# Homework Help: Bending moment

1. Mar 4, 2005

### 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? whats the correct formula for working out when it will bend?
thanks
chris

2. Mar 4, 2005

### faust9

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?

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)?

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Last edited: Mar 4, 2005