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Anchor bolt design

This document provides details of the design of a headed concrete anchor and end plate connection supporting a reinforced concrete beam. Key details include: - Supported member is a hopper applying 5000kg vertical force - Anchor bolt diameter is 20mm - There are 4 anchors in a 2x2 configuration spaced 50mm apart - Concrete strength is 40MPa - Checks are performed to ensure the connection has sufficient capacity for the applied tension and shear loads considering factors like concrete breakout strength, steel strength, pryout strength, etc. with all checks indicating the design is safe.

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Checked by DESIGN OF HEADED CONCRETE ANCHOR & END PLATE SUPPORTING MEMBER RC BEAM D1 = mm ha = mm B1 = mm SUPPORTED MEMBER HOPPER SUPPORTED BEAM END FORCES Factored Compressive force C = kN Tensile force T = kN Vertical force = kN (~5000kg*9.81/1000) Horizontal shear force = kN Moment = kNm CONNECTION DETAILS Bolt details Diameter of anchor do = Diameter of Nut H = Effective cross sectional area of one anchor Ase = Nr of anchor column nc = Nr of anchor rows nr = Nr of bolts n = Spacing of anchor rows (pitch) p = Spacing of anchor columns (gauge) g = Sum of square of 'r' for the bolt group e r 2 = r = Effective anchor embedment depth hef = Eccentricity & Edge distance Horizontal Edge distance for nth column of bolts ca2 = Horizontal Edge distance for 1st column of bolts ca4 = Vertical Edge distance for nth row of bolts ca1 = Vertical Edge distance for 1st row of bolts ca3 = Edge distance bt. anchors and end plt. e' = Eccentricity for vertical shear e = Eccentricity of normal force on group of anchors eN' = (The distance between the resultant tension load on a group of anchors in tension and the centroid of the group of anchors in tension) Eccentricity of shear force on group of anchors, eV' = (The distance between the resultant shear load on a group of anchors in shear and the centroid of the group of anchors in shear) 0.0 1300.0 mm Connection id 150.0 mm 32500.0 500.0 30.0 mm 90.14 2 mm2 150.0 mm 0.0 20.0 mm 0.0 50.0 314.2 mm 2 mm 1325.0 mm 100.0 1055.0 mm 0.0 2000.0 Designed by Date 20-Sep-14 100.0 mm 2 5000.0 4 0.0 50.0 mm 0.0 mm SUBJECT mm 95.0 mm ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 1 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Depth supported member/fin plate Ds = mm Thickness of fin plate/ supported member wed tf = mm Distance between tension bolts to compression edge D = mm mm (ca3) Design strength reduction factor f = mm (ca1) mm mm (ca2 ) (ca4 ) Plate details Depth of end plate Dp = Width of end plate Bp = Thickness of end plate tp = Material strength & grade Grade of bolt = Tensile Strength of bolt futa = Characteristic strength of Concrete (cylinder) fc ' = Yield strength of plate fyp = 1325 12 250 250 2000 560.0 95 1055 N/mm 2 N/mm2 8.8 grade 200.0 mm 20.0 mm 250.0 mm 40.0 N/mm 2 0.75 265.0 2 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 CONNECTION CAPACITY CHECKS SUMMARY TENSION LOAD Remarks 2.5ca1>hef, Blow-out strength check is not required SHEAR LOAD INTERACTION OF TENSILE AND SHEAR LOADING Interaction for single anchor (Nua/fNn+Vua/fVn) = <= 1.2 SAFE Interaction