Re: location of maximum stresses

[paddles069]

With respect to upper figure in the attached diagram, I don't really understand how the moment acts on the beam. I've always understood moments as forces that cause rotation and so when it is drawn as a straight line in the upper figure I'm not sure how that is affecting the beam.

With regards to the lower figure, the solutions state that 'by inspection', the maximum tensile stress is located at point B and the maximum compressive stress is located at point C. Why is this? How do they arrive at this conclusion?

 

[SteamKing]

The moment in the upper figure is shown resolved into its two components in the lower figure (notice the moments shown on the y and z axes). In effect, the beam is being bent about the y and z axes at the same time.

 

[Jupiter6]

It's an understandable question. Treat it as any other beam cross-section, except it's being twisted to the right and twisted upwards, as opposed to a straight on load.

To answer your questions:
Moments are a force applied at a distance from some center. They don't have to cause a rotation and if this is the case, they can be resolved into forces applied, at a certain distance.

I too was thrown off by a lot of these things in sophomore solid mechanics because they were never related to the real world.

Their "by inspection" statement assumes you are familiar with beam cross sections. In cases of T-beams, I think you should treat them as I-beams when "inspecting".

First and foremost, always draw your freebody diagrams or break the problem down into FBD's. Always!

 

[pongo38]

I think the M should have had a double headed arrow, indicating a moment about the axis with the arrow head at its end. In a 3-dimensional sketch, can you sketch the stress distributions separately from the two components? This is how you can see by inspection the quality of the stresses at B and at C.