# 1-5 - CHAP 1 Stress-Strain Analysis 23 5 Find the principal...

This preview shows pages 1–2. Sign up to view the full content.

CHAP 1 Stress-Strain Analysis 23 5. Find the principal stresses and the corresponding principal stress directions for the following cases of plane stress. (a) σ xx = 40 MPa, σ yy = 0 MPa, τ xy = 80 MPa (b) σ xx = 140 MPa, σ yy = 20 MPa, τ xy = −60 MPa (c) σ xx = −120 MPa, σ yy = 50 MPa, τ xy = 100 MPa Solution: (a) The stress matrix becomes 40 80 MPa 80 0 xx xy xy yy   To find the principal stresses, the standard eigen value problem can be written as   0    In The above problem will have non-trivial solution when the determinant of the coefficient matrix becomes zero: 40 80 0 80 0 xx xy xy yy   The equation of the determinant becomes:       2 40 80 80 40 6400 0   The above quadratic equation yields two principal stresses, as 1 102.46MPa and 2 62.46MPa  .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

1-5 - CHAP 1 Stress-Strain Analysis 23 5 Find the principal...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online