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.
I am using one film mateial (Polyester Polyurethane) for some purpose. I have got data sheet from the manufacturer with following details:
Durometer 90Shore A D 2240
Specific Gravity 1.19...
Hi I have a problem with the following question:
A steel violin string has a cross-sectional area of 0.2*10^-6 m^2 and is under tension 83N. If its length under tension is 35cm, find its original length.
I can not seem to solve the question without needing the value of young modulus...
Hi. I've been attempting this modulus problem from my textbook for the past hour and could not find a way to get the correct answer.
Homework Statement
The equation x^2 -(k+2)x + 2k + 1 = 0 ,where k is a constant has two real roots α and β.
1)Express α+β and αβ in terms of k
b) if |α| =...
I hope someone can help. I am an Production Engineer. We have a situation where we have to torque a 16mm copper cable in a box terminal by 4Nm. The cable will be used to carry a high electrical current.
We find that after torqueing (About 5 hours or so) the terminal can be re-tightened back...
We are studying the waterhammer in a Refinery. Since the bulk modulus is involved in this study, we will like to know where to find the bulk modulus at different temperatures and pressures for several refinery fluids such as kerosene, diesel, atmospheric and vacuum residue.
We have found some...
Homework Statement
The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at that point is huge, about 1.13 x108 N/m2.
(a) The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at that point is huge, about 1.13 x108 N/m2...
Homework Statement
Determine Young's Modulous (E) for the following materials:
Metal alloy - Test Piece 1 (TP1)
Low Carbon Steel - Test Piece 2 (TP2)
Copper - Test Piece 3 (TP3)
Each test piece has the same following dimentions - Length 25mm Diamter 4mm
Data:
TP1 = Force(kN) -...
My problem is not knowing the effects of modulus in parts of an equation ( in this case linear ) on the parts of the graph. An elaboration will be like y = |bx| + c , what's the effect on the graph compared to y = bx + c and likewise : y = bx + |c| and y = bx + c or even y = b|x| + c compared to...
Homework Statement
A wire of length L, Young's modulus Y, and cross-sectional area A is stretched
elastically by an amount ∆L. The restoring force is given by Hooke's Law as
k∆L.
b. show that the work done in stretching the wire must be: W = (YA/2L) x (∆L)^2.
The Attempt at a Solution...
Ok so i was wondering if what i am doing is correct, But it gets the wrong minimum point?
So my function is y=|x+4|
1) y^2=x+4
2)2y(dy/dx)=1
3)dy/dx = 1/2y
4)dy/dx = 1/2|x+4|
I set that 0 and get
0=1/(2(|x+4|))
Am i write in thinking this cannot be solved? or missing something...
Hi friends,
My work is related to simulation of the practical testing processes to the software testing methodologies using CAE :cool:
In short, I have an assembly(3d model or CAD data) for which I have to simulate the practical testing process to the software testing and compare the...
Homework Statement
A steel beam is used in the road bed of a bridge. The beam is mounted between two concrete supports when the temperature is 23⁰C, with no room for thermal expansion. What compressional stress must the concrete supports apply to each end of the beam, if they are to keep the...
Homework Statement
A human bone has a youngs modulus of 10^10 N m^-2. It fractures when the compressive strain exceeds 1%. What is the maximum load that can be sustained by a bone of cross sectional area 3cm^2?
Homework Equations?
F= Y*(change in length/ original length)* cross...
1. Two part question.
An elastic cord with cross sectional area 4.00mm^2 needs a force of 3.6N to increase its length by 12%
Part One- Find the Youngs Modulus of Elasticity
Part Two- The unstretched cord is 0.80m long. Find the energy stored in this strain.
[b]2. Homework Equations ...
Homework Statement
6. A steel beam is used in the road bed of a bridge. The beam is mounted between two concrete supports when the temperature is 23⁰C, with no room for thermal expansion. What compressional stress must the concrete supports apply to each end of the beam, if they are to keep the...
Homework Statement
Find all entire functions f(z) with the property that |zf(z)|<=1 for all z in C
Homework Equations
The maximum modulus principle says that the only functions that are entire and bounded are constant functions.
