M'n8 wp =(1+Ba)1z (9) On the other hand when the available moment redistribution is greater than or equal to the quired t redistribu n(Ba≥Br) of at the ntial hinge hogging re is capal de mechanism moment redistribution develops from the hogging moment region to the sagging moment region. Both in hogging and sagging regions a full plastic resistance can be reached by the hinges,and so a full plastic mechanism will develop. The load carrying capacity in this situation can be computed either by: M',8 w,=1+B)亚 (10) (11) Where:is the distance from the side support =( 1+u-1)/ =Mp/Mp is the ratio of the negative on positive moment resistance It is important to notice that when B<B the moment redistribution ratio is then taken as B=Ba,while when B2B then the moment redistribution ratio is then taken as B=Br. The available rotation capacity of a continuous composite beam should be greater or equal to he bea such a 6.Discussion In EC4,it is proposed that by neglecting cracking of concrete slab,40%of moment redistribution is capable if the effective cross-section in the member is in Class 1,and 30% moment redistribution is for cross-section if the member is in Class 2,as it is possible to see from the fig 3. From laboratory tests and computer simulations,it has emerged that the available moment redistribution from the hogging region to the sagging region of continuous composite beams with plastic cross section in both h ging and s ions is not aly 99 tto enab astic but it is greater than 15% wh in th current It is also been found that,for what concern composite beams with two unequal spans,in most cases the results based on the computer simulation are also lower than the required moment redistribution enabling a full plastic design as predicted by Eq.(7). From these results it is possible to deduce that the available moment redistribution in the continuous composite beams is no more a fixed ratio saying 30%or 40%moment reduction at the internal support
On the other hand when the available moment redistribution is greater than or equal to the required moment redistribution ( ) the rotation capacity at the potential hinge in the hogging region is capable of developing a full plastic mechanism for the beam, and full moment redistribution develops from the hogging moment region to the sagging moment region. Both in hogging and sagging regions a full plastic resistance can be reached by the hinges, and so a full plastic mechanism will develop. The load carrying capacity in this situation can be computed either by: Where: is the distance from the side support is the ratio of the negative on positive moment resistance It is important to notice that when the moment redistribution ratio is then taken as , while when then the moment redistribution ratio is then taken as . The available rotation capacity of a continuous composite beam should be greater or equal to the required rotation capacity in order to allow for a full plastic design of the beam. I such a case a full moment redistribution from the hogging region to the sagging region of the beam is permitted. 6. Discussion In EC4, it is proposed that by neglecting cracking of concrete slab, 40% of moment redistribution is capable if the effective cross-section in the member is in Class 1, and 30% moment redistribution is for cross-section if the member is in Class 2, as it is possible to see from the fig 3. From laboratory tests and computer simulations, it has emerged that the available moment redistribution from the hogging region to the sagging region of continuous composite beams with plastic cross section in both hogging and sagging regions is not always sufficient to enable a full plastic design, but it is greater than 15%, which is the value suggested in the current Chinese Design Code [1]. It is also been found that, for what concern composite beams with two unequal spans, in most cases the results based on the computer simulation are also lower than the required moment redistribution enabling a full plastic design as predicted by Eq. (7). From these results it is possible to deduce that the available moment redistribution in the continuous composite beams is no more a fixed ratio saying 30% or 40% moment reduction at the internal support
The characteristics which mainly influence the allowed moment redistribution are the geometry of the cross section and the properties of the materials,because these features influence the rotation capacity of the cross section and the ratio of negative moment resistance to the positive moment resistance of the beam A study proposed by Shiming Chen and Yuanlin Jia [4]provides a design approach to assess the oad fo based on the cap n deper inding on the e rotation capacity o ratio,et r than a propose in order to obtai an this study emerged that the 15%of moment redistribution,allowed by the Chinese Design Code [1]and based on the global uncracked elastic analysis,is not sufficient to enable a full plastic design as in most of the cases the moment at the mid-span is still elastic. Then the current Chinese design method [1]for a continuous composite beam is very conservative.The uniformly distributed load for the ultimate limit state,found using the calculation method proposed by Shiming Chen and Yuanlin Jia [4],is gr eater than the allowed uniformly distribut load ba sed on the current The rea uired me tion is also slightly lower than a fixed dvalue of 40%as that propose in Eurocode 4 [2] for class 1 section by using uncracked section analysis,which means that 40%of moment redistribution is more than that required to develop a full plastic design.However,because the calculated plastic moment resistance (based on the yielding strength)of a composite section reserves a post yielding strength,in most cases,the conservative based on the Eurocode rule is justified. 