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The Masing conditions establish a criterion to relate the loading curve of a hysteretic system (e.g., systems with friction or plasticity) to its complete hysteresis loop. For the field of joint mechanics, where hysteretic models are often used to describe the dissipative, tangential behavior within an interface, the Masing conditions allow for significant computational savings when the normal load is constant. In practice, though, jointed systems experience time varying normal forces that modify the tangential behavior of the system. Consequently, the hysteretic behavior of jointed structures do not adhere to the Masing conditions. In this work, this discrepancy between the Masing conditions and behavior exhibited by jointed structures is explored, and it is hypothesized that if the Masing conditions accounted for variations in normal force, then they would more accurately represent jointed structures. A new set of conditions is introduced to the original set of Masing conditions, yielding a « Masing manifold » that spans the tangential displacement-tangential force-normal force space. Both a simple harmonic oscillator and a built-up structure are investigated for the case of elastic dry friction, and the results show that the hysteresis of both of these systems conforms to the three dimensional Masing manifold exactly, provided that a set of constraints are satisfied, even though the hysteresis does not conform with the original Masing conditions.