Test: Properties of Metals, Simple Stress Strain & Elastic Constants - 1

Isotropic- Identical properties in all directions
Orthotropic- Different properties in all three directions
Homogeneous- A material of uniform composition

Actual area at instant of loading does not remain constant and decreases with increases in elongation actual stress is also called true stress.

The temperature at which the creep becomes an important consideration is called HOMOLOGOUS TEMPERATURE and this temperature is nearly half of the melting point temperature.

Clapeyorn’s Theorem of Three Moments express the relation b/w bending moments at three successive supports of a continuous beam, subjected to a loading on two adjacent span with or without settlement of supports.

The equation for simple bending is given by:

where I = Moment of Inertia, E = Modulus of Elasticity, F = Stress at any fiber at a distance of y from the neutral axis, M = Bending moment and R = Radius of curvature.

For a circle, the radius is constant, hence for pure bending, the arc bend into a circle.

Assumptions made in the theory of Pure Bending :

• The material of the beam is homogeneous and isotropic
• The value of Young's Modulus of Elasticity is the same in tension and compression
• The transverse sections which were plane before bending, remain plane after bending also
• The beam is initially straight and all longitudinal filaments bend into circular arcs with a common centre of curvature
• The radius of curvature is large as compared to the dimensions of the cross-section
• Each layer of the beam is free to expand or contract, independently of the layer, above or below it.

E =0  Slope of Stress- Strain Curve is straight horizontal line. It means at constant stress, strain keeps increasing which is the characteristic property of perfectly plastic material.

Bulk Modulus= K=(-p)/(ⅆv∕v)=1/β=E/3(1-2μ) 

β=compressibility is proportional to reciprocal of E.
 

 AB = b = D cosθ, BC = d = D sinθ