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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.
- 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
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 = deltaparallel 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
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.
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
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)
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