Tensile Stress & Strain, Compressive Stress & Shear Stress - Basic Introduction
Summary
TLDRThe video script explores fundamental concepts of mechanical stress and strain on objects. It explains tensile stress, where a downward force causes objects to stretch, and compressive stress, where an upward force leads to compression. The script delves into the formulas for calculating tensile and compressive strain, emphasizing the importance of understanding an object's ultimate strength, such as concrete's differing tensile and compressive strengths. It also introduces shear stress, its calculation, and the concept of equilibrium in both translational and rotational contexts. The elastic modulus (Young's modulus) and shear modulus are highlighted as key ratios in stress-strain relationships, crucial for predicting an object's deformation under various forces.
Takeaways
- 🔍 Tensile stress occurs when an object is hung from a ceiling and a downward force is applied, causing the object to stretch.
- 📏 Tensile strain is the positive change in length (delta l) of an object when it is stretched, calculated as delta l divided by the original length (l0).
- 🧱 Compressive stress happens when a downward force is applied to a column resting on a surface, causing it to decrease in length.
- 📉 Compressive strain is negative, as the object's length decreases, calculated as negative delta l divided by the original length (l0).
- 🏗️ Concrete's ultimate strength indicates the maximum stress it can withstand without breaking, with tensile strength being lower than compressive strength.
- 🔢 The maximum tensile and compressive strengths of concrete are given as 2 x 10^6 N/m^2 and 20 x 10^6 N/m^2, respectively.
- 📚 Tensile and compressive strengths represent the maximum stress an object can endure, calculated as maximum force divided by area.
- 📉 The elastic modulus (Young's modulus) is used to calculate the change in length (delta l) of an object under tensile or compressive stress.
- ⚖️ Shear stress is experienced when an object is deformed by forces applied in opposite horizontal directions, causing a change in shape.
- 📏 Shear strain is calculated as the horizontal change in length (delta l) divided by the original vertical length (l0).
- 🔄 Shear modulus (G) is the ratio of shear stress to shear strain, used in calculating the deformation under shear stress.
Q & A
What is tensile stress?
-Tensile stress is a type of mechanical stress that results from forces applied to an object that cause it to stretch or elongate. It is calculated as the force applied divided by the area over which the force is distributed.
How is tensile strain calculated?
-Tensile strain is calculated as the change in length (delta l) of an object divided by its original length (l0). It is a positive value when the object's length increases due to the applied force.
What is compressive stress?
-Compressive stress is the mechanical stress that results from forces applied to an object that cause it to decrease in volume. It is also calculated as the force divided by the area, but it results in a decrease in the object's length.
How is compressive strain different from tensile strain?
-Compressive strain is the change in length (delta l) of an object due to compression, which is negative because the object's length decreases. It is calculated as negative delta l divided by the original length (l0).
What is the ultimate strength of concrete?
-The ultimate strength of concrete refers to the maximum stress that the material can withstand before breaking. The maximum tensile strength of concrete is 2 x 10^6 newtons per square meter, and the maximum compressive strength is 20 x 10^6 newtons per square meter.
Why is concrete's compressive strength greater than its tensile strength?
-Concrete's compressive strength is greater than its tensile strength because the material is inherently stronger when resisting compression (being pressed together) than when resisting tension (being pulled apart). This makes concrete well-suited for structures that bear weight but not as ideal for those that experience a lot of tension.
What is the formula for calculating the change in length (delta l) under stress?
-The formula for calculating the change in length (delta l) under stress is delta l = (1 / E) * (F / A) * l0, where E is the elastic modulus or Young's modulus, F is the applied force, A is the cross-sectional area, and l0 is the original length of the object.
What is shear stress?
-Shear stress is the stress that results from forces that cause parallel layers within a material to slide against each other. It is calculated as the force applied divided by the cross-sectional area of the material.
How is shear strain calculated?
-Shear strain is calculated as the change in length (delta l) in the direction of the applied force divided by the original length (l0) in the perpendicular direction. It is a measure of the deformation caused by shear stress.
What is the shear modulus?
-The shear modulus, also known as the modulus of rigidity, is the ratio between shear stress and shear strain. It is denoted by the letter G and is used to describe a material's resistance to shear deformation.
What is the significance of torque in the context of shear stress?
-Torque is significant in the context of shear stress because it represents the rotational force that can cause an object to rotate. When an object is under shear stress, the torques acting on the object must be balanced for the object to remain in equilibrium and not rotate.
How can you ensure an object under shear stress remains in equilibrium?
-An object under shear stress can remain in equilibrium by ensuring that the net force and net torque acting on the system are both zero. This typically involves the application of additional forces that counteract the effects of the applied shear forces and torques.
Outlines
🔴 Tensile and Compressive Stress
This paragraph explains the concepts of tensile and compressive stress. When an object is hung from a ceiling and a downward force is applied, it experiences tensile stress, which is calculated as force divided by the area. The object is in equilibrium with an upward force acting on it, resulting in the object stretching. Tensile strain is the positive change in length (delta l) divided by the original length (l0). Conversely, when a downward force is applied to a column resting on a horizontal surface, an upward force (normal force) acts on it, leading to compressive stress. The compressive strain is the negative change in length (delta l) divided by the original length (l0). The paragraph also introduces the ultimate strength of materials like concrete, which indicates the maximum stress it can withstand before breaking. Tensile strength is lower than compressive strength for concrete, making it stronger under compression than tension.
