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Strength of Materials I: Review Principles of Statics, Internal Resultant Loads (1 of 20) | CPPMechEngTutorials | YouTubeToText
YouTube Transcript: Strength of Materials I: Review Principles of Statics, Internal Resultant Loads (1 of 20)
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[Music]
but before we go to chapter one I would
like you to refresh your memory about
some of the principle of a static which
is very important for you
those are equilibrium so everybody is
familiar with the equilibrium of course
we have 2d problem and we have 3d
problem so 2d problem generally the
forces have X component and y component
so you have three equations I'm not
going to put it down here for
equilibrium so anytime you draw a
Freebody diagram there is it forces and
there could be moment but the moment is
one-dimensional usually if you are
working on the XY plane so the moment
will be about the z axis or the K
direction yes sir so those are the three
equations in 3d you are going to have
six equations and those six equation
again is Sigma FX equal to zero Sigma FY
equal to zero Sigma FZ equal to zero
which are the component along X Y Z also
three moment which are the moment about
x axis y axis and z ax you should be
able to do that through this exercise
one of this problem was 3d and you are
supposed to do that so and in this class
we never use cross-product you should be
able to use your right hand rule by
taking moment about x axis y axis and z
axis actually if you look in the book
they never use our bodies are the
simpler problem but you should be able
to do that I hope that you have
practiced that in your static class so
there are four so I'm going to be
putting it down Sigma M about x axis
equal to 0 Sigma M about the y axis
practice that one and seek for M about
the z axis which in general we can put
it in a vector for
but this is the breakdown of it in a
scalar equation then we need the
centroid and of course in the centroid
we have X bar which is equal to
summation of X I a I divided by
summation of a I and we have Y bar which
is summation of Y I AI divided by
summation of us of course everybody
knows that the denominator are the areas
yes or though what are the numerator any
idea product X and ay no it's not a
product of X and it has a meaning very
important meaning and it's going to
appear several place in in a strength of
material I'm going to for time being
because I don't know how many of you
remember that which is very important
this is qy we call it and this is QX it
has a meaning it has a name it has some
special specification and you through
the example I'm going to show you one
more time because in aesthetic I've put
a lot of emphasis on this Q which is not
as exactly we say the product of X and
ay it is has a lot of meaning on it and
it's going to be used in strength of
metal material alone okay I'm glad you
put it in the red that means you are
going to pay attention to that yes or no okay
okay
and of course we are going to have
moment of moment of inertia of course
moment of inertia
everybody knows the moment of inertia of
a rectangular shape with respect to the
axis that passes through each Center is
equal to what 1/12 of base times height
cubic that's right and then we have for
the circle as well which is PI over 2
these are IX so let's call it I X equal
to that IX I'm sorry it is PI over 4
radius ^ 4
of course the unit is inch ^ 4 see this
is very important to recognize this
process a is the area yes or no it has
the unit of length ^ - yes
q we call it moment first moment of area
and that the unit of length to the power
of 3 why because it's a product of X and
area everybody understand and the moment
of inertia which sometimes is called
second moment will be linked to the
power of four because the Y square da or
X square da as you recall from static
yes or no correct I hope you remember
that yeah okay there is now this is not
sufficient to know the moment of inertia
of special shape like this you need to
know parallel axis theorem so that is
very important parallel axis theory so
therefore you have here you say i X
equal to I X prime X prime passes
through the centroid of the object plus
the area times distance squared don't
worry about it I'm going to do an
example and do all of this in one
example that you see how is being
applied okay so those are the subject
that I'm sure you already know from your
aesthetic especially if you just pass
the static yes hopefully with a or b i
had one student who got c by the way i
want you know the last past quarter he
asked me to lower - C - because he said
he wants to take it again so I want you
to know this happened I actually I have
one also in 219 he did the same thing
I have to a student requesting me to
reduce the C - C - in order to that's
that important would be for you in
future classes static because you are
going to use it a lot you will see it
here anyhow let's do our first example
about this subject before I go into the
real strength of material so go let's go
back to this problem there are a couple
of problem in your handout
then I decided to do this for the other
class so I'm going to do the same for
you guys and therefore draw the picture
is not in your handouts but this picture
is simple so we can do it here so here
let's say this is the cross-section on
of an object that you are designing and
let's say that it is 75 millimeter by 50
attached to a plate here and like this
these are not in a scale so therefore I
just put here 200 millimeter is the
width this is the thickness of the plate
is 25 millimeter the height here is 150
millimeter these are all in millimeter
if I am not putting some of them just
just to save time and here the thickness
of this plate also is 25 minute
this is the object made of these three
pieces together this is the cross
section of a beam or a column in future
in this class that's what we are going
to talk always about the cross section
