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Check Your Understanding If the normal force acting on each face of a cubical 1 .0-m 3 piece of steel is changed by 1.0 × 10 7 N , find the resulting change in the volume of the piece of steel.

63 mL

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Shear stress, strain, and modulus

The concepts of shear stress and strain concern only solid objects or materials. Buildings and tectonic plates are examples of objects that may be subjected to shear stresses. In general, these concepts do not apply to fluids.

Shear deformation occurs when two antiparallel forces of equal magnitude are applied tangentially to opposite surfaces of a solid object, causing no deformation in the transverse direction to the line of force, as in the typical example of shear stress illustrated in [link] . Shear deformation is characterized by a gradual shift Δ x of layers in the direction tangent to the acting forces. This gradation in Δ x occurs in the transverse direction along some distance L 0 . Shear strain is defined by the ratio of the largest displacement Δ x to the transverse distance L 0

shear strain = Δ x L 0 .

Shear strain is caused by shear stress. Shear stress is due to forces that act parallel to the surface. We use the symbol F for such forces. The magnitude F per surface area A where shearing force is applied is the measure of shear stress

shear stress = F A .

The shear modulus is the proportionality constant in [link] and is defined by the ratio of stress to strain. Shear modulus is commonly denoted by S :

S = shear stress shear strain = F / A Δ x / L 0 = F A L 0 Δ x .
Figure is a schematic drawing of an object under shear stress: Two antiparallel forces of equal magnitude are applied tangentially to opposite parallel surfaces of the object. As the result, the object is transformed from the rectangle to the parallelogram, shape. While the height of the object remains the same, top corners move to the right by the Delta X.
An object under shear stress: Two antiparallel forces of equal magnitude are applied tangentially to opposite parallel surfaces of the object. The dashed-line contour depicts the resulting deformation. There is no change in the direction transverse to the acting forces and the transverse length L 0 is unaffected. Shear deformation is characterized by a gradual shift Δ x of layers in the direction tangent to the forces.

An old bookshelf

A cleaning person tries to move a heavy, old bookcase on a carpeted floor by pushing tangentially on the surface of the very top shelf. However, the only noticeable effect of this effort is similar to that seen in [link] , and it disappears when the person stops pushing. The bookcase is 180.0 cm tall and 90.0 cm wide with four 30.0-cm-deep shelves, all partially loaded with books. The total weight of the bookcase and books is 600.0 N. If the person gives the top shelf a 50.0-N push that displaces the top shelf horizontally by 15.0 cm relative to the motionless bottom shelf, find the shear modulus of the bookcase.

Strategy

The only pieces of relevant information are the physical dimensions of the bookcase, the value of the tangential force, and the displacement this force causes. We identify F = 50.0 N , Δ x = 15.0 cm , L 0 = 180.0 cm , and A = (30.0 cm) (90.0 cm) = 2700.0 cm 2 , and we use [link] to compute the shear modulus.

Solution

Substituting numbers into the equations, we obtain for the shear modulus

S = F A L 0 Δ x = 50.0 N 2700.0 cm 2 180.0 cm . 15.0 cm . = 2 9 N cm 2 = 2 9 × 10 4 N m 2 = 20 9 × 10 3 Pa = 2.222 kPa.

We can also find shear stress and strain, respectively:

F A = 50.0 N 2700.0 cm 2 = 5 27 kPa = 185.2 Pa Δ x L 0 = 15.0 cm 180.0 cm = 1 12 = 0.083 .

Significance

If the person in this example gave the shelf a healthy push, it might happen that the induced shear would collapse it to a pile of rubbish. Much the same shear mechanism is responsible for failures of earth-filled dams and levees; and, in general, for landslides.

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Questions & Answers

What is th formular for force
Joseph Reply
F = m x a
Santos
State newton's second law of motion
Seth Reply
can u tell me I cant remember
Indigo
force is equal to mass times acceleration
Santos
The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
Asad Reply
Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?
Sohail Reply
how can one calculate the value of a given quantity
Helen Reply
means?
Manorama
To determine the exact value of a percent of a given quantity we need to express the given percent as fraction and multiply it by the given number.
AMIT
meaning
Winford
briefly discuss rocket in physics
Ibrahim Reply
ok let's discuss
Jay
What is physics
Nura Reply
physics is the study of natural phenomena with concern with matter and energy and relationships between them
Ibrahim
a potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inductance of the inductor that should be connected to the capacitor for the circuit to oscillate at 1125Hza potential difference of 10.0v is connected across a 1.0AuF in an LC circuit. calculate the inducta
Royalty Reply
L= 0.002H
NNAEMEKA
how did you get it?
Favour
is the magnetic field of earth changing
tibebeab Reply
what is thought to be the energy density of multiverse and is the space between universes really space
tibebeab
can you explain it
Guhan
Energy can not either created nor destroyed .therefore who created? and how did it come to existence?
Suzana Reply
this greatly depend on the kind of energy. for gravitational energy, it is result of the shattering effect violent collision of two black holes on the space-time which caused space time to be disturbed. this is according to recent study on gravitons and gravitational ripple. and many other studies
tibebeab
and not every thing have to pop into existence. and it could have always been there . and some scientists think that energy might have been the only entity in the euclidean(imaginary time T=it) which is time undergone wick rotation.
tibebeab
What is projectile?
Nana Reply
An object that is launched from a device
Grant
2 dimensional motion under constant acceleration due to gravity
Awais
Not always 2D Awais
Grant
no comments
Awais
why not? a bullet is a projectile, so is a rock I throw
Grant
bullet travel in x and y comment same as rock which is 2 dimensional
Awais
components
Awais
no all pf you are wrong. projectile is any object propelled through space by excretion of a force which cease after launch
tibebeab
for awais, there is no such thing as constant acceleration due to gravity, because gravity change from place to place and from different height
tibebeab
it is the object not the motion or its components
tibebeab
where are body center of mass on present.
Balwant Reply
on the mid point
Suzana
is the magnetic field of the earth changing?
tibebeab
does shock waves come to effect when in earth's inner atmosphere or can it have an effect on the thermosphere or ionosphere?
tibebeab
and for the question from bal want do you mean human body or just any object in space
tibebeab
A stone is dropped into a well of 19.6m deep and the impact of sound heared after 2.056 second ,find the velocity of sound in air.
Sisco Reply
9.53 m/s ?
Kyla
In this case, the velocity of sound is 350 m/s.
Zahangir
why?
Kyla
some calculations is need. then you will get exact result.
Zahangir
i mean how? isn't it just a d over t?
Kyla
calculate the time it takes the stone to hit the ground then minus the stone's time to the total time... then divide the total distance by the difference of the time
Snuggly
awit lenard. Hahahah ari ga to!
Kyla
Why do we use mochromatic light? If white light is used, how would the pattern change
Dominic Reply
what is the dimension of force
Omolola Reply

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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