## STRESSES AND DESIGN ANALYSIS: HOW THE PROCESS OCCURS?????????

**Reversed stresses** : Those stresses which have same magnitude of stresses but in opposite sense (i.e **σ _{1 = }-σ_{2}**).

Here, **σ _{m}=0** &

**σ**

_{v = }σ_{1 }or σ_{2}**Fluctuating stresses** : Those stresses which have different magnitude of stresses and also induces in a specific direction.

**σ _{m}=**

**σ**&

_{1 }+σ_{2}/2**σ**where ,

_{v = }σ_{1 }– σ_{2}/2**σ**=

_{1}= maximum stress σ_{2}**minimum stress**

In fatigue design , we deal with two types are problems:

**1) Components subjected to completely reversed stresses**

**2) Components subjected to fluctuating loading stresses**

**For reversed stresses** ,since the Mean stress value is zero.

Therefore tensile stresses occupy the first half and Compressive stresses occupy the second half of the stress distribution.

**Whereas, for fluctuating loading stresses**, there comes a definite non zero mean stress value.

Therefore, the stresses here can be purely tensile, purely compressive or Mix of both tensile and compressive.

### DESIGN STRATEGY FOR REVERSED STRESS PROBLEMS:

For designing a component subjected to *completely reversed stresses*, there are further **2 sub conditions** under which study is done.

1) DESIGN FOR INFINITE LIFE

2) DESIGN FOR FINITE LIFE

**DESIGN FOR INFINITE LIFE**

When a component has to be designed for infinite life, **the ENDURANCE LIMIT becomes the failure criteria.** Here, the stress amplitude (**σ**_{f}) should be less than the Endurance Limit (**σ**_{e}) to withstand infinite no. of cycles.

These equations are mainly used in this type of design analysis:

**σ _{a}=S_{e} / FOS τ_{a} = S_{se} / FOS **

Where ;

σ_{a} = Stress amplitude in component (due to bending)

S_{e} = Corrected Endurance Limit in reversed bending

τ_{a} = Stress amplitude in component (due to torsion)

S_{se}= Corrected Endurance Limit in reversed bending

#### DESIGN FOR FINITE LIFE

When a component has to be designed for finite life, the **S N CURVE becomes the failure criteria.** Here, the stress amplitude (**σ**_{f}) is usually greater than the Endurance Limit (**σ**_{e}). It mostly finds applications in steels.

##### PLOTTING TECHNIQUE OF **S N CURVE** :

THE S N CURVE drawn here is a Straight Line AB drawn from **(0.9 S _{ut}) at 10^{3} cycles to S_{e} at 10^{6} cycles** on a LOG-LOG graph paper.

PLOTTING PROCEDURE :

1. Locate point A with coordinates **{log _{10}(10^{3}),log_{10}(0.9 S_{ut})}= {3, log_{10}(0.9 S_{ut})}** .

2. Locate point **B** with coordinates **{log _{10}(10^{6}),log_{10}(S_{e})}= {6, log_{10}(S_{e})}** .

3.Join **AB . **This is the criterion for failure for Finite life problems.

4. Depending upon the Value of the life N given to us, draw a *vertical line* passing through **log _{10}N **on the abscissa, which further intersects AB at point F.

5. Draw a line *FE parallel to abscissa*. **The ordinate at point E i.e log _{10}Sf gives the fatigue strength corresponding to N cycles.**