Search

Variability of deflection prediction models is assessed for cracked prestressed concrete flexural members with bonded steel tendons. Current models for computing deflection are based on an effective moment of inertia (with or without an offset moment for the cracked section response) or a bilinear moment-deflection response using the moment of inertia of the uncracked section before cracking and moment of inertia of the cracked section after cracking. The accuracy of the approaches provided in ACI 318-19, the PCI Design Handbook, and elsewhere are examined for computing immediate deflection using a large database of 180 fully prestressed as well as partially prestressed beams. Parameters considered in the analysis include the effect of tension-stiffening, reinforcement ratio, prestressing type (fully or partially prestressed), cracking moment, concrete elastic modulus, modulus of rupture, and the use of transformed or gross section properties. Results highlight the need for a rational model that can be universally applied to reinforced as well as prestressed concrete flexural members. [ABSTRACT FROM AUTHOR]

The suitability of using CSA A23.3-14 to compute service load deflection of slender concrete wall panels is evaluated. Calculation of deflection using an effective moment of inertia with a reduced cracking moment is reviewed for beams, slabs, and tilt-up wall panels. While the procedure adopted by A23.3 for computing deflection works reasonably well for beams and slabs with reinforcing ratios as low as 0.4%, computed values do not correlate well with existing tests on slender walls and can underestimate deflection significantly. Deflection of slabs with very low reinforcement ratios (less than 0.4%) is also likely to be underestimated. Revisions to A23.3 are proposed for computing deflection. Key words: deflection, effective moment of inertia, service load, tilt-up walls. La pertinence de l'utilisation de la norme CSA A23.3-14 pour calculer la fleche en service de panneaux muraux en beton elances est evaluee. Le calcul de la fleche utilisant une inertie efficace obtenue avec un moment de fissuration reduit est examine pour des poutres, des dalles et des panneaux muraux mis en place par relevement. Bien que la procedure adoptee par la norme A23.3 pour le calcul de la fleche fonctionne raisonnablement bien pour les poutres et les dalles avec un pourcentage d'armature aussi bas que 0,4%, les valeurs calculees different des resultats de tests effectues sur des panneaux muraux elances et peuvent conduire a une sous-estimation considerable de la fleche. La fleche de dalles avec des pourcentages d'armature tres bas (moins de 0,4%) risque vraisemblablement d'etre aussi sous-estimee. Des revisions pour la norme A23.3 sont proposees pour le calcul de la fleche. Mots-cles: fleche, inertie efficace, charge de service, panneaux muraux mis en place par relevement., Introduction Tilt-up concrete walls are a popular form of construction in North America. Tilt-up wall panels are typically slender axial load bearing members subjected to out-of-plane lateral loads from wind [...]

Abstract: Deflection control is an important performance criterion that needs to be satisfied to ensure serviceability of the structure for its intended use. The extent of cracking and amount of [...]

This paper provides a critical evaluation of equations commonly used to compute short-tern1 deflection for steel and fiber-reinforced polymer (FRP) reinforced concrete beams. Numerous proposals have been made for FRP in particular, and the different approaches are linked together by comparing the tension-stiffening component of each method. Tension stiffening reflects the participation of concrete between cracks in stiffening the member response. The Branson equation used in North America and other parts of the world is based on an empirically derived effective moment of inertia to calculate deflection. The tension-stiffening component with this method is highly dependent on the applied level of loading relative to the cracking load as well as the ratio of untracked-to-cracked transformed moment of inertia ([I.sub.g]/[I.sub.cr]) for the beam section. Tension stiffening is overestimated for the high [I.sub.g]/[I.sub.cr] ratios typical with FRP concrete. leading to a much stiffer response and underprediction of member deflection. Deflection of steel reinforced concrete with reinforcing ratios less than 1% is also likely to be underestimated because of higher [I.sub.g]/[I.sub.cr] ratios at these lower reinforcement levels, but not to the same extent. In both cases, service loads are less than twice the cracking load where tension stiffening is most significant. Modifications to Branson's equation for deflection prediction of FRP concrete soften the member response by reducing the tension-stiffening component, mostly by introducing empirical factors that effectively decrease the [I.sub.g]/[I.sub.cr] ratio. An alternative expression for calculating beam deflection is developed with a rational approach that incorporates a tension-stiffening model adopted in Europe. The proposed equation gives an effective moment of inertia that is independent of [I.sub.g]/[I.sub.cr] and works equally well for either steel or FRP reinforced concrete. CE Database subject headings: Deflection; Beams; Concrete, reinforced; Steel.