The Attempt at a Solution
I know that if f(z) is...
If I am given that mica has a modulus of 52GPa parallel to the c-axis and 179 GPa perpendicular to the c-axis, how do I figure out the elastic modulus of a polycrystalline mica where grains are oriented randomly?
I was wondering if anyone could please point me in the direction of some background info on who (and why) someone defined the equations definition of the shear modulus, I've searched in google and wiki and havnt found anything useful. Just a link or something would be great
Homework Statement
My graph doesn't look like a typical stress vs strain plot.
http://dl.dropbox.com/u/2344149/graph.png
* y-intercept set to zero and last 4 data points were ignored
Wire diameter= 1.16 mm
L0= 100.2 cm
\overline{}L'0= 0.015
Young's modulus for steel (actual)=...
in young modulus of a metal bar , we have a horizontal bar on one side we attach some weight so there is some change in angle but no change in length then why it is called young modulus?
Hello,
I've got
|a|^{2} = |a - b + b|^{2}
What can I do with this guy? Usually when the square isn't there I use the triangle inequality and things fall out pretty quick, for example,
|a| = |a - b + b| \leq |a-b| + |b|
Is there something like that I can do with the orginial guy?
Homework Statement
Show that if a, b, c, and d are integers such that a | c and b | d, then ab | cd.
Let m be a positive integer. Show that a mod m = b mod m if a ≡ b(mod m)
Homework Equations
| means "divides," so a | b means "a divides b" or "b can be divided by a"
mod gets the...
I need to multiply 2 matrix in Mathematica but modulus an Integer.
The "Modulus->n" option cannot be used with "Dot" function. You can use Modulus-> n with "Inverse" or even "Det" but not with "Dot". It is something strange.
How should I do it, then? Any idea?
Thank you.
1. The Young's modulus for tin is 4.5x10^10. If the speed of sound in tin is measured to be 2.73km/s , find its density in (kg/m^3) .
a)6.05x10^3
b)23.8x10^3
c)6.35x10^3
d)24.5x10^3
e)6.65x10^3
, E(tin)=4.5x10^10 ,speed of sound in tin=2.73km/s
2. v=sqrt(B/density) -where...
Homework Statement
I'm completing a homework for Young's Modulus and one question asks to estimate the elastic limit for the wire which was used.
I can see where this approximately is on the graph I have drawn. When the question asks to estimate the elastic limit, does this mean to...
Homework Statement
I was given the problem to try experimentally find youngs modulus for normalized steel but when i did the equation the value i got was about 33 GPa. It is supposed to be around 200 isn't it? I cannot figure out what is wrong, am i missing something or is the measured data...
Okay, when I enter into the calculator sqrt(x^2) it equals |x|. Since when? I thought sqrt(x^2) equals x and then when you go to sketch it, it will be a positive diagonal line through the origin whereas |x| is a reflection at the origin.
Homework Statement
2. As engineers, we wish to use a metal bar as a support arm on a crane. The bar has a
Young’s Modulus of 3x106psi . Assuming the rod will need to be 3ft long. Answer the
following questions…
a)If the crane is designed so that the
maximum tensile force on the rod is...
Homework Statement
Multiple choice question about a modulus function, which statement is false?
Below is the multiple choice question about a modulus function (the domain of the function is all reals):
Which one of the following is not true about the function f(x)= | 2x+4 | :
A. The...
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...
Hi,
I have a fairly simple problem which but I'm not sure if it should rather be in a computer science forum for algorithms or something.
Given n vectors, how do you choose the sign of each vector as to maximize the modulus of the sum of the vectors?
Sure you could go through all 2^n...
1. How to calculate cross sectional area and force for Young's Modulus? My main issue is that I don't know my F or my Ao. Help?
e=Constant 2.106
DeltaL=10mm
Lo (original length of elastic)= 200mm
f=?
Ao=?
2. E= FLo
Ao(Delta)L
F= EAoDeltaLength[U/]
Lo
F= [U](2.106)(10mm)(Ao)...
