# What is Shear modulus: Definition and 27 Discussions

In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:

G

=

d
e
f

τ

x
y

γ

x
y

=

F

/

A

Δ
x

/

l

=

F
l

A
Δ
x

{\displaystyle G\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\tau _{xy}}{\gamma _{xy}}}={\frac {F/A}{\Delta x/l}}={\frac {Fl}{A\Delta x}}}
where

τ

x
y

=
F

/

A

{\displaystyle \tau _{xy}=F/A\,}
= shear stress

F

{\displaystyle F}
is the force which acts

A

{\displaystyle A}
is the area on which the force acts

γ

x
y

{\displaystyle \gamma _{xy}}
= shear strain. In engineering

:=
Δ
x

/

l
=
tan

θ

{\displaystyle :=\Delta x/l=\tan \theta }
, elsewhere

:=
θ

{\displaystyle :=\theta }

Δ
x

{\displaystyle \Delta x}
is the transverse displacement

l

{\displaystyle l}
is the initial length of the area.The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M1L−1T−2, replacing force by mass times acceleration.

View More On Wikipedia.org
1. ### A Lame parameter mu = shear modulus derivation (rogue factor of 2)

Hello, I am trying and failing to derive that the shear modulus ##G## is equal to the Lame parameter ##\mu##. I start with the linear, symmetric, isotropic stress-strain formula: $$\sigma = \lambda \mathrm{tr}(\epsilon) \mathrm{I} + 2\mu \epsilon$$ I then substitute a simple (symmetric) shear...
2. ### I Derivation of Voigt's Shear Modulus

How did Voigt derive the average shear modulus of an anisotropic material, G=1/5 (A-B+3C), where 3A=c11+c22+c33, 3B=c12+c13+c23, 3C=c44+c55+c66? The original text is published in German about 100 years ago. I looked for other papers explaining this, but none has explained the derivation. They...
3. ### Shear modulus, finding length of board

Homework Statement A diver stands (80kg) at the end of a diving board, causing the board to dip 10cm. The board has a width of 34cm and a height of 6cm. If the shear modulus of the board is 2x10^6pa, what is the length of the board? (Ans: 5.2m) Homework Equations [/B] F/A=S⋅Δx/h The...
4. ### I Experimental Shear Modulus and Poisson Ratio

I'm designing a 'thing' for my masters project, which has to be 3D printed. I've designed this in Inventor, but it doesn't have PLA (Polylactic Acid), so I've been using Inventor's PMMA (Perspex) thus far. I want to get more accurate figures, so I've had a 1 cm3 block printed to get an exact...
5. ### Shaft radius from shear modulus

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...
6. ### Different values of shear modulus

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...
7. ### Calculating Bulk and Shear Modulus with Young's Modulus and Poisson's Ratio

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
8. ### What is the shear modulus of viton material?

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...
9. ### Shear Modulus, Modulus of rigidity

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...
10. ### Bulk and Shear Modulus Calculations

Homework Statement A material which has a Young’s modulus of elasticity of 250 GN m–2 and a poisons ratio of 0.32, calculate: (a) the bulk modulus of the material (b) the shear modulus of the material. Homework Equations E=3(1−2ν)K 3. The Attempt at a Solution a) E = 3(1−2ν)K K = E /...
11. ### What is the Shear Modulus of This Screw?

I have a screw that is used in our plant that is rated to break at 39 ft/lbs of torque. The diameter of the shaft is .130 inches. What is the shear modulus of the material that is being used. Thanks
12. ### Shear modulus and shear strain relationship?

If a shear force is acting on a rectangular beam, how do I use the value of the shear modulus to calculate if the force applied will fracture the beam? Below I've submitted the data involved. The shear force applied is 1000 N and the cross section area is 28 mm. So the shear force applied is...
13. ### Shear Modulus (G) for Nitronic 50 or XM-19 Hot Rolled Condition

I am looking for shear modulus (G) for Nitronic 50 or XM-19 High strength hot rolled condition UNS - S20910 and ASTM A276-10 it is surprising for me that material standards like ASME or ASTM does not provide shear modulus data..? even checked "http://www.keytometals.com" and...
14. ### Shear modulus of dry spaghetti

While doing an assignment on building with spaghetti I have come across the shear modulus. I need to find the shear modulus in order to use the torsion equation. Does anyone have a value for it by any chance?
15. ### Shear Modulus value for Alu bronze

Hello, Does anyone have the shear modulus value for Alu Bronze CW307G-R680 Cheers Ben
16. ### Determine the modulus of elasticity, Poisson's ratio and the shear modulus.

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...
17. ### Help : Determine shear modulus from tensile test

Hi, i just did a unaxial tensile test for a done specimen. What i got is the stress-strain curve, and poison ratio. May i know how can i determine the shear modulus G12 ? I gt E1, E2 and V12 and V21.
18. ### Shear Modulus of Steel: Help Understanding Imperial Calcs

I am reading through some calculations in a book that refer to an average shear modulus of steel (19700)... they give no units and it has completely thrown me off track while following through the calcs can anybody help? I know the unit is imperial and if i convert some of the other units...
19. ### The theory underlying the shear modulus of metals

Hi, I'm trying to more understand the theory behind the shear modulus for various materials and have come across this text: http://www.scribd.com/doc/49116294/Electronic-Basis-of-the-Strength-of-Materials-Gilman-J-CUP-2003 The chapter on shear modulus starts on page 153 and there is a part...
20. ### Shear Modulus of jiggling jello

Homework Statement A student bumps into a tray of jello. The lime jello is jiggling side to side faster than the orange jello. Both jellos have the same spatial dimensions. Which statement is true? Answer: Lime jello has a higher shear modulus than orange jello Homework Equations...
21. ### Help with Shear Modulus Research

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
22. ### How Do You Calculate Shear Modulus from Poisson's Ratio and Young's Modulus?

hi there, I am completely stuck on this question and was wondering if anyone could help me out here; ''a metal wire has a diameter of 1mm. when subjected to a tensile load of 200N the diameter is 0.99925. if the youngs modulus of the titanium is 110GPa, determine the shear modulus of the...
23. ### Shear modulus as a funtion of temperature

Why does the shear modulus of a metal decrease with increasing temperature, on an atomic scale? Is it something to do with electrons gaining more energy allowing "layers" to slide around more easily??
24. ### Reference for shear modulus vs temperature of glass?

Homework Statement I'm doing some preliminary research for a potential IB extended essay topic. It involves thermal stresses in fused glass; details aren't that important right now. But I need to find a table, equation, or SOME sort of reference that gives me the relationship between the...
25. ### Finding Shear Modulus for Θ = LT/JG Equation

I have a question in an assignment and am using the Θ = LT/JG equation to find the angle of twist in an I section beam to be used in a monorail. I have all other figures to put in the equation but am not sure where i get G value from Help :o) Thank you
26. ### How Does Shear Modulus Affect the Distance Traveled by a Rubber Sole?

A child slides across a floor in a pair of rubber-soled shoes. The friction force acting on each foot is 25 N, the cross-sectional area of each foot is 20 cm2, and the height of the soles is 5.0 mm. Find the horizontal distance traveled by the sheared face of the sole. The shear modulus of the...
27. ### How Is the Shear Modulus of a Sponge Calculated?

A large sponge has forces of magnitude 17 N applied in opposite directions to two opposite faces of area 43 cm2 (see the figure below ). The thickness of the sponge (L is ")3 cm. The deformation angle (g is ")8.4°. (a) What is delta x? (b) What is the shear modulus of the sponge? delta x =...