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STUD ANCHOR DESIGN Combined Tension and Shear

Result Summary                  
Anchor Rod Embedment, Spacing and Edge Distance       OK  
Min Rquired Anchor Reinft. Development Length ratio = 0.86 OK  
Overall         ratio = 0.83 OK  
Seismic Design         Tension =   OK  
          Shear =   OK  

Design Code Reference                  
Welded stud design based on                 Code Abbreviation
ACI 318M-11 Building Code Requirements for Structural Concrete and Commentary Appendix D ACI 318M-11
PIP STE05121 Anchor Bolt Design Guide-2006 PIP STE05121
                Code Reference
Welded Stud Data                    
Factored tensile force Nu = [kN]      
Factored shear force Vu = [kN]      
Concrete strength f'c = [MPa]    
Welded stud material   =          
Stud tensile strength futa = 65.0 [MPa]         ACI 318M-11
      Stud is ductile steel element       D.1
Welded stud diameter da  = [in]   = 19.1 [mm]  
Anchor effective cross section area Ase = 285 [mm2]        
Welded stud head bearing area Abrg = [mm2]        
                PIP STE05121
Welded stud embedment depth hef = [mm] 229   OK   Page A -1 Table 1
Pedestal height ha = [mm] 431   OK    
Pedestal width bc = [mm]          
Pedestal depth dc = [mm]          
                   
                  PIP STE05121
Welded stud edge distance c1 c1 = [mm] 114   OK   Page A -1 Table 1
Welded stud edge distance c2 c2 = [mm] 114   OK    
Welded stud edge distance c3 c3 = [mm] 114   OK    
Welded stud edge distance c4 c4 = [mm] 114   OK    
                  PIP STE05121
Outermost bolt line spacing s1 s1 = [mm] 76   OK   Page A -1 Table 1
Outermost bolt line spacing s2 s2 = [mm] 76   OK    
                  ACI 318M-11
To be considered effective for resisting anchor tension, vertical reinforcing bars shall be located RD.5.2.9
within 0.5hef from the outmost anchor's centerline  
Avg ver. bar center to anchor rod center distance dar = [mm]  
Rebar specification   =        
No of ver. rebar that are effective for resisting anchor tension nv =    
Ver. rebar size No. = 25.4 [mm] dia single rebar area As = 509.0 [mm2]  
Ver. rebar top anchorage option        
                  ACI 318M-11
To be considered effective for resisting anchor shear, hor. reinft shall be located RD.6.2.9
within min( 0.5c1, 0.3c2 ) from the outmost anchor's centerline min (0.5c1, 0.3c2) = 38 [mm]  
           
No of tie leg that are effective to resist anchor shear nleg =    
No of tie layer that are effective to resist anchor shear nlay =    
Hor. tie rebar size No. = 12.7 [mm] dia single rebar area As = 129.0 [mm2]  
For anchor reinft shear breakout strength calc    
                   
Rebar yield strength - ver. rebar fy-v = [MPa]        
Rebar yield strength - hor. rebar fy-h = [MPa]        
Total no of welded stud n =          
No of Welded stud carrying tension nt =          
No of Welded stud carrying shear ns =          
                 
                     
                 
For side-face blowout check use                
No of Welded stud along width edge nbw =          
No of Welded stud along depth edge nbd =          
                  ACI 318M-11
Provide built-up grout pad ?   =           D.6.1.3
                  ACI 318M-11
Seismic design category SDC >= C   =           D.3.3.1
Welded stud load E <= 0.2U Tensile =   Shear =   D.3.3.4.1 & D.3.3.5.1
Welded stud satisfies opion Tensile = Shear = D.3.3.4.3 & D.3.3.5.3
                   
Strength reduction factors                 ACI 318M-11
Anchor reinforcement fs = 0.75           D.5.2.9 & D.6.2.9
Anchor rod - ductile steel ft,s = 0.75   fv,s = 0.65   D.4.3 (a)
Concrete - condition A ft,c = 0.75   fv,c = 0.75   D.4.3 (c)

CONCLUSION
                 
Anchor Rod Embedment, Spacing and Edge Distance       OK ACI 318M-11
Min Rquired Anchor Reinft. Development Length ratio = 0.86 OK 12.5.1
Overall ratio = 0.83 OK  
Tension          
Anchor Rod Tensile Resistance ratio = 0.23 OK  
Anchor Reinft Tensile Breakout Resistance ratio = 0.18 OK  
Anchor Pullout Resistance ratio = 0.29 OK  
Side Blowout Resistance ratio = 0.30 OK  
Shear          
Anchor Rod Shear Resistance ratio = 0.33 OK  
Anchor Reinft Shear Breakout Resistance          
      Strut Bearing Strength ratio = 0.55 OK  
      Tie Reinforcement ratio = 0.69 OK  
Conc. Pryout Not Govern When hef >= 12da       OK  
Tension Shear Interaction          
Tension Shear Interaction ratio = 0.83 OK  
           