of the beam or column is that understood
or a structure this is the cross and now
what we want to do or what is suppose
you are supposed to do in later chapter
which is chapter 4 or 5 always is this
first you are required if you want to do
this strength of material first it is
required to find the centroid of this
object so of course as you see it is not
symmetrical with respect to X but it is
symmetrical with respect to Y so you
have to make a choice here you can put
your x axis here or here on top or
bottom the most customary one is to put
your x axis here your voices again you
have a choice but it is silly to put
your Y axis here the y axis should be
right at the middle because it is
symmetrical so that's our system now so
this is the y axis then we want to
determine the location of the centroid
which I am going to show it with a dot
somewhere here we don't know here is 200
times 25 here is 75 maybe it's a little
bit up there so there
is the location of the centroid of this
object right at the middle because it's
symmetrical so therefore since I chose
this as X so therefore this distance
from centroid to this x-axis we are
going to call it Y bar then we have to
go to this equation we don't care about
X bar because X bar is equal to 0 for
this y-axis yes or no it's symmetrical
so X bar is you now how do we calculate
Y bar now here was was my question
earlier guys what is this
numerator you said it is product of a
times I it's more than that that's it okay
okay
first smaller very good all right now
first of all we are going to divide that
into three area area one area two and
area three so this is the composite
section method and then denominator is
very simple denominator is the area yes
or no so there are four let's put the
area as from top so 75 times 50 plus 150
times 25 plus the last one a 3 which is
200 times 25
so denominator is very simply adding all
the areas no numerator we call it moment
first moment and we call it Q why why a
QX I'm sorry because look it's in rivers
so QX because you are taking moment
about the x-axis the idea is this if
this was flat like that first of all we
are assuming this plate display display
they are all made of the same material
with the same thickness if this doesn't
work in future we will have that in
chapter 4 we get a beam part of it is
wood part of it is still this system
doesn't work so immediately it comes to
your mind or it has to be the same
material so why not change the wood into
still or a still into wood so if you
understand this you understand that
problem immediately so based on that the
same material area would be representing
the weight yes or no yes if
this has a weight where would you put
the weight there you would put the
weight of this object of light system
where you would put it where you would
put it here yes
so that numerator is the first moment of
that area with respect to x-axis and
that's why we call it QX is that current
so we want to write it down here this is
first moment of the area of whatever
area you have about the x-axis of this
similarly the other one is the first
moment about the y-axis so boys knowing
that then the Y become very because in
the in practice some people use okay 75
times 50 represent the weight yes or no
correct if they are the same thickness
is saying who cares about the thickness
and the density because they are all
having the same yes so if you have a
plate like this and it's to a square
foot and one is square foot the weight
of 2 is square is twice as much as one
because they are made of the same
thickness the same material correct or
not yes
so if the weight is there that's the
weight yes or no where do you put the
weight here yes so of course this weight
was usually downward but you are
assuming it's going like that like it
this is flat and the moment of that
about x axis what this time do I need
now look the distance will be there if
they wait here and you take a moment
about here that distance is from here to
here yes or no prey so the distance is
25 150 and 25 so that is 200 yes or no
so there are 4 times 200 as if you are
taking the moment of this weight about
the x axis assuming that was flat this
is how you should have learned this
stuff in the static as well because this
is really what they cheese so then we go
to the second one when we go to the
second one don't forget about this sea
board this is something that you are we
are trying to
this area now the second area this is
the second area let's do it this way now
what's the mass of that that again the
mass represent the area represent the
mass so that is for the weight so it is
equal 250 times 25 where is the location
of that mass it is at the center and
what distance do I need so you can
calculate the distance immediately that
this time you need 75 plus 25 times
hundred so having this in mind life
become much simpler you never make a
mistake by this assuming you are
calculating the moment about certain
axis is that understood yes and that
last one is simple the last one is how
much 200 times 200 times 25 and then
multiplied by what the mass is here and
I need this distance is that correct
that this nurse is 12 and is that how
you learn your aesthetic class yes no
you just fill out the for the table yes
bad bad idea very bad idea everybody
under that is the difference in how you
learn this material so I want you to do
the same thing here in a strength of
material always I'm going to talk about
the concept more than the formula I give
you all the formula all the tools in
today's age with the internet with the
computer they are available you don't
need to remember any of the formula or
any of the equation that's given in the
book yes only only you have to
understand what is good for and how to
use it the most important part this is
the tool will be given to you you know
how to use it that's what I'm talking about
about
all everybody who's using centroid you
should take this at the moment everybody
about certain axes everybody abut but
