# STRESS CONCENTRATION FACTORS CLASS NOTES FOR MECHNICAL ENGINEERING

**STRESS CONCENTRATION**

** ****FACTORS CLASS NOTES FOR **

**MECHANICAL ENGINEERING**

**It is increase in stress due to a **

**discontinuity in a body under loading. **

**Discontinuities are quite common. **

**Stress increase depends on the type **

**and extent of a discontinuity.**

** Stress increases due to the following discontinuities. **

**(i) ****Key seat in a shaft**

**(ii) ****Threads on a bolt**

**(iii) ****Oil holes in a machine part**

**(iv) ****Notch in a machine part**

**(v) ****Groove in a machine part**

**(vi) ****Tool mark(s)**

**(vii) ****Scratches**

**(viii) ****Fillets**

**(ix) ****Splined shaft **

**(x) ****Flaws or inclusions**

**(xi) ****Abrupt change of cross section**

**(xii) ****Dent(s)**

**Stress Concentration Factor, k**

**k=Stress at a discontinuity/stress based on net cross section at the discontinuity**

**k is always greater than 1**

**Stress concentration factor depends on the following criterions.**

**(i) ****Geometry of the discontinuity—It is called Form stress concentration factor**

**(ii) ****Location of the discontinuity in the part**

**(iii) ****Overall dimensions of the part**

**(iv) **** Material(ductile or brittle)**

**(v) ****Type of loading—It is called Load concentration factor**

**(vi) ****Method of manufacture **

**The value of ‘k’ is different under different types of loading for the same continuity. The value of ‘k’ is also different for the same type of load when applied gradually/suddenly/impact load.**

**Firstly k**_{t} is the stress concentration factor in tension

_{t}is the stress concentration factor in tension

**Secondly k**_{c} is the stress concentration factor in compression

_{c}is the stress concentration factor in compression

**Thirdly k**_{b} is the stress concentration factor in bending

_{b}is the stress concentration factor in bending

**Fourthly k**_{tor} is the stress concentration factor in torsion

_{tor}is the stress concentration factor in torsion

**Fifthly k**_{buck} is the stress concentration factor in buckling

_{buck}is the stress concentration factor in buckling

**Sixthly k**_{fatigue} is the stress concentration factor in fatigue (reversal loading)

_{fatigue}is the stress concentration factor in fatigue (reversal loading)

**k**_{complex} is the stress concentration factor in complex loading (more than one type of load acting simultaneously)

_{complex}is the stress concentration factor in complex loading (more than one type of load acting simultaneously)

**DETERMINATION OF ‘k’**

**(i) ****For simple discontinuity—Empirical equations are available.**

**(ii) ****For a complex discontinuity—It is found by photo-elasticity**

**(iii) ****Standard graphs are available for few cases—refer Design of Machine Elements by Spott.**

**Empirical relation for an elliptical hole k = (1+2a/b) σ**

**Where ‘a’ is semi major axis of the ellipse**

**‘b’ is the semi- minor axis of the ellipse**

**If a/b is large, crack will develop**

**When a/b is small, k**_{t} will be relatively small.

_{t}will be relatively small.

**Further when a/b = 1 it becomes a circle. The value of k becomes =3 i.e. stress concentration for a hole is 3 times the normal stress.**

**σ**_{stress concentration }= 3 σ_{normal stress}

_{stress concentration }= 3 σ

_{normal stress}

**HOW TO ACCOUNT FOR STRESS COCEMNTRATION IN DESIGN**

**Design stress = σ**_{design}= k σ_{nominal}

_{design}= k σ

_{nominal}

**This design stress < a**_{llowable }

_{llowable }

**σ**_{allow} = (σ_{yp}/FOS) for ductile materials

_{allow}= (σ

_{yp}/FOS) for ductile materials

**σ**_{allow} = (σ_{ult}/FOS) for brittle materials

_{allow}= (σ

_{ult}/FOS) for brittle materials