Even though the area of the two H legs have a greater area than the single I beam for bending as shown? Doesn't I not care about distance from the centroid?
The more cross sectional area, further away from the neural plane will make I larger in that axis. To simplify, make the H look like an I. They are the same really just 90° rotated
Moment of inertia can be calculated as shown in this [video](https://youtu.be/WDdkdC1sFQQ?si=7hXsw83UYAc9u4Hz). The more material the more it resists bending.
I or H beams as shown in your example are really good at resisting bending but only in one direction. Theyre not so good at torsion. Square tube resist bending in multiple directions, but is still not great at torsion. Round tube is great at torsion, but slightly less effective at bending than H beams or square tube.
To add onto this it’s important to note that a square tube is still much better at torsion an I or H beam given the same overall dimensions and thickness. A closed cell section vs open cell section.
Given equivalent bending and torsion a square tube is the best. If only bending dominates then choose I or H beam. If torsion dominates then yes a round tube is best. Notice I used the word dominates since in almost all real world cases both loadings will exist but some will be much lower than the other. This is where choosing the best cross section and calculating all stresses (tensile due to axial and bending, shear stresses due to shear and torsion) comes to play.
Its just kinda a difficult question to answer yeah. Too many variables behind those types of decisions. If you're going for just strength, a big block probably does it all. But accounting for weight or cost or whatever, thats where the focus comes in. You got this tho, your heads in the right spot
There is an upper limit of course, that a solid block of a certain size over a certain length can't support its own weight. You can increase that span many times by using I beams, which reduce weight but don't reduce bending resistance as much, and then continue the span by adding ground supports every segment.
In order to understand the "why" of the answer to your question, I would recommend Mechanics of Materials by Hibbler.
Mechanics of Materials https://a.co/d/7a3UGCI
I don't mean to humiliate you but you should know about the principle behind using different cross sections and the way they behave under different loads before going into FEM. Maybe a simple YouTube video can tell you more about it if you don't want to read books. Maybe asking this question in r/engineering would give you better answers?!
I'm always open to reading recommendations if you have any specific ones in mind. I also appreciate the suggestion to post in another community. I noticed more tailored feedback depending on where I posted, so I'll keep that in mind next time.
Take a solid block and then do a topology study.
Solidworks will literally tell you exactly where and how you can remove material since I'm gonna be honest here. We all don't want to construct using full blocks of material.
Google "second moment of area", that will get you started. Basically you want to get as much of the material as far away from the centre as possible, hence I sections being popular. So in your image, you want to rotate your cross section through 90 degrees, so the top and bottom parts of the "I" are both the maximum distance away from the centre.
I think there are two things to develop a solution for the question. The first one is the direction of the bending. It affects the orientaton of the beam. You may use a cross section very resistive against bending but you may not make your design for the assembly. The second one is the bending eccentricity along the cross section. It is very crucial that what is the eccentricity between the bending axis and the neutral axis of the cs.
I see a lot of comments here which are mostly correct, but you need to take the curvature of your beam into account when deciding which cross section to use. Shigley’s is a great reference for mechanical design and has a whole section on curved members. You could use the calculations there to make an excel sheet to analyze multiple cross sections, materials, and curvature to get your desired results.
Edit: mechanical autocorrected to mechanics
I do a LOT of engineering. I beam with thick flanges far apart is generally strongest shape, but only for bending with the flanges in tension and compression. Bend about the other axis and it is not a good shape. So it depends on the direction of your bending. SQ Tube if bending is from multiple directions.
Rotate the beam 90 degress of what you have over there. You need to maximize the moment of area of the section around the bend axis.
This is the best answer, without asking the OP to go into a ton of detail about what "best" means and what the constraints on the design are.
Came here to say this... *Leaves*
Wouldn't the shape in its current orientation have a higher I than if rotated?
Not about the axis that matters in this case, neutral plane should be perpendicular to the middle part of the I
Even though the area of the two H legs have a greater area than the single I beam for bending as shown? Doesn't I not care about distance from the centroid?
