Mechanical Principles -- Assignment question

[haruspex]

post #22 where I calculated the denominatiors through the integration process was incorrect

It was already wrong in post #20. In the $\frac {d^2}{dy^2}$ equation you had, correctly, a term $-\frac{(10)(x-0)^2}{2}$. But when you integrated that you got $-\frac{(10)(x-0)^3}{3}$ instead of $-\frac{(10)(x-0)^3}{6}$. Same with the next term.

 

[Al_Pa_Cone]

This is my working out for A when x = 5, and B = 0,

I am completely lost as to how I obtain the value for A when B does not equal 0, I would think A is worth a different value as x changes?
I presume I am plotting onto the graph for the value of B anyway?

Do I need to use the math methods for finding 2 unknowns or is their a much simpler way. Obvioiusly Understanding Calculus is not my strong point in all of this!

Thanks

 

[haruspex]

am completely lost as to how I obtain the value for A when B does not equal 0

A and B are constants, by definition. You correctly found that B must be zero in order that y(0)=0, then you found that A=-76 so that y(5)=0.
There is no more to do, you have the complete equation. Just sketch the curve and see if you get something like the graph I posted.

 

[Al_Pa_Cone]

but what about the deflection values for 2,3and 4 meters as the question requires me to give results in 1 meter increments. Also how would I find out to what level the curve should drop to before it begins to climb back to 0? I would have thought they expect me to plot each point and then build a curve from the known results.

 

[haruspex]

but what about the deflection values for 2,3and 4 meters

Just plug those x values into the equation.
You seem not to understand the statement that A and B are constants. Having determined what they are by considering particular (x,y) pairs, they apply for all x.
Think of it this way. Without knowing A and B, you have an equation which satisfies all the loads, but works no matter how high the two supports are. You can adjust each up and down independently, and the beam displacements will adjust to match. That is equivalent to varying A and B. In the actual set-up, y is defined to be 0 at the left support, and the right hand support is at the same height. A and B must have those values which give y(0)=y(5)=0.

how would I find out to what level the curve should drop to before it begins to climb back to 0

I don't see that asked for in the question as you posted it. If you have to find that, the ideal method would be to find where the gradient is zero. But the gradient equation contains cubic terms, so you would have to solve a cubic equation, which I am sure you are not expected to do. Next best is to plot the curve using some software and read it off the graph. Third best is to calculate y at a number of points; the more the merrier, but the question as you posted it specifies 1m intervals... a bit crude, but that's what it says.

 

[Al_Pa_Cone]

So I think I have the correct method now by inputting my values for x into the formula for each point on the graph with the knowledge that A already sums to -76 for each value of x and B would be the graph plotting figure remaining in from the formula.

I am determined to get this question right as I have spent so much time on it! Really thanks for everything. I would have never been able to get through this on my own. As I am a distance learning student, I don't have any others around me to bounce questions off nor a tutor to quiz when I get stuck. If I don't fully understand the text then I have to just figure it out elsewhere. So thanks so much for all your time!

 

[haruspex]

B would be the graph plotting figure remaining in from the formula

Not sure what you mean by that. Just substitute B=0 and A=-76 in your general equation for EI y as a function of x. Then evaluate for whatever values of x you want.

 

[CivilSigma]

Hey, for part b), an easier approach is to sketch the bending moment diagram, which will be continuous since there are no applied external moments, and then, the maximum bending moment will be located along the beam where the shear diagram is 0. So, you don't need to write all those algebraic equations. Why? Because the moment diagram is the integral of the shear force function over the span of the beam.

 

[Al_Pa_Cone]

Well this is what I have managed to obtain for the method I think I am following correctly. For plotting values at 1 meter increments I now have all positive values for B??
it does however make the arch on a graph, showing it would fit within the deflection diagram #29 if the values had all been Negative?

 

[Al_Pa_Cone]

Maybe I am being stupid, Does B always = 0 throughout the equations, an the values would read
EI y = -74.6 + 0 for x = 1 therefore the plotting point would be -74.6 and no further transposition would be required?

 

[haruspex]

, Does B always = 0 throughout the equations, an the values would read
EI y = -74.6 + 0 for x = 1 therefore the plotting point would be -74.6 and no further transposition would be required?

Yes.

 

[Al_Pa_Cone]

Well well well. Looks like the answer does exist! Thank you so much for your patience. You are a very helpful Tutor and I certainly would not have managed that without your guidance. All the best for the New Year as well!

 

[haruspex]

Well well well. Looks like the answer does exist! Thank you so much for your patience. You are a very helpful Tutor and I certainly would not have managed that without your guidance. All the best for the New Year as well!

You are welcome. I learned something too.

 

[GSXR-750]

Sorry to drag this back up.

I am following the question here but getting vastly different results.
Bending at the 1m mark of 625mm which obviously looks wrong.

Going right back to post #1, I have calculated I as being;

$I = \frac {0.03*0.06^3} {12}$
$= 0.54*10^{-6}$Jumping back to the later posts I have the same formula for IEy= ... as post #39I see the poster omitted (red writing) parts of the formula that was to the right of the part in question but kept the rest of formula in. Why is that?
Using that method though, I then calculated $y$by dividing the result by EI. (210x$10^9$ x 0.54x$10^{-6}$
Leaving these horrifically high numbers.
1m = -0.657m

Any help appreciated.

 

[thor55]

hey guys i was doing this question but don't understand anything and how it works can i get some help i tried to follow the working out in my notes and one of the al_pa_cone.
still don't understand some help will be great.
thank you

 

[haruspex]

hey guys i was doing this question but don't understand anything and how it works can i get some help i tried to follow the working out in my notes and one of the al_pa_cone.
still don't understand some help will be great.
thank you

Which post by al_pa_cone, and where is the first part you do not understand?

 

[thor55]

basically i know that this is a simultaneous equation but like when the integration takes part and the denominators change in post 20
and when he( al_pa_cone) works everything out he has 12 as a dominator in post 24
also when he works out the value for A he has different denominators and that is what is confusing me as to how come there are different denominators
and also the in one of the post i believe you mentioned that if there is a negative number then the term should be ignored bit more info on that too.
because i used used skyciv free calculator and the deflection was towards the bottom and should not be positive
help will be appreciated.
Thank you