基于纽玛克法的变截面波形钢腹板组合箱梁畸变效应分析

Analysis on Distortion Effect of Non-prismatic Composite Box Girders with Corrugated Steel Webs Based on Newmark Method

为研究变截面波形钢腹板组合箱梁(CBGCSWs)在偏心荷载作用下的畸变效应,忽略波形钢腹板的纵向抗弯刚度,通过建立其微段单元平面内、外力系平衡方程,推导了以畸变角为未知量的畸变微分方程,并采用基于共轭梁理论的纽玛克法进行求解,由此建立了偏心荷载作用下变截面CBGCSWs畸变正应力计算理论。以某大跨变截面CBGCSWs桥为工程背景,运用该理论获得了4种不同工况下组合箱梁角点处畸变正应力理论解,并采用空间有限元方法进行了验证,数值解与理论解吻合良好,表明推导的变截面CBGCSWs畸变计算理论正确且精度足够,可供工程参考。在此基础上,比较了变截面CBGCSWs与对应PC箱梁的抗畸变能力,并探讨了横隔板间距、高跨比、宽跨比及钢腹板形状等因素对变截面CBGCSWs畸变正应力的影响规律。结果表明:用波形钢腹板替代混凝土腹板会较大程度削弱箱梁的抗畸变能力,应当引起足够重视;横隔板间距及宽跨比等参数对畸变正应力影响较大,而高跨比及钢腹板形状等则影响很小。

To investigate the distortion effect of non-prismatic composite box girders with corrugated steel webs（CBGCSWs）under eccentric loads,the in-plane and out-of-plane force systems of an infinitesimal segment of non-prismatic CBGCSWs were first established,ignoring the axial stiffness of the corrugated steel web in the longitudinal direction.Then,by taking the distortional angle as the unknown,the governing differential equation for distortion of nonprismatic CBGCSWs was derived.Finally,the governing differential equation was solved using the Newmark method based on the theory of conjugate beam;thus,the calculation theory for the distortional warping normal stress of non-prismatic CBGCSWs under eccentric loads was established.Taking a large-span non-prismatic CBGCSWs bridge as the case study,thedistortional warping normal stresses of angular points of the bridge under four different cases were obtained using the proposed method.The theoretical values were compared with results obtained using the three-dimensional finite element method.The results showed good agreement,indicating that the values obtained from the proposed method are accurate and can be applied in projects as reference.Based on this,the ability of non-prismatic CBGCSWs to resist distortion was compared with that of the corresponding PC box-girder,and the effects of the diaphragm spacing,the depth to span ratio,the width to span ratio,and the dimensions of corrugated steel web on the distortional warping normal stress were investigated.The results show that using the corrugated steel webs to replace concrete webs would largely weaken the ability of the box-girder to resist distortion,and this phenomenon should be further explored.In addition,the effects of the diaphragm spacing and the width to span ratio on the distortional warping normal stress are significant,while the depth to span ratio and the dimensions of corrugated steel web have minimal effect.