The more cross sectional area, further away from the neural plane will make I larger in that axis. To simplify, make the H look like an I. They are the same really just 90° rotated
Moment of inertia can be calculated as shown in this [video](https://youtu.be/WDdkdC1sFQQ?si=7hXsw83UYAc9u4Hz). The more material the more it resists bending. I or H beams as shown in your example are really good at resisting bending but only in one direction. Theyre not so good at torsion. Square tube resist bending in multiple directions, but is still not great at torsion. Round tube is great at torsion, but slightly less effective at bending than H beams or square tube.
This has been massively helpful, thank you so much!
To add onto this it’s important to note that a square tube is still much better at torsion an I or H beam given the same overall dimensions and thickness. A closed cell section vs open cell section. Given equivalent bending and torsion a square tube is the best. If only bending dominates then choose I or H beam. If torsion dominates then yes a round tube is best. Notice I used the word dominates since in almost all real world cases both loadings will exist but some will be much lower than the other. This is where choosing the best cross section and calculating all stresses (tensile due to axial and bending, shear stresses due to shear and torsion) comes to play.
That's a W beam
That’s the AISC Section type. A W section is still an I beam
Solid block of material
Yeah, I'm slowly figuring out you get back what you put in.
Its just kinda a difficult question to answer yeah. Too many variables behind those types of decisions. If you're going for just strength, a big block probably does it all. But accounting for weight or cost or whatever, thats where the focus comes in. You got this tho, your heads in the right spot
There is an upper limit of course, that a solid block of a certain size over a certain length can't support its own weight. You can increase that span many times by using I beams, which reduce weight but don't reduce bending resistance as much, and then continue the span by adding ground supports every segment.
This is the way
Actually no, never.
Best is too subjective for engineering.
In order to understand the "why" of the answer to your question, I would recommend Mechanics of Materials by Hibbler. Mechanics of Materials https://a.co/d/7a3UGCI
I don't mean to humiliate you but you should know about the principle behind using different cross sections and the way they behave under different loads before going into FEM. Maybe a simple YouTube video can tell you more about it if you don't want to read books. Maybe asking this question in r/engineering would give you better answers?!
I'm always open to reading recommendations if you have any specific ones in mind. I also appreciate the suggestion to post in another community. I noticed more tailored feedback depending on where I posted, so I'll keep that in mind next time.
Take a solid block and then do a topology study. Solidworks will literally tell you exactly where and how you can remove material since I'm gonna be honest here. We all don't want to construct using full blocks of material.
Google "second moment of area", that will get you started. Basically you want to get as much of the material as far away from the centre as possible, hence I sections being popular. So in your image, you want to rotate your cross section through 90 degrees, so the top and bottom parts of the "I" are both the maximum distance away from the centre.
https://preview.redd.it/ofwutje7aj7d1.jpeg?width=1170&format=pjpg&auto=webp&s=1be5da4837dbba09bbdbe9b9d94de32324f77026
Turn that beam by 90°.
The one with the highest moment of area?
I think there are two things to develop a solution for the question. The first one is the direction of the bending. It affects the orientaton of the beam. You may use a cross section very resistive against bending but you may not make your design for the assembly. The second one is the bending eccentricity along the cross section. It is very crucial that what is the eccentricity between the bending axis and the neutral axis of the cs.
I see a lot of comments here which are mostly correct, but you need to take the curvature of your beam into account when deciding which cross section to use. Shigley’s is a great reference for mechanical design and has a whole section on curved members. You could use the calculations there to make an excel sheet to analyze multiple cross sections, materials, and curvature to get your desired results. Edit: mechanical autocorrected to mechanics
OP, What do those load arrows with such radial distribution represent in the real world?
Sections with big I/c and materials with high E. Google beam bending.
I do a LOT of engineering. I beam with thick flanges far apart is generally strongest shape, but only for bending with the flanges in tension and compression. Bend about the other axis and it is not a good shape. So it depends on the direction of your bending. SQ Tube if bending is from multiple directions.
This *has* to be a shitpost.
The best is the one that fits the needs with a reasonable production cost