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Von Mises

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hungrydinosaur

Marine/Ocean
Sep 25, 2013
41
Hi All,

I am preparing a excel sheet, where I have the results for an analysis. I have the stresses for Axial, Bend-Y, Bend-Z, Combined, Shear-Y and Shear-Z. What formula do I need to come up with for the von-Mises stress? Thanks in advance.

HD
 
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This depends more on your code than on the fundamentals... Are you designing in ASD or LSD?

Typically (Mx*/øMrx)+(My*/øMry)+(N*/øNr)<=1 or (Mx*/øMrx)^2+(My*/øMry)^2+(N*/øNr)^2<=1 is used. Both are generally considered to be conservative.
 
1) what is von Mises stress ? ie what do you need to know ?

2) knowing that you need principal stresses, how can you determine them from your data ?
consider that peak shear stresses don't coincide with peak bending stresses.

Quando Omni Flunkus Moritati
 
rb1957 is entirely right, and I wasn't sufficiently clear... The normal formula is to combine axial and bending, with shear rarely ever needed to "mix in", hence the formula I sent is the typical column case.

It is very rare to have an element that needs to be checked in shear and bending, but not unheard of. It occurs in large transfer beams and other similarly significant point loads as well as all "high efficiency" materials like CFS.

Here's a summary I wrote for the interns:

Combined Stress Design:

You will very likely be familiar with basic bending, shear and (for some of you) torsional design of members. The classic design problems you will have faced required you to check bending and shear independently. This is sufficient for beams which are simple spans, but fails to meet the fundamental requirements of good design when dealing with continuous and oither more complicated questions. The issue is one of the specific location of the design action and resistance; In a simple span the maximum bending stress and the maximum shear stress could not be further apart – Peak bending occurs at the centre, and peak shear occurs at the support. What happens to this arrangement when we take even the most simple case of a two span continuous beam? Now the peak bending moment occurs at the centre support, as does the peak shear stress. Even so Von Mises is only very rarely a critical issue for materials which are designed elastically (Timber), never for those designed specifically against the assigned load where each is effectively a custom members such as reinforced concrete, and not normally of concern for materials which have large, bulky cross sections (extruded plastics). Note that all cases of elastic design are excluded as the peak bending stress within a cross section occurs at the extreme fibres, and the peak shear stress occurs at or around the centroid.

For each problem you face, a preliminary review of the possibility of combined actions shall be made. Where bending and shear, or bending and torsion, occur in the same location of a member, a suitable combined actions formula shall be applied.

It is not the magnitude of the individual loads which matters, but rather the location and in particular the coincident locations of differing forms of stresses. As a guideline, anything over 75% of the available bending capacity is a high flexural load, and anything above 60% of an available shear capacity is a high shear load. Steel is a critical case in which this is often incorrectly overlooked, however it is interesting to note that the American AISC does not require a combined bending and shear check. Note that both S16 and NZS 3404 do specifically require such a check, and the limits of 75% and 60% are taken from NZS 3404.
 
Seriously though I meant to say that shear and moment stresses are also maximum at the same section for cantilever beams.
 
but not at the same location on the section ... you wouldn't make a principal stress out of max shear stress and max bending stress

Quando Omni Flunkus Moritati
 
True. Perhaps. CEL makes a good point though that the shape and materials at the section of interest are important. In concrete and in WWF sections the shear and moment are designed to be accepted by separate parts of the section.

I have been looking at moment connections in HSS lately and I have been finding that moment and shear stresses are not so clearly separated. Due to slenderness/thin-wall/non-compact type issues, HSS members behave more like elements in a space frame where the stresses in a section are more difficult to localize, especially at connections. In that case I think that Von Mises might be useful to simplify the analysis.

 
Rb1957: What is true for the design of some structures is not of others. In plastic design you must combine the bending and shear in some cases as the section is fully utilised in bending (the whole point of plastic design).
 
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