Numerical Modelling of Lean Duplex Stainless Steel Hollow and Concrete-filled Columns of Square, L-, T- and +-shape Sections under Pure

But for LDSS pipe thickness ≥ 30 mm, the strength ratio for NRS and representative square section tends to 1.0. The deformation capacities of LDSS hollow tubular slender columns are similar regardless of cross-sectional shapes and class classification.

INTRODUCTION 1-11

Lean duplex stainless steel
Concrete-filled tubular column
Objectives of the Investigation
Outline of the Report

Examples of the use of stainless steel materials as structural members in the form of hollow tubular columns in construction fields are shown in Figure 1.2. The following subsections briefly discuss the beneficial factor involved in the use of lean duplex stainless steel (LDSS) material as a structural member and concrete filled tubular columns in construction industries.

LITERATURE REVIEW 12-39

Structural Hollow Tubular Columns

Taking advantage of its corrosion resistance and aesthetic appeal, stainless steel is often used for exposed structural elements (eg Baddoo et al., 1997). Some examples of experimental investigation on stainless steel hollow tubular columns are shown in Figure 2.1.

Structural Concrete-filled Tubular Columns

The studies were focused on assessing the effect of cross-sectional aspect ratio, thicknesses of stainless steel tubes and slenderness of the parts on the strength and structural behavior of such columns. Some examples of recent experimental investigation of stainless steel concrete-filled tubular columns are shown in Figure 2.2.

Structural LDSS Material

Previous Research on LDSS
Design guidance on structural stainless steel

The results were presented in terms of ultimate loads and a comparison with the currently available stainless steel design standards was obtained. The first specific design rules for structural stainless steel were produced in America by AISI (1968) based on the research program carried out by Johnston and Winter (1966).

Structural Tubular Columns with NRSs

Material Modelling

Stainless steel

Ramberg-Osgood model
Rasmussen model
Gardner and Ashraf model

Confined concrete core

Thus, the concrete core experiences a state of multiaxial compression, which increases the deformation capacity and strength of the concrete. The second part of the curve is a non-linear part starting from the proportional ultimate stress (0.5 fcc) to the strength of confined concrete (fcc).

Initial Geometric Imperfections

Local geometric imperfections
Global geometric imperfections

Hollow tubular stainless steel columns can have initial maximum out-of-straightness from L/3000 to L/8000 (where L is the length of the specimen) with an average of about L/6500. Huang and Young (2013) measured the initial -straightness value in the test specimens of thin LDSS hollow tubular columns with needle bottoms.

The Production of Stainless Steel Tubular Sections

Summary of the Literature Review

Many have studied and analyzed the structural behavior of hollow and concrete-filled stainless steel tubular columns with respect to commonly available shapes such as square, rectangular, circular, and elliptical sections. However, relatively little attention is paid to the structural behavior of tubular columns (both hollow and concrete filled) with equal material consumption, as stainless steel is expensive, together with the favorable factors involved in the use of specially shaped sections, such as the NRSs.

NUMERICAL MODELLING OF LEAN DUPLEX

FE Modelling

Boundary conditions and analysis technique
FE mesh
Appraisal of existing material models
Local geometric imperfections

In the present study, linear elastic analysis technique using the *BUCKLING command was used to obtain the relevant eigenmodes, which were subsequently used to represent initial geometric imperfections in subsequent nonlinear analyses. In each load increment, the equilibrium iteration is performed and the equilibrium path is traced in the load displacement space. A suitable mesh size is chosen at a point where there is little improvement in the σcr with further mesh refinement.

Verification of the FE Models

The evolution of the stress-strain curve of the concrete core in CFDSST columns is described in detail in Section 2.7.2. The evolution of the stress-strain curve of the concrete core in CFDSST slender columns with fixed ends is described in detail in Section 2.7.2. However, local buckling of the LDSS tubes is prevented by the concrete core in the CFDSST columns (see Figure 6.4i-l).

Hollow Tubular Stub Column Modeling

Introduction
Development of the FE models

Results and Discussion

Introduction
Deformed shapes of NRSs and square section
Load-axial deformation profile
Strength capacity of NRSs and square section
Deformation capacity of NRSs and square section
Comparison with design codes

Effective area determination
Cross-section resistance
Comparison of FE strengths with design strengths
Reliability analysis of the codes

Reliability analysis of the design standards was also performed based on the FE studies. Development of the FE models for LDSS hollow tubular slender columns with fixed ends was similar to that of the hollow tubular stub columns as discussed in Chapter 3. However, local buckling of the LDSS tube is prevented due to the concrete core in CFDSST columns.