that determining your all the A's are
all the distances is that understood yes
notice there is a big difference between
the two anyhow this ends up I'm not
going to put all the number then I did
it for you so end up to be equal to 95
millimeter so that now we solve this
problem the century
here is somewhere here a little bit
lower so the centroid here now is at
ninety five millimeter that means this
distance from here to here is 70
millimeter and this distance this is not
in a scale I'm sorry that's eighty
millimeter and so so far because the
total was hundred so question number one
was answer the centroid everybody with a
little bit of detail of that question
number two is their moment of inertia
now before I go to the moment of inertia
I want to ask you a question now that I
did that we are going to change this X
this is X is going in static they put an
X here they asked you to calculate
moment of inertia with respect to that x
axis in a strength that's not what we
are going to do it's the strength when
we go to chapter four you will see any
time we do a bending design the cross
section of a beam you need to calculate
the centroid of that cross section then
you need to take write it down the
moment of inertia with respect to the
axis that passes through their centroid
not any arbitrary axis it has a meaning
we will give you the name that's the
procedure so every problem in design
always start with this to first design a
beam design or column even shaft will go
through the same order you always have
to find the centroid for we did that
then we remove this X as this X does not exist
exist
we put our x axis here which passes now
through their center actually it has a
name later on you'll see in chapter or
we call it neutral axis there is a
reason for it that they will talk about
it in chapter four or five that has a
name that goes through the centroid yes
or no now you have to calculate the
second question this is the second
equation you want to find out the moment
of inertia with respect to the axis that
passes through their century so new axis
yes or no correct so let's calculate if
I see my X fact axis here was there and
that was the Q value if I put my xx
here tell me this is the area above an
area below of this x-axis are equal or
this is six by two this is six by two do
you think the centroid is their question
I want to know how how you learned your
centroid at this testing my testing to
know how you learned the stuff this is
the difference in way of learning is the
centroid they're probably not yes or no
right now the area above is six by two
the area below that C is six by two the
two area are equal is that the case
no so what should be equal in order Y
bar C when I put your X here Y bar is
equal to zero yes or no if Y bar is zero
that quantity must be equal to zero for
this x axis not that exact says yes in
order this to be the XL means that two
of the above and few of the below must
be equal and opposite to each other or
total Q must be equal to 0 this is Rises
I can see that you did not learn your
static in that format let's say this is
a seesaw let's say this is 20 inches and
this is 20 inches and you put here an
area which represent the weight exactly
like that this two area are the same yes
or no let's assume these two area are
the same correct this is the centroid
yes however if I want to move that to
this area to this at the centroid and
this become 100 and this become 300 is
this the centroid but look the area on
the left and area on the light are equal
so what is not equal Y this is not
centroid because of the moment everybody
see that this moment if W W times 300 is
much larger that W times 100 in order
this to be centroid I need to put
another depth 3w there is that correct
or now is that centroid 3 w times 100
equal to 300 time w yes so what is equal
there the moment the cube is that
understand that's the cue you are taking
moment of that with respect you look 3 w
time 100 equal to voided you can do it
this way or you can do it vertically and
you're--you they use this 2,000 years
ago as a scale I mentioned that in my
aesthetic class remember don't make a
scale that used in the Roman time they
put one weight on one side and the lots
of weight on the other side because they
are balancing their movement yes that's
what the cue I'm talking about this is a
century but look the area is this is
three times area than that the area
should you put it X through the centroid
the moment of the lower area and the
moment of the first moment the cue of
lower area and the cue of above area
must be equal and opposite this is very
important for future therefore I can't
calculate that let's calculate that now
for this problem I can see that some of
you are looking a little bit surprised
because the other class will response
was a little bit better I must tell you
that because I want always to put you in
the competition with the other class in
order to get a better result everybody
understand her yeah you are aside from
you being in competition with your
classmate you are going to be in
competition with the other class always
I check that too so remember that I have
this area above oops it doesn't work so
no good so I can go red so notice the
red area you have this kind of problem
in a static which is the area above the
centroid and you have the blue area
which is the area below the centroid I
said this to area if you check it I
don't have time to do you will see that
the areas are not the same so what is
the same write it down one more time the
cue of a bob and if you're below must be
equal on sign or opposite like the
seesaw I show you there and therefore
let's check that one so if I go with
their cue of the above now notice the X
is not there X is here this distance is
80 this distance is 50 and I'm
calculating Q of this two area is that
understood yes so I can add that
together this is the Q of above so is
equal to fifty times seventy five times
what now you give me that second number
