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.
(powers of complex numb.):Find the solution of the following equation whose argument is strictly between 90 degrees and 180 degrees: z^6=i?
I don't understand why the modulus of i is 1 and the argument of i can be 90∘ plus any multiple of 360
Hi. I am trying to determine the size of a shaft for a motor I am designing. The thing is, I can't seem to find shear stress alone for steel. I can find shear modulus easy though... But I don't really know the angle of twist. I know torque and I am trying to figure out radius.
Should I just...
Hi everyone!
Please help, I have spent some considerable time to understand the two concepts and still this is nagging at me... I am relating to Structural Engineering, just to let you know guys. My question is ..
Moment of inertia is about distribution of mass, the further away from the axis...
Hi everyone!
Please help, I have spent a considerable time to understand the two concepts and still this is nagging at me... I am relating to Structural Engineering, just to let you know guys. My question is ..
Moment of inertia is about distribution of mass, the further away from the axis the...
Homework Statement
I was doing this experiment: http://practicalphysics.org/shm-cantilever.html
I'm interested in the derivation of the result ω^2 = Exy^3 / 4*M*L^3. I tried to think where it comes from.
How do we even start to derive k from the equation mg = KS where S is the delta in the...
Hi
How to find young's modulus of quantum well semiconductor?
For GaAs- young's modulus E=85 GPa and
For Al0.3Ga0.7As- young's modulus E=84 GPa.
For quantum well Al0.3Ga0.7As/GaAs/Al0.3Ga0.7As
Value of young's modulus is?
A steel cable 3.00 cm 2 in cross-sectional area has a mass of
2.40 kg per meter of length. If 500 m of the cable is hung
over a vertical cliff, how much does the cable stretch under
its own weight? Take Y steel ϭ 2.00 ϫ 10 11 N/m 2 .Y=([L][/o]F)/(A*delta_L)
My attempt of solution...
http://imgur.com/oLMkHBX
How exactly would you calculate E in this? The cross section is a square and it deforms .8 mm. I'm not quite sure what to do since obviously the size of the cross section changes.
Young’s modulus is given as the second derivative of the total energy with respect to the strain divided
by the equilibrium volume.
Can help me for the calculate equilibrium volume and young's modulus?
I'm trying to better understand RSA and Diffie-Hellman exchange and the modulus math that they are base on, there are some questions I have about there properties for which I am unable to find concise explanations about. I'm generally interested in how the commutative, associative...
Homework Statement
By what amount does the 52-cm-long femur of an 73 kg runner compress at this moment? The cross-section area of the bone of the femur can be taken as 5.2×10-4 m2 and its Young's modulus is 1.6×1010 N/m2.
Express your answer to two significant figures and include the...
Homework Statement
So I'm trying to find the modulus and argument of
cosh(iπ)
Homework EquationsThe Attempt at a Solution
so far coshπi = ½(eiπ+e-iπ) I am now a bit stuck as what to do as i have two terms in the form eix and I'm not sure homework to combine them to get the argument?
Hello everybody. I've measured the Young Modulus of PDMS samples both in compression and in tension. From compressive tests I get a Modulus twice as big as the one I get from tensile tests.
Is it normal to get two different values for Young Modulus using tensile or compressive tests? Do you...
If I have something like:
$$\lvert \langle M \lvert \hat{L}_x+i\hat{L}_y \rvert M-1 \rangle \rvert ^2=c$$.
where ##c## is any old real number. If I undid the modulus square to find:
$$ \langle M \lvert \hat{L}_x+i\hat{L}_y \rvert M-1 \rangle=\pm \sqrt{c} $$ Would I not have to consider...
Homework Statement
Find the modulus and argument of
1) cos(i)
2) -3i
Homework EquationsThe Attempt at a Solution
1) So for question 1 i tried
cos(i) = ½(ei2 + e-i2) = ½(e-1 + e) . However this doesn't (as far as I can see!) lead me to the right answer. I was aiming to get it in the form...
Homework Statement
A force stretches a wire by 2mm. A second wire of the same material and with the same area of cross-section and twice the length is also stretched by the same force. What will its stretch be?
Homework Equations
F= (YA/L)ΔL
The Attempt at a Solution
F, Y, and A are all...
Homework Statement
A mild steel wire of length 1 m and cross-sectional area 0.5*10^-2 cm^2 is stretched within elastic limit horizontally between two pillars.A mass of 100 g is suspended from mid-point.Depression at mid-point?
Homework Equations
Sag in metal rod is=WL^3/(4BD^3Y) where...
After completing two experiments to find the shear modulus of a beam, I found two very different results. For test 1, we twisted the beam slowly at very small angles (0.005 - 0.03 rad), only in its elastic form. The torque was found using a torsiometer . In test two a replica of the beam was...
So my question is, if the bulk modulus change by 5%, what is the fractional volume change value? is it times 0.05 or divided by 0.05? or the fractional volume change still the same?
If I have something like ||V>+|W>| That is the modulus of sum of two ket vectors, can I "bra" through the modulus like: <V|(||V>+|W>| )=|<V|V>+<V|W>|?
Thanks,
kq6up
Homework Statement
First question = attached below
Second Question = attached below
Homework Equations
modulus, argument, roots.
