Eccentric Loading (Rivet design) Video Lecture | Design of Machine Elements - Mechanical Engineering

the rivet arrangement let me have a
rivet here one Lydia I will take the
simple problem first it is to be desired
for this load
now this arrangement is symmetrical the
centroidal system is somewhere here this
axis is X this one is y light level this
one is rivet number one near it number
two so for this one to find out a
centered of the system X bar equals to
x1 plus x2 plus x3 plus x4 divided by
the number of limits not equal to 4
suppose this distance is 50 and this
distance is 100 so what is the
x-coordinate of rivet one is zero what
is the x-coordinate of rivet 2 is also 0
what is the x coordinate of rivet 3 is
15 what is the x coordinate of wait for
is also figure 8 divided by 4 so is X
bar equals to 25 unit y bar also what is
y coordinate of rivet 1 0 what is the y
coordinate of rivet to under 40 negative
8 3 I get under but in the y coordinate
of rivet 4 is 0 divided by number of
rivets this one is 2
so your x-coordinate is 25 and Y
quantity is 25 so your first job is to
look at Salford so locate the centroid
of the rivet system assuming a point
mass and by passing their axis through
rivet one that is the lowest rivet on
the left-hand side now from this point
measure the distance between the line of
action of the given force for this
eccentricity e the eccentricity is the
distance between the line of action of
force if your line of action is vertical
you also draw a vertical shift here that
the line of action has will change so in
mechanics we can shape this force to
this point so if we shift this force to
this point the magnet of the force will
remain same but the additional moment
will be generated and that additional
moment will be equals to is f multiplied
by F multiplied by this distance and is
this moment will be clockwise moment so
in this system we can remove this force
and this force will be shifted as it is
here plus one additional moment
so this force will be shifted to this
point and will act in the same direction
now the moment produce at this point so
in this one the moment produce will be
clockwise and this moment we light eyes
f f/a is given by f multiplied by EP and
the force is downward so your system is
basically subjected basically it is a
moment this one is perpendicular to the
plane also so we treat this as torque
one plate is rotating with the other
plane so that will causing a torque so
it is better to describe this one as dot
head twisting moment divide this force
equally into all the four rivets this F
is called as primary shear force F a
primary shear force and this F is
equally divided in all the place so we
have we have F 1 equals to F 2 equals to
F 3 equals to F 4 is same as F divided
by number of rivets so right now I have
folders and we prefer the same direction
so each of them will act vertically
downward so let represent this force
here so in magnitude we will call this
as f 1 and this one is DEP 3 we call
this as f 4 this one is F 1 this one is
f 2
and we are keeping the same direction
basically they are going to act in
opposite direction these are called net
primary dia
so it will cut in this plane and this
plane is circular section so this force
is parallel to the circular section that
is why it is called as primary shear
force now to balance they start the
procedure involved is join reaching like
this so join all the rivet centers with
a given point and on this rivet Center
that is through this one we have to show
one force either this one or either this
one which is perpendicular to the line
of action so this one is the shortest
distance between this point and we want
this type of moment so this moment was
divided equally into four rivers
depending upon their length from this
point so let's call this length equal to
l3 this one is a clockwise moment so I
will retain this shape equals to F 3
Prime and this I will cancel out because
this if I use this one the moment will
be anti-clockwise but if I use this word
my moment is clockwise so cancelled it
about this point we want the moment at
this point s 1 equals to R l4 so moment
about this point should also be
clockwise so shall we go for this
direction or we should go for this
direction we should go for this
direction is always perpendicular to
this
now what about this one we want a
clockwise moment so either direction is
like this and we also want clockwise the
direction is like this so in this
fashion we can finish up the four
direction let call this one is F both
double dash F four dash this one is F
one - this one is f 2 - every time it is
perpendicular each time according to the
definition of moment force particulars
so at every point we have two forces one
is primary and then the second forces
are F 1 F 2 dash F 3 - and F 4 - these
are called as secondary shear force in
this case the secondary forces are
proportional to the length from the
center of rivets that is F 1 - by L 1 a
same as F 2 dash by L 2 a same as f 3
dash by L 3 is same as f 4 dash by L 4
so on the processor plane the total
moment is F into H so total torque
rather total torque is F into E is
equals to F 1 this torque is what what
it is torque is F four dash multiplied
by this length equal to what ello
