The non-linear analysis column analysis by Bridge and Roderick(1978)was used to calculate the axial strength of two typical composite sections:an encased universal column UC section;and a concrete filled square hollow SHS section. An out-of-straightness of L/1000 was used which is the fabrication tolerance specified in AS 4100 Typical residual stresses were used for the steel sections.Shrinkage stresses induced in the steel micro-strain.The members were analysed as pin-ended columns for a range of different slenderness.The results are shown in Figure 4 and are compared with the steel column curves in As 4100.Eurocode 4 also allows the use of such a direct analytical approach for the strength of axially loaded me mbers and specifies the equivalent member imperfection to be used in the order analysis. 04=-1.0 4=-0.5 Steel 4=0.0 ◆ 04=0.5 号0.6 4=1.0 @0.4 ▲Encased I- section 0.2 ■Filled square 0 0 05 1 15 2 2.5 Slendemess Figure 4 Column curves for steel and composite coumns It can be seen from Figure 4 that the column curves in AS 4100 could be adapted for composite columns although it is likely,as a result of this preliminary study,that a lower column curve than that b ed purely on the method of manufacture of the steel section would have to be selected. 4.3.2 Combined axial compression and bending moment In this section,only the in-plane strength of bea coumns is considered as reinforced con and com 05 T suc hape tha -o-pia el columns bent about their ne effects ar r strong axis Page
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 12 | 24 The non-linear analysis column analysis by Bridge and Roderick (1978) was used to calculate the axial strength of two typical composite sections: an encased universal column UC section; and a concrete filled square hollow SHS section. An out-of-straightness of L/1000 was used which is the fabrication tolerance specified in AS 4100. Typical residual stresses were used for the steel sections. Shrinkage stresses induced in the steel and concrete of the encased section were also included assuming a free concrete shrinkage of 600 micro-strain. The members were analysed as pin-ended columns for a range of different slenderness. The results are shown in Figure 4 and are compared with the steel column curves in AS 4100. Eurocode 4 also allows the use of such a direct analytical approach for the strength of axially loaded members and specifies the equivalent member imperfection to be used in the second-order analysis. Figure 4 Column curves for steel and composite columns It can be seen from Figure 4 that the column curves in AS 4100 could be adapted for composite columns although it is likely, as a result of this preliminary study, that a lower column curve than that based purely on the method of manufacture of the steel section would have to be selected. 4.3.2 Combined axial compression and bending moment In this section, only the in-plane strength of beam-columns is considered as reinforced concrete and composite steel-concrete columns are usually of such a shape that out-of-plane effects are not significant. This may not be the case for steel columns bent about their strong axis
ACOMPARISON OF OESIGN METHOO FOR STEEL ENCAONCRETE COLUMN AND STEEL REINFORCEO CONCRETE The applied axial force Nand lar within the column,magnified for second-order effects,is then determined from Equation 1. 4.3.2.1 Reinforced concrete Using the provisions AS 3600,the in-plane strength of a member in combined bending and axial compression is best described with reference to the load-moment interaction curve in Figure 5 e/D=0.05 N (N',M.) Moment M Figure 5 Interoction curve for reinforced concrete Where the larger end eccentricity e2=M2/N*is less than the minimum eccentricity of 0.05D,the end moment M2*(and M1*assuming symmetrical single curvature)is taken as M2*=N*/0.05D)=M1 (14) Using moment magnification.this results in the curved dashed line in Figure 5 which intersects the solid line for cross-section strength at a value of load Nc which can be considered the strength Nc in axial compression.It should be noted that the minimum eccentricity of 0.05D is not in addition to any end eccentricities resulting from the applied loads and end moments. At the level of the design axial force N,AS 3600 assumes that the nominal bending strength available to resist the maximum design bending moment M*(magnified for second-order effects as in Equation 6)is Mu.This is obtained directly from the load-moment interaction curve as shown in Figure 5.The strength is considered sufficient if M*≤Ma (15) ignoring the capacity reduction factor中，otherwise M*sΦMu.The factorΦcan be taken as unity for laboratory tests where material properties and member geometry are accurately known. 4.3.2.25teel Page 13124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 13 | 24 The applied axial force N* and larger end moment M2* for end-loaded braced members can be determined from a global first-order elastic analysis. The maximum design bending moment M* within the column, magnified for second-order effects, is then determined from Equation 1. 4.3.2.1 Reinforced concrete Using the provisions AS 3600, the in-plane strength of a member in combined bending and axial compression is best described with reference to the load-moment interaction curve in Figure 5. Figure 5 Interaction curve for reinforced concrete Where the larger end eccentricity e2 = M2*/N* is less than the minimum eccentricity of 0.05D, the end moment M2* (and M1* assuming symmetrical single curvature) is taken as M2* = N*(0.05D) = M1* (14) Using moment magnification, this results in the curved dashed line in Figure 5 which intersects the solid line for cross-section strength at a value of load Nc which can be considered the strength Nc in axial compression. It should be noted that the minimum eccentricity of 0.05D is not in addition to any end eccentricities resulting from the applied loads and end moments. At the level of the design axial force N*, AS 3600 assumes that the nominal bending strength available to resist the maximum design bending moment M* (magnified for second-order effects as in Equation 6) is Mu. This is obtained directly from the load-moment interaction curve as shown in Figure 5. The strength is considered sufficient if M* ≤ Mu (15) ignoring the capacity reduction factor φ, otherwise M* ≤ φMu. The factor φ can be taken as unity for laboratory tests where material properties and member geometry are accurately known. 4.3.2.2 Steel
