At a point in a quarry wall the stress state can be treated as two-dimensional in the…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Stress, strain and elastic waves in the Earth

Problem

At a point in a quarry wall the stress state can be treated as two-dimensional in the vertical xx-yy plane, with tension taken as positive: σxx=−90 MPa,σyy=−50 MPa,σxy=24 MPa.\sigma_{xx} = -90\,\mathrm{MPa}, \qquad \sigma_{yy} = -50\,\mathrm{MPa}, \qquad \sigma_{xy} = 24\,\mathrm{MPa}. ((a)) Find the mean in-plane stress σˉ=12(σxx+σyy)\bar\sigma = \tfrac12(\sigma_{xx}+\sigma_{yy}) and the deviatoric components τxx\tau_{xx}, τyy\tau_{yy}, τxy\tau_{xy} obtained by subtracting it from the diagonal terms. ((b)) Find the two in-plane principal stresses, and report them as the compressive magnitudes S1≥S3S_1 \ge S_3.

Browse the problem library