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Sideways stress: shear modulus

[link] illustrates what is meant by a sideways stress or a shearing force . Here the deformation is called Δ x size 12{Δx} {} and it is perpendicular to L 0 size 12{L rSub { size 8{0} } } {} , rather than parallel as with tension and compression. Shear deformation behaves similarly to tension and compression and can be described with similar equations. The expression for shear deformation    is

Δ x = 1 S F A L 0 , size 12{Δx= { {1} over {S} } { {F} over {A} } L rSub { size 8{0} } } {}

where S size 12{F} {} is the shear modulus (see [link] ) and F size 12{F} {} is the force applied perpendicular to L 0 size 12{L rSub { size 8{0} } } {} and parallel to the cross-sectional area A size 12{A} {} . Again, to keep the object from accelerating, there are actually two equal and opposite forces F size 12{F} {} applied across opposite faces, as illustrated in [link] . The equation is logical—for example, it is easier to bend a long thin pencil (small A size 12{A} {} ) than a short thick one, and both are more easily bent than similar steel rods (large S size 12{S} {} ).

Shear deformation

Δ x = 1 S F A L 0 , size 12{Δx= { {1} over {S} } { {F} over {A} } L rSub { size 8{0} } } {}

where S size 12{S} {} is the shear modulus and F size 12{F} {} is the force applied perpendicular to L 0 size 12{L rSub { size 8{0} } } {} and parallel to the cross-sectional area A size 12{A} {} .

Bookcase sheared by a force applied at the bottom right toward the bottom left, and at the top left toward the top right.
Shearing forces are applied perpendicular to the length L 0 and parallel to the area A , producing a deformation Δx . Vertical forces are not shown, but it should be kept in mind that in addition to the two shearing forces, F size 12{F} {} , there must be supporting forces to keep the object from rotating. The distorting effects of these supporting forces are ignored in this treatment. The weight of the object also is not shown, since it is usually negligible compared with forces large enough to cause significant deformations.

Examination of the shear moduli in [link] reveals some telling patterns. For example, shear moduli are less than Young’s moduli for most materials. Bone is a remarkable exception. Its shear modulus is not only greater than its Young’s modulus, but it is as large as that of steel. This is why bones are so rigid.

The spinal column (consisting of 26 vertebral segments separated by discs) provides the main support for the head and upper part of the body. The spinal column has normal curvature for stability, but this curvature can be increased, leading to increased shearing forces on the lower vertebrae. Discs are better at withstanding compressional forces than shear forces. Because the spine is not vertical, the weight of the upper body exerts some of both. Pregnant women and people that are overweight (with large abdomens) need to move their shoulders back to maintain balance, thereby increasing the curvature in their spine and so increasing the shear component of the stress. An increased angle due to more curvature increases the shear forces along the plane. These higher shear forces increase the risk of back injury through ruptured discs. The lumbosacral disc (the wedge shaped disc below the last vertebrae) is particularly at risk because of its location.

The shear moduli for concrete and brick are very small; they are too highly variable to be listed. Concrete used in buildings can withstand compression, as in pillars and arches, but is very poor against shear, as might be encountered in heavily loaded floors or during earthquakes. Modern structures were made possible by the use of steel and steel-reinforced concrete. Almost by definition, liquids and gases have shear moduli near zero, because they flow in response to shearing forces.

