In this study, the limit load, shakedown, and ratchet limit of a defective pipeline subjected to constant internal pressure and a cyclic thermal gradient are analyzed. Ratchet limit and maximum plastic strain range are solved by employing the new linear matching method (LMM) for the direct evaluation of the ratchet limit. Shakedown and ratchet limit interaction diagrams of the defective pipeline identifying the regions of shakedown, reverse plasticity, ratcheting, and plastic collapse mechanism are presented, and parametric studies involving different types and dimensions of part-through slot in the defective pipeline are investigated. The maximum plastic strain range over the steady cycle with different cyclic loading combinations is evaluated for a low cycle fatigue assessment. The location of the initiation of a fatigue crack for the defective pipeline with different slot type is determined. The proposed linear matching method provides a general-purpose technique for the evaluation of these key design limits and the plastic strain range for the low cycle fatigue assessment. The results for the defective pipeline shown in the paper confirm the applicability of this procedure to complex 3-D structures.