7.Conclusions To enable a plastic desian for a continuous composite beam the available moment redistribution for the should be gre eater than or at least qual to the r redistrbution required,in order to permit the moment redistribution from the hogging region to the sagging region in the beam. However sometimes the potential moment redistribution in a continuous composite beam is also assessed when the available rotation capacity at the notional hinge fails to satisfy the required capacity capable of plastic design. For what concern two span continuous composite beams with uniform loading and uniform ngthhms are pabte of plasic deinvn there re the full span.The red mo reace as t of negative t 9 mom nt re stance educes,but de diffe rence,c the difference of load in the two spans increases An economic design of a continuous composite beam should be possible using a design approach which assess the load carrying capacity,and then the available moment redistribution, on the rotation capacity of the cross section or on the force ratio.Studies on these subject were conducted by Shiming Chen and Yuanlin Jia [4]. A possible solution in order to increase the resistance of a continuous composite beam is the use of pre-stressing beams.Adding pre-stressing along the steel bottom flange of a composite beam u der positive mo ment will make the be less deflected and in ase the ultir mate capacity,while adding pre-stressing in hog ging region can minate ks in the concrete slab due to the negative bending.Studies founded [5]that exerting prestressing on a
The characteristics which mainly influence the allowed moment redistribution are the geometry of the cross section and the properties of the materials, because these features influence the rotation capacity of the cross section and the ratio of negative moment resistance to the positive moment resistance of the beam. A study proposed by Shiming Chen and Yuanlin Jia [4] provides a design approach to assess the load carrying capacity for a continuous composite beam based on the available capable moment redistribution depending on the rotation capacity or the force ratio, etc. rather than a fixed value of moment redistribution proposed in order to obtain an economic design. From this study emerged that the 15% of moment redistribution, allowed by the Chinese Design Code [1] and based on the global uncracked elastic analysis, is not sufficient to enable a full plastic design as in most of the cases the moment at the mid-span is still elastic. Then the current Chinese design method [1] for a continuous composite beam is very conservative. The uniformly distributed load for the ultimate limit state, found using the calculation method proposed by Shiming Chen and Yuanlin Jia [4], is greater than the allowed uniformly distributed load based on the current design method. The required moment redistribution is also slightly lower than a fixed value of 40% as that proposed in Eurocode 4 [2] for class 1 section by using uncracked section analysis, which means that 40% of moment redistribution is more than that required to develop a full plastic design. However, because the calculated plastic moment resistance (based on the yielding strength) of a composite section reserves a post yielding strength, in most cases, the conservative based on the Eurocode rule is justified. 7. Conclusions To enable a plastic design for a continuous composite beam, the available moment redistribution for the beam should be greater than or at least equal to the moment redistribution required, in order to permit the full moment redistribution from the hogging region to the sagging region in the beam. However sometimes the potential moment redistribution in a continuous composite beam is also assessed when the available rotation capacity at the notional hinge fails to satisfy the required capacity capable of plastic design. For what concern two span continuous composite beams with uniform loading and uniform cross section along the length, not all the beams are capable of plastic design, even if there are plastic cross sections along the full span. The required moment redistribution increases as the ratio of negative to positive moment resistance reduces, but decreases as the span difference, or the difference of load in the two spans increases. An economic design of a continuous composite beam should be possible using a design approach which assess the load carrying capacity, and then the available moment redistribution, on the rotation capacity of the cross section or on the force ratio. Studies on these subject were conducted by Shiming Chen and Yuanlin Jia [4]. A possible solution in order to increase the resistance of a continuous composite beam is the use of pre-stressing beams. Adding pre-stressing along the steel bottom flange of a composite beam under positive moment will make the beam less deflected and increase the ultimate capacity; while adding pre-stressing in hogging moment region can eliminate cracks in the concrete slab due to the negative bending. Studies founded [5] that exerting prestressing on a
continuous composite beam with external tendons will increase the extent of intemnal force and moment redistribution in the beam.It was found that at the ultimate state,the moment redistribution in the prestressed continuous composite beams is greater than that in non- prestressed composite beams. References [1]Chinese standard:Code for design of steel structures.GBJ50017-2003.2003. [2]UNI_EN_1994-1-1.Eurocode 4:Design of composite steel and concrete structures.Part 1-1: General rules and rules for buildings.Brussels:European Committee for Standardization;1992. 131 UNI EN 1993-1-1.Eurocode 3:Design of steel structures.Part 1-1:General rules and rules for buildings.Brussels:European Committee for Standardization;1992. [4]Shiming Chen,Yua lin lia Required and available redistribution of continuous steel-co compos te beams.School of Civil Engineering,Tongi Univer rsity No.1239,Siping Road,Shanghai 200092,People's Republic of China.(Received 20 December 2006;accepted 11 May2007) [5]Shiming Chen,Yuanlin Jia,and Xindi Wang.Experimental study of moment redistribution and load carrying capacity of externally prestressed continuous composite beams.School of Civil Engineering.Tongii University.No.1239.Siping Road.Shanghai 200092.People's Republic of China (Receiv ved July 7,2008.Accepted March 3.2009) [6]Shi ning Che Xindi Wang,and d Yuanlin Jia.A ompa ative study on ontinuous beams pre with ve Republic of China.(Received April 3,2008,Accepted March 4,2009). [7]G.Vasdravellis,B.Uy,E.L.Tan,B.Kirkland.Behaviour and design of composite beams subjected to negative bending and compression.University of Western Sydney,Sydney, Australia.Received 6 February 2012,Accepted 25 July 2012. [81 David a.Nethercot.Composite Construction.Spon Press.Tavlor and francis Group [9]R.P.Johnson.Composite Structures or Steel and Concrete,Volume 1,Second edition. Blackwell Scienti ific Pubblications
