Mechanics of Materials

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Mechanics of Materials
2012-02-26 12:53:01
FE Mechanics Materials

FE - Mechanics of Materials
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  1. 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, thin-walled pressure vessels, beams, eccentrically loaded members, and columns.
  2. Stress
    - 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- = Pnormal to the area / A

    Tao = Pparallel to area / A
  3. 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.
  4. 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 = deltaparallel to area / height = tan theta aprox = theta [ theta is in radians ]
  5. 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
  6. Poison ratio, y
    is a constant that relates the lateral strain to the axial strain for axially loaded members.

    y= Epsionlateral / 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.
  7. 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 = Gtao
  8. 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)
  9. Material Properties

    materials |units (a)| steel|aluminnum |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