8.3 附加偏心距和偏心距增大系数8.3 Additional eccentricity and eccentricity magnifying coefficient 附加偏心距和偏心距增大系数附加偏心距和偏心距增大系数Accidental eccentricity ea（（附加偏心距）附加偏心距）e0+eais called initial eccentricityei（初始偏心距）（初始偏心距）are considered in the calculation.aieee+=01、、 Accidental eccentricity附加偏心距附加偏心距参考以往工程经验和国外规范，附加偏心距参考以往工程经验和国外规范，附加偏心距取取ea=20mm orh/30 两者中的较大值，此处两者中的较大值，此处h是指偏心方向的截面尺寸是指偏心方向的截面尺寸8.3 附加偏心距和偏心距增大系数8.3 附加偏心距和偏心距增大系数8.3 附加偏心距和偏心距增大系数由于施工误差、计算偏差及材料的不均匀等原因，实际工程中不存在理想的轴心受压构件为考虑这些因素的不利影响， 引入由于施工误差、计算偏差及材料的不均匀等原因，实际工程中不存在理想的轴心受压构件。
为考虑这些因素的不利影响， 引入附加偏心距附加偏心距ea(accidental eccentricity)，即在正截面压弯 承载力计算中，偏心距取计算偏心距即在正截面压弯 承载力计算中，偏心距取计算偏心距e0=M/N与附加偏心距与附加偏心距ea之 和，称为之 和，称为初始偏心距初始偏心距ei(initial eccentricity)，aieee+=0参考以往工程经验和国外规范，附加偏心距参考以往工程经验和国外规范，附加偏心距ea取取20mm与与h/30两者中的较大值，此处两者中的较大值，此处h是指偏心方向的截面尺寸是指偏心方向的截面尺寸一、附加偏心距一、附加偏心距二、二、eccentricity magnifying coefficient◆◆◆◆second-order effect will appear due to lateral deflection ，，then cause the additional moment◆◆◆◆If the column is slender, the additional moment can not be neglected.◆◆◆◆The lateral deflection of middle The lateral deflection of middle showed in Fig.showed in Fig. is is f .◆◆◆◆For the section in middle, the For the section in middle, the eccentricity of axial load iseccentricity of axial load is ei+ f ，，and the moment is M =N ( ei+ f ).elxfyπsin⋅=fyxeieiNNN eiN ( ei+ f )le8.3 附加偏心距和偏心距增大系数二、偏心距增大系数二、偏心距增大系数◆◆◆◆由于侧向挠曲变形，轴向力将 产生由于侧向挠曲变形，轴向力将 产生二阶效应二阶效应(second-order effect)，引起附加弯矩，引起附加弯矩◆◆◆◆对于长细比较大的构件，二阶效应引起附加弯矩不能忽略。
对于长细比较大的构件，二阶效应引起附加弯矩不能忽略◆◆◆◆图示典型偏心受压柱，跨中侧 向挠度为图示典型偏心受压柱，跨中侧 向挠度为 f .◆◆◆◆对跨中截面，轴力对跨中截面，轴力N的的偏心距 为偏心距 为ei+ f ，即跨中截面的弯矩为，即跨中截面的弯矩为 M =N ( ei+ f ).elxfyπsin⋅=fyxeieiNNN eiN ( ei+ f )le8.3 附加偏心距和偏心距增大系数二、二、◆◆◆◆ If the section and the If the section and the initial eccentricity are the initial eccentricity are the same, but the slendernesssame, but the slendernessl0/h and the lateral deformation are different, the influence of secondsecond- -order effectorder effect is differentis differentand will cause different failure.elxfyπsin⋅=fyxeieiNNN eiN ( ei+ f )le8.3 附加偏心距和偏心距增大系数Eccentricity magnification factor二、二、Eccentricity magnification factor偏心距增大系数偏心距增大系数◆◆◆◆在截面和初始偏心距相同的情况下，柱的在截面和初始偏心距相同的情况下，柱的长细比长细比l0/h (slenderness)不同，侧向挠度不同，侧向挠度 f 的大小不同，二阶效应的影响程度会有很大差别，将产生不同的破坏类型。
