Calculating the Bending Moment of a Steel Tube

[fcukniles]

Hi,
I need to work out the bending moment of a steel tube, 25mm diameter (3mm thick) 410mm long.

im assuming i have to use youngs modulus in some way? what's the correct formula for working out when it will bend?
thanks
chris

 

[faust9]

Hi,
I need to work out the bending moment of a steel tube, 25mm diameter (3mm thick) 410mm long.

im assuming i have to use youngs modulus in some way? what's the correct formula for working out when it will bend?
thanks
chris

How is the tube supported? This is a very important detail when determing bending moments. Cantalevered beams will have different support reactions than simply supported beams... Essentially what you need to do is determine the support reactions on the tube as if it were solid; additionally, you need to find the point of maximum moment along the tube (this is where the support conditions come into play). Once you know where along the tube the max/min moments are to be found you can then draw a 3D FBD of the cross section and analyze how bending effects the top and bottom(or wherever the max moments may be) differential cross sectional areas of the tube.

See attached picture. The red bar is the tub modeled as a solid and the blue/white pipe is a section of the tube at the point of max moment(under the force in this case). There is a stress relationship \sigma=\frac{My}{I} where M is the moment, y is the distance from the centroid to the point of concern(usually point of maximum stress which occurs at the outer edge of the cross section) and I is the moment of inertia.

Is that what you were looking for?

[edit]The pipe will always bend no matter how much or little it is loaded unless it is supported along a free surface i.e. resting on a flat smooth surface. Are you looking for the yield criteria (max moment just before the onset of permanate plastic deformation)?

 

[thepatientmental]

Hi Chris,

To calculate the bending moment of a steel tube, you can use the formula M = F * d, where M is the bending moment, F is the force applied, and d is the distance from the point of rotation to the force.

In this case, the force is the weight of the tube itself, and the distance from the point of rotation (the center of the tube) to the force can be calculated as half of the length of the tube (205mm).

Now, to determine the force, you need to calculate the weight of the tube. This can be done using the formula W = m * g, where W is the weight, m is the mass, and g is the gravitational acceleration (9.8 m/s^2).

The mass of the tube can be calculated by multiplying its volume (pi * r^2 * h) by its density. As the tube is 25mm in diameter and 410mm long, its volume would be approximately 15,707 mm^3. The density of steel is around 7,850 kg/m^3, so the mass of the tube would be 0.123 kg.

Plugging these values into the formula, we get W = 0.123 kg * 9.8 m/s^2 = 1.206 N.

Finally, we can calculate the bending moment by multiplying the force by the distance: M = 1.206 N * 205mm = 247.23 N*mm.

As for Young's modulus, it is a measure of a material's stiffness, but it is not necessary to use it in this calculation. It is typically used to determine the deflection of a material under a given load, but in this case, we are only interested in the bending moment.

I hope this helps! Let me know if you have any further questions.