📏 Elastic Modulus and Shear Stress
The second paragraph delves into the calculation of the change in length (delta l) of an object under tensile or compressive stress using the elastic modulus (E or Young's modulus). The formula delta l = 1/E * (F/A) * l0 is provided, where F is the force applied, A is the cross-sectional area, and l0 is the original length. The elastic modulus is the ratio of stress to strain. The concept of shear stress is introduced, which occurs when a force deforms an object's shape, like pushing a book. Shear stress is calculated as force divided by area, and shear strain is the change in length (delta l) divided by the original length (l0) in the horizontal direction over the vertical direction. The shear modulus (G) is the ratio of shear stress to shear strain. The paragraph emphasizes the importance of considering shear stress and shear strain when an object's shape is being altered.
⚙️ Translational and Rotational Equilibrium
The final paragraph discusses the conditions for an object to be in equilibrium under shear stress. It illustrates that while the net force on the object may be zero, the net torque must also be zero for equilibrium. This is achieved by the presence of additional forces exerted by the ground that counteract the torques from the applied forces. The forces are arranged such that the torques from the applied forces (F1 and F2) are balanced by the torques from the ground forces (F3 and F4). The paragraph also highlights the need to consider all forces acting on an object, including vertical forces, when drawing a free body diagram. An example of pushing a book down illustrates the horizontal and vertical forces involved and how the ground counteracts these forces to maintain equilibrium.
Mindmap
Keywords
💡Tensile Stress
💡Equilibrium
💡Tensile Strain
💡Compressive Stress
💡Ultimate Strength
💡Elastic Modulus (Young's Modulus)
💡Shear Stress
💡Shear Strain
💡Shear Modulus
💡Translational and Rotational Equilibrium
💡Free Body Diagram
Highlights
An object hanging from a ceiling and subjected to a downward force is under tensile stress, which is calculated as force divided by area.
Tensile stress causes an object to stretch, with tensile strain being the positive change in length (delta l) divided by the original length (l0).
In equilibrium, an upward force equal to the downward force acts on the object, extending throughout its length.
When a column is subjected to a downward force, it experiences compressive stress, which results in a decrease in cell size.
Compressive stress is calculated similarly to tensile stress, but with the area of a circular column being pi times the radius squared.
Compressive strain is negative, indicating a decrease in length, and is calculated as negative delta l divided by the initial length (l0).
The ultimate strength of a material like concrete is the maximum stress it can withstand before breaking, with different values for tensile and compressive strength.
Concrete's maximum compressive strength is significantly higher than its tensile strength, making it strong under compression but weaker when stretched.
The elastic modulus (Young's modulus) is used to calculate the change in length (delta l) under tensile or compressive stress.
Shear stress occurs when a force is applied to deform an object's shape, and is calculated as force divided by the cross-sectional area.
Shear strain is the change in length in the horizontal direction (delta l) divided by the original length in the vertical direction (l0).
The shear modulus (G) is the ratio between shear stress and shear strain, analogous to the elastic modulus for tensile/compressive stress.
An object under shear stress requires additional forces to maintain both translational and rotational equilibrium, as torques must also be balanced.
When drawing a free body diagram for an object under shear stress, it's important to include all forces acting in both the x and y directions.
The ground exerts horizontal and vertical forces to counteract the forces applied by a person pushing down on an object like a book.
Understanding the concepts of tensile, compressive, and shear stress is crucial for analyzing the behavior of objects under various forces.
The elastic modulus and shear modulus are key parameters in determining how materials respond to different types of stress.
Practical applications of these concepts include designing structures that can withstand specific types of stress without failure.