Plus this doggy goes to 1 f 2 - when he
paid by corresponding language and to
this torque is f 3 - f 3 - x length
healthy - x fo so what we had done
actually we had done two steps whatever
the external force is there was equally
shared between all this place and
similarly this moment is it distributed
between the four rivers so we are
claiming the same thing that if this
force is distributed between the four
rivets and this moment is distributed
between the four rivets then this
arrangement is possible that is external
torque is balanced and external forces
also now to solve this equation further
we can take the help of this one now if
you substitute for this so this is F
into e F dash and dash l1 will keep
everything's this f2 - we can calculate
from this so f2 - will be F 1 - x cross
x + 2 he wanted by l1 so and this I
doing as it is next is this F 3 F 3 and
first term so what he get is effort - x
n3 divided by l1 and is again multiplied
by L 3 and the story continue now in
this case F into e I wish to take effort
- by l1 comma so in this one is this
value is l1 square for the retaken
common this L 2 and this at 2 is what I
2 square X L 1 is only taken power so
this L 3 and this earth means l3 squared
so plus L 4 in no L 1 l 2 and 3 and 4
and we know the value of F into e so we
can very compare
really calculator for - once we
calculate f1 - then we can also
calculate F 2 - then f 3 - are the
voltage so in this fashion we can
calculate two forces one is F 1 and 1 is
f 2 - for all the limits this is vector
V bar and this is vector Q Bar and let's
say the angle between there is the fire
now we can rework we want to find out
the resultant of these two to find out
resultant of these two so this one is 5
so this Acker is also fire so this one
is vector Q this one is resultant R so
if you have two forces like this one and
if we know this angle we can find out
resultant of this force so this
resultant we are finding so we will
resolve this into two parts one part is
this and one part is this out of this
this part is Q cos of Phi and this one
is Q sine of for the law whatever
espadrilles we can apply and then find
out this so what is R square this one is
R square this side is total is P plus Q
cos Phi
this one is Q side v so this one equals
to R square equal to P Square plus 2
times PE q into cos 5 plus Q square or
square v + Q square sine square Phi so
this one is R square equal to P Square
plus twice B Q cos of Phi plus Q square
because cos square Phi R sine square Phi
is 1 so value of R is dependent on the
value of P the value of Q
between them now this video if negative
then our will be normally zoom value of
this one is one in that case the R will
be maximized and that is true also if
this vector at this vector they are
acting in the same direction they are
resultant will be maximum value is it
fine now if they are perpendicular so
this value will be zero in that case we
are only p square plus R square you are
knowing this one vector is this other
vector is this is the resultant value
will be given by this vector Plus this
vector if the two vectors are acting in
opposite direction then this value will
be one more than 90 in that case this is
negative and your son will be less so
what that instead of going for this
result for finding for all for you
identify first that which forces as
larger value of this two component all
component has same value of f1 f2 f3 f4
so don't show any interest on that one
then you identify whether F 1 dash is
more F 2 dash is more or F 3 dash is
more or effort now for the present
figure they are symmetrically placed so
right now all these valleys are also
selling because L 1 is same as n 2 a
semi ran 3 & 4 so all these are for same
but if you observe the angle between
these two force if this one angle is
less than 90 if you observe the angle
between these 2 is it less than 90 and
if you observe the Eiger between this
word is it an obtuse angle greater than
if it is greater than 90 this term is
negative it means that resultant of this
and the resultant of this is always less
than the result
this - how to identify the rivet which
is Mabley loaded in that case first step
is that find the debate which has a
maximum value of secondary shear force
no comparison is required for primary
because primer is equal value comparison
only based on secondary shear force if
we observe that a secretary shear force
is also say then you take the decision
based on value of five so this is a
criteria is used for this one this one
is 5 this 5 and this Phi is supposed to
be the almost semi literally but this
Phi is it more than this part so you
have to avoid this and your to our it is
so in this case rivet number three and
rivet number four our we will load it so
we can calculate a resultant value at
reaction three using same equation as f3
square plus two types f3 f3
- in to cause of flex a 5 3 + f3
- square and in this case because of
cylindrical arrangement f3 is same as F
4 and F 3 - is also same as at 4 so this
value will be same as our 4 it means
that the rivet number of 3 and the rivet
number 4 are heavily loaded once we know
the name in loaded then we they will
going to fail in shear so value of R 3
equals 2 it is a case of signal shear so