for group of anchors (Nuag/fNng+Vuag/fVng) = <= 1.2 SAFE PLATE End plate thickness required = < tp SAFE 0.096 Concrete pryout strength of group of anchors 157.16 50.0 0.318 SAFE Concrete pryout strength of an anchor 128.58 12.50 0.097 SAFE Concrete breakout strength for group of anchors 253.80 50.00 0.197 SAFE 0.050 25.00 78.6 SAFE SAFE 0.095 SAFE Concrete breakout strength of an anchor 251.93 12.50 SAFE Steel strength for group of anchors 527.79 50.00 0.095 SAFE Steel strength of an anchor 131.95 Checks Design values Utilization Ratio Capacity(kN) Load(kN) Status Concrete side-face blowout strength of anchor Pullout strength of an anchor Concrete breakout strength of an anchor 0.08 Concrete side-face blowout strength for group of anchor Pullout strength for group of anchors Concrete breakout strength for group of anchors N.A. Steel strength for group of anchors 10.1 N.A. 263.88 0.08 N.A MAXIMUM UTILIZATION RATIO SAFE 10.10 0.16 20.2 12.50 0.58 20.20 10.10 SAFE 0.08 SAFE SAFE 0.26 SAFE 0.25 20.20 10.10 20.2 N.A Steel strength of an anchor Concrete breakout strength for group of anchors near concrete edge 260.59 131.95 SAFE 0.08 Capacity(kN) Load(kN) Status Design values Utilization Ratio Checks 263.89 64.29 131.94 0.32 15.12 20.0 SAFE 3 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 MAXIMUM FORCES IN ANCHORS Shear force Torsion due to horizontal eccentricity in shear Me = V*ev' = Shear force anchor due to moment Vh = Me*r/εr 2 = Vertical shear due to Fm FVm = Fm * cosO O = = Horizontal shear due to Fm FHm = Fm * sin O = Shear force per anchor due to vertical force Vv = 50/4 = Total Shear force per anchor Vua = Shear force for group of anchors Vuag = Tension force Bearing strength of concrete = 0.85fcfc' = Force equilibrium for the design bearing stress T+N = C Considering the moment equilibrium M = T(D-Dp/2)+C(Dp-X/2) 0.85fc'fcbpX(D-X/2)-Fy(D-Dp/2) = M 20.4*200*X(250-X/2)-0*(250-250/2) = 50* 0.1+0*0+0 2.04X^2-1020X+5000 = a = b = c = X1 = -(-1020)+(-1020^2-4*2.04*5000)^0.5/(2*2.04) = X2 = -(-1020)-(-1020^2-4*2.04*5000)^0.5/(2*2.04) = Length of compressive stress block X = mm Compression force resisted by concrete C = kN Tension force transfer to anchors T = kN (Assumed to be transfer to anchors located above the C.G. of end plate) Nos of anchors row effective in tension nrt = (2 ) / 2 = -1020 2.04 5000 0 495.05 4.95 0.0 kN.m kN 12.5 kN 56.3 4.95 20.2 20.2 1.0 12.5 kN 50.0 kN KN 0.00 KN Assuming the shear transfer to anchors as below MPa 20.4 0.00 0.0 4 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Nos of anchors efective for tension nt = 2 * 1 = Tension force on an anchor due to bending T1 = 20.2/ 2 T1 = kN Direct tension force in each anchor T2 = = kN Total tension in each anchor, Nua = T1+T2 = kN Tension force transfer to group of anchors Nuag = = kN STEEL STRENGTH OF ANCHORS As per ACI 318-05 D5.1 Nominal strength of a single anchor in tension Nsa = Ase * futa = 314.16*560/1000 = As per ACI 318-05 D4.4 a(i) f = f Nsa = >Nua SAFE ( ) Nominal strength of group of anchors in tension Nsag = nt * Ase * futa = 2*314.16*560/1000 = f Nsag = > Nuag SAFE ( ) CONCERE BREAKOUT STRENGTH OF ANCHOR Single Anchor min(ca3,1.5hef) mm min((ca1+(nr-1)p), 1.5hef) mm min(ca2, 1.5hef) min((ca4 +(nc-1)g), 1.5hef) mm mm As