Seismic Design         ACI 318M-11
Tension Applicable       OK D.3.3.4
Seismic SDC>=C and E>0.2U , Option D is selected to satisfy additional seismic requirements as per D.3.3.4.3    
                   
Shear Applicable       OK D.3.3.5
Seismic SDC>=C and E>0.2U , Option C is selected to satisfy additional seismic requirements as per D.3.3.5.3    

Assumptions ACI 318M-11
1. Concrete is cracked D.5.2.6, D5.3.6, D.6.2.7
2. Condition A - supplementary reinforcement is provided D.4.3 (c)
3. Load combinations shall be per ACI 318M-11 9.2 D.4.3
4. Anchor reinft strength is used to replace concrete tension / shear breakout strength as per D.5.2.9 & D.6.2.9
    ACI 318M-11 Appendix D clause D.5.2.9 and D.6.2.9  
5. For tie reinft, only the top most 2 or 3 layers of ties (50mm from TOC and 2x75mm after)
    are effective
 
6. Strut-and-Tie model is used to anlyze the shear transfer and to design the required tie reinft  
7. Anchor reinft used in structures with SDC>=C shall meet requirements specified in D.3.3.7 D.3.3.7

CACULATION                  
Anchor Rod Tensile Resistance                 ACI 318M-11
  f t,s Nsa = f t,s nt Ase futa = 383.4 [kN] D.5.1.2 (D-2)
  ratio = 0.23 > Nu OK  
               
Anchor Reinft Tensile Breakout Resistance       ACI 318M-11
Min required full yield tension ldh ldh = 180 degree hook case = [mm] 12.5.2, 12.5.3(a)
Actual development lenngth la = hef - c (50mm) - dar x tan35 = [mm]  
        > 203 OK 12.5.1
             
              ACI 318M-11
Anchor reinft breakout resistance fs Nn = fs x fy-v x nv x As x (la / ld , if la < ld) = 503.1 [kN] D.3.3.4.5, D.5.2.9, 12.2.5
  ratio = 0.18 > Nu OK  
               
Anchor Pullout Resistance             ACI 318M-11
Single bolt pullout resistance N p = 8 Abrg fc' = 145.0 [kN] D.5.3.4 (D-14)
  ft,c Npn = f t,c nt Ψc,p Np = 406.1 [kN] D.5.3.1 (D-13)
  Ψc,p = 1 for cracked conc       D.5.3.6
  f t,c = 0.70 pullout strength is always Condition B D.4.3(c)
Seismic design strength reduction   = x 0.75 applicable = 304.6 [kN] D.3.3.4.4
  ratio = 0.29 > Nu OK  
               
Side Blowout Resistance              
Failure Along Pedestal Width Edge             ACI 318M-11
Tensile load carried by anchors close to edge which may cause side-face blowout        
along pedestal width edge Nbuw = Nu x nbw / nt = 44.5 [kN] RD.5.4.2
  c = min ( c1, c3 ) = 125 [mm]  
  s = s2 = 150 [mm]  
Check if side blowout applicable hef = 355 [mm]         ACI 318M-11
    > 2.5c side bowout is applicable D.5.4.1
Single anchor SB resistance ft,c Nsb = = 164.1 [kN] D.5.4.1 (D-16)
Multiple anchors side blowout              
      work as group ftcNsbgw = (1+s/ 6c) x ft,c Nsb = [kN] D.5.4.2 (D-17)
Seismic design strength reduction   = x 0.75 applicable = 147.7 [kN] D.3.3.4.4
  ratio = 0.30 > Nbuw OK  
               
Failure Along Pedestal Depth Edge             ACI 318M-11
Tensile load carried by anchors close to edge which may cause side-face blowout        
along pedestal depth edge Nbud = Nu x nbd / nt = 44.5 [kN] RD.5.4.2
  c = min ( c2, c4 ) = 125 [mm]  
  s = s1 = 150 [mm]  
Check if side blowout applicable hef = 355 [mm]         ACI 318M-11
    > 2.5c side bowout is applicable D.5.4.1
Single anchor SB resistance ft,c Nsb = = 164.1 [kN] D.5.4.1 (D-16)
Multiple anchors side blowout              
      work as group ftcNsbgd = (1+s/ 6c) x ft,c Nsb = [kN] D.5.4.2 (D-17)
Seismic design strength reduction   = x 0.75 applicable = 147.7 [kN] D.3.3.4.4
  ratio = 0.30 > Nbud OK  
               