的大小不同，二阶效应的影响程度会有很大差别，将产生不同的破坏类型elxfyπsin⋅=fyxeieiNNN eiN ( ei+ f )le8.3 附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNum fmNulNul eiNul flFor the slenderness of short For the slenderness of short columncolumn l0/h≤≤5◆◆ Lateral deformationLateral deformation f compare with initial compare with initial eccentricityeccentricity eiis very small.is very small.◆◆ The moment in the middleThe moment in the middle M=N(ei+f ) is increasing with the increase of the N8.3 附加偏心距和偏心距增大系数◆◆ Until the section reaches ultimate limit states and Until the section reaches ultimate limit states and occursoccurs failure.failure. ◆◆ For a short column ,the deformationFor a short column ,the deformation f is negligible.MNN0M0NusNuseiNumNumeiNum fmNulNul eiNul fl对于长细比对于长细比l0/h≤≤5的短柱的短柱◆◆侧向挠度侧向挠度 f 与初始偏心距与初始偏心距ei 相比很小相比很小, ◆◆柱跨中弯矩柱跨中弯矩M=N(ei+f ) 随轴 力随轴 力N的增加基本呈线性增长，的增加基本呈线性增长，◆◆直至达到截面承载力极限状 态产生破坏。
直至达到截面承载力极限状 态产生破坏◆◆对短柱可忽略挠度对短柱可忽略挠度f 影响8.3 附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNum fmNulNul eiNul flFor the slendernessFor the slenderness l0/h of the middle slender column is 5~30◆◆f can not be neglectedcan not be neglected comparing comparing withwithei. ◆◆f is increasing as the increase of axial load , the speed of the moment in the middle of column span M = N( ei+ f ) is bigger than that of N.◆◆ M is increasing quickly as the increase of N and appears non linear◆◆ Although it will reach the ultimate limit states that the carryiAlthough it will reach the ultimate limit states that the carrying ng capacity is lower than the short columncapacity is lower than the short column. .◆◆ For slender column , we must consider the additional For slender column , we must consider the additional deformation in design.deformation in design.8.3 附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNum fmNulNul eiNul fl长细比长细比l0/h =5~30的中长柱的中长柱◆◆f 与与ei相比已不能忽略。
相比已不能忽略◆◆f 随轴力增大而增大，柱跨中 弯矩随轴力增大而增大，柱跨中 弯矩M = N ( ei+ f ) 的增长速 度大于轴力的增长速 度大于轴力N的增长速度，的增长速度，◆◆即即M随随N 的增加呈明显的非 线性增长的增加呈明显的非线性增长◆◆虽然最终在虽然最终在M和和N的共同作用下达到截面承载力极限状态，但 轴向承载力明显低于同样截面和初始偏心距情况下的短柱的共同作用下达到截面承载力极限状态，但 轴向承载力明显低于同样截面和初始偏心距情况下的短柱◆◆因此，对于中长柱，在设计中应考虑附加挠度因此，对于中长柱，在设计中应考虑附加挠度 f 对弯矩增大的 影响对弯矩增大的 影响8.3 附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNum fmNulNul eiNul fl8.3 附加偏心距和偏心距增大系数For the slenderness of the slender For the slenderness of the slender columncolumn l0/h >30◆◆ The influence of lateral The influence of lateral deformationdeformation f is big.is big.◆◆ Lateral deformation Lateral deformation f is is instable before it reaches the instable before it reaches the ultimate limit states.ultimate limit states.◆◆ The axial load is appeared The axial load is appeared before the interaction line before the interaction line Nu- -Mu◆◆ This failure is instable failure, This f。