per ACI 318-05 D5.2 Nominal concrte breakout strength of an Ncb = ANc/ANco * yed,N * yc,N * ycp,N* Nb anchor in tension 225 95 225 2.0 10.1 Nua*nt 20.2 0.75 175.9 0 / 4 0.0 10.1 kN 131.9 kN 10.1 351.9 kN 263.9 kN 20.2 225 CAPACITY AGAINST TENSION LOADING 5 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Basic concrete breakout strength of an anchor Nb = kc sqrt(fc ' ) hef 1.5 in cracked concrete For cast-in anchors kc = Actual anchor embedment depth h1 = ca,min = mm ca,max = mm Max(Cmax/1.5,max spacing/3) h2 = mm Effective anchor embedment depth hef = If 1.5*h1>Cmax = h2 or h1 = Nb = 10* sqrt(40) *150^1.5 Nb = Modification factor for edge effects yed,N = 0.7 + 0.3 (ca,min/1.5hef) for ca,min <1.5hef = for ca,min >1.5hef yed,N = Modification factor to account for cracking yc,N = Modification factor to account for post-install ycp,N = For cast-in anchors anchors Projected concerte failure area of an anchor ANco = 9 hef 2 (not limited by edge distance or spacing) = 9 *150^2 = Projected concerte failure area of an anchor = (225+95) * (225+225) < ANco ( limited by edge distance or spacing) = ANc = Nominal concrte breakout strength of an Ncb = (144000/202500) * 0.83*1.25*1*116.19 anchor in tension = f Ncb = >Nua SAFE ( ) Group of anchors Basic concrete breakout strength of an anchor Nb = kc sqrt(fc ' ) hef 1.5 in cracked concrete For cast-in anchors kc = Actual anchor embedment depth h1 = ca,min = mm ca,max = mm Max(Cmax/1.5,max spacing/3) h2 Effective anchor embedment depth hef = If 1.5*h1>Cmax = h2 or h1 = Nb = 10* sqrt(40) *150^1.5 = 116.2 10.0 150.0 mm 150.0 mm 95 225 0.83 1.25 1.00 202500.0 mm2 116.2 kN 1.0 10.1 144000.0 mm2 144000.0 mm 2 85.7 kN kN 150 mm 150.0 mm 64.3 kN 150.0 mm 150 95 225 10.0 6 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 min(ca3, 1.5hef) mm (nrt-1)p = mm min((ca1+(nr-1)p-(nrt-1)p), 1.5hef) mm min(ca2, 1.5hef) (nc-1)g min(ca4, 1.5hef) mm mm mm Modification factor for eccentrically loaded anchor group yec,N = 1/(1 + (2e'N / 3hef)) Modification factor for edge effects = 0.7 + 0.3 (ca,min/1.5hef) for ca,min <1.5hef = for ca,min >1.5hef yed,N = Modification factor to account for cracking yc,N = Modification factor to account for post-install ycp,N = For cast-in anchors anchors Projected concerte failure area of an anchor ANco = 9 hef 2 (Not limited by edge distance or spacing) = 9 *150^2 = Projected concerte failure area of group of = (95+0+225) * (225+100+225) (Limited by edge distance or spacing) = < nt ANco ANc = ( mm 2 ) Nominal concrte breakout strength for Ncbg = ANc/Anco yec,N* yed,N * yc,N * ycp,N* Nb group of anchors in tension = (176000/202500) * 1*0.83*1.25*1* 116.19 = f Ncbg = > Nuag SAFE ( ) PULLOUT STRENGTH OF ANCHOR As per ACI 318-05 D5.3 Nominal pullout strength of an anchor Npn = yc,P * Np in tension Pullout strength in tension of an Np = Abrg * 8* fc ' headed bolt or headed bolt 225 100 225 95 225 1.00 1.0 78.6 kN 0.83 1.25 1.00 202500.0 mm 2 176000.0 mm2 20.2 176000.0 mm2 405000 104.8 kN 0 7 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Bearing area of the head of bolt or anchor Abrg = pi() * (30^2 - 20^2 )/ 4 bolt = Pullout strength in tension of an Np = 392.7 * 8 * 40 headed bolt or headed bolt = Modification factor to account for cracking yc,P = Single Anchor