Problem statement
Solution video1
Solution video2
DISCUSSION THREAD
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HOMEWORK 35.A - SUM 24
22 thoughts on “HOMEWORK 35.A - SUM 24”
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Through solving this problem I came to a singular point that experiences pure bending. I understand that this is possible as the criteria is that V=0 and M is not 0, but none of the lecture example problems included single points. Has anyone else gotten a similar result when solving?
I got the same result, and although the lecture examples didn't have such an instance, the contexts from those examples can be applied here, yielding our result.
Yes, I got the same result. It’s hard to base it off the lecture examples because there wasn’t a problem quite like this one.
I got the same result (i.e. point bending). I used the sigma x max formula and substituted the bending moment at the point of pure bending stress to get the max normal stress.
Yes, I encountered the same thing. Despite not seeing an example like this on the lecture, I believe this would be true since the two criteria are met: That the shear force is zero and also that the bending moment is not zero at that point.
I got the same. Even though nothing was in the examples, as there was a range of pure bending, in our case, it is just one point. I was surprised initially to see that, but then, after double checking, I got the same result. So, yeah, there is only one point when V = 0 and M != 0.
I also got the same result. There was a brief example that was changed and mentioned in the context lecture to show that a singular point experiencing pure bending is possible so I think this is a reasonable answer.
I got the same thing. the lecture example doesn't really cover it exactly for this problem, but i got the answer. Then to get the max normal stress, i just used the point of pure bending.
Would the moment be the area under the curve of the shear force graph up until the pure bending point?
Yes, the moment at a given point along a beam can be found by integrating the shear force diagram up to that point.
Yes, if your graph for shear between certain points results in a simple geometric shape you can calculate its area to find the moment between those points.
I think this is true since as said in some of the lecture notes that the bending moment at any section would be the integral of the shear force over that length of the beam.
it is true. Change of Bending moment is equal to the area under Sheer Stress in the particular range. So, yeah, you are right.
Yes, you can just integrate the equations you determined for shear force and graph the integrated functions as moment graph
HW12A presents the exact same scenario as this problem. It's actually interesting to see that what was once a complete assignment in HW12A has now become just a simple step in HW35A.
In this question, there is a certain point where the pure bending is negligible, would the normal stress be maximum at the same point?
I'm assuming that you're asking "if both shear force and bending moment are 0, is that still a point of pure bending stress?" In that case, I believe the answer would be no; only cases where there is no shear force but a nonzero bending moment.
Yes that is what i was asking, thanks!
When taking the integral of the shear force to solve for the bending moment how do you solve for C. When I just took the integral it did not give me the value that I was looking for as it was missing that constant and I am unsure of how to solve for that.
Basically, we have to have a point where we know what bending moment is, which is usually zero. So for example if we know that the bending moment at x=0 is 0 we know our C which would just be zero. So just find a point where you know the value of bending moment and the value there should be how high or low is your graph off of the x axis. If you know that M=0 at x=0 it is pretty simple as the moment diagram is not shifted up or down at all because C=0.
Just to clarify, is the moment highest where V = 0 always, because the moment will be the highest at pure bending?
Yes, the moment is highest where the shear force (V) is zero, as this indicates points of pure bending. At these points, the bending moment reaches a local maximum or minimum since there is no transverse load.