this is PI by 4 d square multiplied by
tau so from this we can find out
diameter of Riveter now for this type of
loading we have to check which one is
going to fill or which rivet is mainly
loaded now from observation of this
figure this one itself is the center of
rivet system so this external force P
will be shown at this point and this P
will cause the moment along this work
and this moment will be equals to P into
e is a clockwise moment so this P is
equally divided and we will show what
force here will show one force here and
will show one force here this is
basically primary shear force this value
is P by 3 this value is also P by 3 and
this value is also P by 3 primary shear
so this P is equally divided between
this Li the secondary force should be
acted at 3 to add one in such a way that
it will cause the moment about the
center of the weight system in a
clockwise direction so if I take this is
a central system then this force will
act in a clockwise direction and this
value will call as f1 - corresponding
distance is l1 and that equals to what a
no moment is caused at point two because
this force will pass at this point and
is the force acting at this point will
be acting this way that equal to f2 -
and the corresponding distance is l2 is
same as a so moment of f2 - about the
center of system is clockwise so this
total value will be equals to R F into e
the forces secondary forces are acting
at equivalent distance it means that f1
- a same as f
so actually we don't have to do any
calculation if you apply if you apply
the law of pendulum of this force is it
a heavily loaded and is it a least
loaded because this is they are acting
in opposite direction so is this the
weight is heavily loaded so design is
based on the rivet number three can we
find out f2 - yes we can find out a
production that equal to 1 P multiplied
by E
F 1 divided by L 1 multiplied wash l1
squared plus l2 squared we are just done
this this one is P multiplied by G f-111
a is a and this one is a square plus a
square e to a square so f 1 equals to P
into e divided by 2 divided by doing so
you can just put up this value so this
one is able to donate so design is based
on this value equal to PI by 4 into d
square multiplied by tau so the order of
shear stress will be tau 3 is more than
tau 2 is more than power
so just by observation you are set to a
somewhere here so sector is somewhere
here so this distance is 40 40 and this
distance is 30 30 this the force 10
kilonewton is equally divided in all
four rivers so 2.5 2.5 at all pluses
this one is primary shear force 2.5 to
find out the value of secondary shear
force will join of this with this sector
and this radial distance is saved for
all of them for this one we equals 240
this distance equals 230 so this
distance equals 240 square plus 30
square that equal to 50 so it means that
lol is same as n to a same as l3 is same
as L 4 equals 250 now this is the their
lengths are same their forces is also
simply because force is proportional to
length so f 1 - f 2 - F 3 - equals to F
4 all secondary forces are saying how to
calculate the forces we have a formula
external force P multiplied by D must
equals to F 1 - by L 1 into bracket l1
squared plus l2 squared plus l3 square
plus L 4 squared is same as 4 times and
once so this answer come out to be 5 so
all these forces are equals to 5
kilogram to show the direction of this
force you have to first connect your
rivet Center to G draw perpendicular in
this direction such that such that the
rotation of this force will develop the
clockwise moment because this P also
will produce clockwise moment so once
you decided what direction continue this
every time this is perpendicular to that
so every time is perfect
to length so we know all these forces
this one is f2 - this one is f3 now we
want to find out this angle that we are
calling as and then file this excel that
we are polygons I can find
we were only considered this to process
that is these two rivets because there
actually is less than 90 now this limit
will never fill because angle is more
than 90 and this rivet will never fill
either of this ankle or that angle
because in both cases it is greater than
90 so only we will go for either 2 or
either 3 but both are symmetrically
placed so this file this file is also
said so to find out that value of 5 I
will consider here a right angle
triangles like this here this line and
this grid line make an angle of 90 so
this one is 90 minus 1 this one is 90
minus 5 so this angle must equals to 5
so this fire is this length is 40 this
length is 40 this length is 40 and this
height equal to 130
so they side from here to here is 30 so
we can very well find out that fine so
tan Phi is 30 divided by 40
so that equals to thirty six point eight
six of parallelogram of forces resultant
force at R 2 is same as R 3 F 2 square
plus F 2 dash square plus 2 times F 2
into f2 - hit - cos theta that is
classified so put 4 f2 equals to 2.5 f2
- we are just a great equal to 5 and
angle Phi equals to 36.8 6 suppose we
are given tau equals to 90 mega Pascal
so can we calculate the diameter of
rivet so that will be equals to R 2
equals to PI by 4 into d square
multiplied by tau that is 90 from this
we can find out diameter