Fiber-reinforced concrete used in structural applications requires characteristic material properties that can be easily incorporated into existing design procedures. This paper investigates the postcracking response of reinforced concrete tension members made with both plain and steel fiber-reinforced concrete (SFRC). Loading was either monotonic or cyclic, and shrinkage effects are included in analysis of the member response. Tension-stiffening results are used to determine the average tensile response of concrete after cracking, and an expression is developed to predict this smeared behavior as a material property for cracked SFRC, as well as to estimate crack spacings. Specimens with steel fibers exhibited increased tension stiffening and smaller crack spacings, which both contributed to a reduction in crack widths. The postcracking tensile strength of fiber concrete at the cracks is the determining factor affecting behavior and is a fundamental material property used to predict tension stiffening and crack behavior for conventionally reinforced SFRC. The uniaxial strength of SFRC immediately after cracking governs serviceability behavior, while the postcracking strength at larger deformations governs strength design and is responsible for tension stiffening after yielding of the reinforcement. Cyclic loading did not have a significant effect on either tension stiffening or crack width control for the specimens tested. CE Database subject headings: Bonding; Cracking; Concrete, reinforced; Shrinkage; Stiffening.

The uniaxial stress-strain response has been measured for air-dried plain-concrete cylinders, nominally 100 mm in diameter and 250 mm long, loaded in compression at both a slow static rate of about 10 microstrains per second and a much higher impact rate of between 5 and 10 strains per second. Design concrete strengths of 30 and 50 MPa were tested. Static loading was carried out in a hydraulic testing machine, and a guided free-falling mass was used for impact loading. The impact and static responses are compared to provide some insight into the behavior of concrete during hard-impact loading. Differences in behavior are identified for various strength and deformation characteristics. Although the maximum strength and corresponding axial strain, the energy-absorption capacity at failure, and the secant modulus all increase during impact loading, the initial tangent modulus does not appear to change very much. Other characteristics such as volumetric strain and Poisson's ratio are also studied. A simple physical model is used to help explain observed changes.

The ACI 318 Building Code computes time-dependent deflections from creep and shrinkage as the product of immediate deflection from sustained loads and a deflection multiplier that depends on the duration of loading and amount of compression reinforcement. An alternative methodology is proposed that extends the approach developed for an effective moment of inertia Ie, recently adopted by ACI 318-19 for computing immediate deflection to include time-dependent deflections from creep under sustained load and shrinkage. Separate components are developed for creep and shrinkage deformation based on a rational tension stiffening model that accounts for the reduced member stiffness from creep, shrinkage warping of the uncracked and cracked sections, and loss of stiffness from a lower cracking moment that results as tensile stresses develop in the concrete from restraint to shrinkage and cause additional cracking. Comparison is also made with the Eurocode 2 approach. Validation with long-term test data shows close agreement within a few percent for the proposed approach and Eurocode 2 approach. ACI 318-14 underestimates deflection by 27% and ACI 318-19 overestimates deflection by 23% for the test results evaluated in this study. [ABSTRACT FROM AUTHOR]

The ACI 318 Building Code permits calculation of immediate deflections for cracked prestressed concrete slabs and beams based on either a bilinear moment deflection relationship or an effective moment of inertia. The effective moment of inertia Ie is taken as a weighted average of the uncracked moment of inertia Ig and cracked moment of inertia Icr. Accuracy of deflection calculations based on Ie depends on the value of cracking moment and requires an upwards shift in the Icr response. A new approach is proposed for computing service load deflections of cracked prestressed members. The proposed approach is compared with the existing ACI 318 approaches using the measured load-deflection response of prestressed beams and is shown to provide a more accurate and consistent prediction of deflections than the existing approaches. An alternative trilinear model that is much simpler but not as accurate is shown to provide reasonable results as well. It is recommended to compute deflection of cracked prestressed members using the trilinear approach except in those instances where higher accuracy is needed. [ABSTRACT FROM AUTHOR]