the third number that's the area times
where is the mass is here
what distance do I need to take the
moment about the new x-axis yes or no so
what distance is that 80 plus 25
half of 25 the bus is here so this is 25
plus 80 is that correct you're taking
movement about the x-axis rail but
correct we call it you X so there are 4
x 105 so that is it now for this little
red area so that is a key by 25 time
what distance come on guys give me that
distance the mass is here so what this
time do I need I need 40 so just one
second so if you multiply this together
if my number is correct so if you
multiply that together you will get this
number four four hundred seventy three
thousand four hundred seventy three
thousand seven hundred fifty was the
unit see that's what again another
subject that you want to understand here
area come on guys listen to me area is
length to the power of two doesn't
matter millimeter to the power of two
inch to the power of two what is the Q
you just said it mathematically is area
times distance which we call it u so
what's that then the unit of that length
to the policy automatic if you think
about it this is the logic about it
that's what I want you to think the
logic of that tells you since I'm
multiplying area about the distance
which like a weight that I'm doing that
was not weight this area because area
represent the weight because it's made
of the same material and the same
thickness remember that yes that is the
idea behind it
therefore this become length to the
power of three so automatically become
millimeter to the power you don't have
even to think about it because you know
that you shouldn't know that this is the
fact we are going to use that often in
me2 18 and then of course Q of the block
you had a question now before I go very
okay now if you go one further there was
the unit of moment of inertia because
moment of inertia is the second moment
you have to multiply it by another
distant therefore you become to the
power of four so it goes from a to Q
remember that a Q I is that that in that
rest we use sometimes Q in a strength of
material area everybody knows what the
area is so is Q is the first moment I is
the second moment or moment of inertia
which I'm going to do next so Q up there
below area of the in this case blue area
now I have this Q and that U with
respect to this X I'll now you put the
number yourself 200 times 25 is the area
so you don't need to use sign you know
that this moment like the C so what that
moment if this moment goes like that
this moment goes like this everybody
understand it yes or no correct okay
that's the idea of the right hand rule
okay 200 times 25 times what what
distance this is the center what
distance do I need 70 plus 12 and half
so that is 82 and half trick so 82 and
half plus this little area yes or no
that little area is 70 times 25 times
what times 35 I'm glad okay so when you
do that calculation at home you will see
that for this end up to four hundred
seventy three thousand seven hundred
fifty millimeter that means our nice 95
is correct because the Q of a Bob and Q
of the below with respect to the neutral
axis must be equal and opposite yes or
no don't forget that for when we get to
later chapter is that understood
can I erase that down yes now the next
is moment of inertia which of course
requires parallel axes to you
so again I let's calculate IX I'm going
to bypass iy because iy we don't need it
that so I X equal to but I just put the
number there just to show you one more time
time
this works but then the number is not
essential here so IX is equal to
actually if you look at it this one this
is one of the quizzes by there I forgot
to ask if this is one of the quizzes I
have as a student to do in the past if
you go to the quiz page you will see
that picture there I'm sorry I didn't
mention that go to the page and go to
page I don't know go go go further than
last pages last couple of pages go
through no I just no no no no there to
page 14 you see that picture there I
should have mentioned that is that
everybody see that picture exactly like that
that
yes yeah that's part of a question not
the whole quail you have 15 minute to do
all of that plus the first part of it
but you can do it when you do your
homework of course yes after you do the
homework or practice this then you can
do all of that easily everybody
understood it now IX what is IX I need IX
IX
area 1 I X of area 3 and IX of area 2
let's do the first one now how do I do
that first I had knee to the centroid
that's the centroid and this is X Prime
is that correct or the X prime passes
through the centroid of a want to worry
about it I just wanted to know that this
type of question was going to be asked
from you in first quiz yes so there was
I act concentrate on this one I don't
want you to miss that
what is IX prime first you see that you
need IX prime which is passes through
the centroid which is 112 I already
given it to you
112 of base time height cubic yes or no
so it is 1/12 of base what is the base
base is this area base is 75 you are
quiet or at times but I'll need input 50
to the power of 3 but that's not
sufficient that's the moment about X
prime and I'm taking moment about the X
so the therefore requires parallel axis
theory of the distance between the two
axis is d is that correct or not
plus the area area which is 7
five times 50 times distance squared
distances fear we already calculate that
that's 80 plus 80 plus 25 that is 105 to
the power of two don't forget that so it
becomes millimeters to the power of four
everybody that is the moment of inertia
of area one let's do moment of area of
the third one so this is for the second
one this is for the third one the third
one is easy so I'm doing that first is
that correct what's the moment of
inertia of this with respect to that
x-axis with the same routine again I
have to put a X prime axis here yes or
no correct
you guys remember your parallax story
yes or no if you don't do that you could
