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Re: ACI 318 - Defintion of Vp in Eq. 11-12 (Prestressed Concrete Des...

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In answer to your question about where there is an example calculating Vp - it is done in Lin and Burns. (3rd edition, 1981)

It is quite a simple calculation,  you just calculate the distance over which you have a vertical rise in the tendon,  then take that percentage of the force in the tendon.

For your example,  you have a 63 beam - say that the tendons are flat for about 7 ft in the middle of the beam and the low point is at about 2.5 in.  At a point five feet away from the end of the beam, the tendons might be at 21 in.  You probably have 243 kips in the beam (9 tendons).

You have a horizontal distance of (63-7)/2 - 5 = 23 ft = 276 in.
You have a vertical distance of  21 - 2.5 in.  = 18.5 in.

Vp is 18.5/276 * 243 = 16.3 kips

This calculation is only really applicable if your profile is a simple parabola though. With reverse curvature, as is norminally found in the profiles for continuous members, it is difficult, if not impossible to calculate Vp.   It is more difficult, if not more impossible, to calculate Vp when you have several changes in curvature.  In these instances, Vp can change sign.

Gail Kelley