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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 = 0.87 OK  
Overall         ratio = 0.82 OK  
Seismic Design         Tension =   OK  
          Shear =   OK  

Design Code Reference                  
Welded stud design based on                 Code Abbreviation
ACI 318-14 Building Code Requirements for Structural Concrete and Commentary ACI 318-14
PIP STE05121 Anchor Bolt Design Guide-2006 PIP STE05121
                Code Reference
Welded Stud Data                    
Factored tensile force Nu = [kips]      
Factored shear force Vu = [kips]      
Concrete strength f'c = [ksi]    
Welded stud material   =          
Stud tensile strength futa = 65.0 [ksi]         ACI 318-14
      Stud is ductile steel element       2.3 & 17.3.3 (a)
Welded stud diameter da  = [in]          
Anchor effective cross section area Ase = 0.442 [in2]        
Welded stud head bearing area Abrg = [in2]        
                PIP STE05121
Welded stud embedment depth hef = [in] 9.00   OK   Page A -1 Table 1
Pedestal height ha = [in] 17.00   OK    
Pedestal width bc = [in]          
Pedestal depth dc = [in]          
                   
                  PIP STE05121
Welded stud edge distance c1 c1 = [in] 4.50   OK   Page A -1 Table 1
Welded stud edge distance c2 c2 = [in] 4.50   OK    
Welded stud edge distance c3 c3 = [in] 4.50   OK    
Welded stud edge distance c4 c4 = [in] 4.50   OK    
                  PIP STE05121
Outermost bolt line spacing s1 s1 = [in] 3.00   OK   Page A -1 Table 1
Outermost bolt line spacing s2 s2 = [in] 3.00   OK    
                  ACI 318-14
To be considered effective for resisting anchor tension, vertical reinforcing bars shall be located R17.4.2.9
within 0.5hef from the outmost anchor's centerline  
Avg ver. bar center to anchor rod center distance dar = [in]  
No of ver. rebar that are effective for resisting anchor tension nv =    
Ver. rebar size No. = 1.000 [in] dia single rebar area As = 0.790 [in2]  
Ver. rebar top anchorage option        
                  ACI 318-14
To be considered effective for resisting anchor shear, hor. reinft shall be located R17.5.2.9
within min( 0.5c1, 0.3c2 ) from the outmost anchor's centerline min (0.5c1, 0.3c2) = 1.50 [in]  
           
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. = 0.500 [in] dia single rebar area As = 0.200 [in2]  
For anchor reinft shear breakout strength calc    
                   
Rebar yield strength - ver. rebar fy-v = [ksi]        
Rebar yield strength - hor. rebar fy-h = [ksi]        
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 318-14
Provide built-up grout pad ?   =           17.5.1.3
                  ACI 318-14
Seismic design category SDC >= C   =           17.2.3.1
Welded stud load E <= 0.2U Tensile =   Shear =   17.2.3.4.1 & 17.2.3.5.1
Welded stud satisfies opion Tensile = Shear = 17.2.3.4.3 & 17.2.3.5.3
                   
Strength reduction factors                 ACI 318-14
Anchor reinforcement fs = 0.75           17.4.2.9 & 17.5.2.9
Anchor rod - ductile steel ft,s = 0.75   fv,s = 0.65   17.3.3 (a)
Concrete - condition A ft,c = 0.75   fv,c = 0.75   17.3.3 (c)

CONCLUSION
                 
Anchor Rod Embedment, Spacing and Edge Distance       OK ACI 318-14
Min Rquired Anchor Reinft. Development Length ratio = 0.87 OK 25.4.3.1
Overall ratio = 0.82 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 = 0.29 OK  
Shear          
Anchor Rod Shear Resistance ratio = 0.33 OK  
Anchor Reinft Shear Breakout Resistance          
      Strut Bearing Strength ratio = 0.54 OK  
      Tie Reinforcement ratio = 0.69 OK  
Conc. Pryout Not Govern When hef >= 12da       OK  
Tension Shear Interaction          
Tension Shear Interaction ratio = 0.82 OK  
           
