Theories of failure (TOF) and its concept has a great importance in design section.

In **TOF** , it is important to be perquisite with the knowledge of various notations and terms used in this theory.

**This blog puts emphasis on all these terms and notations.**

*1.STRESS *

The internal resistance offered by a body against an acting load.

*STRESS = RESISTING FORCE /AREA*

**TYPES OF STRESSES:**

**a.NORMAL STRESSES** : Stresses acting along the axis of load . Denoted by** σ **. Causes change in volume of an object.

** σ = F/A ** F= Resisting force

**b.SHEAR STRESSES**: Stresses acting due to a tangential load along the face of body. Denoted by **τ **(Greek: tau). Causes change in overall shape of the body.

** τ = F/A**

#### 2.STRENGTH :

A material’s capacity to sustain load without getting failed.

**a.YIELD STRENGTH ( σ _{yt} )** : The strength of a material at its yield point. Usually defined for ductile materials.

**b.ULTIMATE STRENGTH ( σ _{ut} )** : The strength of a material at its ultimate point. Usually defined for brittle materials.

#### 3.STRAIN :

Change in dimensions to the original dimensions.

**a.** **Longitudinal strain **: Strain that occurs because of Normal stress. Denoted by ε. Here, length is the varying dimension.

**ε = ΔL / L**

**b. Shear strain : **Strain that occurs because of Shear stress. Denoted by γ . Here, angle is the varying dimension.

**γ = 90 – α**

#### 4. POISSON RATIO :

Ratio of lateral strain to longitudanal strain .** Denoted by µ**.

**µ = (Δd/d) / (ΔL/L) **

#### 5. FACTOR OF SAFETY :

Factor of safety (FOS) is the ratio of maximum allowable stress (yield or ultimate) to the maximum working stress.

**FOS = (Max. allowable or permissible stress)/ (max .working stress) = σ _{max} or σ_{yt} or σ_{ut} / σ_{working}**

**FOS is one of the important aspects of THEORIES OF FAILURE.**

#### 6.PRINCIPAL STRESS AND STRAINS :

Stresses and strains acting along the principal plane of a body.

σ_{1} = Max.principal normal stress

σ_{2} = Min. principal normal stress

τ_{1} = Max. principal shear stress= τ_{max}

**τ**_{2 }= Min. principal shear stress

#### CONDITION OF FAILURE IN A MACHINE ELEMENT

A machine element is said to be undergo failure in two conditions :

**On undergoing permanent deformation:**Usually this condition is analysed in ductile materials .It is due to the fact that Permanent deformation (plastic deformation) occurs after*yield point.***On material breakdown or fracture :**Usually this condition is analysed in brittle materials . It is due to the fact that with no yield point , this material breaks on*fracture point.*

#### FAILURE CRITERIA :

- STRENGTH CRITERIA (STATIC LOADING) :

2.STIFFNESS / RIGIDITY CRITERIA( STATIC LOADING DEFLECTION):

3.FATIGUE LOADING/DYNAMIC LOADING CRITERIA :

4.BUCKLING CRITERIA (COLUMNS):