beams. The strengthened beams exhibited capacity enhancements of 21.6 to 46% compared to the equivalent unstrengthened beams, demonstrating the potential effectiveness of the prestressed CFRP strap system. Nonlinear finite element (FE) predictions, which incorporated the load history, reproduced the observed experimental behavior but either underestimated or overestimated the post-cracking stiffness of the beams and strap strain at higher load levels. These limitations were attributed to the concrete shear models used in the FE analyses.

The sensitivity of vibration characteristics of reinforced concrete beams under incremental static and cyclic loading

The use of changes in vibration properties for global damage detection and monitoring of existing concrete structures has received great research attention in the last three decades. To track changes in vibration properties experimentally, structures have been artificially damaged by a variety of scenarios. However, this procedure does not represent realistically the whole design-life degradation of concrete structures. This paper presents experimental work on a set of damaged reinforced concrete beams due to different loading regimes to assess the sensitivity of vibration characteristics. Of the total set, three beams were subject to incremental static loading up to failure to simulate overloading, and two beams subject to 15 million loading cycles with varying amplitudes to produce an accelerated whole-life degradation scenario. To assess the vibration behaviour in both cases, swept sine and harmonic excitations were conducted at every damage level. The results show that resonant frequencies are not sensitive enough to damage due to cyclic loading, whereas cosh spectral and root mean square distances are more sensitive, yet more scattered. In addition, changes in non-linearity follow a softening trend for beams under incremental static loading, whilst they are significantly inconsistent for beams under cyclic loading. Amongst all examined characteristics, changes in modal stiffness are found to be most sensitive to damage and least scattered, but modal stiffness is tedious to compute due mainly to the difficulty of constructing restoring force surfaces from field measurements. © (2013) Trans Tech Publications.