Research On The Second-order Effect Of Two Cross Reinforced Concrete Bent-frames And The Effective Length Of Bent-columns

The stipulation of equivalent length of bent frame column in current “Code fordesign of concrete structures” introduced from the former Soviet union has not changedin the last fifty years, and lacks theoretical basis. Yet current studies of the equivalentlength of bent frame column, or exist conceptual issues, or still need to be furtherverified and improved. Based on this situation, the thesis author’s research teamundertook the project of China Academy of Building Research, i.e.“the research onfollow-up questions of second-order effect law” in the “Code for design of concretestructures (GB50010-2010)”. On the basis of existing research results in the team andthrough a series of numerical examples, this paper studied the second-order effect lawand the equivalent length values of columns in two-span bent RC frame.This paper takes crane tonnage, bent span, top and bottom column altitude ratio and reference wind pressure as four variables, and then according to the general atlasdesigned two bins of two-span bent RC frame models with a bin of the same altitudeand another bin of different altitude. For each bent model, make first-order andsecond-order elastic analysis under the action of load combinations using the finiteelement analysis software ETABS. And then determine the most unfavorable loadcombinations of each control column section in bent according to the second-orderanalysis results. At last, find out the moment magnifier using analysis data of themost unfavorable load combinations, and back calculate the equivalent lengthl0ofeach column in bent frame through the l0method. In the process of the researchwork, the achievements in this paper are as follows:(1) Briefly reviewed the l0method which could approximately consider thesecond-order effect of bent columns, and then simply combed regulations on secondorder effect in02edition and10edition “Code for design of concrete structures”.(2) Discussed the various load effect on the bent frame structure in detail,compared the differences between “Load code for the design of building structures” GB50009-2012and GB50009-2001in the bent frame structure of load combinations, andproved that the two different kinds of load combinations has a little influence on theresearch results of the paper using a example of single span bent, and the results of theexample, moment magnifier and equivalent length factor, show a very goodstability. (3) The second-order effect and the equivalent length of two span equal altitudebent column were studied with34examples. Found out that, in the four influencingfactors, crane tonnage, bent span, top and bottom column altitude ratio andreference wind pressure, the most important influencing factor for the second-ordereffect and the equivalent length of bent column is top and bottom column altitude ratio. And the regularity is shown as follows. With the increase of the top and bottomcolumn altitude ratio, the moment magnifier of bent upper column decreased,and the equivalent length factor also decreased; With the increase of the top andbottom column altitude ratio, the moment magnifier of bent lower columndecreased, but the equivalent length factor increased.(4) With the top and bottom column altitude ratio as influencing factor,suggested values of equivalent length factor for two span equal altitude bentcolumn are given. And the rationality of the proposed solution is verified by somenumerical examples.(5) The second-order effect and the equivalent length of two-span unequal altitudebent column were discussed simply with9examples. Discovered that the law of thesecond-order effect and the equivalent length of two span unequal altitude bent columnis basically consistent with the equal altitude bent column, and the top and bottomcolumn altitude ratio is still the most important influencing factor.(6) Compared the moment magnifier and equivalent length factor of sidecolumns in two-span equal altitude and unequal altitude bent frame with thoseparameters in one-span bent frame, discovered that the variation of the momentmagnifier and equivalent length factor in the three kinds of bent columns arebasically the same, and their value range was similar, most of the equivalent lengthcoefficient values can be contained by the suggested values of two-span equalaltitude bent, so we can consider that the proposed solution of equivalent lengthcoefficient for two span equal altitude bent columns can also be applied to two spanunequal altitude bent columns. Moreover, it is safer to use the proposed solution of twospan equal altitude bent in the middle columns of two span unequal altitude bent.