Nonlinear models for design of circular RC columns under ultimate and service states

2021 ◽  
Author(s):  
Helena Barros ◽  
Carla Ferreira ◽  
Joaquim Figueiras ◽  
Mário Pimentel
Keyword(s):  
Reinforced Concrete ◽  
Nonlinear Models ◽  
Bending Moment ◽  
Constitutive Law ◽  
Equilibrium Equations ◽  
Linear Elastic ◽  
Compressive Stresses ◽  
Steel Bar ◽  
Tension And Compression ◽  
Definition Of

<p>The present paper is dedicated to the ultimate and to the service design of circular reinforced concrete sections under axial load and bending moment, according to Eurocode 2 [1].</p><p>The objective of the present work is to develop design equations for circular reinforced concrete sections, solving the equilibrium equations by mathematic symbolic software. The concrete only supports compressive stresses and the steel can hold both tension and compression. The nonlinear equation of EC2 [1] is used for compressed concrete in the ultimate design. The steel is considered to have a linear elastic constitutive law up to the yield stress, followed by a plastic behaviour. The ultimate design condition is posed in terms of maximum strains for the most compressed concrete fibre or for the tensioned steel bar, permitting the definition of interaction abacuses, shown in the present paper.</p>

3D Hyperelastic Constitutive Model for Yarn Behaviour Description

2012 ◽  
Vol 504-506 ◽  
pp. 267-272 ◽  
Author(s):  
Adrien Charmetant ◽  
Emmanuelle Vidal-Sallé ◽  
Philippe Boisse
Keyword(s):  
Longitudinal Shear ◽  
Constitutive Law ◽  
Energy Potential ◽  
Double Curvature ◽  
Axial Tension ◽  
Proposed Model ◽  
Tension And Compression ◽  
Bias Extension ◽  
Definition Of ◽  
Continuous Material

The preforming stage of the LCM composite manufacturing processes lead to fibrous reinforcement deformations which may be very large especially for double curvature shapes. Those deformations have significant influence on the second stage of the process, i.e. the injection of the resin. A way to predict accurately the spatial distribution of the permeability tensor consists in simulating for various configurations, the deformed shape of the reinforcement at the scale of the yarns. Mesoscopic scale analyses of textile reinforcements generally consider the yarns as a continuous material despite their fibrous nature. In order to have an accurate simulation tool, it is necessary to build up a constitutive law which accounts for the physical specificities linked to the microstructure of the yarns. Several models exist with reasonable accuracy. The present paper proposes a new approach in the hyperelasticity framework. The proposed model is based on the definition of mathematical invariants linked to the four main deformation modes of the yarn material: tension, compaction, longitudinal shear and transverse shear. The strain energy potential build up with those invariants is identified using classical fabric material tests: uni- and bi-axial tension and compression. The model has been validated on laboratory tests such as bias extension tests and gives promising results.

scholarly journals Numerical Simulation of Corroded Reinforced Concrete Beam Strengthened by a Steel Plate with Different Strengthening Schemes

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Huang Tang ◽  
Jianxin Peng ◽  
Linfa Xiao ◽  
Xinhua Liu ◽  
Jianren Zhang
Keyword(s):  
Reinforced Concrete ◽  
Corrosion Rate ◽  
Bearing Capacity ◽  
Steel Plate ◽  
Steel Strip ◽  
Reinforced Concrete Beam ◽  
Constitutive Law ◽  
Bottom Surface ◽  
Bond Slip ◽  
Tension And Compression

This paper proposes 3D nonlinear finite element (FE) models to predict the response of corroded reinforced concrete (RC) beam strengthened using a steel plate. Five FE models are developed based on the tests carried out by the authors in a previous investigation, in which three models are used to simulate the corroded RC beams with different schemes. The FE models use the coupled damaged-plasticity constitutive law for concrete in tension and compression and consider the bond-slip between the corroded tensile steel bar and concrete. The cohesive element is also used to model the cohesive bond between the steel plate and concrete. The FE results of load-deflection and the crack distribution are compared with the test data. The FE results are consistent with the test results. The influence of the thickness of the steel plate, the thickness, and location of the U-shaped steel strip on the bearing capacity of the strengthened corroded beam is analyzed through FE models. The results show that the thickness of the steel plate on the bottom surface should not exceed 4 mm for the flexure-strengthened and combined strengthened beams with a 10% corrosion rate. It is most reasonable to improve the bearing capacity using the 3 mm and 2 mm of thick U-shaped steel strips for the shear-strengthened and combined strengthened beams, respectively. The most reasonable location of the U-shaped steel plate is at the end of the steel plate for beams with a 10% corrosion rate.