Span-depth ratio (ℓ/h) expressions are developed for steel-reinforced concrete one-way slabs and beams to satisfy deflection control and flexural strength requirements. The expressions are presented as functions of reinforcement ratio and specified deflection-to-span limit. A comparative study is performed to evaluate the effects of effective moment of inertia, shrinkage restraint, construction loads, sustained live load, long-time deflection multiplier, support conditions, and deflection limits on the resulting span-depth ratios. A comparison is also made with minimum thickness values prescribed by ACI 318 that are a function of span and support conditions only. Effects of various input parameters are considered in examples involving a simply supported rectangular beam and an interior span of a continuous one-way slab. The results of the study indicate some of the limitations associated with the ACI 318 minimum thickness requirements. [ABSTRACT FROM AUTHOR]

The effects of shrinkage restraint cracking and loading history on defection of reinforced concrete flexural members are discussed. It is shown that deflections of lightly reinforced members (less than 0.8% reinforcement) are highly sensitive to both shrinkage restraint cracking and loading history, whereas deflections of more heavily reinforced members are insensitive to these effects at full service load. Results of a deflection example are presented along with recommendations for changes to the ACI 318 Building Code. Proposed changes include a) adoption of a cracking moment equal to two-thirds the value currently specified in the Code to account for shrinkage restraint stresses; and b) evaluation of deflection using an effective moment of inertia based on the full dead plus live service load to account for preloading from construction loads prior to installation of nonstructural elements. Both effects are evaluated using an alternative formulation for the effective moment of inertia that works well over a wide range of reinforcing ratios and for fiber-reinforced polymer (FRP)-reinforced concrete. [ABSTRACT FROM AUTHOR]

The effective moment of inertia expression proposed by Branson in 1963 and incorporated into the ACI Code is reevaluated. It is found that Branson's expression is valid for members with steel reinforcement ratios greater than 1%. This expression, however, overestimates member stiffness at lower reinforcement ratios and gives a member deflection less than expected as demonstrated by comparison with test results. Branson's approach also underestimates deflection of slender walls with a central layer of reinforcement, as well as deflection of fiber-reinforced polymer (FRP)-reinforced concrete beams. An alternative expression is presented that is shown to be valid for all reinforcement ratios for both steel and FRP reinforcement. [ABSTRACT FROM AUTHOR]

Comments on the study "Analytical Model to Predict Nonlinear Flexural Behavior of Corroded Reinforced Concrete Beams," by Tamer El Maaddawy et al. Use of a bond to control deflection of the computed beam response; Calculation of deflection from elongation of the reinforcement between cracks; Relation of the method of computing deflection with the concept of tension stiffening.

Axial tension members made of both normal- and high-strength concrete are used to investigate tension stiffening and cracking of reinforced concrete to determine experimentally if any relationship exists between concrete strength and post-cracking behavior. Tension stiffening represents the tensile strength of concrete between cracks in a reinforced concrete member and can significantly affect member stiffness, deflection, and crack widths under service loads. Large-scale specimens using 40 and 80 MPa concrete were reinforced with either 15M or 20M bars to give a corresponding reinforcing percentage of 1.3 and 2%, respectively. An empirical model is proposed to predict the average tensile response of concrete after cracking. When this relationship is expressed as a normalized stress-strain response, it is independent of concrete strength and the reinforcing steel ratio as long as shrinkage is included in analysis of the member response. When shrinkage is ignored, the higher strength concrete exhibits a corresponding greater decrease in tension stiffening because of the higher shrinkage values that developed in this concrete. Crack spacing is not affected by the strength of concrete for the type of specimens tested. Hence, any decrease in crack width for a given load level occurs because of the increase in tension stiffening attributed to a concrete having a higher tensile cracking strength. [ABSTRACT FROM AUTHOR]

Discusses the stress and strain relationship of reinforced concrete subjected to biaxial tension. Role of shrinkage in the tensile stress-strain relationship derived by the authors; Significance of differences in shrinkage between concrete batches; Determination of the average tensile force carried by the concrete between cracks.

An abstract of the article "Shrinkage Restraint and Loading History Effects on Deflections of Flexural Members," by Andrew Scanion and Peter H. Bischoff is presented.