Nominal pullout strength of an anchor Npn = 1.4* 125.66 = f Npn = >Nua SAFE ( ) Group of anchors Nominal pullout strength of group of anchor Npng = 2 * 175.92 = f Npng = > Nuag SAFE ( ) CONCRETE SIDE-FACE BLOWOUT STRENGTH OF ANCHOR Single anchor As per ACI 318-05 D5.4 Nominal side-face blowout strength of an anchor Nsb = 13 ca1 sqrt(Abrg) sqrt(fc') ca1 = mm Abrg = Perpendicular distance to ca1 ca2 = mm If ca2 < 3ca1, Nsb shall be multiplied by a factor (1+ca2/ca1)/4 (1+ca2/ca1)/4 = Nominal side-face blowout strength of an anchor Nsb = 13 * 95 * sqrt(392.7) * sqrt(40)*1 = Nominal side-face blowout strength of an anchor Nsb = anchor in tension f Nsb = >Nua SAFE ( ) 2.5ca1>hef, Blow-out strength check is not required 392.70 mm2 125.66 kN 1.40 175.92 kN 131.9 kN 10.1 351.8 kN 263.9 kN 20.2 95 1.0 392.70 392.70 mm2 1325.0 154.8 kN N.A. kN N.A. kN 10.1 8 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Group of anchors For multiplie headed anchors Nsbg = (1+s/6ca1) Nsb Spacing of outer anchors along the edge s = Nominal side-face blowout strength of Nsbg = (1+100/(6*95))*154.78 group of anchors in tension Nominal side-face blowout strength of Nsbg = group of anchors in tension 2.5ca1>hef, Blow-out strength check is not required f Nsbg = > Nuag SAFE ( ) STEEL STRENGTH OF ANCHOR As per ACI 318-05 D 6.1 Nominal strength of an anchor in shear Vsa = Ase * futa = 314.16*560/100 = f Vsa = > Vua SAFE ( ) Nominal strength of anchor group in shear Vsag = n * Ase * futa 4*314.16*560/1000 = f Vsag = > Vuag SAFE ( ) Nominal strength of anchor group f Vsag = f* nc * Ase * futa in shear (for no. of columns of anchors) = BREAKOUT STRENGTH OF ANCHOR Single anchor As per ACI 318-05 D 6.2 Nominal breakout strength of an anchor for shear force perpendicular to the edge Vcb = AVc/AVco * yed,V * yc,V * Vb Basic concrete breakout strength of an anchor Vb = 0.6 (le/da) 0.2 sqrt(da)sqrt(fc ' ) ca1 1.5 in cracked concrete le = min.( hef, 8da) = Actual edge distance ca1 = 100.0 mm 175.9 kN 131.9 kN 181.9 kN N.A. kN N.A. kN 12.5 703.7 kN 527.8 kN 50.0 263.9 kN 150.0 mm 1055.0 mm CAPACITY AGAINST VERTICAL SHEAR LOADING 20.2 9 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 min(ha, 1.5ca1) mm min(ca2, 1.5ca1) min((nc-1)g+ca4, 1.5ca1) mm mm ca2max = mm ca2min = mm ha = s = mm Minimum free edge distance ef = Min(ha,ca2min) = Effective anchor edge distance ca1 = if ef< 1.5ca1= max(ca2/1.5,ha/1.5,S/3 or Ca1) = Vb = 0.6 * (150/20)^0.2 * sqrt(20) * sqrt(40) * 1055^1.5 Vb = Modification factor for edge effects yed,V = 0.7 + 0.3 (ca2/1.5ca1) for ca2 <1.5ca1 = for ca2 >1.5ca1 yed,V = Modification factor to account for cracking yc,V = Projected concrete failure area of an anchor AVco = 4.5 ca1 2 (Not limited by corner influence, spacing, or member thickness) = 4.5 *1055 ^ 2 AVco = Projected concrete failure area of an anchor = (1325 + 1582.5) * 500 (Limited by corner influence, spacing, or member thickness) = < Avc0 AVc = Nominal concrete breakout strength of an Vcb = (1453750/5008612.5) * 0.95*1.4*870.14 anchor for shear force = f Vcb = > Vua SAFE ( ) 2000 1325 500 1582.5 500.0 mm 100.0 870.1 kN 1055.0 mm 1325.0 500.0 mm mm2 mm 2 5008612.5 1453750.0 1.0 0.95 1.40 mm 2 335.9 kN 251.9 kN 1453750.0 12.5 10 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Group of anchors min(ha, 1.5ca1) mm min(ca2, 1.5ca1) (nc-1)g min(ca4, 1.5ca1) mm mm mm Basic concrete breakout strength of an anchor Vb = 0.6 (le/do) 0.2 sqrt(d0)sqrt(fc ' ) ca1 1.5 in cracked concrete Where, le = min.