What is Modulus of elasticity: Definition and 36 Discussions
An elastic modulus (also known as modulus of elasticity) is a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form:
δ
=
def
stress
strain
{\displaystyle \delta \ {\stackrel {\text{def}}{=}}\ {\frac {\text{stress}}{\text{strain}}}}
where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter. Since strain is a dimensionless quantity, the units of
δ
{\displaystyle \delta }
will be the same as the units of stress.Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are:
Young's modulus (E) describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.
The shear modulus or modulus of rigidity (G or
μ
{\displaystyle \mu \,}
Lamé second parameter) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity.
The bulk modulus (K) describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as volumetric stress over volumetric strain, and is the inverse of compressibility. The bulk modulus is an extension of Young's modulus to three dimensions.Two other elastic moduli are Lamé's first parameter, λ, and P-wave modulus, M, as used in table of modulus comparisons given below references.
Homogeneous and isotropic (similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below at the end of page.
Inviscid fluids are special in that they cannot support shear stress, meaning that the shear modulus is always zero. This also implies that Young's modulus for this group is always zero.
In some texts, the modulus of elasticity is referred to as the elastic constant, while the inverse quantity is referred to as elastic modulus.
Hello All :
i am reviewing charlse kettle book introduction to solid state physics and came across an equation in the 3ed chapter which is a bit unclear
hope that physics forums members can clear it more if that possible
the equation 1st mentioned in the 3ed chapter page number 84
it is about...
Could I please ask for help with the following question?
Four uniform rods of equal length l and weight w are freely jointed to form a framework ABCD. The joints A and C are connected by a light elastic string of natural length a. The framework is freely suspended from A and takes up the shape...
I realized that the tension in the rod is not uniform and found it to be ##T = Wx/L## I found this by splitting the rod into two sections one of length ##x## and the other of length ##L-X## where x is the length from the base of the hanging rod
To find the total elongation in the rod I...
For an anisotropic material, is there any way to analytically determine the elements of the stiffness matrix?
For orthotropic and isotropic materials, there are analytical expressions relating the stiffness matrix elements to the elastic modulus and poisson's ratio, but I do not believe this...
Which modulus define a property of fluids??
The above mentioned question was asked in my college internals. The answer they suggested was sheer modulus.
Any explanations??
So I'm trying to understand how the modulus works in metals. I understand that when the temperature rises, that means that the modulus decreases. But I do not understand exactly what it is or how it affects the way that the molecules would vibrate for instance, as kinetic sound energy moved...
I am trying to find a formula to show the modulus of elasticity (MOE) of a panel of three layers of different materials when I know the MOE value of the three individual materials. This is for a Plastic Laminated Panel where, the top and bottom layers are plastic laminate (i.e. Formica) .028"...
I am constructing a glutamine beam as part of a project and need to estimate the load at which the beam fails in bending and the load that will give deflection of length/200.
I have been allowed to do a none destructive test on each piece of timber to be used in my beam. This has given me a...
Homework Statement
Stress = 320 MPa
Max Elastic Moment = Stress*Z
Max Plastic Moment = Stress*S
Solve the maximum moments and compare the % increase
Beam is an I beam with dimensions: (b and d)
Top Flange = 25*10
web = 10*180
Bottom Flange = 200*8
Homework Equations
see above
The Attempt at...
I am a part C mechanical engineering student and require some advice for my individual project, which is based on the high strain-rate testing of a particular glass filled composite material using a split-Hopkinson pressure bar (SHPB) experiment.
I gathered the results on a SHPB test rig and...
Hello lol first post . so I've done an experiment in determining the modulus of rigidity for a bar of an unknown material (torsion experiment). I have been asked to analyse the results, which I still have no idea what that means and find the material with the G value that i have. I've been...
Hi,
I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...
Hi,
I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...
Homework Statement
Grade 1020 Steel has a yield strength of 42ksi and E modulus of 30 mpsi. Another grade of steel has yield strength 132 ksi. What is its E modulus?
Homework Equations
E=FL/EA
This is the equation i should be using to find e modulus I thing
The Attempt at a Solution
I don't...
I'm learning about Hooke's law and modulus of elasticity (also known as youngs modulus) but it seems I am being taught it differently in maths and physics.
In maths I am taught that T=λx/l and λ is the modulus of elasticity, measured in Newtons.
In physics I am taught that T=λAx/l where λ is...
I appreciate your help with this problem from a Three point Bending Test in Wood samples
Homework Statement
Force: 2400 N
Deflection: 4.3 mm
Span: 343 mm
Length: 392 mm
b: 24.01 mm
d: 24.25
MOE: 16445.15 MPa
How can I calculate the Modulus of Elasticity with shear corrected...