not pass this class parallel axis story
is essential part is like calculating
area anytime you are designing something
later on in this this book moment of
inertia replaces the area everybody
understand as simple as you calculate
the area of a circle or a square or
rectangular you should be able to
calculate moment of inertia this week is
the best week to refresh your memory or
do whatever learning to do if you want
to do a static without learning this is
no good
notice what I put here three subject
equilibrium centroid at the moment have
these are the most important part that
is going to be repeated again and again
and again so don't be surprised I can
see some surprises on your eye
by the way throughout the course I look
into your eyes I want you to look into
my I know exactly exact how my lecture
registered to you
I can see it immediately so don't hide
anything from me so don't put your head
down I want to look into your eyes this
is the technique I have to work before
so I hopefully work with you guys
because if I don't see that it is not
there is some problem there I may
explain it one more time everybody
understand what I'm saying this so
therefore now the third part I need the
moment of inertia with respect to this X
prime which is again 1/2
well of base time height cubic yes or no
so it is 1/12 of base which is 200 times
25 because that is routine plus again
there is a distance between X Prime and
X because we are taking moment of
inertia with this this is the question I
asked you to do yes or no
so therefore the distance again is 70
plus 12 and so 82 and a half so area
I need the area 200 times 20 time
distance square which is 82 and a half
that's right
to the power of 2 so you can calculate
that now remaining the middle part so
remember that you have to do exactly the
same thing here too so if I consider it
being at one piece still I have to write
112 base base is 25 times height is 153
however does this X passes through the
centroid of that piece no it passes
through the centroid of the whole object
but the centroid of this piece only this
space is where this is 150 where is the
centroid of that 1/100 so it is 75 so I
have a 5 millimeter distance that's my
distance between the two axes yes or no
everybody see what I'm talking about yes
so there you see this is the centroid of
a 1 this is centroid of a 2 you need the
centroid of a 3 which is at 75 and 75
everybody understand so there is a
distance of 5 millimeters so you have to
use that plus the area so plus 25 times
150 I'm sorry that's the area times 150
but that has to be multiplied only by 5
to the power of 2 so that would be your
I X I Y is simple I'm not going to do it
or don't waste your time so that is the
centroid this is the review of the cue
centroid moment of inertia yes a little
five yes all right
so this is I put it here a little bit
bigger is that correct or not where is
our total centroid not first of all this
is 150 where is the centroid of this
page shape
this here so here should be 75 here
should be but where is our x-axis that
I'm taking moment about is it there look
the distances are given it is 70 and 80
so where is the x axis the x axis is
here see that so the distance this
become your X Prime and this is your X
that the distance is 5 the set s that
blue dot is the centroid of the entire
picture is not the centroid of that
seventh centroid of 150 by 25 is that 75
everybody knows that yes okay all right
all right good
everybody clear about that ok now let's
go to the first example now what did
discussion that we have here which is
very important you guys know this is the
first time you are going through this
rate of material this was already a t so
I'm going to erase that
now the first subject that I've I want
to discuss with you guys which is not in
the book but it is very important
actually it is in Chapter seven of your
static book is external load versus
internal or call it actions not note
because that gives you a different idea
there now there is a big difference
between a static and a strength of
material and you have to understand that
that's exactly what's sitting there
external load versus external example
let me give you an example here that you
will see what happened there when we do
this kind of problem let's say we have
here a beam here everybody should draw a
legend let's say this beam is 8 foot long
long
it is a
in here roller there and I say the
weight of this beam is 100 pound per
foot how do you find a reaction this is
such a simple abc's of aesthetic
everybody knows that so what's the
weight of the beam now I just want to
show you some very important factor here
the weight of the beam is 800 yes or no
100 counter foot it's 8 feet it is 800
where do you put it at the middle of the
beam because it's the same weight is
that there's no problem there don't be
this don't be surprised some of you are
surprised maybe you are afraid to say
that that is something you have done it
many many times even in high school yes
or no yes so you put the 800-pound there
so don't worry about it I'm not talking
about this yet because that is the total
weight W is equal to 100 pound per foot
multiplied by 8 feet feet and feet drops
out so it's 800 pound you put it at the
centroid and then you calculate the
reaction now you are removing this you
calculate the reaction here and here it
is symmetrical so this become 400-pound
this is 504 and this is 400 because it's
symmetrical yes or no this you have done
it many many times yes or no that's no
problem there the problem is this in a
strength of material we do the same
thing when we want to calculate the
reaction which was fine now let's say
somebody wants to because this object
first of all in a static object usually
will rigidbody if you go to chapter 4 or
5 don't remember is that if you chapter
4 it was the equilibrium of rigid but
right now you are not only more longer
rigidbody if I have a beam like that you
put it your hand you put a load at the
