Nonlinear FE models were developed using the commercial package ABAQUS and analyzes were performed to understand the behavior of RC columns under torsional loading with and without FRP strengthening. Similarly, the analysis is performed in MATLAB using the FRP Torsion Softened Membrane Model (SMMT-FRP). 5.1.
5.5.4 (c) Moment and twist behavior of columns with and without FRP under torsion and equal axial loads.
LIST OF TABLES
CH APTER – 1
IN TRODU CTION
CH APTER -1
- GEN ERAL
- STRU CTU RAL STREN GTH EN IN G W ITH FRP COM POSITES
- Advantages of Composites
- N ECESSITY FOR STREN GTH EN IN G
- RESEARCH M OTIVATION
- OBJECTIVES AN D SCOPE
For this, nonlinear finite element (FE) models (square and circular columns) are created in ABAQUS and numerical analysis is performed to predict the global and local behavior of columns wrapped with and without FRP. The overall moment and twist behavior of RC columns with and without FRP was observed and compared with the FE model, which showed good agreement. Initially, nonlinear FE models are created to predict the global and local behavior of RC square and circular columns with and without FRP.
The aim of the study is to understand the overall torque-rotation behavior of RC circular columns strengthened with FRP composites and to understand the significance of FRP by performing varying parametric studies.
CH APTER-2
LITERATU RE
REVIEW
CH APTER -2
LITERATU RE REVIEW
- BEH AVIOR OF RC COLU M N S U N DER TORSION
- BEH AVIOR OF RC BEAM S U N DER TORSION
- FRP STREN GTH EN ED BEAM S
- BEH AVIOR OF FRP STREN GTH EN ED RC COLU M N S
The main findings of the study were: (i) The pattern of concrete cracks in the reinforced beams has a greater longitudinal distribution compared to individual cracks. ii). A significant increase in crack strength was observed when RC beams were reinforced with FRP plates oriented along the longitudinal direction of the beam. After the relocation of the plastic hinge, the confinement of a repaired area showed an increase in performance in terms of force and displacement capacity.
The main findings of the study are: The addition of external insulation to plain specimens, in various layered formats, significantly improved the ductility behavior.
CH APTER-3
FIN ITE ELEM EN T
AN ALYSIS
CH APTER -3
FIN ITE ELEM EN T AN ALYSIS
- IN TRODU CTION
- ELEM EN TS
- M ATERIAL M ODELS
- Concrete – Damage Plasticity M odel
- Steel
- PROCEDU RE – DYN AM IC EXPLICIT
- STEEL – CON CRETE IN TERFACE
- LOAD AN D BOU N DARY CON DITION S
- M ESH IN G
It is believed that there are mainly two failure mechanisms, namely tensile cracking and compressive crushing of the concrete material. The variation of the damage variables with stress states was also specified under tension and compression. The default values of the failure ratios are taken from the literature (Mondal and Prakash, 2015c).
The ratio of ultimate biaxial compressive stress to ultimate uniaxial compressive stress was taken as 1.16. The absolute value of the ratio of uniaxial tensile stress at failure to uniaxial compressive stress at failure was assumed to be 0.1, although the default value is 0.09. The dimensions and properties of the modeled round column are summarized from Prakash (2009), and for square columns the same is summarized from Tirasit and Kawasima (2007a, 2007b).
For the strengthening of columns subjected to torsional loading, ductility is one of the main factors to be considered. In this study, all degrees of freedom are restricted to the bottom of the column. The relative positions of the regions that are part of the rigid body remain constant throughout the analysis.
A reference point was created at the center of the surface and assigned as the rigid body reference point. The constant axial load applied to the circular columns is very less compared to the dimension of the column.
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SOFTEN ED M EM BRAN E
M ODEL FOR TORSION -FRP
CH APTER -4
SM M T-FRP) 4.1 IN TRODU CTION
SOFTEN ED M EM BRAN E M ODEL FOR TORSION
Later, Jeng and Hsu (2009) extended SMM to RC membrane elements subjected to torsion and proposed a theory named Softened Membrane Model for Torsion (SMMT). In this model, Jeng and Hsu (2009) considered the strain gradient of concrete supports in the shear flow zone by modifying the constitutive relationships of concrete. They observed that the strain gradient created by the bending of concrete struts under torsional loading leads to higher tensile strength and stiffness than that under shear condition in a membrane element.
The behavior of circular and non-circular sections under torsion is very different due to changes in shear flow properties and deformation. In the case of square/rectangular columns, the strain-gradient effect is significant due to deformation of the cross-section. However, the strain-gradient effect in circular sections is not very significant as that in the case of rectangular sections.
To incorporate this correction, Anand.et al. 2015) developed a new strain hardening model by modifying the descending/post-peak part of the constitutive tensile law for concrete. 44 | P a g e I I T H an improved softened membrane model (SMMT-FRP) considering the influence of FRP composites on the compressive behavior of cracked concrete. A new concrete strain-hardening relationship is also recommended, which also included bidirectional stress states in its formulations.
But the SMMT-FRP model proposed by Anand.et.al (2015) is limited to rectangular sections. This study compiled all the modifications required in the existing SMMT-FRP model using theories developed by Jeng and Hsu (2009) and Anand.et al. 2015) to make it applicable for circular sections.
