A COMPARISON OF OESIGN METHOO FOR STEELENCDNCRETE COLUMNS AND STEEL REINFORCED CONCRETE where Is and Ic are modulus, e the second moments of area of the steel and c concrete,Es is the steel elas is the ncrete seca urocode2,andBdig th ratio of nentloading to the total loading to account for creep effects using a reduced perma modulus approach.For the short term loading used in laboratory strength tests,Bd=0. An alternative(Bridge et al 1986)to Equation 8 is a modification to Equation9 where EI=167MubD/(1+(tBd) and E/is the secant flexural stiffness of the cross-section corresponding to the "balanced"moment capacity Mub of the cross-section taken to occur(Rotter 1982)when the neutral axis is at mid- depth D/2 of the composite section and the extreme concrete fibre strain in compression is 0.003 (Bridge 1990).The advantage of Equa tionis that the value of Mub takes into account the particular material and geometric configuration of the cross-section and hence obviates the need for the calibration and correction factors used in Equation 8. 4.2 Section strength The section strength is defined as the load and moment capacity of a cross-section i.e.a short column without any overall member instability.The pure moment capacity(zero axial load)is denoted by Muo and the pure axial compressive load capacity(zero moment)is denoted by Nuo. 4.2.1 Reinforced concrete 4.2.1.1 Strength The can be caculated on the basis and strain-co patibility considerations.This requires knowledge of the geometry of the cross-section and the stress-strain relationships for both the concrete and the reinforcement.Most codes allow simplified rectangular stress blocks to be used for the concrete stress distribution.For a range of practical cross-sections.load-moment interaction curves have been calculated and provided in design handbooks(eg.CCAA HB71-2002).A typical reinforced concrete curve is shown in Figure 2. Page 7124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 7 | 24 where Is and Ic are the second moments of area of the steel and concrete, Es is the steel elastic modulus, Ec is the concrete secant modulus and ϕt is the creep coefficient (Eurocode 2), and βd is the ratio of permanent loading to the total loading to account for creep effects using a reduced modulus approach. For the short term loading used in laboratory strength tests, βd = 0. An alternative (Bridge et al 1986) to Equation 8 is a modification to Equation 9 where EI = 167MubD/(1 + ϕt βd) (9) and EI is the secant flexural stiffness of the cross-section corresponding to the “balanced” moment capacity Mub of the cross-section taken to occur (Rotter 1982) when the neutral axis is at middepth D/2 of the composite section and the extreme concrete fibre strain in compression is 0.003 (Bridge 1990). The advantage of Equation 9 is that the value of Mub takes into account the particular material and geometric configuration of the cross-section and hence obviates the need for the calibration and correction factors used in Equation 8. 4.2 Section strength The section strength is defined as the load and moment capacity of a cross-section i.e. a short column without any overall member instability. The pure moment capacity (zero axial load) is denoted by Muo and the pure axial compressive load capacity (zero moment) is denoted by Nuo. 4.2.1 Reinforced concrete 4.2.1.1 Strength The section strength can be calculated on the basis of equilibrium and strain-compatibility considerations. This requires knowledge of the geometry of the cross-section and the stress-strain relationships for both the concrete and the reinforcement. Most codes allow simplified rectangular stress blocks to be used for the concrete stress distribution. For a range of practical cross-sections, load-moment interaction curves have been calculated and provided in design handbooks (eg. CCAA HB71-2002). A typical reinforced concrete curve is shown in Figure 2
Reinforced Concrete 0.8 Composite 0.6 系 0.4 Steel -Eq.1 0.2 Steel-Analysis. Steel-Eq.2 0 0 0.5 1 1.5 Moment Capacity M/Muo Figure 2 Load-moment interaction curves 4.2.1.2 Local buckling Local buckling of the reinforcement is restrained by the concrete surrounding the reinforcement Tests by Hudson(1966)on reinforced concrete columns with or without ties showed that the concrete alone apparently provided sufficient restraint against reinforcement buckling such that the absence of ties seemingly had no effect on the maximum load capacity of the columns. However,ties and tie spacing are required (AS3600)to provide positive restraint and to ensure a more ductile performance in the post-ultimate region,i.e.provision against brittle failure. 4.2.25teel 4.2.2.1 Strength The strength of a bare steel cross-section can also be determined by analysis on the basis of equilibrium and strain-compatibility considerations.The results are shown by the curve marked anaysis n typica Universal Beam nsection bent about its major axis.However,as the moment capacity is not enhanced with the application of low levels of axial compressive load,as it
