Studies On The P-Δ Effect Of The Vertical Loads On High-rise Steel Structures

In steel structure industry, it is of great importance to consider the P-â–³effect on strength and stability. Especially when it comes to high-rise steel structures, the additional internal force and displacement caused by this effect cannot be ignored and should be treated very carefully. Therefore, Code for Design of Steel Structures. (GB50017-2003) and other related codes used by western countries put great emphasis on this area. Moreover, many scholars have proposed different simplified methods in order to consider the P-â–³effect in a computationally more efficient way, such as Higgins iteration method, negative-stiffness method and amplification-coefficient method. However, most of these methods have only been used in plane-frame steel structures.In this paper, a novel iteration method is proposed to study the P-â–³effect efficiently and its accuracy and reliability is verified in several plane-frame steel structures tests. First, lateral load is applied to the initial structure configuration to calculate the first-order displacement. Second, we apply the vertical load to the deformed structure. Then the initial structure configuration can be updated using the additional lateral displacement which is caused by the vertical load. It should be noted that, at this key stage, we actually obtain an artificial structure configuration which will always be updated from the initial structure with only new additional displacement caused by vertical force. In next step, we again apply the vertical load to the artificial structure configuration and then update the initial structure with the new additional lateral displacement once more. Therefore, we get a new artificial structure configuration. The iteration process mentioned above should not stop until the additional displacement caused by vertical load can be negligible. In other words, the new artificial structure configuration occupies nearly the same spatial position with the initial configuration. As a result, the total displacement of the structure is the addition of first-order displacement and those additional displacements. What's more, after updating the initial structure with the total displacement, the final internal forces can be easily calculated by linear analysis.Last, accuracy and reliability of the proposed iteration method is verified through solving several different high-rise steel structures tests. Comparing with the results of nonlinear finite element method, we can find that that the P-â–³effects increase simultaneously with the floor height. In addition, both the P-â–³effects and the relative error between iteration method and nonlinear FEM vary with different layouts and locations. In sum, the proposed method is very effective and computationally efficient in analyzing P-â–³effects.