Combined Loading on an L-shaped beam

  • #1
morpheus343
29
4
Homework Statement
Find Fx and Fy.
I tried calculating σα,σb,σc,σd using σ=εE for each point since i know the strains for each point. Then took the section from the top to points a,b. Fx will create a bending moment M and Fy is axial force, so for a: σα=-Fy/A - Mz/Iyy which has 2 uknowns the Fy and M. I do the same for point b: σb=-Fy/A +Mz/Iyy and solve a 2x2 system and find Fy and M. Not sure so far
Relevant Equations
stress
Screenshot 2023-09-20 155607.png
Screenshot 2023-09-20 155716.png
Screenshot 2023-09-20 155716.png
 
Last edited:
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  • #2
morpheus343 said:
Homework Statement: Find Fx and Fy.
I tried calculating σα,σb,σc,σd using σ=εE for each point since i know the strains for each point. Then took the section from the top to points a,b. Fx will create a bending moment M and Fy is axial force, so for a: σα=-Fy/A - Mz/Iyy which has 2 uknowns the Fy and M. I do the same for point b: σb=-Fy/A +Mz/Iyy and solve a 2x2 system and find Fy and M. Not sure so far
Relevant Equations: stress

View attachment 332254
Can you break the diagram into two pictures so the text is larger?
 
  • #3
Should be visible now
 
  • #4
morpheus343 said:
Should be visible now
Ok, go ahead and replace ##F## with its effective loading at the top of the column so we are clear.

Then proceed with finding the reaction forces at the base. It's a good idea to produce shear moment diagrams, as it should help you find an error (I believe) you are making.
 
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  • #6
I need to add a moment at the top?
 
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  • #7
I'm assuming they have given the length of the beams?
 
  • #8
No
 
  • #9
morpheus343 said:
No
:wideeyed:

Are they the same length? Does it say anything about their length?
 
  • #10
No measurements given for any of them. It said the strains have been calculated with rosettes, not sure if that matters for the solution or it's just filler talk.
 
  • #11
I think it's just to explain how you came to find said strains IMO. let's just call them both length ##L## for now ( I am now certainly unsure of how to get a numerical answer...), but lets continue so you can see the issue with what you were proposing.
 
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  • #12
I don't know if you go stuck or not, but have you had any luck finding reaction forces and/or producing a shear moment diagrams ( or just using the relevant equations to determine the internal moment ) ?
 
  • #13
Furthermore, its preferable that you format your math using LaTeX Guide. It doesn't take long to learn, and it makes the communication process much smoother.
 
  • #14
The internal moment at a random length x is M=Mtop+Fx*x ?
 
  • #15
morpheus343 said:
The internal moment at a random length x is M=Mtop+Fx*x ?
You have the right idea, but you are applying things incorrectly. What do you find for the reaction moments, forces at the base of the column. Please draw a diagram turning that portion horizontal.

Also, please follow the link I gave and reply with latex for math. It’s really not a difficult thing to learn. It is certainly not too much to ask given the fact that you are receiving free help.
 
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  • #16
1695229943631.png
 
  • #17
morpheus343 said:
View attachment 332272
What direction is the moment at B? And what is its value in terms the assumed beam length ##L##?
 
  • #18
counterclockwise?
 
  • #19
morpheus343 said:
counterclockwise?
It's the external effect of ##F_y## (applied at distance ##L##) on the beam. Just like the forces. What direction is it?
 
  • #20
you mean it should be clockwise to counteract the rotation that Fy creates?
 
  • #21
Fx * when perpendicular
 
  • #22
morpheus343 said:
you mean it should be clockwise to counteract the rotation that Fy creates?
No it should be clockwise because it is the rotation ##F_y## creates. We are not looking at an internal force there. We are looking at external forces/loads at ##B##. We are replacing the external loading condition out at the end where ##F## is applied, with an equivalent external loading condition at the column.
 
  • #23
morpheus343 said:
Fx * when perpendicular
These are perfect opportunities to use LaTeX Guide for math formatting. I'm not going to ask again.
 
  • #24
I get it now
 
  • #25
F_y , not sure why it's not showing correctly in preview i copied your LaTeX code
 
  • #26
morpheus343 said:
F_y , not sure why it's not showing correctly in preview i copied your LaTeX code
You don't have it in delimiters that lets it know to execute it as latex code.

Code: 
##F_y##

makes inline Latex Code

Like this ##F_y##

If you want an equation centered by itself use:

Code: 
$$ F_y $$

Like this:

$$ F_y$$
 
  • #27
##F_y## okay thanks
 
  • #28
morpheus343 said:
##F_y## okay thanks
Also there is a "glitch" ( side effect of trying to save processing power on the site) where if there is no latex in the thread, then latex will not show up in preview.
 
  • #29
morpheus343 said:
I get it now
So are you good on the whole problem, do you see the issue?

Your shear/moment diagrams suggest you might be having sign convention issues, and the internal moment should be ## M(x) = M_A - F_x x ##

##M_B## is negative according to convention, so it has to cross the axis.
 
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  • #30
I am not really sure, so if i cut the beam at points ##a## and ##b## ,both ##F_x## and ##F_y## will create a bending stress and ##F_y## also a normal stress? Would this be the way to solve it, cutting 2 times once at ##a## , ##b##, and once at ##c##,##d##
 
  • #31
In order to find the bending moment at each point
 
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  • #32
morpheus343 said:
In order to find the bending moment at each point
Yes, the moment at section ##a-b## and ##c-d## are defined by ##M(x)## which is a function of ##F_x, F_y##.

Before you were applying the same moment at point ##b## and ##d##. But they are ##10 ~ \rm{cm}## apart. So they don't have the same internal moment.

You have two other points to consider, so maybe you can even solve for ##L##, I don't know...You'll have to try that out.

To me it appears as though section ##a-b## is at ##\frac{L}{2}## but that isn't specified anywhere - I'm skeptical, but who knows.

Also, it’s not clear whether or not the height of the I beam ( ##20 \rm{cm}## )is to be neglected against ##L##, that would factor into your external moment.
 
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  • #33
I see, i will work the algebra and see if i can solve it, but i think there are too many unknowns.(##F_x##, ##F_y##, ##M_B##, ##L##, ##x## distance). And i only have 4 equations, one of each of the combined stress at each point. Thank you for your time and help
 
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