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Strength of Materials Cheat Sheet (DRAFT) by

Strength of Materials - GATE XE & ME

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Strain - Stress Graph

Slope of the curve is Young's Modulus
Young's Modulus (E) = Δσ / Δε
Perfectly Elastic Bodies retain their shape in elastic region

Rigid vs Plastic Bodies

Perfect Rigid body an ideal physical model of a solid object that does not deform, bend, stretch, or change shape in any way when forces or torques are applied to it
Perfectly Plastic Body does not regain its original shape or size at all when an external deforming force is removed, remaining perman­ently deformed

Static Equili­brium Equation

∑ Fx = 0 ; ∑ Fy = 0 ; ∑ Fz = 0 ;
∑ Mx = 0 ; ∑ My = 0 ; ∑ Mz = 0 ;
 

Assump­tions in SOM

1. Material is said to be Homoge­neous & Isotropic
2. Material obeys Hooke's Law (Assume to be within stress & strain region)
3. Member is assumed to be prismatic (Cross section & dimensions are assumed to be same through the length)
4. Load is assumed to be static load
5. Self weight of the component is neglected
6. Member is assumed to be under static equation
Homoge­neous : A material is said to be homoge­neous when it exhibits same elastic properties at any point in a given direction
Isotropic:A material is said to be isotropic when it exhibits same elastic properties in any direction.
Every Homoge­neous material need not be isotropic & vice versa
Anisot­ropic : A material is said to be anisot­ropic when it exhibits direction dependent elastic properties

Classi­fic­ation of Loads - Applic­ation

With Respect to Time :
1. Static Load - Dead Load & Gradually Applied Load
2. Dynamic Load - Impact / Shock / Suddenly Applied Load

With Respect to Cross Section :
1. Normal Load - Axial Loads & Eccentric Axial Load
2. Shear Load - Transverse Shear load & Eccentric transverse load

With Respect to distri­bution load :
1. Distri­buted Load
- Uniformly Distri­buted Load
- Uniformly varying Load
- Uniformly Distri­buted Moment
2. Concen­trated Load
- Concen­trated Point Load
- Concen­trated Moments