00:01
Hi everybody so here this is here in the textbook so you can see this is symmetric just like this part the left side of fg and the right side of fg is symmetric actually so we only need to find one side and the same will be applied applicable for the next side also that's just like the force that d will be equal to h the force that we will be equal to j likewise so now this pratt roof with loading and support as shown in this figure so here the bc is a zero force member this bc this is a zero force member so b c is a zero first member and here in point l you can see a support and in point a there is another support so in point a there is one support that is pin support in point a there is pinned support pin support so because of this support because the support because the support the type of support is pinned support there will be two forces one vertical let's name the vertical force as a y and there will be one horizontal force also horizontal let's name the horizontal as a x so now in this question we are going to find the find this part the love side of fg so here there is a way here and a horizontal force a x also so all the measurements are given in the matrix there is one kilo newton two kilo not and two kilo and one kilo and two kilo and one kilo and forces and every measurement is given in newton itself in meter itself so now to use the method of joins let's start with an analysis of this free body diagram of the center trust then we will look for joints connecting maximum two members with the unknown internal forces to solve with force equilibrium equations so let's take let's just write for the other one also like in point l in point l there is rolosopon and you know the speciality of flora support because of this type of support there will be one vertical reaction so let's name that reaction as ly so now let's go to equation of equilibrium let's take summation it's and on it's equal to zero that gives us a x equal to zero now now let's take summation of momentum at l equal to zero so at l equal to zero gives us the distance 12 meter to 1 kiloton plus the 10 meter into 2 kiloons plus the 10 meter into 2 kiloons force plus then the next distance will be 8 meter 8 meter into 2 kiloton force plus 6 meter into 1 kilo newton force plus sorry here actually the sign is minus minus 12 meter into a byte equal to 0 so so here you can see this or these things like 2 plus 2 plus 2 plus 2 plus 2 is the distance.
05:45
So 2 4, 6, then again 8, 10, 12.
05:52
This is 12 meter into 1.
05:56
The 1 kilo, the 1 kilo will be here also.
05:59
So that 1 plus the next 2 kiloton, 2 kiloton will be here also.
06:06
2, 4.
06:08
So that is 10 meter away.
06:10
So that into 2 kiloton, the next distance is 8 meter, 8 meter into the next 2 kiloton.
06:17
The next distance is 6 meter, 6 meter into 1 kiloton minus the 12 meter into a while will be equal to 0.
06:30
So here from this equation we can directly we will directly get the value for a way that is the a way will be equal to 4 .5 kiloat 4 .5 kilo time so we got the value for a way also now let's move to each joint and so for each joints so first take let's take joint a so for joined a if this is joined a there will be one force a way adding vertically upward and there will be one force one kilo tonne actually this is vertically downward sorry for my drawings and there will be another force fab add some sland slope and there will be another force fac at some other slope and we we know the distance here this is two meter and this is one meter so the hypotenuse that will be root 5 that is 2 square 4 plus 1 5 root of 4 plus 1 5 root 5 is the hypotenuse so and here the distance is this is 2 and this is also 2 so the hypotenuse will be root of 2 square 4 plus 4 root of 8 hypotenuse will be root 8 so you got the distances now let's resolve this summation along y equal to zero gives us a y minus one kilo newton minus for f a c the sign will be opposite by hypotenuse that is 1 by root 5 1 by ruff 5 fac c minus for f a b the sign will be opposite by hypotenuse will be 2 by root 8 2 by root 8 f a b equal to zero now here we will get an equation of fac and fab as we just found the value for a y substitute the value for a y here and then we can write an equation for fac and fab that is 1 by root 5 fac minus 2 by root 8 if a b will be equal to minus 3 .5 so let's name this equation as equation number a now let's resolve along x senses summation along its equal to zero que says minus of 2 by root h will be f a b plus 2 by root 5 facc equal to 0 so that is 2 by root 8 fab means the this adjacent this is 2 so this adjacent distance to by hypotenuse root 8 and for fac this adjacent distance 2 by hypotenuse root 5 so here we got an equation of fab and fac another equation of fab and fac so let's name this as b so from a and b from the equation a and b we can write we will get the values of fab and fac that will be if a b will be equal to so serving these two equation gives us fab that will be seven root two seven to that means rotate by root 5 f ac is that that that will be the equation we will get after solving this so from that substituting the values we will get fab equal to 7 root 2 kiloton 7 root 2 kilo and f a b is going inward so that creates compression denoted as denoted by the letter c now f ac c is 7 root 5 by 2 7 root 5 by 2 kilo ton and this fac is going outward from the point a so that creates tension denoted by the letter t.
13:04
Now he solved for joint a now let's move to the next join that is joint c so for joint c so for the joint c so for the join c the diagram looks like there will be be one first f -c -e and just opposite to this there will be under f -a -c and vertically upward there will be one f -b -c -c -c -s -f now this distance this is two this is one so the hypotenuse will be root 5 and here also, this is 2, this is 1, so the hypotenuse will be root 5.
14:14
Now let's resolve for joint c, that is summation along h .c equal to 0, qsas, fce minus facc equal to 0.
14:34
That is fce, that is, we just found the value for facc here, that is 7.
14:44
Root 5 by 2 so if c will be equal to 7 root 5 by 2 kilo newton and here fc is going out from the point c that creates tension denoted by the letter t now let's find summation along y equal to 0 that gives us f b f b c will be be c will be so there is only fpc in the y direction so fpc will be equal to zero so now let's move to that next join that will be joined b join for join b the dynamic will look like it's a big complicated there will be a kilo -noten, particularly upward.
15:58
This is two -kilon -tongotan force and there will be f -b -d and just opposite to that there will be f -a -b.
16:19
And also, particularly downward, there will be f -b -c.
16:29
Now let's use screen for indicating the distances.
16:35
This is 2, this is also 2, so the hypotenuse will be root age.
16:44
Now here, here also the distances are same.
16:51
This is 2, this is 2, hypotenuse will be root age.
16:58
Now let's go in service.
17:00
This for join b summation lm by equal to 0 uses the opposite by hypotenuse that is 2 by root 8 2 by root 8 fab minus this 2 kilo tonneous minus again opposite by hypotenuse 2 by rotate fbd will be equal to zero so from here we already know the value for fab so the fbd we can directly write we will get the value for fbd as 5 root 2 hilo -nooter and the fbd is going inward to the point b so that creates compression denoted by the letter c now summation the law it's equal to zero yes us f be e plus adjacent by hypotenuse that is also 2 by rotate f a b minus again adjacent by hypotenuse that is also 2 by rotate fbd equal to 0 so we got the value for fbd just substitute the value of fbd and we know the value of fab we just found the value of fab as 7 root 2 just substitute that value also though so we will get the value for fbe from this equation that is minus 2 newton and the fbe the fbe the yeah it's actually going in word so that creates compression let's create compression yeah now let's move to the next one sorry for the confusion actually there is one here yeah we know that it's pretty clear this is fbe so here the fbe is the fbe is actually going outward so that means that means yeah that means it creates tension denoted by the letter b now let's move to the next joint that is joint e for a joint e, let's draw the diagram first.
21:06
If this is e, there will be f -e -g here, and just opposite to that, there will be f -c -e -e.
21:22
There will be f -c -e and vertically upward f -d -e, and here horizontally f -b.
21:41
Now let's note.
21:46
Not the distances also.
21:48
This will be two, this will be one, so the hypotenuse will be root 5.
21:53
Here also the distance is 2, 1 and hypotenuse root 5.
22:06
Yeah...