# Why is it unwise to choose cylindrical horizontal beam

I heard that it is unwise to choose cylindrical horizontal beam. My question is why?

• For what application? – feetwet Feb 7 '15 at 17:59
• Did you hear this about hollow cylinders, solid cylinders or both? – Air Feb 7 '15 at 20:44

The strength of a horizontal beam is defined based on a property called the section modulus. Shapes that have more material distributed near the top and the bottom have a higher section modulus. This is why I-shaped beams or tall rectangles are common choices. Round shapes, on the other hand, have most of their material concentrated around the center of the shape, and very little at the top and the bottom, so they don't make very strong beams. That means a round beam would need a lot more material to achieve the same strength as a taller shaped beam.

You could see this intuitively if you take a ruler or other piece of thin material you have handy and try to bend it. You'll notice that in the flat direction, it's very weak and easy to bend. In the wide direction though, it's quite strong. Even though the piece of material is the same size, having more of it at the top and bottom makes it stronger.

The reason for this isn't too hard to understand, when a beam bends it can't stay perfectly straight. In order to form a curve it has to change shape slightly. The top of it gets compressed (pushed inwards) and the bottom part experiences a tensile stress (gets pulled apart.) As you move closer to the center, there is less stress of each type. In fact, when you get to the middle, the beam is neither getting pulled apart or pushed together, it is called the 'neutral axis.' So the top and bottom have to be strong to resist the compression and tension, but the center only has to be strong enough to keep everything attached.

If you did really want to use a cylindrical shape for a horizontal beam (maybe for visual reasons or wind resistance) a round tube would be more efficient than a solid cylinder, because it has less material around the neutral axis. It still wouldn't be as efficient as a rectangular tube or traditional structural shape though.

• It would perhaps be more clear and precise to state that in the flat direction the ruler is less stiff and in the wide direction it is more stiff. Unless the ruler material is anisotropic, the strength doesn't change with orientation, and unless failure is intended, strength does not play a role in beam design except for material selection. – wwarriner Feb 8 '15 at 5:54
• Stiffness is the property that the user observes, but the strength of the beam is changed when you change the orientation of the loads applied. the material strength doesn't change, but the beam strength does. Since the section modulus is the moment of inertia (which controls stiffness) divided by the extreme fiber distance, strength and stiffness are correlated for a given material, and for an intuitive understanding of section properties, we don't need to differentiate. – Ethan48 Feb 8 '15 at 19:06

A cylindrical beam is probably not the best beam for given situation. This doesn't mean that there are no specific situations where a cylindrical beam would be useful.

Pros

• Can resist the same load in any direction or combination of directions. It is as strong in the horizontal direction as the vertical direction.
• No need to worry about or check the Lateral Torsional Buckling (LTB) limit state.
• Works well as beam-column (moments and axial loads together).
• The circular shape may have less surface area than other shapes when considering things like painted area or ice buildup.

Cons

• Not as efficient (weight of material per strength) as an I-shape for loads in only one direction.
• Sections may be difficult to find or more costly than more common shapes.
• Connections at the ends and to other members coming in from the side are more complicated.
• Stiffeners under areas of concentrated loads are harder to design and fabricate.

Unless one of the items in the "Pros" list greatly outweighs the "Cons", a cylindrical beam is probably not the best option.

The use of a cylindrical horizontal beam is unwise in that it has added weight that offers no added strength.Therefore you are paying for unneeded material which is unwise,unless aesthetic concerns require the use of the cylinder shape. Highly unusual lateral loads might make the use of a cylindrical beam an option but those forces are normally addressed with other design components.

• Couldn't you inscribe the cylinder inside a prism instead of circumscribing it? That way, you'd use less material. – HDE 226868 Feb 8 '15 at 1:18
• @HDE226868 I don't quite understand your question here, but if you're still curious, you could post it as a question of its own with a sketch. – Ethan48 Feb 11 '15 at 16:38
• @Ethan48 This answer seems to assume that the cross-section of the cylinder is larger than a cross-section of a square. This is essentially circumscribing the cross-section. I'm suggesting inscribing it instead, which would actually weigh less. Did I misinterpret it? – HDE 226868 Feb 11 '15 at 16:40
• I think what they meant (but didn't explicitly state) is that for a given beam strength requirement, the cylindrical beam will weigh more. Certainly you can make circular beams smaller than other cross sections, but they will be weaker than other cross sectional shapes with the same area. – Ethan48 Feb 11 '15 at 16:44