I'm inputing data into a SolidWorks material profile, but I'm having difficulty determining the value of the elastic modulus (psi) of steel reinforced concrete
i'm looking at the following source for material properties:
http://www.fhwa.dot.gov/pavement/pccp/pubs/05081/chapt3.cfm [for...
Homework Statement
By considering the force-separation curve for two adjacent atoms in a solid, f(x), show that the Young’s modulus can be expressed on the microscopic scale as:
Y = - \frac{1}{x_0} \frac{df}{dx}\right| |_{x=x_0}
(the | is meant to go allt he way form the top to bottom of...
Homework Statement
a) List all integers, A, that is in the range where A is greater than -51 and less than 51 such that it also satisfies: A is congruent to 7 (mod 17)
b) has a set of representatives modulo 17, made up entirely of multiples of 3
Homework Equations
Only need to know...
Homework Statement
A 0.46 m long guitar string, of cross-sectional area 1.1 10-6 m2, has Young's modulus Y = 2.20 109 N/m2. By how much must you stretch the string to obtain a tension of 10 N?
Homework Equations
?
The Attempt at a Solution
I don't know how to begin this...
can someone tell me a direct way of solving modulus containing equations other than taking different cases with all terms ,
i mean if we have an equation of the kind |a|+|b|-|c|-|d|=|e|+|f| ,where a,b,c..are some expressions , i cannot take 12 cases! , there would definitely be some technique...
Homework Statement
Find the inverse of
y=|x-4|
Homework Equations
-
The Attempt at a Solution
i tried y+4=|x|
replacing y with x,
x+4= |y|
and I am quite stuck because of the modulus sign.
do i go on with x+4=y or -x-4=y?
Homework Statement
Onto a thick brass rod we attach equally long glass thread. At what temperature change will the glass thread break if the temperature coefficient of linear expansion for brass is
α1= 20 x 10 ^-6 K^-1, and for glass is α2= 7 x 10^-6 K^-1? Young’s (elastic) modulus for glass...
Homework Statement
Onto a thick brass rod we attach equally long glass thread. At what temperature change will the glass thread break if the temperature coefficient of linear expansion for brass is
α1= 20 x 10 ^-6 K^-1, and for glass is α2= 7 x 10^-6 K^-1? Young’s (elastic) modulus for...
I am investigating the Young's Modulus of certain materials and what factors have an effect on the Young's Modulus of materials.
I am going to be altering the temperature, my hypothesis being that increasing the temperature will lower the E of the materials.
Are there other factors I could...
the reasons:
1. For low molecular weight materials, modulus drops rapidly with increasing temperature.
2. For High molecular weight amorphous materials, modulus drops to a secondary plateau region called the rubbery plateau (polymer entanglement prevents chain slippage). With further...
in the following question, how do i find the changle in AB, the change in AD and the change in AC?
http://lh4.ggpht.com/_H4Iz7SmBrbk/Sv_hYT83rYI/AAAAAAAAB8s/7l5YRXMxVfQ/s912/Capture.JP what i have done is used the following
\sigmaxx=E*\epsilonxx
\deltaAB=\epsilonAB*AB
since AB is on the x...
Hi everyone, :smile:
Apologies if this is in the wrong section, I'm still relatively new to the forum. :blushing:
I'm an engineer studying Young's modulus in building materials. I have a passing interest in physics, but let's say my knowledge of the subject is far from exhaustive...
Homework Statement
Let g(z) be a function that is analytic and non-constant on D = {|z| < 1}. Suppose that Max |g(z)| \leq \frac{1}{r} for all 0< r <1, |z| = r. Use the Maximum Modulus Principle (or corollary) to prove that |g(z)| < 1 for all z \in D.
Homework Equations...
1. Consider a steel guitar string of initial length L=1.00 meter and cross-sectional area A=0.500 square millimeters. The Young's modulus of the steel is Y=2.0 \times 10^{11} pascals. How far ( Delta L) would such a string stretch under a tension of 1500 Newtons?
Use two significant figures in...
Homework Statement
Im confused as to how you obtain that,
77 is congruent to -1 mod 26
-77 is congruent to 1 mod 26
-11 is congruent to 15 mod 26
Homework Equations
The Attempt at a Solution
Some help would be great thanks