Mechanics of Materials

- 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, thin-walled pressure vessels, beams, eccentrically loaded members, and columns.

- is force per unit area

- typical units of stress are lbf/in² , 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

- 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.

- 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 ]

- 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

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.

- 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

- 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)

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