Seismic Design         ACI 318-14
Tension Applicable       OK 17.2.3.4
Seismic SDC>=C and E>0.2U , Option D is selected to satisfy additional seismic requirements as per 17.2.3.4.3    
                   
Shear Applicable       OK 17.2.3.5
Seismic SDC>=C and E>0.2U , Option C is selected to satisfy additional seismic requirements as per 17.2.3.5.3    

Assumptions ACI 318-14
1. Concrete is cracked 17.4.2.6, 17.4.3.6, 17.5.2.7
2. Condition A - supplementary reinforcement is provided 17.3.3 (c)
3. Load combinations shall be per ACI 318-14 5.3.1 17.3.3
4. Anchor reinft strength is used to replace concrete tension / shear breakout strength as per 17.4.2.9 & 17.5.2.9
    ACI 318-14 clause 17.4.2.9 and 17.5.2.9  
5. For tie reinft, only the top most 2 or 3 layers of ties (2" from TOC and 2x3" 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 17.2.3.7 17.2.3.7

CACULATION                  
Anchor Rod Tensile Resistance                 ACI 318-14
  f t,s Nsa = f t,s nt Ase futa = 86.19 [kips] 17.4.1.2 Eq 17.4.1.2
  ratio = 0.23 > Nu OK  
               
Anchor Reinft Tensile Breakout Resistance       ACI 318-14
Min required full yield tension ldh ldh = 180 degree hook case = [in] 25.4.3.1, 25.4.3.2
Actual development lenngth la = hef - c (2 in) - dar x tan35 = [in]  
        > 8.00 OK 25.4.3.1
             
              ACI 318-14
Anchor reinft breakout resistance fs Nn = fs x fy-v x nv x As x (la / ld , if la < ld) = 112.30 [kips] 17.2.3.4.5, 17.4.2.9, 25.4.10.1
  ratio = 0.18 > Nu OK  
               
Anchor Pullout Resistance             ACI 318-14
Single bolt pullout resistance N p = 8 Abrg fc' = 32.66 [kips] 17.4.3.4 Eq 17.4.3.4
  ft,c Npn = f t,c nt Ψc,p Np = 91.44 [kips] 17.4.3.1 Eq 17.4.3.1
  Ψc,p = 1 for cracked conc       17.4.3.6
  f t,c = 0.70 pullout strength is always Condition B 17.3.3(c)
Seismic design strength reduction   = x 0.75 applicable = 68.58 [kips] 17.2.3.4.4
  ratio = 0.29 > Nu OK  
               
Side Blowout Resistance              
Failure Along Pedestal Width Edge             ACI 318-14
Tensile load carried by anchors close to edge which may cause side-face blowout        
along pedestal width edge Nbuw = Nu x nbw / nt = 10.00 [kips] R17.4.4.2
  c = min ( c1, c3 ) = 5.00 [in]  
  s = s2 = 6.00 [in]  
Check if side blowout applicable hef = 14.00 [in]         ACI 318-14
    > 2.5c side bowout is applicable 17.4.4.1
Single anchor SB resistance ft,c Nsb = = 38.33 [kips] 17.4.4.1 Eq 17.4.4.1
Multiple anchors side blowout              
      work as group ftcNsbgw = (1+s/ 6c) x ft,c Nsb = [kips] 17.4.4.2 Eq 17.4.4.2
Seismic design strength reduction   = x 0.75 applicable = 34.50 [kips] 17.2.3.4.4
  ratio = 0.29 > Nbuw OK  
               