middle like that put it load at the
middle this object is going to bend if
this was a rigid body it who not being
two bending is that correct and that
bending is the issue we want to address
in future chapter 4 and chapter 4 now
when you look at this the bending are
different from this point to this point
to that point somewhere is going to go
down more than the other so we have to
go to go inside the body
and see what is happening in this body
this body this is what we are going to
do in the next few classes hold it with
you it's going to be like that pull it
this is purely tension we are going to
do week one or two then we can put it
like a column and push it down which
would be purely don't look at it that's
a buckling that's Amy 2:19 we talked
about that okay that it if this was
purely compression it would be
compressed down yes or no chapter one
and two this is the preview of coming
attractions guys so free will be about
tension and compression or two Force
member depending what's happening inside
the body which we call it a stress
strain etcetera so all of that coming in
future then in Chapter three instead of
force we are going to apply a moment
look at my tongue a moment like that
that moment like that moment like that
which is the moment about x-axis look
what happened to this object this object
is going to be twisted we call it
torsion or twist is that the last
chapter three in chapter four which was
just showing it the object is going look
at the moment the change this is this
moment now this moment causes this to
bend that's chapter four and five
chapter six is something else and
Chapter seven we put it all together so
we just have fun to get that let's put
it this way anyhow so what I'm saying
that you have to go inside the body
which you have done it in a static once
remember in a static when you went to
the trusses you were determining the
internal tension or compression remember
the internal forces you were cutting it
and finding the internet that's exactly
what we are doing here however look what
problem I have here let's say that this
is four feet and four feet and I want to
go here three feet here and make a cut
here and determine what is happening
inside the body of the material because
that determines the strength of material
to what which chapter to go now if I
draw it like that this is three feet and
here I put four hundred pound there is
no here forces here there is a force
here 400 is that correct
is that correct
what about the weight of the beam you
see that that for her 800 years with
that is because you were looking at
entire system this you cannot do you
have to go back to the original system
the original system is this guy's a
uniform node of no big very careful a
uniform load of intensity of how much
100 pound per foot because this beam and
the other beam are going to deflect
differently everybody understand that
now if I cut it at 3 feet how much dough
do I have there 300 everybody understand
what I'm saying that so that balance so
that changes the scenario so now don't
write it that all I want you to
understand that that there is a 300 here
then we are going to find out the
internal forces at this point which
would be either horizontal force or
vertical force or a moment exactly so
instead of now know that you understand
remember always do it this way that's
the you your problem number 9 and 11 is
all about that for aesthetic purposes
you can put one single load abandon you
want to cut the beam you have to go to
original back to original no the load
could be uniform it could be in triangle
Road slope road etc it's even a parabola
that you have to do integration
everybody understand what I'm saying
that so if you are looking at the weight
of the wing of airplane it's not the
constant it must be some some parabola
yes or no so then you have to use the
integration you learn it all about that
now let's go to an example in the book
in the handout but I've way to put it
there I don't want you to look at the
solution we are subject still is
internal action so this is the the
structure there is a beam here a b c is
a pin connection at k and also it is a
pin connection and right here this is C
this is the
and this is paint connection to the wall
these two are at the same level and this
distance is six feet that is four feet
and four feet exactly what I said there
and the load here is a uniform load so
we are considering the weight of the top
beam we are not considering the weight
of this one for neglecting that and the
weight is given 50 pound per foot this
is the question and we want to calculate
the internal actions at point B while
you guys are standing there outside for
looking from the window what's the
problem there let's let me check those
you want to come in you're welcome
why are you standing there watching for
next class okay all right okay so how do
we do that guy we want to calculate the
internal force of the what should i do
first you know that from a static you
have to find the reaction at all the
support yes first yes all right so of
course you have to draw a free body
diagram of the member let's say ABC
correct this is the free body diagram
come on guys these are basically static
that we are not talking about here at
Point a it is a pin so what should I put
that point eight guys a x and a y now
hot water would the load there remember
the load is a uniformly distributed load
of 50 pound per foot now if I want only
reaction I can replace it with one
single load what's that single though
that single load is 50 times eight so it
is 400 so I can put here at 400 right at
the middle 400 pound here now we come to
this point that point seems to be a
the pain to CX and CY Harvick looking at
member CD member CD is a two-force
member so the force should be in the
direction of CD so I should not put
their two forces I should put one force
in the direction of CD which the slope
is as you see there the slope is four
run three rice because eight and six
which is the same is that career corner