continuous composite beam with external tendons will increase the extent of internal force and moment redistribution in the beam. It was found that at the ultimate state, the moment redistribution in the prestressed continuous composite beams is greater than that in nonprestressed composite beams. References [1] Chinese standard: Code for design of steel structures. GBJ50017-2003. 2003. [2] UNI_EN_1994-1-1. Eurocode 4: Design of composite steel and concrete structures. Part 1-1: General rules and rules for buildings. Brussels: European Committee for Standardization; 1992. [3] UNI_EN_1993-1-1. Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings. Brussels: European Committee for Standardization; 1992. [4] Shiming Chen, Yuanlin Jia. Required and available moment redistribution of continuous steel–concrete composite beams. School of Civil Engineering, Tongji University, No. 1239, Siping Road, Shanghai 200092, People’s Republic of China. (Received 20 December 2006; accepted 11 May 2007) [5] Shiming Chen, Yuanlin Jia, and Xindi Wang. Experimental study of moment redistribution and load carrying capacity of externally prestressed continuous composite beams. School of Civil Engineering, Tongji University, No. 1239, Siping Road, Shanghai 200092, People’s Republic of China. (Received July 7, 2008, Accepted March 3, 2009) [6] Shiming Chen, Xindi Wang, and Yuanlin Jia. A comparative study on continuous steelconcrete composite beams prestressed with external tendons: Experimental investigation. School of Civil Engineering, Tongji University, No. 1239, Siping Road, Shanghai 200092, People’s Republic of China. (Received April 3, 2008, Accepted March 4, 2009). [7] G. Vasdravellis, B. Uy, E.L. Tan, B. Kirkland. Behaviour and design of composite beams subjected to negative bending and compression. University of Western Sydney, Sydney, Australia. Received 6 February 2012, Accepted 25 July 2012. [8] David A. Nethercot. Composite Construction. Spon Press, Taylor and Francis Group. [9] R.P. Johnson. Composite Structures or Steel and Concrete, Volume 1, Second edition. Blackwell Scientific Pubblications
A comparison of design method for steel encased concrete columns and steel reinforced concrete columns. Analysis,Design,Example Claudio De Filippis Abstract This paper is the result of research aimed at highlighting the different methods of design for steel column,steel reinforced concrete column and composite column.The comparison has been extended also to the steel structures to better understand some aspects of the design and because there are many similarities.The technical codes to which reference is made are:As 3600 AS4100 and Eurocode 4. Then we will see how different approaches lead to very similar results.Not only in well design of the column will be analysed but also the manner in which certain effects are taken into account. After a brief introduction on the composite column are explained materials,security factors and calculation of strength in different condition. At the end of the paper it is a practical example of analysis of a structure using the three differen construction methods.This example lead us to better understand the real gains in all three case
A comparison of design method for steel encased concrete columns and steel reinforced concrete columns. Analysis, Design, Example Claudio De Filippis Abstract This paper is the result of research aimed at highlighting the different methods of design for steel column, steel reinforced concrete column and composite column. The comparison has been extended also to the steel structures to better understand some aspects of the design and because there are many similarities. The technical codes to which reference is made are: AS 3600, AS4100 and Eurocode 4. Then we will see how different approaches lead to very similar results. Not only in well design of the column will be analysed but also the manner in which certain effects are taken into account. After a brief introduction on the composite column are explained materials, security factors and calculation of strength in different condition. At the end of the paper it is a practical example of analysis of a structure using the three different construction methods. This example lead us to better understand the real gains in all three case. TONGJI UNIVERSITY – Course of Composite structure Claudio De Filippis
ACOMPARISON OF OESIGN METHOO FOR STEEL ENCAONCRETE COLUMN AND STEEL REINFORCEO CONCRETE 1 Introduction concrete encas t-ro stee on or a cor steel and is s gen as a load- aring memb in a comp ypica osite columns with fully and partially concrete encased tlons are ustrated in Fig.1. b=b (b) (c) Figure 1 Typical cross-sections of fully and partiolly concrete encased columns In a composite column both the steel and concrete would resist the external loading by interacting together by bo and friction.Supplementary reinforcement ir the concrete encasement prevents excessive spalling of concrete both under normal load and fire conditions. Page 1124
A COMPARISON OF DESIGN METHOD FOR STEEL ENCASED CONCRETE COLUMNS AND STEEL REINFORCED CONCRETE COLUMNS P a g e 1 | 24 1 Introduction A steel-concrete composite column is a compression member, comprising either a concrete encased hot-rolled steel section or a concrete filled tubular section of hot-rolled steel and is generally used as a load-bearing member in a composite framed structure. Typical cross-sections of composite columns with fully and partially concrete encased steel sections are illustrated in Fig. 1. Figure 1 Typical cross - sections of fully and partially concrete encased columns In a composite column both the steel and concrete would resist the external loading by interacting together by bond and friction. Supplementary reinforcement in the concrete encasement prevents excessive spalling of concrete both under normal load and fire conditions