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Re: shear design

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Here's my "proof" of the design for shear-friction reinforcement at
non-keyed 
construction joints: 
 
1. I concur with three general statements made in ACI 318 R11.7.7. which 
suggest the following: i) where there is direct tension across a joint, 
reinforcement must be provided to resist the tension in addition to the 
shear-friction reinforcement; ii) where there is direct compression across a 
joint, the shear-friction reinforcement may be reduced accordingly; iii)
when 
considering flexure only on a joint, the tension and compression are in 
equilibrium, i.e. T=C. 
 
2. For shear alone, Av = V/uFy (I will leave "phi" out of the formulas to 
simplify typing).  Av equals the total reinforcement across the joint
(tension 
and compression faces).  
 
3. For tension alone, As = T/Fy.  For tension plus shear, Total As = T/Fy + 
V/uFy.   
 
4. For compression plus shear, V = u(C + AvFy) or Av = V/uFy - C/Fy. 
 
5. Combining shear plus compression plus tension: As = T/Fy + V/uFy - C/Fy.  
If T and C are due to flexure only, T = C, so As = V/uFy = Av.  Thus, 
shear-friction reinforcement is not affected by flexure.