- N avier’s Principles of M echanics
- Stress Equilibrium Equations
- Strain Compatibility Equations
- Constitutive Laws of M aterials
- Constitutive relationship of concrete in compression
- Constitutive relationship of concrete in tension
- Constitutive relationship of mild steel bars embedded in concrete
- Constitutive relationship of FRP
- Constitutive relationship of concrete in shear
- Additional equations for torsion
- Solution Algorithm for SM M T-FRP
The presence of tensile cracks in the primary compression plane softens the stress-strain behavior of the concrete struts. In this model, a compressive stress strain ratio of softened concrete is also used, as in the case of SMM. Zhang (1995) found that the softening coefficient (𝜁) is also a function of the concrete compressive strength.
However, in a torsional member, the angle of twist (𝜃) causes bending in the wall of the member, which in turn causes bending of the diagonal concrete struts. The circular AB members would be subjected to certain bending loads after cracking due to the differences in the ratios of the longitudinal and transverse reinforcements and because concrete is an inelastic material. A deformation gradient is visible in the main directions, which affects the behavior of the membrane element.
Therefore, a rational shear modulus is included in the SMMT, which relates the concrete shear stress to the shear strain as follows: In a torsional element, the twist angle θ also causes bending in the element wall, which in turn causes bending of the concrete struts. The area in the outer part that is compressed is considered to effectively resist the shear flow.
The expressions for the area (𝐴0) and the perimeter (𝑃0) of the shear current are shown in Eq. The torque (Τ) and twist (𝜃) in the element can be calculated from the expressions given in Eqns. Deformation in a membrane element in any direction is a function of not only stress in that direction but also stress in the perpendicular direction.
As in the SMMT, the first two fundamental equilibrium equations are Eq. 2) are added and subtracted to obtain the following two equations, which are used as convergence criteria for the solution procedure.
CH APTER-5
RESU LTS
RESU LTS AN D DISCU SSION
PART-I
PART-II
Torque Vs Twist
PARAM ETRIC STU DY
- EFFECT OF TH ICKN ESS OF FRP SH EET
- U N STREN GTH EN ED COLU M N S
- FRP STREN GTH EN ED COLU M N S
Parametric study has been carried out by varying the parameters such as thickness of FRP sheets, number of layers of FRP sheets, alignment of FRP sheets and increasing the axial load. The overall torque–rotation behavior predicted by varying the thickness of FRP sheets from 1 mm to 3 mm is shown in Fig. 5.5.1. But there is a significant increase in post-peak behavior, which can be observed in the form of increased peak torsional moment, which shows the effect of increasing the thickness of FRP sheets.
The overall torque and buckling behavior predicted by varying the number of constant thickness FRP layers is shown in Figures 5.5.2 (a) and 5.5.2 (b). It was observed that the peak torsional moment and the post-peak behavior increased significantly with the increase of FRP sheet layers. Here, the bond characteristics between multiple layers of FRP panels are assumed to behave as a perfect bond.
Here, the predictions developed for different alignments of FRP with respect to transverse direction (Fig. 5.5.3) show that FRP is more effective in resisting cracking and increasing the maximum torsional moment when aligned at an angle of 600. The effect of axial compression is investigated by predicting the torque-rotation behavior of the reinforced concrete circular column subjected to axial compression in addition to torsion. Since the axial compression dominates, the failure will be sudden in the form of crushing of concrete.
At low levels of axial compression, the torsional capacity of a section is improved as in the case of axial compression and bending interaction diagram. Any contribution of longitudinally aligned fibers to the axial compressive strength of a concrete element must be neglected.
Torque-Axial Interaction Curve
The maximum compressive stress in the confined concrete (𝜀𝑐𝑐𝑢) given in the equation below should be limited to 0.01 per code to prevent excessive cracking and resulting loss of concrete integrity.
CH APTER-6
CON CLU SION S
CH APTER – 6
CON CLU SION S
SCOPE FOR FU TU RE STU DY
REFEREN CES
The axial-torsional behavior of FRP-wrapped columns shows a significant contribution of FRP in terms of peak torsional capacity and tip behavior. Finite Element Analysis of Confined Concrete Columns." Proceedings of the Fifth International Symposium on the Application of High-Strength/High-Performance Concrete, Sandefjord, Norway. Modeling the Bond and Slip Behavior of Confined Large-Diameter Reinforcing Bars." III ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN, Corfu, Greece.
Modeling and Simulation of Reinforced Concrete Beams: Coupled Analysis of Imperfectly Bonded Reinforcement in Fracture of Concrete.” Master's thesis 2013:42, Department of Applied Mechanics: Division of Solid Mechanics, Gothenburg, Sweden. Behavior of normal strength FRP wrapped concrete columns under eccentric loading. Engineering Structures Journal, Elesvier,72, pp 503-511. Torsion of structural concrete - behavior of reinforced concrete rectangular members.” Torsion of Structural Concrete, SP-18, American Concrete Institute, Detroit, MI.
Identification of parameters of a constitutive plasticity model of concrete damage.” Fundamentals of Civil and Environmental Engineering, no. Diagonal Compression Field Theory - A Rational Model for Structural Concrete in Pure Torsion.” Journal of the American Concrete Institute, 71, p. Nonlinear finite element analysis of RC bridge piers under torsion with and without axial compression.” Journal of Bridge Engineering, ASCE Library, 04015037.
Panchacharam, S and Belarbi, A "Rotational Behavior of Concrete Beams Reinforced with FRP Composites", First FIB Congress, Osaka, Japan, Oct-2002.
