**ME 310 - Mechanics of Materials II Stress Transformation and**

Principal Stresses -

28th Oct - 11th Nov 2013

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

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