The generalized Hook’s law

Notes 3

 "Equlibrium"

Introduction :

Equilibrium is the foundation of any science .Each science sees it with different point of view and present it in away which suits the nature of the proposed problem. In the case of studying static structure, equilibrium is essential to model any structural problem, and it means that the structure will be able to sustain the applied external load without movement ,in other words, the external generalized forces equals the support reactions and the structure internal forces equal the external loads.

STRESS AND STRAIN :

Average stress =force /area     (vector )
There are two types of stress :

1-Axial stress ( axis line is parallel to surface area ) .
2- shear stress (axis line is normal to surface area –Tangential stresses )( friction betweeen two surfaces causses shear stress) .

Shear Bolt :

 << Poisson Ratio >>

* where ν is poisson ratio ..

HOOK'S LAW :

The generalized hook’s law : 
a

Applying  a hydrostatic  pressure :
a

a
SO ,the dilatation (reduction in the  volume / original volume ) will be :aa

a
For  the problem to be physically acceptable the volume must decrease , so :
a

a

Volumetric Strain :

Volume =Length x weight  x  height
 

      V=LWH

a

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