Conclusions

NUMERICAL MODELLING OF LEAN DUPLEX

FE Modelling

FE mesh
Initial geometric imperfections

The following subsections present various details to obtain a reliable FE model representation of LDSS hollow tubular slender columns as also followed by several researchers. Linear elastic analysis technique was initially performed on the fixed-end hollow tubular slender column FE models to extract both local and global buckling mode shapes. This imperfection size was applied at the center of the column in the plane of the major weaker axis for all of the investigated hollow tubular slender fixed-end columns.

Verification of the FE models

This demonstrates the ability to predict the loading and deformation capacities of the LDSS hollow tubular fixed-end slender columns. The design strengths of the CFDSST stub columns took into account the concept of effective width, as detailed in section 3.5.7.1, given in EN to account for the effect of local buckling on the LDSS pipe. The main objective is to study the effects of cross-sectional geometries on the strength and behavior of the fixed-end slender CFDSST columns with NRSs and a representative square cross-section.

Hollow Tubular Slender Column Modeling

Introduction

Results and Discussion

Introduction
Buckling strength of NRSs and square section

Class 3 sections
Class 4 sections

Class 3 sections
Class 4 sections

Design strengths

The axes of flexural buckling are based on the constraints of cross-sectional dimensions considered in the present study (see Figure 4.5). However, for Class 4 sections, Ae of the cross section is used to account for the reduction in resistance due to local bending effects and detailed in Section 3.5.7.1. A  higher, for both Class 3 and Class 4 sections, the European specification gives a conservative estimate of strengths compared to the American specification, which gives a slightly conservative value, in the design of thin hollow tubular LDSS columns.

Conclusions

Based on reliability analyses, it can be seen that except for Class 3 LHC, both codes show βo ≥ 2.5 when compared to FE results. Considering the lower limit of βo = 2.5 suggested by the ASCE specification for structural members, it can be concluded that both specifications can be adopted for all the design of thin LDSS hollow tube columns with fixed bottom, except for LHC of class 3, where a suitable modification can be used after systematic studies (including experiments). Unlike Class 3 sections, the cross-sectional shape becomes increasingly important as  decreases, however, the cross-sectional shape becomes unimportant for very high sections, as it also happens for Class 3 sections.

NUMERICAL MODELLING OF CONCRETE-FILLED

FE Modelling

FE mesh
Concrete core material model
Modelling of concrete-steel tube interface

Similar analysis technique as mentioned in Section 3.2.1 was followed, and the modified RIKS method was used in the non-linear analyzes of the CFDSST stub column FE models in line with. Due to the thin nature of the LDSS tube adopted in the FE models (i.e. D/t > 29.2); insufficiently constrained concrete material model was adopted. Dai and Lam (2010) studied different friction coefficient (µ) (i.e. in the tangential direction), from 0.1 to 0.5, between the two interaction planes of the outer concrete core surface and the LDSS tube inner surface.

Verification of the FE Models

Therefore, increasing the thickness of the LDSS tube is more beneficial to increase the strength of the CFDSST buttress columns rather than the concrete strength. Furthermore, lower values of δu for the representative square section can be attributed to early buckling of the LDSS tube thus providing less restraint on the concrete core compared to the NRSs. Therefore, increasing the thickness of the LDSS tube is more beneficial to increase the strength of the CFDSST buttress columns rather than the concrete strength.

Concrete-filled Tubular Stub Column Modeling

Introduction

Results and Discussion

Introduction
Influence of the LDSS tube

Cross-section resistance

S2 defines the ultimate strength capacity of the CFDSST stub column and is dependent on the cubic strength of the concrete (see Figures 5.7a and b), cross-sectional shapes and the thickness of the LDSS pipe. LDSS pipe with concrete significantly increases the strength capacity of the CFDSST stub columns, but at the cost of a decrease in εu (i.e., ε at Pu) with increasing concrete strength. Figures 5.9a and b show that the influence of the LDSS pipe alone (excluding the involvement of the concrete core and the confinement effect) on the Pu decreases with increasing concrete strength and increases with increasing thickness of the steel pipe.

Conclusions

Based on the reliability analyses, it can be seen that except for CFDSST stub columns with +-shaped section, both codes show β0 ≥ 2.5 when compared with the actual FE results. Considering the lower limit of β0 = 2.5 suggested by the ASCE specification for structural members, it can be concluded that both specifications can be adopted for all design of CFDSST stub columns except CFDSST stub columns with +-shaped section, where a suitable modification can be employed after systematic studies (including experiments). However, for CFDSST stub columns, design based on American specifications tends to be slightly more reliable compared to European specifications.

Introduction

FE Modelling

Concrete core material model
Initial geometric imperfections

The first global buckling mode shapes are then used as initial geometric imperfections pattern to perturb the geometry of the slender columns similar to that followed in Chapter 4 for the FE analyzes of the hollow tubular slender columns with fixed ends. However, global geometric imperfections were considered as they are one of the most important effect factors on the ultimate strength (Galambos, 1998). This imperfection size was applied at the midspan of the column in the plane of the weaker major axis for all CFDSST slender column FE models with fixed ends.