Uniaxial Constitutive Equation of Ice From Beam Tests

1985 ◽  
Vol 107 (4) ◽  
pp. 511-515 ◽  
Author(s):  
P. C. Xirouchakis ◽  
T. Wierzbicki
Keyword(s):  
Strain Rate ◽  
Direct Method ◽  
Elastic Beam ◽  
Bending Moment ◽  
Uniaxial Stress ◽  
Analytical Technique ◽  
Linear Elastic ◽  
Beam Depth ◽  
Tension And Compression ◽  
Extensional Strain

A method is proposed to obtain ice uniaxial stress, strain, strain-rate relations from beam tests. The basic advantage of the proposed analytical technique is that it is a direct method of reducing beam test data. So, no assumption is made with regard to the ice constitutive behavior. The proposed method is an extension of Gillis and Kelly’s procedure to account for different ice response in tension and compression. It is also an extension of the procedure reported by Mayville and Finnie to account for ice response dependence on strain rate. Furthermore, it is shown that the expressions presented by Mayville and Finnie are only valid when the bending moment, with respect to the zero strain axis, is assumed independent of the centroidal extensional strain. A simple example of a linear elastic beam with a Young’s modulus that varies linearly with the beam depth is worked out to show that these earlier given expressions are not applicable in that case.

scholarly journals Analytical solution for the resistance of composite beams subjected to bending

2020 ◽  
Vol 323 ◽  
pp. 01013
Author(s):  
Marek Lechman
Keyword(s):  
Analytical Solution ◽  
Bending Moment ◽  
Composite Beams ◽  
Bending Moments ◽  
Equilibrium Equations ◽  
Good Convergence ◽  
Linear Elastic ◽  
Eurocode 2 ◽  
Strain Relationship

The paper deals with the resistance of steel and concrete composite beams, named BH beams, subjected to bending. They are structurally connected with prefabricated or cast in situ slabs, forming floor slab system. The beams under consideration consist of the reinforced concrete (RC) rectangular core placed inside a reversed TT welded profile. The stress-strain relationship for concrete in compression of the RC core is assumed for nonlinear analysis according to Eurocode 2. For reinforcing and profile steels linear elastic – ideal plastic model is applied. The normalized ultimate bending moment determining the resistance of the BH beam is derived by integrating the equilibrium equations of the bending moments about the horizontal axis of the RC core rectangle, taking into account the physical and geometrical relationships. The presented model was verified by tests carried out on two BH beams subjected to bending. The comparisons made indicated good convergence between the analytical solution and the experimental results in ultimate bending moments.

Strength decay of RC sections for chloride attack

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Stefania Imperatore ◽  
Angelo Leonardi ◽  
Zila Rinaldi
Keyword(s):  
Reinforced Concrete ◽  
Axial Force ◽  
Design Methodology ◽  
Bending Moment ◽  
Strength Reduction ◽  
Analytical Tool ◽  
Structural Safety ◽  
Chloride Attack ◽  
The One ◽  
Definition Of

Purpose Corrosion of reinforcement, and mainly the one induced by chloride attack, is one of the leading causes of deterioration in reinforced concrete structures. Then, it is very important to develop a simplified analytical tool, able to simulate the corrosion processes and the consequences for the structural safety. Design/methodology/approach Aim of this paper is the definition of a simplified integrated procedure, able to predict the decay with the time of the bending moment and axial force resistance of a reinforced concrete section, exposed to a chloride attack. Starting from various literature findings, the rebar mass loss in time is evaluated and related to the chloride distribution and content in time. Then the mechanical properties of the corroded rebars are evaluated by means of strength decay laws developed by the authors. Finally, moment curvature relationships and bending moment – axial force (M-N) interaction envelopes are defined. Findings The strength variation with the time can be easily evaluated and then the life cycle and the timing of repair or rehabilitation strategies can be estimated. Originality/value The proposed methodology can be considered a very simple, but useful tool for a first analysis of the strength reduction in time, due to chloride pitting corrosion, before performing more complex and time-spending analyses.

Microscopic Numerical Simulation of Reinforced Concrete Damage Evolution under Uniaxial Tension and Compression

2012 ◽  
Vol 424-425 ◽  
pp. 439-442
Author(s):  
Jian Yun Chen ◽  
Ming Zhang ◽  
Zhi Guang Liu
Keyword(s):  
Reinforced Concrete ◽  
Numerical Simulations ◽  
Damage Evolution ◽  
Aggregate Model ◽  
Brittle Damage ◽  
Steel Bar ◽  
Random Aggregate ◽  
Tension And Compression ◽  
Concrete Damage ◽  
The Impact

Based on the mesoscopic random aggregate model and brittle-damage constitutive model, the numerical simulations of tension and compression are performed on reinforced concrete, and the thickness method is employed to simulate the interface between steel bar and concrete. Then a series of samples are generated randomly based on Weibull distribution’ mechanical parameters, and these samples are used to investigate meso damage evolution process of reinforced concrete, as well as the impact of parameter selection on macro-strength characterization of reinforced concrete. The results of numerical simulations effectively reveal the accumulation of tensile damage of meso-units, which lead to the failure of reinforced concrete. In conclusion, this research provides an innovative method to investigate the mechanical properties of interface between steel bar and concrete.