Young's Modulus of Elasticity Problems - URGENT
Homework Statement
Calculate Young's Modulus of Elasticity for the three materials using the graphs only.
Stress (N/m2) Strain
70 0.06
100 0.11
150 0.22
200 0.35
220...
The engineering yield strength, the modulus of elasticity, the original diameter and final diameter of a wire are given. That wire is stretched and it diameter decreases. I am trying to find the engineering strain just before yield and the corresponding true strain.
So I assume I will find...
Homework Statement
How to calculate the modulus of elasticity algebraically? Especially that of a pine wood rectangular cantilever beam? I have a few measurements here. The area inertia is .413 cm^4, the length of the unsupported part of the beam is at 40 centimeters(the whole beam is around 66...
Mechanical principles - Stress and modulus of elasticity
Homework Statement
A 2.2m long steel towing bar of solid circular section diameter of 45mm is expected to carry a maximum load of 210 kN. The safety factor is 4; and for the steel the UTS is 540 MNm-2 and the modulus of elasticity is...
Hey guys,
I recently did a compression lab with different materials (wood and pvc pipe) and I have to plot the stress/strain curves given the data collected, as well as find yield strength (0.2% offset), ultimate compressive strength, and modulus of elasticity. I've already calculated...
Homework Statement
A rod with a diameter of 1.00 in and length of 6.0 ft undergoes an axial deformation of 0.150 in when subjected to an axial force of 52.0 kip. The diameter of the rod decreases by 0.0007 in at this load. Determine the modulus of elasticity, Poisson's ratio and the shear...
Bare with me as I'm brand new to all of this, and my inexperience may show, but i have what may be a simple question to some of you. I'm conducting a lab experiment in my Materials lab I will be testing the the strength of 3 different Aluminum 6061 specimens. I have an L beam, thin walled...
Attached is the graph and small part of table that i have chosen from the elastic range (first column extension, second column load) from a tensile test. I am trying to calculate youngs modulus of elasticity but can't seem to get a figure close to that of the common figure for the material...
I'm trying to figure out how to calculate the modulus of elasticity for a board clamped to a surface plate at one end and free-floating on the other. I've measured the deflection with a 1k weight at the free end of the board. So I've got that data as well as the dimensions of the free-hanging...
Homework Statement
Calculate the deflection at the end of a rod whose dimensions are 1m x 0.1m x 0.1m, when a load of 100N is applied. The modulus of elasticity is given as 1 x 1011 (N/m2)
Homework Equations
d = PL/AE where
d = end deflection of bar in metres (in m)
P = the applied...
Homework Statement
Lets say a wire has Youngs modulus Y, Initial length L area A and is supporting some external load/force of magnitude F...its extension is dl..We say that the Potential energy of wire is 1/2(YA/L)(dl2)...But i am having a problen with the energy changes...
Homework...
After making a chart in Excel and obtaining the equation " Y= 3E+07x+2445.3 "
Now i need to calculate the modulus of elasticity. I know that the slope of the equation gives the modulus of elasticity.
but I have no clue how to even begin solving the equation Y= 3E+07x+2445.3I do know...
new to physics can some one please help me with b and c
Load (kN) 0 20 30 50 60 73 90 94
Extension (mm) 0 0.150 0.225 0.375 0.453 0.550 0.900 1.100
a) Draw a graph with load on the y-axis and extension on the x-axis...
Hi,
I need the compressibility of diesel, depending on density, pressure(0-200bar) and temperatur.
Do you know where to find these values?
Thanks
Inkog
Hello, having some problems with calculating young's modulus, please help.
[b]1. A Strain gauge records the following strain when a block of material is pulled:
Force(N) Strain(%)
100 0.01
1000 0.1
2000 0.179
3100 0.9
Area of block =...
a structural steel rod has a radius of .5 inches and length of 32 in. 4000 lb force stretches along its length. modulus of elasticity is 29 x 10^6 psi.
Need to figure out stress on rod, the elongation of rod due to force, and strain on rod due to force
Homework Equations
The...
I've got a computer plot showing relations between stress and strain for steel. But how can I find the modulus of elasticity (E) from the graph? Isn't it so that E=(stress/strain)? The thing is that I get very different answers when I compute E in this way for various points on the graph.
Is it possible to find the yield stress of a material with only modulus of elasticity and Poisson's ratio?
I was given a problem that:
What is the min. aluminum needed to support a block (10 Newton) to 1 meter high? E=70GPa and v=0.3 are the only given aluminum properties.
I would know...