( hef, 8d0) = Actual edge distance ca1 = ca2max = ca2min = ha = s = Minimum free edge distance ef = Min(ha,ca2min) = Effective anchor edge distance ca1 = if ef< 1.5ca1= max(ca2/1.5,ha/1.5,S/3 or Ca1) = Vb = 0.6 * (150/20)^0.2 * sqrt(20) * sqrt(40) * 1055^1.5 Vb = Modification factor for eccentrically loaded yec,V = 1/(1 + (2e'V / 3ca1)) anchor group = Modification factor for edge effects yed,V = 0.7 + 0.3 (ca2/1.5ca1) for ca2 <1.5ca1 = for ca2 >1.5ca1 yed,V = ca2,min = mm Modification factor to account for cracking yc,V = Projected concrete failure area of an anchor, AVco = 4.5 ca1 2 (Not limited by corner influence, spacing, or member thickness) = 4.5 *1055 ^ 2 AVco = Projected concrete failure area for groups of AVc = (1325 + 100+ 1582.5) * 500 < nc AVc (Limited by corner influence, spacing, or member thickness) = = mm 2 AVc = 2000 1582.5 500 1325 100 150.0 mm mm 2 1055.0 mm 500.0 mm 870.1 0.95 1.40 1055.0 mm mm 1325 mm 500.0 mm mm2 1503750.0 5008612.5 kN 1.0 1.0 mm 2 10017225 1503750.0 150.0 mm 11 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Nominal concrete breakout strength for Vcbg = AVc/AVco * yec,V* yed,V * yc,V * Vb group of anchors in a single row for shear force = (1503750/5008612.5) * 1*0.95*1.4* 870.14 = f Vcbg = > nc*Vua SAFE ( ) Group of anchors min(ha, 1.5ca1) mm min(ca2, 1.5ca1) (nc-1)g min(ca4, 1.5ca1) mm mm mm Basic concrete breakout strength of an anchor Vb = 0.6 (le/do)0.2 sqrt(d0)sqrt(fc ' ) ca1 1.5 in cracked concrete Where, le = min.( hef, 8d0) = Actual edge distance ca1 = ca2max = ca2min = ha s Effective anchor edge distance ca1 = if ef< 1.5ca1= max(ca2/1.5,ha/1.5,S/3 or Ca1) = Vb = 0.6 * (150/20)^0.2 * sqrt(20) * sqrt(40) * 1205^1.5 Vb = Modification factor for eccentrically loaded yec,V = 1/(1 + (2e'V / 3ca1)) anchor group = Modification factor for edge effects yed,V = 0.7 + 0.3 (ca2/1.5ca1) for ca2 <1.5ca1 = for ca2 >1.5ca1 yed,V = Modification factor to account for cracking yc,V = 1807.5 100 1325 mm 500 347.5 kN 150.0 mm 500.0 260.6 kN 25.0 2000 mm 150.0 kN 1205.0 mm 1.00 1.0 1205.0 mm 1.40 0.92 1325 mm mm 1062.2 12 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Projected concrete failure area of an anchor, AVco = 4.5 ca1 2 (Not limited by corner influence, spacing, or member thickness) = 4.5 *1205 ^ 2 AVco = Projected concrete failure area for groups of = (1325 + 100+ 1807.5) * 500 < n Avco (Limited by corner influence, spacing, or member thickness) = = mm 2 AVc = Nominal concrete breakout strength for Vcbg = AVc/AVco * yec,V* yed,V * yc,V * Vb group of anchors for shear force = (1616250/6534112.5) * 1*0.92*1.4* 1062.16 = f Vcbg = > Vuag SAFE ( ) CONRETE PRYOUT STRENGTH OF ANCHOR Single anchor As per ACI 318-05 D 6.3 Nominal pryout strength of an anchor Vcp = kcp * Ncb kcp = Nominal concrte breakout strength of an anchor Ncb = Nominal pryout strength of an anchor Vcp = 2* 85.72 = f Vcp = > Vua SAFE ( ) Group of anchors Nominal concrte breakout strength for Ncbg = Nominal pryout strength for group of anchor Vcpg = kcp * Ncbg = 2* 104.77 = f Vcpg = > Vuag SAFE ( ) INTERACTION OF TENSILE AND SHEAR FORCES Lowest design strength in tension f Nn = min. ( 131.95, 64.29, 131.94, N.A. ) of an anchor = > Nua SAFE ( ) 338.4 kN 253.80 kN mm 2 mm2 6534112.5 12.5 104.8 kN 50.0 2.0 85.7 kN 209.5 kN 157.2 kN 50.0 171.4 kN 128.6 kN 64.3 kN 10.1 26136450 1616250.0 1616250.0 mm 2 13 / 14
