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標題: AISI開口斷面翹曲常數之數值化分析
Numerical Evaluations for Warping Constants of AISI Open Sections
作者: 邱培智
Chiu, Pei-Chi
Contributors: 呂東苗
D. M. Lue
國立中興大學
關鍵字: American Iron & Steel Institute;open thin-walled section;shear center;unit warping;normalized unit warping;warping constant
美國鋼鐵協會;開口薄壁斷面;剪力中心;單位翹曲;法化單位翹曲;翹曲常數
日期: 2002
Issue Date: 2012-08-17 16:33:04 (UTC+8)
Publisher: 土木工程學系
摘要: 九二一集集大地震發生之後,儘管鋼結構具有較佳的抗震能力,但是不難從許多災區中發現鋼構造物的倒塌。由於這些倒塌的鋼結構大多是使用熱軋型鋼,而熱軋型鋼本身的自重較大,所以,一旦遭受地震作用時便會產生較大的慣性力,因此導致結構物損壞的機率增加,有鑑於此,假使能大量的使用冷軋鋼,藉著冷軋鋼之自重小、可回收性高等優點,相信能大幅度的改善鋼結構因強震而損壞的情形。
冷軋鋼中常見之開口斷面(open section)構件受到扭力作用時應考慮純扭曲應力(pure torsional shear stress)與翹曲應力(warping stress)之產生,而翹曲應力則包括翹曲剪應力(warping shear stress)與翹曲正向應力(Warping normal stress),其中翹曲剪應力之分析所面臨之困難為翹曲常數(warping constant, Cw)之計算。雖然許多常見開口斷面之翹曲常數已有現成公式可用,但是這些現成公式一般而言相當複雜。開口斷面翹曲常數之取得,必須先計算斷面剪力中心之位置,再依此計算翹曲常數,其過程牽涉複雜之積分運算,並不容易。
本研究以一階分析(first-order analysis)為基礎,推導翹曲常數理論公式之積分式,考慮斷面由薄壁板元素(thin-walled plate element)所組成,將理論積分式改成數值公式,再將數值公式編寫成Visual Fortran電腦程式,由電腦執行開口斷面翹曲常數之運算工作。所有電腦計算結果將與現有公式計算結果作一比較,並提供AISI / LRFD Cold-Formed Steel Manual[1](P.Ⅴ—26∼34)所列舉斷面之翹曲常數值Cw計算流程及結果供業界參考。
Steel structures are mostly made of hot-rolled steels which have larger self-weight as compared with cold-formed steels. Rolled steel structures will, therefore, have a larger inertia force created when structures are subjected to a seismic force. Although a cold-formed steel has a better performance than a rolled steel when structure is subjected to later forces including earthquake and wind , the evaluation of cold-formed steel structures is more complicated than rolled steel structure.
When a cold-formed steel member is subjected to torsion, the stress analysis of section includes pure torsion stress and warping stresses which are composed of warping shear and warping normal stresses. The evaluation of pure torsion stress is quite straightforward and is well defined. However, the analysis of warping shear stress is not an easy task for general practicing engineers. The difficulty comes from the evaluation of warping constant (Cw) of open section. Although the formulas of warping constant are available for many practical sections, the given formulas are written in quite complicated forms. The calculation of warping constant, which includes the locate the shear center of section and the calculation of warping constant, is not a routine process and is a tough task for most practicing engineers.
This study intends to obtain the theoretical formulas derived based on first-order analysis. The theoretical formulas are obtained and expressed in terms of mathematical integration. Considering the fact that the section is made of thin-walled plate elements, the theoretical formulas can be written in terms of numerical expressions. The numerical expressions are then rewritten in terms of Fortran language. The work of warping constant evaluation is finally carried out by computer. The computer-assisted results of warping constants are compared with the known ones provided by the current AISI / LRFD cold-formed steel manual. The accuracy of the results is quite encouraged.
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