The Attempt at a Solution
For the 1st question I've gotten the modulus, the principal argument and the abs. of z^1/4 which was something like 1.5335 I believe. The...
Homework Statement
See image.
Homework Equations
pressure = density*gravity*depth
The Attempt at a Solution
The pressure at 5000 ft according to the book is 322,000 psf. This makes sense because density*gravity*depth = 2*32.2*5000 = 322,000 psf. How do I apply the bulk modulus equation to...
Homework Statement
If the bulk modulus for water at
70∘F is 319 kip/in^2, determine the change in pressure required to reduce its volume by 0.3%.
Homework Equations
E = dP/(dV/V)
E - Bulk Modulus
dP - change in pressure
dV - change in volume
V - volume
The Attempt at a Solution
Well I just...
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...
This question is killing me.
I know the graph is non-monotonic so i have to split up finding F(Y) for -1<Y and Y<1 but then what do I do with the modulus? >.<
Any help would be greatly appreciated! Thank you so much x
1. Homework Statement
h = 17.2 cm
A = 12.32cm2
E = 410 MPA
Fapp = 6130 N
2. Homework Equations
Stress
σ = F/A where F is force applied and A is cross sectional area of side where force is applied
Strain
ε = ΔL/L where L is the length of the bar and ΔL is the change of length of bar
Young's...
Hi Can any please help:
My course work is asking for me to calculate the Bulk modulus and shear modulus for a material that has a Young's modulus of elasticity of 250GN m-2 and a Poisson's ratio of 0.32?
Any help will be great thanks
Simon
Hello guys,
does anyone know if there is a specific relationship between the modulus of elasticity and crystal structure/microstructure? I know that YM is basically derived from the chemical bonding, but how about the other two? As much as I know it should be not affected by the microstructural...
Hi, PF! In the study of mass transfer involving chemical reactions, I have seen the use of two different non-dimensional parameters which apparently quantify the same ratio. These are the second Damköhler number and the Thiele modulus, which are defined as
\textrm{Da}^{\textrm{II}} =...
Hi,
I was looking some exercices on internet about the poisson's ratio. I have just one question.
How can i calculate the young's modulus and poisson's ratio when i know that a material is purely elastical.
I calculate circonferential et longitudinal contraints and i have write the cauchy...
I've tried searching online for one in what I can only guess would be called a reduced algebraic form, and I cannot find it.
To make matters worse, for me, at least, I do not have the mathematics knowledge necessary to understand advanced functions, series, and transformations of mathematics...
Hi, I have a question regarding calculating Young's modulus for a flat spring. I have a flat spring shown as the left one in the image. Now I fix the bottom of the spring and exert a force F on top of it and it bends for distance of d. Is there any way to calculate young's modulus for this...
i am new to rubber components , now i am developing a bladder for pulsation dampener, so for that i need to check the spring rate or elasticity of viton material and to determine the thickness for the bladder, I am struggling a lot to find the shear modulus of rubber, if have this valve i have...
Homework Statement
The figure shows the stress-strain curve for a material. The scale of the stress axis is set by s = 280, in units of 10^6 N/m2. What are (a) the Young's modulus and (b) the approximate yield strength for this material?
Homework Equations
E=stress/strain
The Attempt at a...
Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of...
Sorry if the answer is very simple, but I just had a question regarding error propagation when using a modulo operator in intermediate steps. For example, I have ## \theta = arctan(\frac {A}{B}) ## and then I do ## \theta ## % ##2\pi## (modulo ##2\pi##). This gives me an answer between ##...
Homework Statement
I am struggling with a part of the question. Please see diagram in the attached.
Calculate the relevant Elastic Modulus and select the lightest suitable beam section assuming a maximum allowable bending stress of 120 Mpa ?
Homework EquationsThe Attempt at a Solution
To...
Homework Statement
I have the following table
Load 25 50 75 100 125 150 160 170
Extension 0.38 0.75 1.15 1.53 2.8 8.6 15 28
and I need to:
1. Plot the stress – strain or (load-extension) graph and determine
(a) Approximate value of the elastic limit
(b)...
Homework Statement
In the figure, a 128 kg uniform log hangs by two steel wires, A and B, both of radius 1.15 mm. Initially, wire A was 2.80 m long and 2.00 mm shorter than wire B. The log is now horizontal. Young's modulus for steel is 2.00 × 1011 N/m2.
What are the magnitudes of the forces...
Homework Statement
Homework Equations
E= (F/A) x (L/ΔL)
The Attempt at a Solution
I know that since the material is the same, the Young modulus should be the same. However, when I try to find the ratio of the second wire to the first, I get the answer C. For the first wire, E= 4FL / d2Δl...
If a rod with cross section area A and length L is lying on a smooth table with one end being pulled by f Newtons and other end by 2f Newtons.
What force I can use in calculating Young's Modulus and why?
my doubt is whether it will be 3N or 1.5N and why?
Stretched length is given.
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 have been undertaking a project investigating the strain sensitivity of a particular glass filled composite.
From my quasi-static results, the stress-strain curves seem to be reasonable and match that of the mechanical material properties...
Homework Statement
A nano-tube having cross sectional area A and length L extends ΔL when a force F is applied normally to one of the cross-sectional surfaces. Show that if N tubes are connected end-to-end the then Young's modulus of the fibre does not change.
Homework EquationsThe Attempt at...