Group side blowout resistance ftc Nsbg = = 295.4 [kN]  
               
Govern Tensile Resistance Nr = min ( f Nsa, f Nn, f Npn, f Nsbg ) 295.4 [kN]  
               
Anchor Rod Shear Resistance             ACI 318M-11
  f v,sVsa = f v,s ns Ase futa = 332.3 [kN] D.6.1.2 (a) (D-28)
Reduction due to built-up grout pad   = x 1.0 , not applicable = 332.3 [kN] D.6.1.3
  ratio = 0.33 > Vu OK  
               
Anchor Reinft Shear Breakout Resistance       ACI 318M-11
Strut-and-Tie model is used to anlyze the shear transfer and to design the required tie reinft  
STM strength reduction factor fst = 0.75       9.3.2.6
               
        
               
Strut-and-Tie model geometry dv = 55 [mm] dh = 55 [mm]  
  θ = 45    dt = 78 [mm]  
Strut compression force Cs = 0.5 Vu / sinθ = 78.6 [kN]  
               
Strut Bearing Strength             ACI 318M-11
Strut compressive strength fce = 0.85 f'c = 30.4 [MPa] A.3.2 (A-3)
               
* Bearing of Welded stud              
    Anchor bearing length le = min( 8da , hef ) = 152 [mm] D.6.2.2
    Anchor bearing area Abrg  = le x da = 2903 [mm2]  
    Anchor bearing resistance  Cr = ns x fst x fce x Abrg = 265.0 [kN]  
        > Vu OK  
* Bearing of ver reinft bar              
   Ver bar bearing area Abrg  = (le +1.5 x dt - da/2 -db/2) x db = 6270 [mm2]  
   Ver bar bearing resistance  Cr = fst x fce x Abrg = 143.1 [kN]  
   ratio = 0.55 > Cs OK  
               
Tie Reinforcement              
* For tie reinft, only the top most 2 or 3 layers of ties (50mm from TOC and 2x75mm after) are effective
* For enclosed tie, at hook location the tie cannot develop full yield strength fy . Use the pullout resistance in
    tension of a single hooked bolt as per ACI 318M-11 Eq. (D-15) as the max force can be developed at hook Th
* Assume 100% of hor. tie bars can develop full yield strength
 
Total number of hor tie bar  n = nleg (leg) x nlay (layer) = 4    
              ACI 318M-11
Pull out resistance at hook Th = ft,c 0.9 fc' eh da = 17.5 [kN] D.5.3.5 (D-15)
  eh = 4.5 db = 57 [mm]  
               
Single tie bar tension resistance Tr = fs x fy-h x As = 40.1 [kN]  
               
Total tie bar tension resistance fsVn = 1.0 x n x Tr = 160.2 [kN] D.3.3.5.4 & D.6.2.9
  ratio = 0.69 > Vu OK  
               
Conc. Pryout Shear Resistance              
The pryout failure is only critical for short and stiff anchors. It is reasonable to assume that for general
cast-in place headed anchors with hef > = 12da , the pryout failure will not govern
               
  12da = 229 [mm] hef = 355 [mm]  
        > 12da OK  
               
Govern Shear Resistance Vr = min ( fv,sVsa , fsVn ) = 160.2 [kN]  
               
Tension Shear Interaction             ACI 318M-11
Check if Nu >0.2f Nn and Vu >0.2f Vn = Yes       D.7.1 & D.7.2
      Nu / f Nn + Vu / f Vn = 1.00   D.7.3 (D-42)
  ratio = 0.83 < 1.2 OK  
               
Seismic Design              
Tension     Applicable     OK  
Option D is selected. ACI 318M-11
User has to ensure that the tensile load Nu user input above includes the seismic load E, with E increased
by multiplying overstrength factor Ωo
D.3.3.4.3(d)
                   
Seismic SDC>=C and E>0.2U , Option D is selected to satisfy additional seismic requirements as per D.3.3.4.3    
               
Shear     Applicable     OK  
Option C is selected.             ACI 318M-11
User has to ensure that the shear load Vu user input above includes the seismic load E, with E increased
by multiplying overstrength factor Ωo
D.3.3.5.3(c)
               
Seismic SDC>=C and E>0.2U , Option C is selected to satisfy additional seismic requirements as per D.3.3.5.3    
                   

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