Unequal Flange I Beam Torsion (open section, non-uniform thickness)
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- Опубликовано: 7 сен 2024
- Here an open section with non-uniform thickness and non-continuous median lines is analyzed to determine the maximum permissible torque it may withstand, applying a factor of safety. Under this torque, the angle of twist per unit length is found, as well as the absolute angle of twist and torsional springrate, assuming the length of the member is known. These analytical steps were applied to a standard unequal flange I beam cross-section that was looked up out of tabular data.
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This example was recorded on January 21, 2018. All retainable rights are claimed by Michael Swanbom.
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The secret here is that the three segments can be analyzed as independent rectangles in terms of shear stress with respect to twist, and their torques summed to find the total torque. Thus we get the relationship between torque and peak shear stress--exactly what I was needing. Thank you!
You have summed it up nicely (pun intended). I'm glad I could help! Thanks for watching!
Thank you Dr. Swanbom! I'm glad you've shared your passion for engineering and teaching with the world.
Hey everyone - if you have a known torque and require estimating the torsional shear stress in an I-beam (or C-channel; the formula is the same), then using the same method in this lecture, the formula is:
τ = (3 * T * tmax) / (Lw * tw^3 + Ltf * ttf^3 + Lbf * tbf^3)
Where τ is torsional shear stress
T is the torque
tmax is the maximum of either the flange thickness or web thickness; usually this is the flange thickness in most steel sections.
Lw is the length of the web between flanges
tw is the thickness of the web
Ltf is the length of the top flange
ttf is the thickness of the top flange
Lbf is the length of the bottom flange
tbf is the thickness of the bottom flange
Note - if you were to mistakenly use τ = Tr/J (only correct for solid circular shafts) and you used J as the torsion constant listed in structural tables for the cross-section, then this method vastly over-estimates the stress.
Do you know how if it's a composite, how to translate the angle formula? or do you know how can I get this information? thanks
Thanks for sharing. Very thorough. I guess this confirms that, for i beams, the web contributes very little in resisting torsion
Yes, the thinner segments of the cross-section do not contribute as much to resisting torsion.
Thanks for watching!
The best explaining torsion in beam.. Thanks a lot
I'm glad you found it helpful! Thanks for watching!
Superb!! Thank you.
I'm glad you found it helpful! Thanks for watching!
Best explanation ever!
Thank you a lot. It was very helpfull.
I'm glad I could help!
Gracias ahora puedo hacer mi tarea
You're welcome, I'm glad I could help!
u da best
thanks! glad it helped!
Thanks for very interesting stuff. I'm missing a discussion or mention of why you are not considering warping at all (or am I missing something?).
This lecture and another you gave which included torsion of a solid square cross section beam helped me get very close to a solution for an I beam problem. When I implemented some strain gauges for various I-beams and solid cross sectional beams, the measured results were about 25% less than expected but close enough to allow an extrapolated approach to then be used to derive the final design. Could you possibly indicate the textbook you were referencing in this lecture regarding the 300ASB155I-Beam? Thanks so much!
Correction to my previous comment - I had a large error in measurement because the torque measurement tool being used (a torque screwdriver) was very inaccurate. When the measurement was made using a fairly accurate torque wrench, the difference between the measurement and the calculation was less than 5%.
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Thank you sir for great video! Today I learnt new things)) Just one question. Is it possible to find miment of inertia about x and y axis and sum up them together then find maximum distance after that we cal calculate shear stress. Shear stress = (Mtorquemoment x r ) / ( Ix + Iy). Is it correct sir?
Thanks Prof,
does this formula & analytical steps apply to T beam?
Can I get reference textbook name.
Yes, You can use this method on a T beam. I use Shigley's Mechanical Engineering Design, 10th edition in this course. Thanks for watching!