In the present paper, the quasi-static uniaxial stress-state methodology to estimate the endurance limit was extended to biaxial stress-state cases. The Infrared thermography (IRT) quasi-static uniaxial stress-state methodology was applied to estimate the endurance limit of a low carbon steel structural-pipe material commonly used in oil and gas pipelines. The quasi-static uniaxial test results were verified by confrontation with data obtained with the application of IRT rapid cyclic assessment tests and theoretical estimates. In continuation, the quasi-static method was extended to biaxial stress states that exist in nominal and hot-spot points located on the surface of six actual-size pipeline specimens with geometric anomalies that were tested under hydrostatic internal pressure. The six pipeline specimens were constructed with API 5L Grade B (324 mm external diameter and 6.35 mm thickness) with plane headed caps. The pipe specimens had geometric dent-anomalies (15% depth related to the external diameter). All specimens were fatigue tested and cracks initiated and grew after thousands of cycles, the number of cycles depending on the ranges of the internal pressure applied. Results obtained showed that the quasi-static biaxial method predicted satisfactorily the location of the hot spots where fatigue cracks initiated in all six tested specimens.