Verification of the FE Models

Strength Analysis of Concrete-Filled Thin-Wall Steel Box Columns.'' Journal of Constructional Steel Research. Analysis and design of concrete reinforced thin-walled steel tubular columns under axial compression. Experimental study of the seismic behavior of concreted steel tubular columns with TL section.

Concrete-filled Tubular Slender Column Modeling

Introduction

Results and Discussion

Introduction

Design strengths

The FE results were compared with currently available stainless steel design standards such as European (EN) and American (ANSI/AISC) specifications for their applicability in the design of CFDSST slender columns with fixed ends. As the current design standards are based on stainless steel material it is the applicability of these codes in the design of slender fixed-end CFDSST columns is evaluated by FE studies. Figures 6.10 to 6.12 show a plot of Pu vs. L/D for slender fixed-end CFDSST columns with NRS and a representative square section.

Conclusions

For the design of CFDSST fixed slender columns with square and L-shapes, the American specification is more reliable compared to the European specification, and vice versa for the design of CFDSST fixed slender columns with T-shapes and +-shaped parts. For the design of CFDSST fixed slender columns with square and L-shapes, the American specification is more reliable compared to the European specification, and vice versa for the design of CFDSST fixed slender columns with T-shapes and +-shaped parts. Dimensions and areas of the cross-section % deduction in ex. CHAPTER 6 - NUMERICAL MODELING OF SLIM COLUMNS WITH FILLED CONCRETE.

CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK 149-157

Hollow tubular stub columns of NRSs and square section

The deformation capacity also increases with increasing thickness for all the analyzed hollow tube stub columns. For dense sections, FE predicts forces above both the codal forces (European and US specifications) by about 28% for all the sections studied. Based on the FE studies, it can be deduced that for slender sections, the US spec.

Hollow tubular slender columns of NRSs and square section

However, for LDSS hollow tubular stub columns, design based on European specification tends to be slightly more reliable compared to the American specification, except for +-shape section, where the American specification tends to be more reliable. However, the design of hollow tubular slender column with L-shaped section by the American specification tends to be critical where it predicts the FE strengths. European specifications tend to be more reliable compared to the American specification and vice versa in the design of Class 4 sections.

Concrete-filled tubular stub columns of NRSs and square section

Concrete-filled tubular slender columns of NRSs and square section

However, the European specification gives a conservative estimate of strengths compared to the American specification for square and L-shaped sections and vice versa in the case of T-shaped and +-shaped sections.

Suggestions for further work

Loading Conditions
In-fill Materials
Other Suggestions

Examples of the use of stainless steel hollow tubular columns

Few examples of composite stainless steel-concrete column sections

Examples of the use of lean duplex stainless steel material

Examples of the use of concrete-filled stainless steel tubular columns

Examples of experimental test on stainless steel hollow tubular columns

Examples of experimental test on stainless steel concrete-filled

Examples of experimental test on LDSS hollow tubular columns

Tested specimens of specially shaped reinforced concrete

Schematic diagram of stainless steel and carbon material

Illustration of the stress-strain curve of the Ramberg-Osgood model with

Equivalent uniaxial stress-strain curve for confined and

Identification of partial products (slabs, blooms and billets) and

Examples of hollow tubular sections formed from different processes

Boundary conditions applied to a square LDSS hollow tubular stub

Typical mesh convergence study of FE models

First eigen buckling modes for (a) SHC; (b) LHC, (c) THC, & (d) +-HC

Stress strain curve of the lean duplex stainless steel material

Variation of P with δ for 80x80x4-SC2

Specimen cross-sections of (a) square and (b-d)NRSs

Typical failure modes for hollow tubular stub columns with NRSs

Effect of cross-sectional shape on the load capacity of hollow

Variation of P u with cross-sectional shapes

Variation of perfentage P u /P u(sq) with cross-sectional shapes

Effect of cross-sectional shape on the deformation capacity

Schematic diagam showing determination of B e

Variation of P u with t for LDSS hollow tubular stub columns

Typical boundary conditions applied to fixed-ended slender

Typical lowest eigen modes for fixed-ended hollow tubular slender

Typical deformed shapes for hollow tubular slender column

Von-Mises stress (superimposed on deformed shape) at P u for

Von-Mises stress (superimposed on deformed shape)

Typical variation of P with δ with varying lengths (Class 3 SHC)

Variation of ε u with for Class 3 sections

Variation of ε u with  for Class 4 sections

Variation of P nom with  for Class 3 sections

Variation of P nom with  for Class 4 sections

Typical Boundary conditions applied to CFDSST stub column FE models

Concrete-filled steel tubular stub column specimens

Comparison of the experimental and FE failure modes for the