Concrete in Compression

One hundred years ago, engineers were debating whether density, aggregate gradation, or water cement ratio controls the strength of concrete. Today, those debates have been settled, but the factors that control the behavior of concrete in compression remain controversial. The debate has now shifted to the roles played by cement paste, the interfacial transition zone between paste and aggregate, and the relative stiffness of the components. While all three ingredients play significant roles, the properties of cement paste and the heterogeneous nature of the material appear to be the key factors in the response of concrete in compression. This article highlights some of the research that demonstrates the roles played by the various constituents, with emphasis on microcracking, interfacial bond strength, and models of concrete. The reader is directed to Reference 1 for a more complete discussion of the subject

Corrosion-Resistant Steel Reinforcing Bars

The corrosion of reinforcing steel in highway structures results in maintenance and replacement costs in the United States that are measured in billions of dollars. These costs would be greatly reduced and the durability and design life of reinforced concrete structures greatly enhanced if the corrosion resistance of reinforcing steel were improved. This study involves the evaluation of a concrete reinforcing steel which has shown superior corrosion-resistant properties. Previous evaluations have concentrated on the corrosion resistance of the steel in the atmosphere, which can be quite different than obtained for steel in contact with concrete. Emphasis in this study is placed on the corrosion resistance of the steel in concrete structures. The new steel differs from steel used in standard U.S. practice in a number of ways. Additional alloying elements (copper, chromium, and phosphorus) are used, along with a special heat treatment, to provide the corrosion-resistant properties of the steel. The bars possess lower carbon content than is usual, and the phosphorous content exceeds that allowed in ASTM specifications. The bars are quenched and tempered immediately following the rolling operation, a step that places the exterior of the bars in compression. The apparent corrosion-resisting mechanisms include the formation of a corrosion-retarding layer of copper chloride-<:apper hydroxide at the steel surface in the presence of chloride, the formation of phosphorous oxides, which serve as corrosion inhibitors, the formation of iron-chromium oxide at the steel surface, which is a poor conductor and, thus, reduces the corrosion rate, and the reduction of microfractures in the surface from the rolling operation due to the quenching and tempering process. The corrosion products that form are much denser than for normal reinforcing steel, which further reduces the availability of oxygen and water at the steel surface. The reduced microfractoring lowers the surface area available for corrosion. The study is carried out in four overlapping stages. Stages l and 3 are dedicated to understanding the corrosion protection mechanisms and the degree of corrosion protection when the steel is subjected to different chloride concentrations and different deicing chemicals. Stage 2 involves the evaluation and comparison of the new reinforcement to standard reinforcing steel using accepted time-to-corrosion tests. Stage 4 consists of a determination of the mechanical properties of the new steel, as affected by the alloying process. The study involves the evaluation of four types of steel, representing combinations of alloying elements and heat treatment. The steels include two conventional steels, one hot-rolled and one subjected to heat treatment immediately following the hot-rolling operation, and two forms of corrosion-resistant steel, one hot-rolled and one heat-treated. The experimental results and analyses demonstrate that the microalloying procedure improves the corrosion resistance of steel reinforcing bars cast in concrete and subjected to deicing chemicals. The resulting corrosion rate is approximately one-half of the corrosion rate exhibited by conventional reinforcing bars. The use of the quenching and tempering heat treatment following hot rolling appears to provide some additional corrosion resistance, when used in conjunction with the microalloying procedure. The heat treatment produces a reinforcing steel with higher yield and tensile strengths. A phosphorous content in excess of that allowed under current AS'IM requirements does not cause the corrosion resistant steel in this study to be brittle. The tests indicate that the new reinforcing steel should not be combined with conventional reinforcement in reinforced concrete structures. The new steel performs well when used in conjunction with an epoxy coating and offers the potential of economically providing a measurable improvement in the corrosion performance of reinforced concrete structures subjected to chlorides and deicing chemicals. Implementation of the new reinforcing steel will require additional corrosion tests to fully document the corrosionresistant properties of the reinforcement, the development of standard specif'JCations for the material, and the execution of demonstration projects in which the new reinforcing steel is applied in practice. Special attention should be given to using the new steel in conjunction with epoxy coating

Design of composite beams with web openings

Design techniques for composite beams with web openings have been under development for well over 30 years. During the past decade, these efforts have reached a level of maturity that allows for an accurate assessment of strength and the development of economical designs. This paper describes the behavior of steel}concrete composite beams with web openings and summarizes the key aspects of strength design and deflection calculation

