__consider__lumped Mass & Masless supporting structure.

What is lumped mass & What is massless Supporting.

A lumped mass is a dead that can be applied to a node in a static stress,natural frequency or modal superposition analysis.

lumped mass & massless supporting structure can be analysis linearly elastic as well as enelasticstructure subjected to eq force.

**What is linearly elastic ?**

linear elasticity is the mathematical study of the way solid object deform and end up internally stressed due to prescribed loadsing situations.

A force-displacement relationship which is both linear & elastic.

For a structure,this means the deformation is proportional to the loading,and deformation disappear on unloading.

**Example:- if due to moment M,deflection is D then deflection for 2M is 2D.**

**linear Elastic:-**The cuve is the linear and holds the same equation for both loading and unloading.

**Non-linear elastic:-** the curve is Non linear and holds the same equation for both loading & unloading(not true for structural steel but can be true for material like rubber)

#What is Non-Linar elastic analysis /

**1.Materal Non-linearity**

When the material move into the zone beyond its yield strengths,it no longer behaves in alinear fashion.there are many things that happen when material go into this zone.

**-permanent deformations**

**-Cracking**

**-Beam rotations**

**-Energy Dissipation**

**Benefit of Non-Linear Analysis over Linear anlysis **

A linear analysis cannot give a complete picture are what can happen to the structure if an earthquake hits Today we have the ability to create a mathematical model which to around 90% of the accuracy can gives us results which again depends on modelling assumptions and the detail at which it is done but it gives us idea whether everything is okay or not but to everyone’s almost surprise,the linear dynamic analysis gives as far off result** **

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