Using the provisions AS 4100,the in-plane strength of a member in combined bending and axia compression is considered sufficient if MSM 6 where Mi is the in-plane moment capacity given by M=(1-9Mu0 (17 and Nc is the capacity in axial compression determined from the column curve appropriate to the column cross-section.Column curves for steel members are shown in Figures 3 and 4. N x壬 peo N (N,M) Moment M This procedure can also be described in terms of a load-moment interaction diagram and is shown in Figure 6 for comparison with concrete and composite interaction diagrams.The full section strength is denoted by the dashed line and it can be seen that the section moment strength corresponding to the applied axial load Nis not utilised(difference between the solid and dashe lines at N*).As member imperfections are not explicitly included in AS 4100 for the analysis of the design moment M*,this difference in the lines accounts for the additional moments arising from member imperfections.It is particularly conservative for members bent in double curvature where imperfections can have little or no effect on the design moment M. 4.3.2.3 Composite Page 14 124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 14 | 24 Using the provisions AS 4100, the in-plane strength of a member in combined bending and axial compression is considered sufficient if M * ≤ Mi (16) where Mi is the in-plane moment capacity given by ( ) (17) and Nc is the capacity in axial compression determined from the column curve appropriate to the column cross-section. Column curves for steel members are shown in Figures 3 and 4. Figure 6 Interaction curve for steel members This procedure can also be described in terms of a load-moment interaction diagram and is shown in Figure 6 for comparison with concrete and composite interaction diagrams. The full section strength is denoted by the dashed line and it can be seen that the section moment strength corresponding to the applied axial load N* is not utilised (difference between the solid and dashed lines at N*). As member imperfections are not explicitly included in AS 4100 for the analysis of the design moment M*, this difference in the lines accounts for the additional moments arising from member imperfections. It is particularly conservative for members bent in double curvature where imperfections can have little or no effect on the design moment M*. 4.3.2.3 Composite
ACOMPARISON OF OESIGN METHOO FOR STEEL ENCAONCRETE COLUMN AND STEEL REINFORCEO CONCRETE Using the provisions of Eurocode 4,the in-plane st ength of a member in combined bending and compression is best described with reference to the load-moment interaction curve in Figure 7 N'M Moment curve for composite members The curved dashed line in Figure7 is the locus of axial load and the second-order moments arising acting on an imperfect colu mn with only an initial bow imperfection as prescribe in Table 6.5 of Eurocode 4.This equivalent bow imperfection is larger than actual member out-of straightness to account for residual stresses and other member imperfections.The column strength Nc in axial compression is where this dashed line intersects the cross-section strength defined by the solid line.Alternatively,Nc is obtained with the use of the appropriate column curve in Eurocode 3 for the steel section using the slenderness A of the equivalent pin-ended column.At the level of the design axial force N*,the remaining bending strength available to resist the maximum design bending M*(magnified for second-order effects as in Equation 1 and including imperfections)is uMuo.The strength is considered sufficient if M*≤Muo (18) If the simplified plastic stress distribution procedures of Eurocode 4 are used to determine the load-moment interaction equation,then the strength is considered sufficient if M*s amuMuo (19 where am is 0.9 for lower steel rades 235 to355 and 0.8 for higher steel grades 420 and 460.The reduction factor m the unc onservatism in the strength calcu ations using full plastic stress blocks for the steel and concrete which ignore considerations of strain. Page 15124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 15 | 24 Using the provisions of Eurocode 4, the in-plane strength of a member in combined bending and compression is best described with reference to the load-moment interaction curve in Figure 7. Figure 7 Interaction curve for composite members The curved dashed line in Figure 7 is the locus of axial load and the second-order moments arising from axial load acting on an imperfect column with only an initial bow imperfection as prescribed in Table 6.5 of Eurocode 4. This equivalent bow imperfection is larger than actual member out-ofstraightness to account for residual stresses and other member imperfections. The column strength Nc in axial compression is where this dashed line intersects the cross-section strength defined by the solid line. Alternatively, Nc is obtained with the use of the appropriate column curve in Eurocode 3 for the steel section using the slenderness λ of the equivalent pin-ended column. At the level of the design axial force N*, the remaining bending strength available to resist the maximum design bending M* (magnified for second-order effects as in Equation 1 and including imperfections) is μMuo. The strength is considered sufficient if M* ≤ μMuo (18) If the simplified plastic stress distribution procedures of Eurocode 4 are used to determine the load-moment interaction equation, then the strength is considered sufficient if M* ≤ αmμMuo (19) where αm is 0.9 for lower steel grades 235 to 355 and 0.8 for higher steel grades 420 and 460. The reduction factor αm accounts for the unconservatism in the strength calculations using full plastic stress blocks for the steel and concrete which ignore considerations of strain
COMPARISON OF DESIGN METHOD FOR STEEL ENCASEOCONCRETE COLUMNS AND STEEL REINFORCEO CONCRETE 5 Real design example Following I repot part of the analys of an high rise building under high seismic forces as here taken Zone iy as pe rl51893:2002w re building is situated,a typical office building plan is selected with area.This cor rative study has been expounded by"D.R.Panchal and P.M.Ma waimin tion of th ar exp es in R.C.C.,steel and composit ng is snown Just tr mn part of the esults.be cause is the aspect in which we are interested 5.1 Architectural details 42.00 Figure Plan view of the building Page 16124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 16 | 24 5 Real design example Following I repot part of the analys of an high rise building under high seismic forces as here taken Zone IV as per IS 1893 : 2002 where building is situated, a typical office building plan is selected with area covering 24 m x 42 m. This comparative study has been expounded by “D. R. Panchal and P. M. Marathe” aiming a clear exposition of the different advantages in R.C.C., steel and composite structure design. Following is shown just the column part of the results, because is the aspect in which we are interested. 5.1 Architectural details Figure 8 Plan view of the building