# Probability of Failure Under a Biaxial State of Stress

*by*R. A. Heller, Virginia Polytechnic Inst &, State Univ, United States,

S. Thangjitham, Virginia Polytechnic Inst &, State Univ, United States,

**Document Type:**Proceeding Paper

**Part of:**Probabilistic Methods in Civil Engineering

**Abstract:**

Structural components are subjected to uniaxial stress states only infrequently. Even under such simple conditions as direction tension or bending the presence of holes, cutouts and other stress concentrations produce bi- or tri-axial stress states. Similarly, combined load conditions, such as biaxial tension, combined tension and torsion, internal pressure with torsion, etc., in some cases require the nonlinear combination of stress components. Yet most structural reliability and probability of failure calculations are based almost exclusively on the simple, linear stress-strength interference principle. The paper considers the probability of failure of a thick walled metal cylinder subjected to statistically distributed pressure and torsional loads. Each random load is a band limited white noise with relatively low frequencies so that dynamic effects will not be present. Because the loads are repeated, the probability of failure increases in each load step.

**Subject Headings:**Tension | Failure loads | Biaxial strength | Biaxial loads | Stress analysis | Load factors | Structural reliability | Cylinders

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