# SIMPLE STRESS

STRESS is the intensity of force inside a solid. The basic unit of stress is the Pascal (Pa) which is Newton per square metre. In engineering it is more convenient to measured as the force (N) per square mm. This gives the common engineering unit of stress, MPa.

**Lecture Notes**: Simple-Stress.pdf Simple-Stress.one

Image | Video Lesson Description and Link | Duration | Date | Download |

Simple Stress | 30:53 min | 20140826 |

**Simple Stress**

Property | Formula | Units | Example |

DENSITY: Mass per unit volume | = Mass (kg)
/ Volume (m^{3}) |
kg / m^{3} |
Steel = 7800 |

STRENGTH: How much Stress it can 'take' Ultimate Strength (max stress before breaking) Yield Strength (max stress before plastic) Stresses: Tensile & Compression (Axial), Shear Fatigue: Max stress under millions of reps Working/Allowable; 'Safe' stress, design value |
= Force (N) / Area (mm^{2}) |
MPa | 1020 Steel UTS = 400MPa 1020 Steel YS = 200MPa 1020 Steel SS = MPa Steel Grade 250 FS = 207MPa 1020 ATS = 120MPa |

HARDNESS: Resistance to indentation or abrasion | Size or depth of indent | varies | HRC55 (Rockwell) etc |

STIFFNESS: How much Stress for a certain
Strain Young's Modulus, Elastic Modulus |
= Stress (MPa) / Strain | MPa | 1020 Steel E = 205GPa |

TOUGHNESS: Energy to break | = Area under Stress-Strain curve | J / m^{2} |
Charpy Test (Joules) |

ELASTICITY: Ability to Stretch with plasticity | = Strain at yield | % | 1020 Steel: 0.01% @ yield |

PLASTICITY: Permanent deformation: Ductility = tensile plasticity Malleablility = compressive plasticity |
= (L2 - L1) / L1 | % | 1020 Steel: 25% |

POISSON'S RATIO: side strain to axial strain | v = ex / ey | - | 1020 Steel v = 0.29 |

DEFINE | Formula | Units | Diagram |

Axial Stress (Tension or Compression) | Stress = Force / Area | MPa | |

Axial Strain (Tension or Compression) | Strain = extension / original Length | - | |

Shear Stress |
Stress = Force / Area | MPa | |

Modulus of Elasticity (Young's Mod) | E = Stress / Strain | GPa | Slope of Stress:Strain diagram |

Modulus of Rigidity (Shear Mod.) =~ 0.4E | G = S. Stress / S. Strain | GPa | Slope of S.Stress:S.Strain diagram |

Shear Strain | Strain = movement / original Depth | - | |

Shear in Detail: Shear Strain is usually small enough to ignore the changes in L with angle. Angle is in radians. Area is the zone that would slide apart assuming it broke in shear. |

## What is a Stress?

STRESS is the intensity of force inside a solid.

It has the same units as Pressure (Pa, kPa, MPa, etc), so you could think of stress as pressure in a solid. The difference is, pressure acts equally in every direction, but stress has a certain direction.

Stress = Force/Area

The base unit for pressure and stress is the Pascal (Pa), but this is way too small for engineering use - except perhaps when measuring the pressure of air conditioning ducts or something. Certainly nothing compared to the stress required to break steel. In most engineering situations, the strength of a material is measured in MPa (MegaPascals)

Stress (MPa) = Force (N) / Area (mm2)

**COMMON MISTAKE: (FORCE
DOUBLING).** When drawing a Free Body Diagram of a
component under stress, you will always end up with a pair of forces
(e.g. 1 up, 1 down). This is the *definition* of
stress - that the cross-sectional area has to sustain the 2 forces
trying to tear it apart. If you add the 2 forces together you are
probably making a mistake! (Besides, if you did try to add them they
would cancel each other out anyway, since they are in opposite
directions.)

**Worked Example 1**:
Tensile force of 5kN acting on a 6mm diameter rod. What is the stress?

**Worked
Example 2**: A block made of 40MPa concrete with
dimensions as shown. What is the maximum load (mass) it can support?

**Worked
Example 3**: Tensile force of 1kN, with steel of
UTS=750MPa and Factor of Safety of 2.5. What is maximum force?

**DIFFERENT SYMBOLS:** Watch out for different symbols for stress. Ivanoff (and some TAFE
publications) use **f** but the rest of the
world (internet and other textbooks) use the Greek symbol sigma .

So where does the ** f** come from for stress?

It appears in the Steel Structures Code AS 4100 (Workbook here)

But for everything else, stress is Sigma. σ

This is so universal that even Autodesk Inventor calls the axial stress Sigma X (axial stress in the X direction).

## Tensile, Compressive and Shear stress

There are 3 types of stress in the world;

- Tensile = pulling apart
- Compressive = squashing together
- Shear = sliding apart

Any of these 3 types of stress are calculated the same way, with the same units - it the area that is different. Always think of what area must be broken when the component fails (the broken area).

#### Questions:

Assignment: Do all questions
(Ivanoff)

Questions 25:1 to 25:11 (Read
Chapter 25.1-4: Tensile Stress)

Questions
26:1 to 26:5 (Read Chapter 26.1-2: Compressive Stress)

Questions 27:1 to 27:16 (Read Chapter 27.1-2: Shear Stress)