yes now do you think this item is under
tension or compression this is Ferris
less than of a strength of material is
it under tension is going to be crush or
it's going to be expanded what do you
think putting a load on top crush so it
should be in compression or if I put it
in tension mode the answer will come
negative remember but since I do it
absolutely it is in compression I'm
going to put it in compression mode
knowing the answer comes positive is
that understood
so which side is for compression upward
or downward your God past me2 814 not in
my class come on guys going toward the
joint is compression going away from the
joint is in tension yes or no all you
know it don't be afraid express it I
want to participate everybody understand
it yes if you know it that's okay if you
don't that's a good word to two doesn't
matter we can the reason I'm saying that
because I want everybody be on board you
either knew it or no right when you give
me the wrong answer that's good too
because if I correct you never for you
never forget it you understand what the
process worked that's what I'm saying
that don't be afraid you are stood and
you are in class you need to make a
mistake but you have to commit yourself
to something everybody on this either
fifty-fifty chance that you are either
correct or incorrect however that's the
learning process so if you are learning
there but these are something of course
you should know it from the past yes so
let's call it f CD is that correct so
that's the F remember CD right the rest
now is very simple now I have only three
unknown so I can solve it yes or no by
taking moment about point a of course
you see the rest this is the free body
diagram or
essential part of your analysis in every
structure so Freebody diagram you cannot
bypass that so Sigma M at or about a
equal to 0 would give you nothing there
so you give you this is for feet and
that's for feet so there is 400 times 4
and that is negative because it's going
clockwise then here it has two component
horizontal component doesn't have any
mode we got that that load goes through
this point I didn't draw it correctly
but goes through that point
so let's opinions there let's say that
so therefore since it goes through that
so the horizontal component does that
have a load we're up in the moment and
the vertical component has a moment but
vertical component is 3/5 yes or no so
therefore 3/5 of the force FCB
time distance of 8 and is this way so it
goes that way therefore it is positive
become equal to 0 this is the force
that's the distance you calculate fcd
become equal to 333 point 3 usually we
go three-digit however here I went to
four-digit to calculate fcd as soon as
you calculate fcd you can calculate a x
and a y which is not a big deal here
everybody can do that so let me give you
the answer so ax become equal to minus
two hundred sixty six point seven pound
and a y actually become two hundred huh
so this is the extent of a static which
everybody can do if you can draw of
course the correct free body diagram
correct now next the question that we
are embracing to do what happened if I
cut it at point B now look point B is
here first of all you have a big problem
is 400 is right on top of point B but is
that a correct assumption put in the 400
then I just already mentioned that
that's that that's invalid everybody
know that so if I want to cut it I have
to go back to that so we go back here
and make a cut here everybody understand
so you
have some load on the left some road on
that some part of it depends where you
are here you are at the middle so there
are four next is free body diagram of a
B so we are going to put it in the
middle here so here it is the free body
diagram of a now what force do I have at
a the force do I have at a we already
been determined is a negative two
hundred sixty six point seven so this
rod has a two hundred points they're
going this way yes or no prick let's go
a step by step before I put anything
else that requires here to do what this
is point B let's forget about anything
else because I haven't put the rest of
it because of this force I should have
an internal force going to the rod so
this beam or this rod is on there
tension or compression tension of two
hundred sixty six point seven which will
be the subject of next to lecture
everybody the rest of those problem are
like that so here I put here a force
here now in the static you call this
vxvy and MBEs change that that's going
to change now is not DX it has a name
this force is normal to the
cross-section yes or no therefore we
call it normal force so please don't go
forth give you normal stress normals
great give normal strain anytime you
have a section you have a column all the
load coming on the section everybody
understand that is force pushing the
column down everybody this force it's
not BX anymore if we call it and be
normal why not about one more time
normal to cross section to the cross
section of the beam everything is about
the cross section in me2 18 write it
down in your note every material that we
are talking about is about the cross
section of an object and is of course
laying come into the picture don't get
me wrong the length determined
everything but when you design something
this column has certain cross section
why this is this big because there is
lots of load on it if it was less load
the cross section become
smaller everybody understand what I'm
saying the leg of this chair you are
sitting there is there about 3/4 of an
inch diameter everybody understand if
you put a giant here you have to make it
four inch diameter everybody understand
what I'm say the weight determining the
the usefulness of the ideas nevertheless
this is normal force do not please do
not make it B X B Y B Z this is normal
force and this force would be what this
force going up on the other side will be
going down so it would be shear forces
everybody the one that in the section we
are going to share cursor me he
