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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 = 0.86 OK  
Seismic Design         Tension =   OK  
          Shear =   OK  

Design Code Reference                  
Welded stud design based on                 Code Abbreviation
CSA A23.3-14 Design of Concrete Structures Annex D CSA A23.3-14
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]         CSA A23.3-14
      Stud is ductile steel element       D.2
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    
                  CSA A23.3-14
To be considered effective for resisting anchor tension, vertical reinforcing bars shall be located Figure D.10
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] single rebar area As = 509.0 [mm2]  
Ver. rebar top anchorage option        
                  CSA A23.3-14
To be considered effective for resisting anchor shear, hor. reinft shall be located Figure D.17B
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] 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 =          
                  CSA A23.3-14
Provide built-up grout pad ?   =           D.7.1.3
                  CSA A23.3-14
Seismic design IEFaSa(0.2) ≥0.35   =           D.4.3.3
Welded stud load E <= 0.2U Tensile =   Shear =   D.4.3.5.1 & D.4.3.6.1
Welded stud satisfies opion Tensile = Shear = D.4.3.5.3 & D.4.3.6.3
                   
Strength resistance factors                 CSA A23.3-14
Concrete fc = 0.65           8.4.2
Steel anchor and reinforcing bar fs = 0.85   Rar = 0.85   8.4.3 a)  D.6.2.9   D.7.2.9
Anchor rod - ductile steel Rt,s = 0.80   Rv,s = 0.75   D.5.3 a)
Concrete - condition A Rt,c = 1.15   Rv,c = 1.15   D.5.3 c)

CONCLUSION
                 
Anchor Rod Embedment, Spacing and Edge Distance       OK CSA A23.3-14
Min Rquired Anchor Reinft. Development Length ratio = 0.86 OK 12.5.1
Overall ratio = 0.86 OK  
Tension          
Anchor Rod Tensile Resistance ratio = 0.26 OK  
Anchor Reinft Tensile Breakout Resistance ratio = 0.19 OK  
Anchor Pullout Resistance ratio = 0.31 OK  
Side Blowout Resistance ratio = 0.30 OK  
Shear          
Anchor Rod Shear Resistance ratio = 0.34 OK  
Anchor Reinft Shear Breakout Resistance          
      Strut Bearing Strength ratio = 0.55 OK  
      Tie Reinforcement ratio = 0.72 OK  
Conc. Pryout Not Govern When hef >= 12da       OK  
Tension Shear Interaction          
Tension Shear Interaction ratio = 0.86 OK  
           
Seismic Design         CSA A23.3-14
Tension Applicable       OK D.4.3.5
Seismic IEFaSa(0.2)>=0.35 and E>0.2U , Option D is selected to satisfy additional seismic requirements as per D.4.3.5.3    
                   
Shear Applicable       OK D.4.3.6
Seismic IEFaSa(0.2)>=0.35 and E>0.2U , Option C is selected to satisfy additional seismic requirements as per D.4.3.6.3    

Assumptions CSA A23.3-14
1. Concrete is cracked D.6.2.6, D.6.3.6, D.7.2.7
2. Condition A - supplementary reinforcement is provided D.5.3 c)
3. Anchors shall be designed for factored load combinations specified in CSA A23.3-14 clause 8 D.4.2
4. Anchor reinft strength is used to replace concrete tension / shear breakout strength as per D.6.2.9 & D.7.2.9
    CSA A23.3-14 Annex D clause D.6.2.9 and D.7.2.9  
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 where Rd>2.5 shall meet requirements specified in D.4.3.8 D.4.3.8

CACULATION                  
Anchor Rod Tensile Resistance                 CSA A23.3-14
  Nsar = fs nt Ase futa Rt,s = 347.6 [kN] D.6.1.2  Eq D.2
  ratio = 0.26 > Nu OK  
               
Anchor Reinft Tensile Breakout Resistance       CSA A23.3-14
Min required full yield tension ldh ldh = 180 degree hook case = [mm] 12.5.2, 12.5.3 b)
Actual development lenngth la = hef - c (50mm) - dar x tan35 = [mm]  
        > 203 OK 12.5.1
             
              CSA A23.3-14
Anchor reinft breakout resistance Nnr = fsx fy-vx nv Asx Rarx (la / ld , if la < ld) = 465.3 [kN] D.4.3.5.5, D.6.2.9, 12.2.5
  ratio = 0.19 > Nu OK  
               
