The prior replies were considering flanged and flued type expansion joints which are covered in Section VIII, Div 1, Appendix 5. The question I believe is addressing thing walled bellows type expansion joints, which are covered in Appendix 26.
The stress equations in Appendix 26 are essentially the same as in EJMA. The fatigue equation in Apendix 26 is more conservative as it is a design equation with safety factors, whereas the EJMA fatigue curve is based on average data. The stress limits are different, and the more recent EJMA editions have added a number of equations dealing with limit load and stability failure modes, which are not found in the current Section VIII rules.