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Considering inclined resolved flexural force components in shear design

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WJA

Structural
May 9, 2016
12
AASHTO LRFD (9th ed) Art. 5.7.2 includes the following text:
"The component of inclined flexural compression or tension, in the direction of the applied shear, in variable depth members shall be considered when determining the factored shear force where its effect is detrimental (increase in shear load) but may be considered if its effect is beneficial (decrease in shear load). "

I'm pretty sure I know how to implement this, but I would like to be 100% sure, as it's having quite a large effect on the shear force in my structure. Can anyone point me towards an example showing how the inclined component of flexure is considered in shear?
 
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If the taper is such that compression side is inclined: resolve compression "C" into its force components (inclined compression "N", horizontal compression "C = Tension / cosine(angle)" and "Q_inclined = vertical shear from inclined compression") and calculate
Q_total = Q + Q_inclined

where "N = normal force", so "sin(angle) = Q_inclined/N ---> Q_inclined = N*sin(angle)". The angle is the inclination of the taper on the compressed side.

I found this formula by googling "shear force tapered RC beam" and opening the figure related to the article "Shear performance analysis of a tapered beam with trapezoidally corrugated steel webs considering the Resal effect" on the first page of results. If the compressed side is angled "in the other direction" (e.g., simply supported beam with taper increasing the height of the compressed top face towards the midspan), the effect would be beneficial (reduce shear).
 
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