Tensile Stress & Strain, Compressive Stress & Shear Stress - Basic Introduction

Summary

The 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

00:00

🔴 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.

05:01

📏 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.

10:05

⚙️ 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.

Keywords

💡Tensile Stress

Tensile stress is a type of mechanical stress that results from forces applied to stretch an object. It is defined as the force per unit area applied to an object and is a key concept in the video as it discusses how objects behave when subjected to stretching forces. In the script, tensile stress is illustrated by hanging an object from a ceiling and applying a downward force, causing the object to stretch.

💡Equilibrium

Equilibrium refers to a state where all forces acting on an object cancel each other out, resulting in no net force. The video uses the concept of equilibrium to explain that when a downward force is applied to an object, there must be an equal and opposite upward force to maintain equilibrium. This is a fundamental principle in understanding how forces interact with objects.

💡Tensile Strain

Tensile strain is a measure of the deformation of an object under tensile stress. It is defined as the change in length (delta l) of an object divided by its original length (l0). The video emphasizes that tensile strain is positive when the object's length increases upon stretching. It is a critical parameter in assessing how much an object can stretch before failure.

💡Compressive Stress

Compressive stress is the force per unit area that tends to compress or squeeze an object. It is the opposite of tensile stress and is discussed in the context of a column resting on a surface and subjected to a downward force. The video explains that compressive stress leads to a decrease in the object's volume or size, which is different from tensile stress that causes elongation.

💡Ultimate Strength

Ultimate strength, as mentioned in the video, is the maximum stress an object can withstand before it breaks or fails. The concept is crucial for understanding the limits of materials like concrete under different types of stresses. The video provides specific values for the ultimate tensile and compressive strength of concrete, highlighting that concrete is stronger in compression than in tension.

💡Elastic Modulus (Young's Modulus)

The elastic modulus, also known as Young's modulus, is a measure of the stiffness of a material. It is the ratio of stress to strain, indicating how much a material deforms under stress. The video uses this concept to explain how to calculate the change in length of an object under tensile or compressive stress, which is essential for understanding material behavior under load.

💡Shear Stress

Shear stress is the force that causes an object to deform in a parallel plane to the applied force. It is calculated as the force per unit area and is distinguished from tensile and compressive stress by the direction of the force relative to the object. The video illustrates shear stress by describing how an object like a box deforms when pushed in a particular direction.

💡Shear Strain

Shear strain is a measure of how much an object's shape changes under shear stress. It is defined as the change in the shape of the object (delta l in the horizontal direction) divided by its original length (l0 in the vertical direction). The video explains that shear strain is a key factor in understanding how objects deform when shear forces are applied.

💡Shear Modulus

The shear modulus, often denoted as G, is the ratio of shear stress to shear strain. It is a measure of a material's resistance to shape change when a shear force is applied. The video discusses the shear modulus in the context of calculating the deformation of an object under shear stress, emphasizing its role in material science.

💡Translational and Rotational Equilibrium

Translational and rotational equilibrium are states where an object is not moving or rotating. The video explains that for an object to be in equilibrium under shear stress, not only must the net force be zero (translational equilibrium), but also the net torque must be zero (rotational equilibrium). This concept is illustrated with the example of forces acting on an object, emphasizing the need for balancing forces and torques.

💡Free Body Diagram

A free body diagram is a graphical representation that shows all the forces acting on an object. The video instructs on the importance of including all forces, both horizontal and vertical, when drawing a free body diagram to analyze the object's state of stress. This tool is fundamental for visualizing and solving problems in mechanics.

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