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Self-Weight Eccentricity

Question:

The attached model is of a concrete pier. Since the pier cap cross-section is asymmetrical, I would expect there to be some torsion due to self-weight. The results show that the torsion is nearly constant along the length of the pier cap for "SW" (Static Load Case 1), but for "Slab DC" (Static Load Case 7), there is a linear variation in torsion. Shouldn't these two load cases produce torsion diagrams of similar shape?
Answer:

Hello,

Thanks for getting in touch.
The beam torsion Mx is obtained by multiplying the load with the eccentricity of the load from the centroid of the section.  Meaning, actually there should be no torsion due to self-weight!  Though, in this case, we are getting torsion due to self-weight, because the section properties are changing in between.  This is still quite low as compared to other torsional moments (0.3 kips-ft for self-weight as compared to 116 kipsft for slab load).  This can be checked by simply applying a UDL at section CG.
However, we will get a relatively larger torsional moment in the beam, if the load is eccentric to CG of section.  I've attached an excel file here for a simple section thats added to the model.  
As for the torsional reaction, that is again applied load x eccentricity.  But now, the eccentricity is calculated as the distance between the applied load and support location.  Hope this clarifies the doubt.
Creation date: 9/19/2019 6:26 AM (nandeep)      Updated: 9/19/2019 3:57 PM (nandeep)
Files   
20190912 Pier 1 - modified.mcb
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20190912 Pier 1 - modified.zip
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Beam Torsion.xlsx
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