工字型钢框架极限承载力分析的通用广义屈服函数

工字型钢构件空间受力下的精确广义屈服函数为隐式函数,不便使用,而现有的近似显式函数不能全面考虑截面几何参数的影响,在适用性和精度方面普遍存在问题。为此,通过合理选择工字型截面几何参数,研究建立了具有广泛适用性的工字型截面齐次广义屈服函数,据此提出了平面和空间受力下框架结构极限承载力分析的高效线弹性迭代方法。研究了工字型截面几何参数对广义屈服函数计算精度的影响;选择腹板面积与单翼缘面积之比γ1和翼缘宽度与腹板厚度之比γ2作为截面几何参数,通过回归分析建立了同时适用于平面和空间受力,且能够全面反映工字型截面几何特征的通用齐次广义屈服函数;通过有策略地缩减高承载单元的弹性模量,建立了工字型截面框架结构极限承载力分析的高效高精度线弹性迭代方法。通过对比分析验证了该方法具有良好的计算精度和效率以及较强的适用性。

A GENERALIZED YIELD FUNCTION FOR THE ULTIMATE STRENGTH OF STEEL FRAMES WITH I-SECTIONS

The exact generalized yield function of steel members with I-sections under spatial loading is usually implicit and inconvenient to use, while current approximate explicit generalized yield functions cannot fully consider the geometry of I-sections, leading to inaccuracy and unsuitability for engineering applications. To overcome this problem, a homogeneous generalized yield function is proposed for I-sections with wide applicability and high fitting accuracy that fully considers sectional geometry. An efficient linear elastic iteration method is presented for the ultimate strength of frame structures with I-section members under plane loading and spatial loading. The influence of the cross sectional geometry on the generalized yield function is investigated. Choosing the ratio of web to flange section area γ₁ and the ratio of flange width to web thickness γ₂ as the sectional geometric parameters, a homogeneous generalized yield function is developed for I-section members under plane loading and spatial loading by regression analysis. By strategically reducing the elastic modulus of the highly stressed elements, an efficient and accurate linear elastic iteration method is presented for the ultimate strength of steel frame structures with I-section members. The comparative investigation shows that the proposed method has a wide range of application with high computation efficiency.