Raymond Ian Gilbert

Time-Dependent Behaviour of Concrete Structures

Time-Dependent Deformation Background Creep of Concrete Shrinkage of Concrete Time-Analysis - The Basic Problem Material Properties Concrete Steep Reinforcement References Design for Serviceability - Deflection and Crack Control Introduction Design Objectives and Criteria Design Actions Design Criteria for Servicability Maximum Span-to-Depth Ration Minimum Thickness Deflection Control by Simplified Calculation Crack Control References Uncracked Sections - Axial Loading Preamble The Effective Modulus Method The Principle of Superposition - Step-by-Step Method The Age-Adjusted Effect Modulus Method (AEMM) The Rate of Creep Method (RCM) Comparison of Methods of Analysis Uncracked Sections - Axial Force and Uniaxial Bending Uncracked Sections - Axial Force and Biaxial Bending Introductory Remarks Overview of Cross-Sectional Analysis Short-Term Analysis of Reinforced or Prestressed Concrete Cross Sections Long-Term Analysis of Reinforced or Prestressed Concrete Cross Sections Using the Age Adjusted Effective Modulus Long-Term Analysis of Reinforced Prestressed Concrete Cross Section Using the Step-by-Step Procedure Composite Steel-Concrete Cross Sections References Cracked Sections Introductory Remarks Short-Term Analysis Time-Dependent Analysis (AEMM) Short- and Long-Term Analysis Using the Step-by-Step Method References Members and Structures Introductory Remarks Deflection of Statically Determinate Beams Statically Indeterminate Beams and Slabs Two-Way Slab Systems Slender Reinforced Concrete Columns Temperature Effects Concluding Remarks References Stiffness Method and Finite Element Modelling Introduction Overview of the Stiffness Method Member Loads Time Analysis Using AEMM Time Analysis Using SSM Time Analysis Using the Finite Element Method Analysis of Cracked Members References Appendix: Analytical Formulations - Euler-Bernoulli Beam Model

Time-Dependent Cracking and Crack Control in Reinforced Concrete Structures

The paper reviews an investigation of cracking under sustained service loads for reinforced concrete flexural elements and restrained direct tension members. Reliable design models using the tension chord model are presented and are shown to be suitable for predicting the time varying width and spacing of cracks caused by bending and/or shrinkage. Also reported are crack widths and crack spacings from laboratory tests on 12 beams and slabs subjected to sustained loads for periods up to 400 days in order to quantify the effects of steel area, steel stress, bar diameter, bar spacing, concrete cover and concrete shrinkage. In addition, crack widths and spacings induced by shrinkage in eight restrained direct tension members are reported.Predictions made using the analytical design models are compared to the experimental observations and agreement is satisfactory.

Numerical Analysis of Continuous Composite Beams Under Service Loading

This paper presents a method for the service-load analysis of continuous composite beams. Both short-term and time-dependent analyses are carried out, in which cracking, creep and shrinkage of the concrete slab are considered. The time-dependent response of individual cross-sections is modelled using the Age-Adjusted Effective Modulus Method coupled with a relaxation procedure, and the lengthwise or longitudinal analysis of the member makes use of the force method of structural analysis. Both propped and unpropped construction may be modelled. The numerical solution requires iteration, but is suited to straightforward spreadsheet or conventional programming on a personal computer, on which the analysis is performed rapidly. The scope of the method is demonstrated in a simple example of the behaviour of a two-span beam with the same sustained loading that is cast propped or unpropped.

Strain Localization and its Impact on the Ductility of Reinforced Concrete Slabs Containing Welded Wire Reinforcement

Welded wire fabric (WWF) is commonly used in reinforced concrete (r.c.) slabs. WWF is classified in Australia as Class L or low ductility reinforcement and, as such, the characteristic strain at peak stress (termed the uniform elongation) is not less than 0.015 and the ratio of tensile strength to yield stress (0.2% proof stress) is not less than 1.03. A r.c. slab containing low ductility steel usually fails in bending by fracture of the tensile reinforcement at the critical section, well before the concrete in the compression zone becomes overstressed, and the conventional understanding of ductile under-reinforced flexural failure is not valid. The failure is brittle and results in complete collapse of the span, often with little or no warning. This paper explores the collapse load behaviour of slabs containing WWF, highlighting the great significance of strain localization in lightly reinforced slabs and its adverse impact on ductility. The results of tests on several simply-supported and continuous one-way slabs reinforced with WWF are used to illustrate the discussion.

DESIGN OF DISTURBED REGIONS IN REACTIVE POWDER CONCRETE BRIDGE GIRDERS

This paper details the benefits of using reactive powder concrete (RPC) to carry bursting forces in prestressed bridge girders. Tests were conducted on 3 RPC, 150 MPa, deep beams with results reported herein. A finite element analysis of a 35-m prestressed RPC bridge girder is also provided. The most important potential advantages of using RPC in bridge engineering are described.

