Abstract: 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.