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 8 | 24 Figure 2 Load-moment interaction curves 4.2.1.2 Local buckling Local buckling of the reinforcement is restrained by the concrete surrounding the reinforcement. Tests by Hudson (1966) on reinforced concrete columns with or without ties showed that the concrete alone apparently provided sufficient restraint against reinforcement buckling such that the absence of ties seemingly had no effect on the maximum load capacity of the columns. However, ties and tie spacing are required (AS 3600) to provide positive restraint and to ensure a more ductile performance in the post-ultimate region, i.e. provision against brittle failure. 4.2.2 Steel 4.2.2.1 Strength The strength of a bare steel cross-section can also be determined by analysis on the basis of equilibrium and strain-compatibility considerations. The results are shown by the curve marked analysis in Figure 2 for a typical Universal Beam section bent about its major axis. However, as the moment capacity is not enhanced with the application of low levels of axial compressive load, as it
A COMPARISON OF DESIGN METHOD FOR STEELENCAONCRETE COLUMNS AND STEEL REINFORCED CONCRETE is for cross-sections containing concrete where been traditional in steel standards such asAS 4100 to use a simple linear expression of the form =1- (10) For doubly symmetric compact I-sections bent about the major-axis,a closer approximation to the analytical result is permitted by AS 4100 where: ÷=118-≤10 (11 The corresponding equations in ANSI/AISC 360-05 are even closer to the analytical solution 4.2.2.2 Local buckling The strength can be redued by lcal buckling of the section.This is a function of the slenderness Ae of the plate elements defined in As 4100 as Ae=b/tv(fy/250)for flat plate elements,and Ae=do/t(fy/250)for circular hollow sections.When Ae exceeds the plate element vield slenderness limit Aey.the actual width b is replaced by a reduced effective width be which can carry the yield stress where: b=b:2≤b (12) This process is similar to other steel codes(ANSI/AISC360-05,BS 5950 and Eurocode 3). 4.2.3 Composite 4.2.3.1 Strength As for reinforced concrete,the strength of a composite cross-section,as defined by its load- moment interaction curve,can be calculated on the basis of equilibrium and strain-compatibility considerations in coniunction with appropriate material stress-strain relationships(Eurocode 4. ANSI/AISC 360-05). This process is a little more complex than for a reinforced concrete as the steel section in the composite member has its own inherent stiffness without the concrete.A typical curve is shown in Figure 2 for an I-section encased in concrete and bent about its maior axis.For simple cross- sections such as concrete filled rectangular tubes,concrete filled circular tubes,partially encased sections and fully encased -sections,Eurocode 4 provides simplified plastic calculations resulting in an approximation using four straight lines. For circular concrete filled tubes,Eurocode 4 allows for an additional increase in strength of the concrete due confinement by the steel tube
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 9 | 24 is for cross-sections containing concrete where the axial load reduces cracking, it has been traditional in steel standards such as AS 4100 to use a simple linear expression of the form: (10) to represent the load-moment interaction curve in a conservative manner as shown in Figure 2. For doubly symmetric compact I-sections bent about the major-axis, a closer approximation to the analytical result is permitted by AS 4100 where: ⌊ ⌋ (11) The corresponding equations in ANSI/AISC 360-05 are even closer to the analytical solution. 4.2.2.2 Local buckling The strength can be reduced by local buckling of the steel plate elements forming the crosssection. This is a function of the slenderness λe of the plate elements defined in AS 4100 as λe=b/t√(fy/250) for flat plate elements, and λe=do/t(fy/250) for circular hollow sections. When λe exceeds the plate element yield slenderness limit λey, the actual width b is replaced by a reduced effective width be which can carry the yield stress where: (12) This process is similar to other steel codes (ANSI/AISC 360-05, BS 5950 and Eurocode 3). 4.2.3 Composite 4.2.3.1 Strength As for reinforced concrete, the strength of a composite cross-section, as defined by its loadmoment interaction curve, can be calculated on the basis of equilibrium and strain-compatibility considerations in conjunction with appropriate material stress-strain relationships (Eurocode 4, ANSI/AISC 360-05). This process is a little more complex than for a reinforced concrete as the steel section in the composite member has its own inherent stiffness without the concrete. A typical curve is shown in Figure 2 for an I-section encased in concrete and bent about its major axis. For simple crosssections such as concrete filled rectangular tubes, concrete filled circular tubes, partially encased Isections and fully encased I-sections, Eurocode 4 provides simplified plastic calculations resulting in an approximation using four straight lines. For circular concrete filled tubes, Eurocode 4 allows for an additional increase in strength of the concrete due confinement by the steel tube