generally say it like that so these are
they have name of course you said there
is a moment other words it will not be
in equilibrium this is MV 2 now the
first two classes we are going to go
through the normal forces and shear
forces actually next subject which I had
10 more minutes I will talk about normal
forces and shear forces and stresses due
to that now hold on one sec well upward
or downward
what VB yes okay alright and then MB so
now chapter 1 chapter 1 and 2 is about
this - if your video chapter 3 we don't
have it here because you don't have a
torsion here chapter 4 and 5 is about
their bending and I said that and at the end
end
now let's put the load thing they lured
here was how much now this is only 4
feet so the load is like that is I just
put it in fashion because I don't want
that so how much load is that now the
load is 4 feet times what times 50 so it
is only 200 because the half of the beam
yes so where do I put that 200 at the
center like that this is 200 pound and
the distance is 2 feet and 2 feet
because that's the center of the
rectangle this is the loading system
that Freebody diagram does not show it
everybody understand that
don't make that mistake this doesn't
understand ok
now everything is simple so what's the
value of M b and b will be two hundred
sixty six point six seven pound
it is in the tension mode so if it was
like this it would be in the compression
mode once the shear force oh I'm sorry
we forgot something here there was an a
why here see you through this discussion
I forgot to put there so let's remove
this and do it correctly so there was a
to hunt this was a boy as well is that
correct or not yes
but notice if you look at your handout
they put this one downward not upwards
so be careful here you have a choice to
put it there is a reason for it I cannot
explain it out to you actually I will
explain to you later on for time being
you are going only by static either put
it upward or downward the answer come
according to where you put it is that
correct but if you want to understand
that we have to wait until we talk about
this the shear and what happened to the
sign of that everybody understand sign
of that normal force is very simple if
it is tension we call it plus you have
seen it in the study if it is
compression we call it - not a
statically plus about it you just
because it's pull or push so that we
talk about that later on today we don't
have done let's calculate so MB of
course is two hundred sixty six point
seven pound and it is in tension if I
want to calculate shear force I have to
write Sigma FY equal to zero yes or no
correct sick boy oh boy equal this was
Sigma FX what I did not use it Sigma FY
equal to plus 200 - 200 plus shear at B
of course shear at me at that time
become equal to zero because the balance
is zero there is that correct order yes
and then the moment how do I calculate
the moment the last this is for chapter
four and five how do we calculate moment
notice this blue ones or internal
remember the subject was external versus
internal in MA - eighteen all the
chapter is all about this blue one and
what happens to the object here due to
this blue one is that understood which
in a fact I am going to tell you is that
the real load that real note has to be
in the different format we talk about
the stresses etc etc but statics tell me
I should have something
that is that career corner yes and then
if I want to calculate the end where
should I take the moment about take the
moment about point he usually this is
the difference from a static now this
time because I want to avoid all of that
you should always take the moment about
point B not the point
again this is different from a static
notice here I took the moment about a
because I wanted the reaction that was a
static this is the strength now I take
off you always take the moment because
you don't want these two to appear in
your equation everybody so take the
moment about point B where you cutting
it so Sigma M where should I put it here
so I can erase that now Sigma M become
Sigma M at B equal to zero so you have
two hundred times for going negative
this one doesn't have any movement plus
two hundred times two this way positive
Plus don't forget there is M be sitting
there yes or no plus M be correct equal
to zero now I want you to understand
that this is totally different from that
some people in this class even in me2 19
they make a mistake between the two MB
is the amount of moment sitting at that section
section
yes sir Sigma M be equal to zero means
taking moment about point B and summing
it up everybody understand I have made
that very clear aesthetic unfortunately
some of you eventually make make a mistake
mistake
that means this moment this moment this
moment this moment if they have any and
this together must be equal to zero
everybody clear about that yes so as you
see it ends up like that many people
write this and say equal to Mb or some
dating and B equal to zero because they
said they write it like that they think
this is M be some people write it like
that totally right when we put Sigma M
at B this is a sentence summation of the
moment about point B equal to zero
everybody understand it gave that
pattern correct all right so
did you see what I did here so MV become
equal to Mb become 400 positive could
discover the pound foot that means that
direction is correct there a whole beam
is going to bend like this not like that
yes which is this how much time do we have
have
I don't know what happened two minutes
how much it's two minutes over twenty
thirty two okay okay next thing the
first thing we are going to do next next
class which is now looking at fcd
everybody under and then this rod would
be only on their tension or compression
in these cases comforter then I talked
about the stresses strain etcetera
etcetera about members which fuel is the
strength of material all right okay I'll
let you go this time
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