Deflection Calculation and Control -Australian Code Amendments and Improvements

This paper describes the behavior of reinforced and prestressed concrete flexural members under sustained service loads and outlines recent developments in the design of concrete structures for the serviceability limit states, particularly with regard to deflection and crack control. The effects of concrete cracking, creep and shrinkage on cross-sectional stresses and deformation are demonstrated and discussed for a wide range of actions and reinforcement layouts. Recent amendments to the serviceability provisions of the Australian Standard for Concrete Structures AS3600 are presented and the background to, and reasons for, the proposed changes are explained. The paper also highlights the inadequacies of the existing deflection calculation procedure in ACI 318M-99 and suggests ways to improve it. A method is proposed for calculating the time-dependent deflection of reinforced and prestressed concrete members taking into account the time-dependent effects of creep and shrinkage, including the loss of stiffness caused by shrinkage induced cracking and the breakdown of tension stiffening with time. The method is illustrated by several examples.

A layered cylindrical quadrilateral shell element for nonlinear analysis of RC plate structures

This paper proposes a simple and accurate 4-node, 24-DOF layered quadrilateral flat plate/shell element, and an efficient nonlinear finite element analysis procedure, for the geometric and material nonlinear analysis of reinforced concrete cylindrical shell and slab structures. The model combines a 4-node quadrilateral membrane element with drilling or rotational degrees of freedom, and a refined nonconforming 4-node 12-DOF quadrilateral plate bending element RPQ4, so that displacement compatibility along the interelement boundary is satisfied in an average sense. The element modelling consists of a layered system of fully bonded concrete and equivalent smeared steel reinforcement layers, and coupled membrane and bending effects are included. The modelling accounts for geometric nonlinearity with large displacements (but moderate rotations) as well as short-term material nonlinearity that incorporates tension, cracking and tension stiffening of the concrete, biaxial compression and compression yielding of the concrete and yielding of the steel. An updated Lagrangian approach is employed to solve the nonlinear finite element stiffness equations. Numerical examples of two reinforced concrete slabs and of a shallow reinforced concrete arch are presented to demonstrate the accuracy and scope of the layered element formulation.

In-Plane Nonlinear Analysis and Buckling of Tied Circular Arches

A nonlinear theory is developed in this paper to investigate the elastic in-plane buckling of shallow tied circular arches under uniformly distributed radial loading, in which the effects of the prebuckling deformation and geometric nonlinearity are included. Prescriptive formulae for the elastic buckling loads of tied arches are derived, as well as the critical stiffness that delineates between the possibility that the arch will buckle, or that it will not buckle, in its plane of loading. The relationship between the buckling load and a modified slenderness parameter of the arch is also discussed. The paper also includes the results of two short-term tests undertaken on shallow reinforced concrete tied arches, and the solutions are also analysed using the well-known ABAQUS software. The consistency of the critical loads and the load versus deflection responses demonstrates the accuracy and practicability of the analytical results derived in the paper.

AS3600 Creep and Shrinkage Models for Normal and High Strength Concrete

The Australian Standard for Concrete Structures, AS3600, is currently being reviewed, with amendments introduced to facilitate the use of 500 MPa reinforcing steel in the design of concrete structures. This paper is primarily concerned with the instantaneous and time dependent strength and deformation characteristics of concrete up to 100 MPa. The factors that have been considered in the current review are discussed and the models that have been developed for predicting the tensile strength, the elastic modulus, the creep coefficient and the shrinkage strain for the full range of applicable concrete strengths are presented.

Tests on RC Slabs Reinforced with 500 MPa Welded Wire Fabric

Abstract Welded wire fabric, with a characteristic yield strength of 500 MPa, is commonly used by the Australian building industry in reinforced concrete slabs. Such steel has recently been classified in the steel reinforcement standard AS/NZS4671-2001 as Class L (low ductility). Reinforcement is classified as Class L if the minimum specified lower characteristic uniform elongation is at least 0.015 and the ratio of yield stress to ultimate tensile strength exceeds 1.03. A reinforced concrete flexural element reinforced with welded wire fabric invariably fails by fracture of the tensile reinforcement and the conventional understanding of ductile under-reinforced flexural failure is not valid. At the ultimate moment, fracture of the tensile steel may occur well before the concrete in the compression zone becomes overstressed, certainly well before the extreme compressive fibre strain reaches 0.003 (as specified in the Australian Standard for Concrete Structures, AS3600-2001). This can be readily shown using a simple cross-sectional analysis, assuming plane sections remain plane and enforcing the requirements of equilibrium and compatibility. It is important to verify the theoretical predictions with experimental results, as the catastrophic failure mode resulting from fracture of the tensile steel has direct consequences on ductility, warning of failure, moment redistribution in indeterminate structures and the validity of many of the routine approximations and simplifications made in the analysis and design of reinforced concrete structures. This paper presents experimental results of three simply supported and three continuous slabs, reinforced with Australian welded wire fabric, designed in accordance with AS3600.2 All slabs were observed to fail in a brittle and catastrophic manner, namely by fracture of the welded wire fabric, at the most heavily loaded section. The results have important implications for consulting structural engineers, code writers, and the builders, owners and users of concrete structures.