Anchor Pullout Resistance             CSA A23.3-14
Single bolt pullout resistance Npr = 8 Abrg fc fc' Rt,c = 94.3 [kN] D.6.3.4  Eq D.16
  Ncpr =  nt Ψc,p Npr = 377.1 [kN] D.6.3.1  Eq D.15
  Ψc,p = 1 for cracked conc       D.6.3.6
  Rt,c = 1.00 pullout strength is always Condition B D.5.3 c)
Seismic design strength reduction   = x 0.75 applicable = 282.8 [kN] D.4.3.5.4
  ratio = 0.31 > Nu OK  
               
Side Blowout Resistance              
Failure Along Pedestal Width Edge             CSA A23.3-14
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]  
  c = min ( c1, c3 ) = 125 [mm]  
  s = s2 = 150 [mm]  
Check if side blowout applicable hef = 355 [mm]         CSA A23.3-14
    > 2.5c side bowout is applicable D.6.4.1
Single anchor SB resistance Nsbr = = 167.3 [kN] D.6.4.1  Eq D.18
Multiple anchors side blowout              
      work as group Nsbgrw = (1+s/ 6c) Nsbr = [kN] D.6.4.2  Eq D.19
Seismic design strength reduction   = x 0.75 applicable = 150.6 [kN] D.4.3.5.4
  ratio = 0.30 > Nbuw OK  
               
Failure Along Pedestal Depth Edge             CSA A23.3-14
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]  
  c = min ( c2, c4 ) = 125 [mm]  
  s = s1 = 150 [mm]  
Check if side blowout applicable hef = 355 [mm]         CSA A23.3-14
    > 2.5c side bowout is applicable D.6.4.1
Single anchor SB resistance Nsbr = = 167.3 [kN] D.6.4.1  Eq D.18
Multiple anchors side blowout              
      work as group Nsbgrd = (1+s/ 6c) x Nsbr = [kN] D.6.4.2  Eq D.19
Seismic design strength reduction   = x 0.75 applicable = 150.6 [kN] D.4.3.5.4
  ratio = 0.30 > Nbud OK  
               
Group side blowout resistance Nsbgr = = 301.2 [kN]  
               
Govern Tensile Resistance Nr = min ( Nsar, Nnr, Ncpr, Nsbgr ) 282.8 [kN]  
               
Anchor Rod Shear Resistance             CSA A23.3-14
  Vsar = fs ns Ase futa Rv,s = 325.9 [kN] D.7.1.2 a)  Eq D.30
Reduction due to built-up grout pad   = x 1.0 , not applicable = 325.9 [kN] D.7.1.3
  ratio = 0.34 > 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.7.2.2 a)
    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 CSA A23.3-14  Eq D.17 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    
              CSA A23.3-14
Pull out resistance at hook Th = fc 0.9 fc' eh da Rt,c = 15.2 [kN] D.6.3.5  Eq D.17
  eh = 4.5 db = 57 [mm]  
               
Single tie bar tension resistance Tr = fs x fy-h x As x Rar = 38.6 [kN] D.7.2.9  Eq D.43
               
Total tie bar tension resistance Vnr = 1.0 x n x Tr = 154.3 [kN] D.4.3.6.4 & D.7.2.9
  ratio = 0.72 > 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 ( Vsar , Vnr ) = 154.3 [kN]  
               
Tension Shear Interaction             CSA A23.3-14
Check if Nu >0.2f Nn and Vu >0.2f Vn = Yes       D.8.2 & D.8.3
      Nu / f Nn + Vu / f Vn = 1.04   D.8.4  Eq D.46
  ratio = 0.86 < 1.2 OK  
               
Seismic Design              
Tension     Applicable     OK  
Option D is selected. CSA A23.3-14
User has to ensure that the tensile load Nu user input above includes the seismic load E, with E increased
by multiplying overstrength factor RdRo=1.3 or as specified in NBCC clause 4.1.8.18
D.4.3.5.3 d)
                   
Seismic IEFaSa(0.2)>=0.35 and E>0.2U , Option D is selected to satisfy additional seismic requirements as per D.4.3.5.3    
               
Shear     Applicable     OK  
Option C is selected.             CSA A23.3-14
User has to ensure that the shear load Vu user input above includes the seismic load E, with E increased
by multiplying overstrength factor RdRo=1.3 or as specified in NBCC clause 4.1.8.18
D.4.3.6.3 c)
               
Seismic IEFaSa(0.2)>=0.35 and E>0.2U , Option C is selected to satisfy additional seismic requirements as per D.4.3.6.3    
                   

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