Cyclic Behavior of High Strength Concrete Beams

Four high strength, lightly reinforced concrete beams were fabricated and tested to evaluate member response under severe cyclic loading. Concrete strengths varied from 11 • 31 0 to 12,860 psi with reinforcement ratios of 0.68 and 1 • 02%. Nominal stirrup strength was approximately 170 psi for all specimens. The applied shear stress ranged from 1 45 to 210 psi. The measured energy dissipation capacity for the beams investigated in this study was compared to specimens fabricated with concrete strengths between 4000 and 6000 psi. Based on a statistical analysis of research representing five major studies, recommendations are made to improve the cyclic performance of reinfor·ced concrete beams. The findings show that for beams with similar geometry, strength and load history, an increase in concrete strength improves.cyclic performance. The primary factor influencing cyclic behavior is the applied shear stress. Results also indicate that the use of reduced stirrup spacing and increased beam widths provide improved eye lie performance. Increases in beam width appear to be the most effective means to improve the cyclic performance of beams subjected to severe seismic loading

Anchorage of High-Strength Reinforcing Bars with Standard Hooks: Initial Tests

This report describes the initial tests on the anchorage strength of standard hooked bars in concrete. The goal of the testing is to determine the effects embedment length, side cover, tail cover, quantity of transverse reinforcement, location of longitudinal reinforcement, concrete strength, bar size, and bar bend on the anchorage strength of hooked bars in concrete. Initial tests have been performed on No. 5 and No. 8 bars, with 90° and 180° hooks, cast in concrete with a nominal compressive strength of 5000 psi. Further testing will also include No. 11 bars and concrete strengths up to 15,000 psi. The goal of this study is to gain a firm understanding of the anchorage strength of hooked bars in concrete as a function of the key variables and use the data to establish reliability-based design expressions for development length. Thus far, the testing apparatus has been fabricated, the testing procedures have been established, and the initial specimens have been tested. The test results agree qualitatively with those in previous studies and show that hook strength increases with increased embedment length, side cover, and confining reinforcement. The results also show that hook strength is greater for hooks anchored within a column core than for hooks anchored outside of the core. The latter case is appropriate to hooks anchoring bars at the end of cantilever beams

Non-optimality of the Greedy Algorithm for subspace orderings in the method of alternating projections

The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm and that one can obtain estimates for the rate of convergence in terms of quantities describing the geometric relationship between the subspaces in question, namely their pairwise Friedrichs numbers. We consider the question of how best to order a given collection of subspaces so as to obtain the best estimate on the rate of convergence. We prove, by relating the ordering problem to a variant of the famous Travelling Salesman Problem, that correctness of a natural form of the Greedy Algorithm would imply that $\mathrm{P}=\mathrm{NP}$, before presenting a simple example which shows that, contrary to a claim made in the influential paper [Kayalar-Weinert, Math. Control Signals Systems, vol. 1(1), 1988], the result of the Greedy Algorithm is not in general optimal. We go on to establish sharp estimates on the degree to which the result of the Greedy Algorithm can differ from the optimal result. Underlying all of these results is a construction which shows that for any matrix whose entries satisfy certain natural assumptions it is possible to construct a Hilbert space and a collection of closed subspaces such that the pairwise Friedrichs numbers between the subspaces are given precisely by the entries of that matrix.Comment: To appear in Results in Mathematic

Quantitative Backscattered Electron Analysis Techniques for Cement-Based Materials

Backscattered electron imaging and x-ray microanalysis are used to identify phases within polished epoxy impregnated cement paste sections. A silicon-magnesium standard is applied and an objective procedure is developed for the calibration of the scanning electron microscope and the image analysis system, so that the L;tensity of individual phases in cement paste appears within reproducible ranges when using backscattered electron imaging, The techniques allow for consistency in quantitative analysis of cement microstructure. Image analysis of cement phases is carried out and a statistical basis is established for the number of frames that must be analyzed to obtain a satisfactory level of confidence in the data. Backscattered electron imaging of polished surfaces of cement paste can be used to distinguish the phases within unhydrated cement particles and the phases of cement I hydration products. The existence of calcium hydroxide within inner product is confirmed, For image analysis, the number of frames required for a selected level of confidence decreases as the magnification decreases, while the total area required increases as the magnification decreases. To achieve a desired level of confidence in image analysis for the phases of hydrated cement paste, unhydrated cement particles require the greatest number of frames, while inner product and calcium silicate hydrate require the least number of frames

Effects of Traffic Induced Vibrations on Bridge Deck Repairs

The effects of traffic induced vibrations on concrete-steel bond strength and concrete compressive strength was studied for full depth repairs of reinforced concrete bridge decks. The specimens had blockouts to represent full depth patch repair areas. Two bar sizes, #5 and #8, two topcovers,3in. and 1-1/2 in., and four slumps, ranging from 1-1/2 in. to 7-1/2 in., were used. The bond tests used modified cantilever specimens. Standard 6 in. x 12 in. cylinders were used for the study of the effect of traffic induced vibrations on compressive strength. Based on the results, traffic induced vibrations are not detrimental to the qua 1 i ty of repair concrete when low slump concrete is used and the reinforcing bars are securely fastened to the structure before the concrete placement. They may be detrimental when medium slump (4 to 5 in.) concrete is used. They are, however, detrimental to the quality of repair concrete when high slump concrete is used. Bond strength of #5 bars is affected more detrimentally than that of #8 bars when subjected to the traffic induced vibrations