Failure Along Pedestal Depth Edge             ACI 318-14
Tensile load carried by anchors close to edge which may cause side-face blowout        
along pedestal depth edge Nbud = Nu x nbd / nt = 10.00 [kips] R17.4.4.2
  c = min ( c2, c4 ) = 5.00 [in]  
  s = s1 = 6.00 [in]  
Check if side blowout applicable hef = 14.00 [in]         ACI 318-14
    > 2.5c side bowout is applicable 17.4.4.1
Single anchor SB resistance ft,c Nsb = = 38.33 [kips] 17.4.4.1 Eq 17.4.4.1
Multiple anchors side blowout              
      work as group ftcNsbgd = (1+s/ 6c) x ft,c Nsb = [kips] 17.4.4.2 Eq 17.4.4.2
Seismic design strength reduction   = x 0.75 applicable = 34.50 [kips] 17.2.3.4.4
  ratio = 0.29 > Nbud OK  
               
Group side blowout resistance ftc Nsbg = = 69.00 [kips]  
               
Govern Tensile Resistance Nr = min ( f Nsa, f Nn, f Npn, f Nsbg ) 68.58 [kips]  
               
Anchor Rod Shear Resistance             ACI 318-14
  f v,sVsa = f v,s ns Ase futa = 74.70 [kips] 17.5.1.2 Eq 17.5.1.2a
Reduction due to built-up grout pad   = x 1.0 , not applicable = 74.70 [kips] 17.5.1.3
  ratio = 0.33 > Vu OK  
               
Anchor Reinft Shear Breakout Resistance       ACI 318-14
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       Table 21.2.1 (g)
               
        
               
Strut-and-Tie model geometry dv = 2.250 [in] dh = 2.250 [in]  
  θ = 45    dt = 3.182 [in]  
Strut compression force Cs = 0.5 Vu / sinθ = 17.68 [kips]  
               
Strut Bearing Strength             ACI 318-14
Strut compressive strength fce = 0.85 f'c = 4.4 [ksi] 23.4.3
               
* Bearing of Welded stud              
    Anchor bearing length le = min( 8da , hef ) = 6.00 [in] 17.5.2.2
    Anchor bearing area Abrg  = le x da = 4.50 [in2]  
    Anchor bearing resistance  Cr = ns x fst x fce x Abrg = 59.67 [kips]  
        > Vu OK  
* Bearing of ver reinft bar              
   Ver bar bearing area Abrg  = (le +1.5 x dt - da/2 -db/2) x db = 9.90 [in2]  
   Ver bar bearing resistance  Cr = fst x fce x Abrg = 32.81 [kips]  
   ratio = 0.54 > Cs OK  
               
Tie Reinforcement              
* For tie reinft, only the top most 2 or 3 layers of ties (2" from TOC and 2x3" 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 318-14 Eq 17.4.3.5 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 318-14
Pull out resistance at hook Th = ft,c 0.9 fc' eh da = 3.95 [kips] 17.4.3.5 Eq 17.4.3.5
  eh = 4.5 db = 2.250 [in]  
               
Single tie bar tension resistance Tr = fs x fy-h x As = 9.00 [kips]  
               
Total tie bar tension resistance fsVn = 1.0 x n x Tr = 36.00 [kips] 17.2.3.5.4 & 17.5.2.9
  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 = 9.00 [in] hef = 14.00 [in]  
        > 12da OK  
               
Govern Shear Resistance Vr = min ( fv,sVsa , fsVn ) = 36.00 [kips]  
               
Tension Shear Interaction             ACI 318-14
Check if Nu >0.2f Nn and Vu >0.2f Vn = Yes       17.6.1 & 17.6.2
      Nu / f Nn + Vu / f Vn = 0.99   17.6.3 Eq 17.6.3
  ratio = 0.82 < 1.2 OK  
               
Seismic Design              
Tension     Applicable     OK  
Option D is selected. ACI 318-14
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
17.2.3.4.3(d)
                   
Seismic SDC>=C and E>0.2U , Option D is selected to satisfy additional seismic requirements as per 17.2.3.4.3    
               
Shear     Applicable     OK  
Option C is selected.             ACI 318-14
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
17.2.3.5.3(c)
               
Seismic SDC>=C and E>0.2U , Option C is selected to satisfy additional seismic requirements as per 17.2.3.5.3    
                   

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