The Identification And Recommendations For Improvement Of The Analytical Method Of The P-Δ Effect For Structures In Current Codes

The basic law of the second order effect and methods of considering it forreinforced concrete structures are of guiding significance in engineering design.Although significant developments of the law of second order effect and practicalmethods to take it into account have been made by the academia in deferent countries inrecent years, due to the characteristics of reinforced concrete structures, a vast array ofimportant problems still remain to be studied in this field thereby perfecting the currentpractical design methods which are not precise enough. Under the background thatChinese national codes and regulations have been revised recently, thoroughinterpretation of the revised provision on the second order effect in these codes andregulations is made and analyses and researches on some unsettled issues are conductedin this paper. The research findings that are of limited importance are as follows:(1)By way of summarizing related provisions on the second order effect inChinese national codes and regulations of vision1989,2001and2010, this paperintroduces the distinctions of the provisions on the second order effect and evaluates themethods of practical design considering the second order effect in these various visions.In addition, analyses and interpretations on the background of provisions related to thesecond order effect in different visions of codes and regulations have been made andtheir flaws have been pointed out. Technically, this part of work here is aimed togeneralize the characteristics of provisions related to the second order effect in differentvisions of codes and regulations and to summarize the heritage and development ofideas and methods for provisions related to the second order effect in codes andregulations from vision1989to2010.(2)It is clarified that the lateral deformation for frame structures is mainlycharacterized by shear-type deformation and that deformation for shear wall structuresis chiefly characterized by flexure-type deformation. However, the lateral deformationfor frame-shear wall structures and frame-core tube structures etc. exhibit sundrycharacteristics on the basis of different relationships between the stiffness of their framepart and shear wall (core tube) part. This paper proposes the method of distinguishingthe structural floor drift, and utilizing this method, it is possible to clarify itscharacteristics of deformation for each type of structures.(3)In terms of structures with lateral displacements, the law of the P-Δ effect is described in graphic detail under both situations that the P-Δ effect of structures istriggered by flexure-type deformation and shear-type deformation. Apart from that, thelaw how the P-δ effect affects the P-Δ effect is illustrated. Meanwhile, in termsof structures without lateral displacements, this paper summarizes the law how theP-δ effect influences these structures again so as to more accurately understand thelaw of the P-δ effect.(4)The concept and procedure of computing the P-Δ effect caused byshear-type deformation and flexure-type deformation respectively utilizing conventionaliterative method are provided. Through theoretical derivations and comparisons ofcomputing cases, it is clarified that the iterative method of equivalent virtual lateralforce is capable of computing the P-Δ effect of structures triggered by flexure-typedeformation and shear-type deformation separately. Therefore, it is justifiable that theiterative method of equivalent virtual lateral force is able to computing the P-Δ effect of structures with different types of deformation. Currently, a great deal ofgeneral-purpose software (for instance Sap2000, ETABS, PKPM, etc.) utilizesgeometric stiffness based finite element method, which is named the method of virtualcolumn as well, to consider the P-Δ effect of structures. This paper describes thismethod thoroughly and displays the process of geometric stiffness based finite elementmethod utilizing frame structures with single floor and single span. In addition, thispaper explains that the idea of geometric stiffness based finite element method and thatof the iterative method of equivalent virtual lateral force are uniform through theoreticalderivations and analyses of computing cases. Because of this, this method is also able tobe applied to compute the P-Δ effect of structures with different characteristics oflateral deformation, which affords us more useful tools in selecting sensible methods tocompute various types of structures.(5)According to related Chinese codes and regulations, the finite element methodor simplified elastic method can be applied to compute the P-Δ effect of structures,and the influence of inelastic properties on the components’ stiffness of reinforcedconcrete structures should be taken into consideration when computing the momentmagnification factors of different structural components. Whereas, each analysissoftware doesn’t explicitly clarify how to consider the stiffness reduction whenanalyzing the second order effect of structures, hence this paper carries out preliminaryexplanation on questions how to consider the stiffness reduction when analyzing thesecond order effect of both seismic and non-seismic structures and makes effort to propose procedures of considering stiffness reduction coefficients in analyzing thesecond order effect of structures.