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ENGR5004 / Week 8
Old spec Statics Session 15 ExampleTutorialOld spec ENGR216Third5 min

ENGR216 (old spec) Statics session 15 worked example (slide 11) official answers

A square element is in plane stress with σx=σy=100\sigma_x = \sigma_y = 100 MPa (tension) and τxy=50\tau_{xy} = 50 MPa (positive, i.e. upwards on the right face). Calculate the normal and shear stresses on the plane whose normal makes an angle θ=30∘\theta = 30^\circ (counterclockwise) with the xx axis.

Square element with sigma_x on the vertical faces, sigma_y on the horizontal faces and positive shear tau_xy (upwards on the right face, rightwards on the top face); an oblique cut whose normal is at angle theta to x.
Square element with sigma_x on the vertical faces, sigma_y on the horizontal faces and positive shear tau_xy (upwards on the right face, rightwards on the top face); an oblique cut whose normal is at angle theta to x.
Formulas you may need
  • Stress transformation: σx′=σx+σy2+σx−σy2cos⁡2θ+τxysin⁡2θ\sigma_{x'} = \dfrac{\sigma_x+\sigma_y}{2} + \dfrac{\sigma_x-\sigma_y}{2}\cos2\theta + \tau_{xy}\sin2\theta, τx′y′=−σx−σy2sin⁡2θ+τxycos⁡2θ\tau_{x'y'} = -\dfrac{\sigma_x-\sigma_y}{2}\sin2\theta + \tau_{xy}\cos2\theta (learn this)