Hollow circular tube versus hollow rectangular shaft

[daniel wood]

Sportnut:
If I am using exact same aluminum material, with exact same thickness of gauge and I construct a 4ft long hollow circular tube that is 1" diameter, and I also construct a 4ft long hollow rectangular shaft that is 1" square, which would be more resistant to bending?

 

[Bill_K]

Hard to say, but the circular pipe would resist bending equally in all directions. Whereas the square pipe would be great in horizontal and vertical directions but would quickly fail if you tried to bend it along a diagonal (making it diamond-shaped)

 

[daniel wood]

Thanks Bill. I appreciate your response.

 

[AlephZero]

The square tube would be stiffer because more of the material is further from the centerline.

The stiffness ratio (from the second moments of area) is (1/12) / (pi/64) = about 1.7

Post #2 is wrong. The square tube is also equally stiff for bending in any direction, though this is not so "obvious" as it is for a circular tube.

 

[pmacias]

I cannot provide a definitive answer without conducting further research and analysis. However, there are a few factors that may affect the resistance to bending in this scenario.

Firstly, the shape of the cross-section alone may not determine the resistance to bending. The material properties, such as the elastic modulus and yield strength, also play a significant role. Therefore, it is important to consider the specific type of aluminum material being used.

Additionally, the orientation of the applied force and the direction of the bending moment may also impact the resistance to bending. For example, if the force is applied at the center of the tube or shaft, the circular tube may be more resistant to bending due to its symmetrical shape. However, if the force is applied at the corner of the square shaft, it may experience less bending compared to the circular tube.

Furthermore, the length of the tube or shaft may also affect its resistance to bending. A longer tube or shaft may experience more bending due to the increased leverage of the applied force.

In conclusion, the resistance to bending of a hollow circular tube versus a hollow rectangular shaft is not solely determined by their shape, but rather by a combination of factors including material properties, orientation of applied force, and length. Further analysis and experiments would be needed to determine which shape would be more resistant to bending in a specific scenario.