Math Problem Statement

The state of plane stress at a point is given below. Find the normal stress () acting on a plane inclined at 30o (CCW) to the x axis.              = 90 MPa           = -60 MPa                    = 20 MPa

Solution

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Math Problem Analysis

Mathematical Concepts

Plane Stress
Stress Transformation
Inclined Plane

Formulas

σθ = (σx + σy) / 2 + (σx - σy) / 2 * cos(2θ) + τxy * sin(2θ)

Theorems

Stress Transformation Equations

Suitable Grade Level

Undergraduate Engineering