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Stress Transformation & Principal Stresses

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on 19 November 2013

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Transcript of Stress Transformation & Principal Stresses

ME 310 - Mechanics of Materials II Stress Transformation and
Principal Stresses -
28th Oct - 11th Nov 2013

Principal Stresses and maximum shear stresss
How many different values can stress have at a point - the plane stress case
Examples
Combined Stresses Design examples
Stress invariants and Design
Graphical Method of Stress transformation - The Mohr Circle
Derivation
The transformation equations for plane stress
Why stress transformation !
Stress components at a point for a given loading dependent on orientation of co-ordinate system.
An infinite number of stress components can be defined depending on the orientation of co-ordinate system used.
These components are not arbitrary and can be expressed as function of angle from any fixed set of reference co-ordinate orientation.
For design purpose we need to find out where these components will attain their maximum or minimum values.
Stress value is a function of coordinate system orientation
Home work
7.1 -7.5 I.H Shames
9.1 to 9.6 R.C. Hibbeler

Prepared and presented by
Dr R S Choudhry
rizwan@ceme.nust.edu.pk
For flash animations used in this prezi
the originals can be found at
http://web.mst.edu/~mecmovie/
with thanks and acknowledgment to
Dr Timothy A. Philpot

Assignment 2:
1. Derive the transformation equations for a three dimensional stress state
2. Question 7.30 Introduction to Solid Mechanics I.H. Shames
3. Prepare a spreadsheet solution or computer code to calculate stresses at any orientation from the given set of input stress state.
Submission date 11 Nov 2013 - Assignment is to be completed in groups of maximum 6 students. A short viva may be held to access individual contribution
Full transcript