Questions & Answers

How submarines floats one water the same time sink in water
Courage Reply
A submarine has the ability to float and sink. The ability to control buoyancy comes from the submarine'strim or ballast tanks which can be filled with either water or air, depending on whether the submarine needs to floator sink. When the submarine floats it means its trim tanks are filled with air
Arif
what is work
Ojo Reply
Force times distance
Karanja
product of force and distance...
Arif
Is physics a natural science?
Adebisi Reply
what is the difference between a jet engine and a rocket engine.
Samuel Reply
explain the relationship between momentum and force
Joseph Reply
A moment is equivalent multiplied by the length passing through the point of reaction and that is perpendicular to the force
Karanja
How to find Squirrel frontal area from it's surface area?
Pooja Reply
how do we arrange the electronic configuration of elements
Muhammed Reply
hi guys i am an elementary student
benedict Reply
hi
Dancan
hello
adolphus
are you an elementary student too?
benedict
no bro
adolphus
yes
Che
hi
Miranwa
yes
Miranwa
welcome
Miranwa
what is the four equation of motion
Miranwa
what is strain?
SAMUEL
Change in dimension per unit dimension is called strain. Ex - Change in length per unit length l/L.
ABHIJIT
strain is the ratio of extension to length..=e/l...it has no unit because both are in meters and they cancel each other
adeleke
How is it possible for one to drink a cold drink from a straw?
Karanja Reply
most possible as it is for you to drink your wine from your straw
Selina
state the law of conservation of energy
Sushma Reply
energy can neither be destroy or created,but can be change from one form to another
dare
yeah
Toheeb
it can neither be created nor destroyed
Toheeb
its so sample question dude
Muhsin
what is the difference between a principle and a law?
Mary Reply
where are from you wendy .?
ghulam
philippines
Mary
why?
Mary
you are beautiful
ghulam
are you physics student
ghulam
laws are ment to be broken
Ge
hehe ghulam where r u from?
Muhsin
yes
dare
principle are meant to be followed
dare
south Africa
dare
here Nigeria
Toheeb
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
Ayoka
Rules are meant to be broken while principals to be followed
Karanja
principle is a rule or law of nature, or the basic idea on how the laws of nature are applied.
tathir
what is momentum?
prakash Reply
is the mass times velocity of an object
True
it is the product of mass and velocity of an object.
The momentum possessed by a body is generally defined as the product of its mass and velocity m×v
Usman
momentum is the product of the mass of a body of its velocity
Ugbesia
what about kg it is changing or not
vijay Reply
no mass is the quantity or amount of body so it remains constant everywhere
Ahsan
yes
Siyanbola
remains constant
taha
mass of an object is always constant. and that is universally applied.
Shii
mass of a body never changes but the weight can change due to variance of gravity at different points of the world
Saheed
what is hookes law
Joshua
mass of an object does not change
SAMUEL
Is weight a scalar quantity
esther Reply
weight is actually a force of gravity with which earth attracts us downwards so it is a vector quantity. and it has both direction and magnitude
Ahsan
ty
Denise
weight is the earth pull of the body
Ugbesia
why does weight change but not mass?
Theo
Theo, the mass of an object can change but it depends on how you define that object. First, you need to know that mass is the amount of matter an object has, and weight is mass*gravity (the "force" that attracts object A to the object B mass).
Nicolas
So if you face object A with object B, you will get a different result than facing object A with object C, so the weight of object A changes but not its mass.
Nicolas
Now, if you have an object and you take a part away from it, you are changing it mass. Lets use the human body and fat loss process as an example.
Nicolas
When you lose weight by doing exercise, you are being attracted by the same object before and after losing weight so the change of weight is related to a change of mass not a change of gravity.
Nicolas
The explanation of this is simple, we are composed of smaller particles, which are itself objects, so the loose of mass of an object actually is the separation of one object is two different ones.
Nicolas
But if you define an object because of its form and characteristics and not the amount of mass, then the object is the same but you have taken a part of it mass away.
Nicolas
Theo, weight =mass. gravity, here mass is fixed everywhere but gravity change in different places so weight change not mass.
ABHIJIT
yup weight changes and mass does not. That's why we're 1/3 our weight on the moon
clifford
weight is the product of mass × velocity w=m×v = m(v-u) but v=u+1/2at^ weight is a scalar quantity mass of an obj is the amount of particles that obj cont
Usman
mass is fixed always while weight is dynamic
Usman
Why does water wet glass but mercury does not?
Yusuf
thanks guys
Theo
Yusuf Shuaibu, for water the Adhessive force between water molecules and glass is greater than the cohessive force between it's own molecules but for Mercury the cohessive force will be greater in comparison with adhessive force. For this water wet glass but Mercury does not.
ABHIJIT
in electrostatic e bonite rod electron is static. they cannot flow to other. because static. is it correct?
prabir Reply
Is weight a scalar quantity
esther
wieght is the vector
ghulam
yes
Mohet
Yes
Karanja
Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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