**STUDY OF FLUCTUATING STRESSES :WHY IT IS IMPORTANT IN DESIGN???**

**Fluctuating stresses??? WHAT, HOW AND WHY????**

Till now, IN THE PREVIOUS BLOGS, we learned about static loading and its related stresses.

IN CASE IF YOU MISSED IT , PLZ REFER TO THE LINK BELOW:

https://mechomotive.com/wp-admin/post.php?post=3355&action=edit

**Static loading is that loading which does not change w.r.t magnitude and direction. **

But we see that many practical applications seemed to work on specific loading conditions. These acting forces changed in magnitude OR direction OR both.

These forces , so called fluctuating forces depend on magnitude OR direction OR both magnitude and direction.

FLUCTUATING STRESS: The stresses produced from fluctuating forces and loading system.

### NEED OF FLUCTUATING STRESS STUDY:

*Nowadays, many of the industries work on fluctuating stress and loads.*

It came into study by the following observation:

**“About 80% of the components failed due to fatigue failure occurring due to fluctuating stresses.”**

So, study of fluctuating stresses came needed to make design safer.

*Since, c*yclic *stress variations were irregular and non-analytic, various models came in suggestion for the study.*

AT LAST, Sine curve came to be taken as the easiest and popular model.

*This model was based on Stress -Time relationship.*

## CYCLIC STRESS MODELS – BASED ON “**SINE CURVE MODE**L”

Before going for cyclic stress study , Let’s have a glance on some important terms

**1. MAXIMUM STRESS: Maximum stress of the system. Denoted by σ _{max}_{ }.**

**2. MINIMUM STRESS: Minimum stress of the system. Denoted by σ _{min}.**

**3. MEAN STRESS: Sum average of the MAX. and MIN. stress of the system. Denoted by σ _{m}.**

**σ _{m}= σ_{max }+ σ_{min}/2**

**4. VARIABLE STRESS/STRESS AMPLITUDE: Average of the difference of the MAX. and MIN. stress of the system. Denoted by σ _{v}.**

**σ _{v}= σ_{max }– σ_{min}/2**

There are main 3 important mathematical models for Cyclic Stresses :

### 1. FLUCTUATING STRESSES/ ALTERNATING STRESSES :

These stresses show changes in a sinusoidal manner w.r.t time. It has some maximum value as well as minimum value stress.

So, there is a fixed mean stress value as well as variable stress value. These stresses can be – Tensile, Compressive or Partial tensile and partial compressive.

**Here, σ_{max }& σ_{min} ≠0**

**Therefore , σ_{m} & σ_{v} ≠0**

**σ _{m}= σ_{max }+ σ_{min}/2**

**σ**_{v}= σ_{max }– σ_{min}/2**2. REPEATED STRESSES:**

These stresses show changes in a sinusoidal manner w.r.t time. But, here the variation starts from the origin (i.e 0,0).

**Therefore, σ_{m}_{in}=0_{ }& σ_{m}_{ax}= Definite value**

*σ _{m}= σ_{max }+ σ_{min}/2* = σ

_{max}/2

** σ_{v}= σ_{max }– σ_{min}/2 = σ_{max}/2**

### 3. REVERSED STRESSES :

These stresses show changes in a sinusoidal manner w.r.t time. But , here the maximum value and minimum value stresses are equal in magnitude ,but opposite in direction.

**Therefore, σ _{min}=-σ & σ_{max}=+σ**

*σ _{m}= σ_{max }+ σ_{min}/2* = 0

*σ _{v}= σ_{max }– σ_{min}/2* = σ

*In fluctuating stress analysis , tensile stress is taken as positive, while compressive stress is taken as negative.*