The concrete and steel columns subjected to a combination of vertical load and horizontal earthquake action are used to study the influence of correlations between loads in failure function on design reliability of seismic capacity of columns. According to the current Code for Design of Concrete Structures and Code for Design of Steel Structures, the correlations between moment and axial force are analyzed for different columns. Through comparisons of different columns in several frame structures, the similarities and differences are investigated between the load interaction curves and those considered in codes. It is indicated that the load interaction curves under this combination match well with those considered in codes for RC columns with compression failure and steel columns with I-shaped section, and they are all negatively correlated straight lines approximately; the load interaction curve of RC column with tension failure is largely different from that considered in codes, and obviously has some positive correlation parts. Based the complex failure function, reliability of columns under this combination is analyzed with the Monte Carlo method and current statistics of load and resistance. The results show that:(1)the reliability indexes of seismic capacity vary lightly with different load effect ratios based on axial force for steel columns and RC columns with compression failure, and are close to those based on the codes; (2)the reliability indexes vary greatly with different load effect ratios based on axial force for RC columns with tension failure, and are also largely different from those based on the codes; (3)the reliability indexes are lower than those based on the codes for RC columns with tension failure when the load effect ratio based on axial force is negative, as a consequence, the current reliability-based design method of columns may be unsafe in this case.