click the bell icon to get latest videos

from Ekeeda Hello friends welcome back to the subject of machine design 1 we are

right now learning about this c Frame design and today we are going to look at

a numerical which is based on C frame design so this is a C frame which we are

familiar with given with this particular cross section the cross section here is

T the load is given which C frame is going to support which is 10 kilonewton

the distance between the point of curvature or the center point of

curvature and the endpoint of the load or the application of flowed given is

thousand millimeter the thickness term is given for the inner radius so inner

radius is basically twice the thickness this thickness term is basically

associated with the cross section the cross section has been given like this

where this lip thing is 3t this is the thickness T this is the base of 0.75

times the T the height given is 3t and the distance between the neutral axis

and this given is 2 T which is this one so basically this particular curve which

is the first fiber is nothing but this one and rest of the part of T is nothing

but this one so anywhere across this is considered this section X X looks like

this so the problem statement says that determine the dimensions of the C frame

shown this side in short all the dimensions are parametric there in terms

of e so we need to find out the thickness T it is sufficient to find out

thickness T so as to completely define the dimension of this given C frame they

have provided us with this material property which is the ultimate stress

200 Newton per millimeter square and factor of safety three students one

thing that we need to understand is so low value of the ultimate

indicates that this particular material must be a brittle material though this particular aspect doesn’t

impact this numerical directly but that gives us a better understanding about

different material properties so the low value of this particular ultimate

tensile strength indicates that it is a brittle material so let’s move ahead to

find out the thickness T so that it can define the parametric terms completely

so it can be seen that the cross-section is subjected to two types of stresses

the first one is direct stress and the second one is the bending stress it is quite obvious that bending stress

will be maximum at the inner fiber and the directors will act over the

complete surface or cross-section in the adverse case both these dresses

will act together and that’s why the total stress will be considered using

both of them together so it comes out to be VI which is the bending stress at the

inner surface the formula simply becomes bending moment to H I area of cross

section with eccentricity and the inner radius but the direct stress will be

given by the load P divided by area of cross section we have been given the

ultimate stress value and we have been given factor of safety so let us write

the expression here itself it’s going to be two hundred divided by three so this

is what the main expression that we are going to look at and evaluate the answer

for the unknown parameter T now let us proceed one by one let’s start with the

value R and for the given cross section now given cross section is a section and

from PhD data book we can easily figure out this particular

expression the substitute the values of the available parameters of certain

terms we need to understand precisely because the cross-section values are

given but we need to convert them in terms of the radii in different radii of

curvature so let us start one by one so before we input the expression let’s do

it beside it is understood that the radius value or the thickness value has

to be T in a case the next expression is the width the inner width will of course

will be three times the T the H size which is basically three times just T we

haven’t given the cross-section the inner radius is directly given which is

nothing but 2 times the T so it is quite obvious that outer radius which is

nothing but the inner radius plus the H value comes out to be 5 times 3t and the

last thing is the actual thickness expected in our problem is 0.75 times

the T value there’s mention it T – for the sake of understanding so these are

nothing but the parameters that we can figure out based on the given images or

figures let’s substitute these values here comes out to be T you in the log to the base e if we see this again each and every term

of this expression is in terms of T so T is the main common parameter that we

need to take out so the final our n value comes out to be three four times DT the value will also

be in millimeter and that’s a first finding let me quickly revise that this

particular expression which is quite lengthy need not mugga we can always

find him from PhD data book for the reference purpose moving ahead let us

find out the component R where RI is 2t the H value here is 3d pío values T Bahai values 3t minus 0.75 times DT

there’s nothing – component of T that we have here also it becomes you we seen that this term is also in terms

of tea and at the end we can find it out like odd is equal to three times the

expression number two so moving ahead with other parameters we

can easily figure out the value of e comes out to be the value of H however is comes out to be and area of cross-section for this

particular T is the wave area plus the flange area you so these are the important parameters

that we have found out now let’s move ahead to find out the bending stresses

direct stresses and equate them to the main equation so the bending stress will

be basically force into radius R the force that we have been given is 10 kilo

Newton which makes it 10 into 10 raised to 3 the value R here is 3 times DT so

it makes it newton millimeter and hence the bending stress at the

inner radius or inner fiber comes out to be you area of cross section and the inner radius which is two times

DT after evaluating this expression we get Sigma inner value is equal to so the

bending moment in this case will become this particular expression where R is

nothing but the radius from thee or the radius of curvature or the distance of

the curvature of radius from the center axis and hence it actually becomes 2

times T plus thousand and hence this particular expression comes out to be 2t

plus thousand newton per newton millimeter in that

case this expression does not remain the valid i heard of this when we are going

to find out the bending moment equation and find out the bending stress let’s

substitute the values the value here comes out to be 2t plus thousand after

using this expression we’ll get a very straightforward but lengthy expression

in terms of T let me write it down for you you the expression since is of the stress

we’ll have this unit Newton per millimeter square whereas the

directories in our case will become / area of cross section and then we have arrived with the

expression that we have already derived their substitute D values after

substituting the value of this and this we can understand that there is only one

unknown which is T and therefore solving this expression we will get the value of

T is equal to let me write down this another side which is two hundred

divided by three let me quickly revise after substituting

these two expressions here which is quite lengthy I am avoiding that step

and directly switching back to the next step

where we can find out thickness T and it comes out to be in terms of a quadratic

equation let’s write down the quadratic equation and that is you now this quadratic equation can be

expanded like this and after evaluating this expression

we’ll get T is equal to or T is equal to 100 millimeter – the

value our model is same we have to refer to thee since the thickness T is

directly proportional or inversely proportional with the value of stress

and hence we are to go for the lower value and therefore T is equal to 99

point two millimeter is the optimum solution for the given cross section so

there we end with this particular numerical it metrically revise what we

have done is you consider the C frame and its design analysis says that there

are two types of stresses that may induce which is direct stress and the

bending stress based on which we have written similar expression then we went

on finding Sigma bending and Sigma T in order to find out Sigma bending there

supposed to find out the bending moment and in order to find our we have gone

through different parameters like RN r b RI centricity e h i etcetera etcetera

after finding out those expression we obtain this particular quadratic

equation after solving which Yordy solution so that was from my side thank

you so much for watching this video if you like this video please subscribe to

equator thank you you