scholarly journals Homogenization of cohesive fracture in masonry structures

2019 ◽  
Vol 25 (2) ◽  
pp. 181-200 ◽  
Author(s):  
Andrea Braides ◽  
Nicola A Nodargi
Keyword(s):  
Growth Conditions ◽  
Energy Functionals ◽  
Linear Elastic ◽  
Compressive Stresses ◽  
Functions Of Bounded Deformation ◽  
Contact Surfaces ◽  
Definition Of ◽  
Functional Setting ◽  
Unilateral Conditions ◽  
Limit Energy

We derive a homogenized mechanical model of a masonry-type structure constituted by a periodic assemblage of blocks with interposed mortar joints. The energy functionals in the model under investigation consist of (i) a linear elastic contribution within the blocks, (ii) a Barenblatt’s cohesive contribution at contact surfaces between blocks, and (iii) a suitable unilateral condition on the strain across contact surfaces, and are governed by a small parameter representing the typical ratio between the length of the blocks and the dimension of the structure. Using the terminology of [Formula: see text]-convergence and within the functional setting supplied by the functions of bounded deformation, we analyze the asymptotic behavior of such energy functionals when the parameter tends to zero, and derive a simple homogenization formula for the limit energy. Furthermore, we highlight the main mathematical and mechanical properties of the homogenized energy, including its non-standard growth conditions under tension or compression. The key point in the limit process is the definition of macroscopic tensile and compressive stresses, which are determined by the unilateral conditions on contact surfaces and the geometry of the blocks.

Methodology of studying the mechanical properties of composite materials (reinforced concrete)

2018 ◽  
Vol 84 (12) ◽  
pp. 61-67
Author(s):  
V. A. Eryshev
Keyword(s):  
Mechanical Properties ◽  
Reinforced Concrete ◽  
Experimental Studies ◽  
Analytical Relationship ◽  
Hardened Concrete ◽  
Deformation Model ◽  
Joint Work ◽  
Concrete Shrinkage ◽  
Axial Tension ◽  
Tension And Compression

The mechanical properties of a complex composite material formed by steel and hardened concrete, are studied. A technique of operative quality control of new credible concrete and reinforcement, both in laboratory and field conditions is developed for determination of the strength and strain characteristics of materials, as well as cohesion forces determining their joint operation under load. The design of the mobile unit is presented. The unit provides a possibility of changing the direction of loading and testing the reinforced element of the given shape both for tension and compression. Moreover, the nomenclature of testing equipment and the number of molds for manufacturing concrete samples substantially decrease. Using the values of forcing resulting in concrete cracking when the joint work of concrete and reinforcement is disrupted the values of the inherent stresses and strains attributed to the concrete shrinkage are determined. An analytical relationship between the forces and deformations of the reinforced concrete sample with central reinforcement is derived for axial tension and compression, with allowance for strains and stresses in the reinforcement and concrete resulted from concrete shrinkage. The results of experimental studies are presented, including tension diagrams and diagrams of developing axial deformations with an increase in the load under the central loading of the reinforced elements. A methodology of accounting for stresses and deformations resulted from concrete shrinkage is developed. The applicability of the derived analytical relationships between stresses and deformations on the material diagrams to calculations of the reinforced concrete structures in the framework of the deformation model is estimated.

Effect of Torsion on Collapse Bending Moment for 24-Inch Diameter Schedule 80 Pipes With Wall Thinning

2012 ◽  
Author(s):  
Kunio Hasegawa ◽  
Yinsheng Li ◽  
Bostjan Bezensek ◽  
Phuong Hoang
Keyword(s):  
Power Plants ◽  
Bending Moment ◽  
Combined Loading ◽  
Bending Moments ◽  
Compressive Stresses ◽  
Wall Thinning ◽  
Nominal Thickness ◽  
Calculation Results ◽  
Loading Modes ◽  
Local Wall Thinning

Piping items in power plants may experience combined bending and torsion moments during operation. Currently, there is a lack of guidance in the ASME B&PV Code Section XI for combined loading modes including pressure, torsion and bending. Finite element analyses were conducted for 24-inch diameter Schedule 80 pipes with local wall thinning subjected to tensile and compressive stresses. Plastic collapse bending moments were calculated under constant torsion moments. From the calculation results, it can be seen that collapse bending moment for pipes with local thinning subjected to tensile stress is smaller than that subjected to compressive stress. In addition, equivalent moment is defined as the root the sum of the squares of the torsion and bending moments. It is found that the equivalent moments can be approximated with the pure bending moments, when the wall thinning length is equal or less than 7.73R·t for the wall thinning depth of 75% of the nominal thickness, where R is the mean radius and t is the wall thickness of the pipe.

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