Transcripts
now let's say if we have an object hang
it from a ceiling
and we decide to apply a downward force
to it
this object is under tensile stress
the tensile stress
is force divided by area
now because this object is in
equilibrium if there's a downward force
there must be an upward force
acting on the object
and that upward force
and the downward force extends
throughout the object
so whenever an object stretches it is
under tensile stress now the tensile
strain of the object
is the change in the fracture length of
the object so let's say this is
the original left l0
then when it stretches it's going to
become longer
and so this new length or the change in
life that's delta l
so the tensile strain
is going to be positive
delta l divided by l zero and keep in
mind delta l is the change between the
final length
and the initial length
now let's say if we have a column
that rests
on a horizontal surface
and if we apply a downward force on this
column
then there's going to be an upward force
acting on two
which is basically equates to the normal
force
exerted by
the surface
now a portion of that normal force is
going to be equal to the downward force
that we apply to it
the normal force is going to be the sum
of this force plus the weight of the
object but if we take out the weight of
the object then the portion of the
normal force is going to be equal to
that downward force
and those two forces causes compression
it causes the object to decrease
in cell f
so this object
is under compressive
stress
so the compressive stress
it's still force divided by area
so in this case we have a circular
column
so the area is going to be pi r squared
here's the original length of the column
and delta l
is the change in life so this time
delta l is negative because
the length of the object decreased
so the compressive strain of the object
is negative
delta out divided by l initial
now you need to be familiar with
the maximum stress that an object can
have
so for instance
let's use concrete as
an example
the ultimate strength tells you the
maximum stress
that an object can have without breaking
into two parts or breaking into pieces
for example the maximum
tensile strength of concrete
is 2 times 10 to the 6
newtons per square meter
and the maximum compressive strength
of concrete
is 20
times 10 to the six
newtons per
square meters
so if you're dealing with the maximum
tensile strength
that's going to be equal to the maximum
force
divided by the area
if you're dealing with the maximum
compressive strength
that will also equal the maximum force
over area
so when you hear the words tensile
strength compressive strength
it tells you the maximum stress that can
be applied to material
so these values represents the maximum
force
over area
now notice that
concrete's compressive strength is
stronger than its tensile strength
so what this means is that concrete
is very difficult to compress if you try
to compress it
it's going to be strong in this
direction however
if you try to
stretch concrete
let's say if you try to pull it apart
it's weaker in this direction
so it's a lot easier to pull apart
concrete than to compress it
so concrete is very useful if you're
trying to put weight on it but if you're
trying to stretch it
it's not as strong in that direction
now don't forget about this equation
when you're dealing with tensile stress
or compressive stress
if you need to calculate the change in
the length of the object
that is delta l
you can use this formula
delta l is going to be 1 over e
where e is the elastic modulus or
young's modulus
times f over a
f is the force applied
a is the cross sectional area times
the original length l0
now young's modulus or the elastic
modulus you can look it up in a table
and it's important to know that the
elastic modulus is the ratio between the
stress applied
and the strain of the object or the
fractional change in the length of the
object
so this is another equation that is
useful
so make sure to use the elastic modulus
when dealing with an object under
tensile stress or compressive stress
now what about if an object is under
shear stress
so let's say
if we have an object like a box or book
and we apply a force
the object
is going to
in this direction it's going to deform
like this
and it turns out that there's another
force acting on it
the force that you apply to the right
the ground is going to apply another
force towards the left
and so it's going to deform
like the shape that you see here
now let's turn this into a 3d structure
so this is the cross sectional area
that's a
and this is the original left
and this is delta l
when dealing with shear stress
so we're going to have a very similar
formula to the last example
delta l
is going to be 1 over g
times f divided by a
times l initial
now this equation is very similar to the
last example
the only difference is we have a g
instead of e
e represented the elastic modulus which
is the ratio between stress and strain
in this example g
is the shear modulus
which is the ratio between
shear stress
and shear strain
so it's still stress over strain but
just with a different type of situation
now the shear stress
is still force divided by area
and the shear strain
is delta l in the horizontal direction
divided by l zero in the vertical
direction so that's a little different
so keep this in mind
the shear stress
that's acting on the object is the ratio
between the force applied
and the cross-sectional area
and the shear strain
is simply
delta l divided by l zero
so g the shear modulus
is going to be f divided by a
the stress
divided by the strain delta l over l
zero
so let's review what we've learned
let's say if you have an object
with two forces
pulling the object causing it to
increase and left
this object is under tensile stress
and whenever you have an object
where the forces
are decreasing the length of the object
this object is under compressive
stress
it's being compressed
into a shorter object
and whenever you apply a force
to change the shape of the object
basically let's say if you push your
hand on a book and you push it down and
towards the
right and you cause it to deform in this
direction
then this object
is under
shear stress
my drawing is terrible but you get the
picture
now there's something else you need to
be familiar with
when an object is under
shear stress
so i'm just going to draw a 2d version
of the object
so we know we have a force in this
direction and there's a force in this
direction
so the net force is zero because we have
one going in the positive x direction
and another going in a negative x
direction
but what about the torques
is the net torque of this system zero
let's call this f1 and f2
relative to the center of mass
f1 wants to create
a clockwise torque
which is basically a negative torque
f2
also wants to rotate the object this way
in the clockwise direction
so that's another
negative torque
so this object's not balanced it wants
to rotate in this direction
so for it to remain in equilibrium there
must be another force
a downward force
that prevents it from rotating and this
force
is not the only force exerted by the
ground but the ground must also exert an
upward force
so let's call this f3
and f4
so notice that f3
creates a counter-clockwise torque
and the same is true for f4
it creates another counterclockwise
torque
and a counterclockwise torque is a
positive torque
so now
the torques are balanced so the net
torque acting on the system is zero
and the net force
acting on the system is zero
so it's in
translational and rotational equilibrium
so these aren't the only forces acting
on the object
you have two forces acting on the in the
x direction and two forces in the y
direction
so this one is in a positive x direction
this is in the negative x direction
this one is in the negative y direction
and that one is in the positive y
direction
so if you have to draw a free body
diagram don't forget about the two
vertical forces
so let's say if you have a book
and you push down on the book with your
hand
there is a horizontal force that you
apply and there is a vertical force that
you apply in the downward direction
and so the ground is going to exert
a horizontal force to counteract this
one and a vertical force to counteract
the downward force that you apply
you
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