Young's Modulus
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ScribdTranslationsYoung's Modulus
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ScribdTranslationsYoung's modulus
The Young's modulus or longitudinal elastic modulus is a parameter that
characterizajavascript:void(0)the behavior of an elastic material, according to the
direction in which a force is applied. This behavior was observed and
studied by the English scientist Thomas Young.
For a linear elastic and isotropic material, the Young's modulus has the same value.
for a tension than for a compression, being a constant independent of
effort as long as it does not exceed a maximum valuemojavascript:void(0)called limit
elastic, and it is always greater than zero: if a bar is pulled, it increases in length.
Both the Young's modulus and the elastic limit are different for the various
materials. The modulus of elasticity is an elastic constant that, like the limit
elastic, can be found empirically through tensile testing of the material.
In addition to this longitudinal elasticity module, the modulus of
transverse elasticity of a material
Isotropic materials
Linear materials
For a linear elastic material, the longitudinal modulus of elasticity is a constant.
(for stress values within the range of complete reversibility of deformations).
In this case, its value is defined as the cocisthmusjavascript:void(0)between the tension and the
deformation that appears in a straight bar stretched or compressed made with the
material for which the modulus of elasticity is to be estimated:
Where:
it is the longitudinal modulus of elasticity.
it is the pressure exerted on the cross-sectional area of the object.
It is the unit deformation at any pointojavascript:void(0)from the bar.
The previous equation can also be expressed as:
So, given two geometrically identical mechanical bars or prisms but made of
different elastic materials, when subjecting both bars to identical deformations, we
higher tensions will be induced the greater the modulus of elasticity. Thus
analogous, we have to be subjected to the same force, the previous equation rewritten as:
It indicates that the deformations are smaller for the bar with a higher modulus of
elasticity. In this case, it is said that the material is stiffer.
Non-linear materials
When certain materials are considered, such as copper, where the curve of
stress-strain does not have any linear segment, a difficulty arises as it does not
the previous expression can be used. For that type of nonlinear materials, they can
define comparable magnitudes to the Young's modulus of linear materials, since
the tensile stress and the deformation obtained are not directly
proportional.
For these nonlinear elastic materialsthejavascript:void(0)is defined some type of
apparent Young's modulus. The most common way to do this is to define the
mean secant modulus of elasticity, as the increase in applied stress to a
material and the corresponding change to the unit deformation it experiences in the
direction of application of effort:
Where:
it is the secant modulus of elasticity.
it is the variation of the applied effort
it is the variation of the unit deformation
The other possibility is to define the tangent modulus of elasticity:
Anisotropic materials
There are several non-exclusive 'extensions' of the concept. For elastic materials, no.
isotropic Young's modulus measured according to the previous procedure does not give values
constants. However, canofjavascript:void(0)to prove that three constants exist
elasticsEx, EyyEzsuch that the Young's modulus in any direction is given
by
and where they are the direction cosines of the direction in which we measure the
Young's modulus with respect to three given orthogonal directions.
Dimensions and units
The dimensions of Young's modulus are In the
International System of Units its units are or, more contextually,
MODULUS OF ELASTICITY IN CONSTRUCTION
Material Approximate Elasticity Modulus Value (Kg/cm)2)
E = 30000 - 50000
In Mexico, it can be calculated according to the NTC 2004 of
masonry, in the following way:
Byajavascript:void(0)brick masonry of
Mamposterjavascript:void(0)dayclay and other piecesjavascript:void(0), except for those of
of brick concretetojavascript:void(0):
Em = 600 fm* for loadjavascript:void(0)short
duration
Em = 350 fmfor sustained loads
fmdesign compressive strength of the
masonry, referred to the gross area.
Hardwoods (in the
direction parallel to the
E = 100000 - 225000
fibers
Softwoods (in the
direction parallel to the
E = 90000 - 110000
fibers
Steel
E = 2100000
Cast iron
E = 1000000
Glass
E = 700000
Aluminum
E = 700000
Concrete (Cement) of
E=
Resistance:
110 Kg/cm2. 215000
130 Kg/cm2. 240000
170 Kg/cm2. 275000
210 Kg/cm2. 300000
300 Kg/cm2. 340000
380 Kg/cm2. 370000
470 Kg/cm2. 390000
Rocks: E=
Basalt 800000
Coarse-grained granite and in
100000 - 400000
general
Quartzite 100000 - 450000
Marble 800000
Limestone in general 100000 - 800000
Dolomites 100000 - 710000
Sandyajavascript:void(0)in
-616000
general
Limestone sandstone 30000 - 60000
Schistose clay 40000 - 200000
Gneiss 100000 - 400000
BIBLIOGRAPHY
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http://en.wikipedia.org/wiki/Young's_modulus