4.2.3.2 Local buckling For fully encased steel sections,Eurocode 4 allows the effects of local buckling to be neglected provided that:the cover is not less than 40 mm nor less than one-sixth of the width b of the flange; ongitudinal reinforcement with an area not less than 0.3%of the concrete cross-section is provided;and ties are provided to Eurocode2 which has similar provisions. 4.3 Member strength 4.3.1 Axial load 4.3.1.1 Reinforced concrete Reinforced concrete design standards traditionally do not make use of a column curve which accounts for the effects of geometric and material imperfections.Instead,axially loaded members are treated as beam-columns with the load being applied at a minimum eccentricity of 0.05D(AS 3600)or 0.03D+15mm (ACI 318-05).Using this minimum eccentricity applied at both ends of a pin-ended column,an can be generated for reinforced columns using a non-linear column analysis(Bridge and Roderick 1978)for a range of column slenderness.The results of the analysis for a typical rectangular reinforced column are shown in Figure 3 and are compared with the column curves for steel members in as 4100.It can be seen from Figure 3 that even for a column of zero slenderness(ie.a cross-section),the axial column strength Ncis less than the pure ax compressive load capacity Nuo for reinforced concrete columns as a result of using the value of 0.05D for the minimum eccentricity of load. Page 10124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 10 | 24 4.2.3.2 Local buckling For fully encased steel sections, Eurocode 4 allows the effects of local buckling to be neglected provided that: the cover is not less than 40 mm nor less than one-sixth of the width b of the flange; longitudinal reinforcement with an area not less than 0.3% of the concrete cross-section is provided; and ties are provided to Eurocode 2 which has similar provisions to AS 3600. 4.3 Member strength 4.3.1 Axial load 4.3.1.1 Reinforced concrete Reinforced concrete design standards traditionally do not make use of a column curve which accounts for the effects of geometric and material imperfections. Instead, axially loaded members are treated as beam-columns with the load being applied at a minimum eccentricity of 0.05D (AS 3600) or 0.03D + 15mm (ACI 318-05). Using this minimum eccentricity applied at both ends of a pin-ended column, an equivalent column curve can be generated for reinforced columns using a non-linear column analysis (Bridge and Roderick 1978) for a range of column slenderness. The results of the analysis for a typical rectangular reinforced column are shown in Figure 3 and are compared with the column curves for steel members in AS 4100. It can be seen from Figure 3 that even for a column of zero slenderness (i.e. a cross-section), the axial column strength Nc is less than the pure axial compressive load capacity Nuo for reinforced concrete columns as a result of using the value of 0.05D for the minimum eccentricity of load
ACOMPARISON OF OESIGN METHOO FOR STEEL ENCAONCRETE COLUMN AND STEEL REINFORCEO CONCRETE 4=-1.0 a=-0.5 Steel 0.8 46=0.0 4=0.5 0.6 .04=1.0 0.4 Reinforced Concrete 0.2 (equivalent) 0 0 0.20.40.60.81 1.21.41.6 Slenderness Fiaure 3 Column curves for steel and reinforced concrete 4.3.1.2 Steel The axial load capacity Nc for steel columns is determined in AS 4100 from a series of five column curves as shown in Figure 3.Each curve is defined by a member section constant ab which reflects the method of manufacture of thecom section which in turn influe the degree of out-of straightness of the member and the level of residual stress,factors which affect the column capacity.For example,RHS and CHS sections are relatively straight with low membrane residual stresses and are therefore designed to the upper curve with ab=-1.0.Multiple column curves are also used in Eurocode 3 and BS 5950 whereas ANSI/AISC 360-05 continues to use a single column curve as in the past. 4.3.1.3 Composite n Eurocode 4,the axial load capacity of c can be detern umn cu de n sing the erness A IS Ca d The appropriate co rve dep nds on the ure ne composite umn similar to the procedure umns in AS 4100.In fact,the mn curves in Eurococ 3 are very simila r to those in. which are shown in Figures 3 and 4.A similar design approach to Eurocode 4 is used in ANSI/AISC 360-05 which uses only a single column curve. =腰 (13) Page 11124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 11 | 24 Figure 3 Column curves for steel and reinforced concrete 4.3.1.2 Steel The axial load capacity Nc for steel columns is determined in AS 4100 from a series of five column curves as shown in Figure 3. Each curve is defined by a member section constant αb which reflects the method of manufacture of the column section which in turn influences the degree of out-ofstraightness of the member and the level of residual stress, factors which affect the column capacity. For example, RHS and CHS sections are relatively straight with low membrane residual stresses and are therefore designed to the upper curve with αb = -1.0. Multiple column curves are also used in Eurocode 3 and BS 5950 whereas ANSI/AISC 360-05 continues to use a single column curve as in the past. 4.3.1.3 Composite In Eurocode 4, the axial load capacity of composite steel and concrete columns can be determined from the column curves in Eurocode 3 for the design of steel structures using the slenderness λ as defined in the equation (4) in which the buckling load Ncr is calculated using an effective stiffness. The appropriate column curve depends on the method of manufacture of the steel section used in the composite column, similar to the procedure used for steel columns in AS 4100. In fact, the column curves in Eurocode 3 are very similar to those in AS 4100 which are shown in Figures 3 and 4. A similar design approach to Eurocode 4 is used in ANSI/AISC 360-05 which uses only a single column curve. √ (13)