## 1 Introduction  
Extreme events (i.e., terrorist attacks, vehicle impacts, explosions, etc.) often cause local damage to building structures and pose a serious threat when one or more vertical load-bearing components fail, leading to the progressive collapse of the entire structure or a large part of it. As it is difficult to predict the probability of occurrence and the magnitude of extreme events, it is neither practical nor possible to design a structure against them through the traditional methods for conventional loads. To avoid progressive collapses, alternative load paths must be available for the load supported by the damaged column to be transferred to neighboring elements. Most current studies on progressive collapse focus on regular RC frame structures [1; 2; 3], and relatively few studies focus on irregular RC frame structures. However, with the increase in building height and complexity and the wide application of irregular building structures, progress collapse accidents often occur [4; 5]. Under the action of accidental load, the asymmetric distribution of mass and stiffness of an irregular structure is more likely to cause the failure of this structure than of a regular structure. The alternate load path method (APM), a significant design approach to reduce progressive collapse, has been mentioned by a number of design codes including GSA [6] and DoD [7]. The APM allows local failure to occur when subjected to an extreme load, but seeks to provide an alternate load path so that the initial damage can be contained and major collapse can be averted. For designing new buildings or checking the capacity of a structure, the technique can be employed. Adding a new structural member to provide additional alternate load paths is a classic approach for strengthening structural systems against progressive collapse. For example, [PERSON] et al. [8] studied the progressive collapse of both unbraced and braced semi-rigid jointed steel frames in order to evaluate the contribution of bracing to improving the progressive collapse resistance. [PERSON] et al. [9] proposed a steel bracing design method based on incremental dynamic analysis (IDA)in order to explore the influence of steel bracing on RC frame resistance to progressive collapse. [PERSON] et al. (2010), in order to improve the progressive collapse resistance of general RC frame structures under local component failure, applied X-tension reinforcement to the progressive collapse resistance design. [PERSON] et al. (2011) proposed a strengthening method to improve the collapse resistance of RC frame structures by installing steel cables of a preset length at the bottom of the beams. The test and analysis results showed that the ultimate resistance of the modified substructure is 90-255% higher than that of the unmodified substructure when two steel cables with diameters of 10 or 14 mm are used as beam and column components. [PERSON] et al. (2012) added a truss steel system (i.e., \"roof truss\") to the roof layer of the building, aiming to define an alternative load path, which was investigated as a retrofit solution. [PERSON] et al. (2013) proposed a method of cap trusses and steel struts to resist the progressive collapse of intermediate RC frame structures. It was found that the axial forces in the removed columns were transferred to adjacent columns by alternative paths using cap trusses to prevent partial or integral failure, or to delay the occurrence of progressive collapse. Because collapse tests cost a lot of money and the test process is complicated, numerical simulation is still the main method to study the progressive collapse resistance of a structure. [PERSON] et al. (2014) analyzed in detail the influence of finite element modeling and analysis techniques (including the solution process, mesh size, element type, column-removal time, damping, strain rate and output-related problems) on the nonlinear dynamic column-removal response of steel frame structures. [PERSON] et al.