
Mechanics of Materials 1
 deals with the elastic behaviour of materials and the stability of members.
 mechanics of materials concepts are used to determine the stress and deformation of axially loaded members, connections, tortuonal members, thinwalled pressure vessels, beams, eccentrically loaded members, and columns.

Stress
 is force per unit area
 typical units of stress are lbf/in^{2 }, Ksi, and MPa.
 There are two primary types of stress: normal stress and shear stress.
 With normal stress, o, the force is normal to the surface are alpha?
 With shear stress, T, the force is parallel to the surface are:
o = P_{normal to the area }/ A
Tao = P_{parallel to area }/ A

Linear Strain, Epsilon
 is a change of the length per unit of length
 Linear strain mah be listed as having unites of in / in, mm / mm, percent or no units at all.

Shear Strain, Tao
 is an angular deformation resulting from shear stress.
 shear strain may be presented in units of radians, percent or no units at all.
Epsilon = delta / L
Tao = delta_{parallel to area} / height = tan theta aprox = theta [ theta is in radians ]

Hooke'a law
 is a simple mathematical statement of the relationship between elastic stress and strains: stress is proportional to strain.
 For normal stress, the constant of proportionality is the modulus of elasticity ( Youngs modulus ), E
o = E*epsilon

Poison ratio, y
is a constant that relates the lateral strain to the axial strain for axially loaded members.
y= Epsion_{lateral }/ Epsilonaxial
Theoretically, Poison's ratio could vary from zero to 0.5 but the typical values are 0.35 for aluminum and 0.3 for steel.

Hookes Law  2  shear modulus
 Hooke's law may also be applied to a plane element in pure shear/
 For such an element, the shear stress is linearly related to the shear, strain, Tao , by the shear modulus ( also known as the modulus of regidity ) G.
Tao = G_{tao}

Hooke's Law 3
Modulus of Elasticity / Shear modulus / Poison's Ratio
 For an elastic isotropic material , the modulus of elasticity, shear modulus and Poinsons ratio are related by
G= E/ 2(1+V)
E = 2G(1+V)

Material Properties
materials units (a) steelaluminnum Cast Iron WoodFir
Modulus of  Mpsi 29.0... 10.0 .......  14.5.......  1.6
elasticity, E  GPa 200.0 69.0......... 100.0.......11.0
modulus of  Mpsi 11.5.. 3.8............ 6.0.......... 0.6
rigidity, G  GPa  80....26.0............ .41.4....... 4.1