Checked by Connection id Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Lowest design strength in tension f Nng = min. ( 263.89, 78.58, 263.88, N.A. ) of group of anchors = > Nuag SAFE ( ) Lowest design strength in shear f Vn = min. ( 131.95, 251.93, 128.58 ) of an anchor = > Vua SAFE ( ) Lowest design strength in shear f Vng = min. ( 527.79, 253.8, 157.16 ) of group of anchors = > Vuag SAFE ( ) Inetraction check for single anchor Nua Vua = (10.1 / 64.29) + (12.5/ 128.58) f Nn f Vn = <= 1.2 SAFE Inetraction check for group of anchors Nuag Vuag = ((20.2 / 78.58) + (50/ 157.16) f Nng f Vng = <= 1.2 SAFE END PLATE THICKNESS Edge distance = mm Number of bolts in tension side nf = Tension in group of anchors T1 = Nua*nf = kN Moment on plate due to tension Mt = T1*ev = kNm Thickness of end plate required = SQRT(6*M2/(Bp*fyp)) = SQRT((6*2.02*10^6/(200*265)) = mm > SAFE ( ) 20.2 12.5 50.0 100 78.6 kN 128.6 kN 157.2 kN + + 0.58 tp 20.2 0.25 20.0 2.02 15.12 treq2 2 14 / 14

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Anchor bolt design

  • 1.
    Checked by DESIGN OFHEADED CONCRETE ANCHOR & END PLATE SUPPORTING MEMBER RC BEAM D1 = mm ha = mm B1 = mm SUPPORTED MEMBER HOPPER SUPPORTED BEAM END FORCES Factored Compressive force C = kN Tensile force T = kN Vertical force = kN (~5000kg*9.81/1000) Horizontal shear force = kN Moment = kNm CONNECTION DETAILS Bolt details Diameter of anchor do = Diameter of Nut H = Effective cross sectional area of one anchor Ase = Nr of anchor column nc = Nr of anchor rows nr = Nr of bolts n = Spacing of anchor rows (pitch) p = Spacing of anchor columns (gauge) g = Sum of square of 'r' for the bolt group e r 2 = r = Effective anchor embedment depth hef = Eccentricity & Edge distance Horizontal Edge distance for nth column of bolts ca2 = Horizontal Edge distance for 1st column of bolts ca4 = Vertical Edge distance for nth row of bolts ca1 = Vertical Edge distance for 1st row of bolts ca3 = Edge distance bt. anchors and end plt. e' = Eccentricity for vertical shear e = Eccentricity of normal force on group of anchors eN' = (The distance between the resultant tension load on a group of anchors in tension and the centroid of the group of anchors in tension) Eccentricity of shear force on group of anchors, eV' = (The distance between the resultant shear load on a group of anchors in shear and the centroid of the group of anchors in shear) 0.0 1300.0 mm Connection id 150.0 mm 32500.0 500.0 30.0 mm 90.14 2 mm2 150.0 mm 0.0 20.0 mm 0.0 50.0 314.2 mm 2 mm 1325.0 mm 100.0 1055.0 mm 0.0 2000.0 Designed by Date 20-Sep-14 100.0 mm 2 5000.0 4 0.0 50.0 mm 0.0 mm SUBJECT mm 95.0 mm ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 1 / 14
  • 2.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Depth supported member/fin plate Ds = mm Thickness of fin plate/ supported member wed tf = mm Distance between tension bolts to compression edge D = mm mm (ca3) Design strength reduction factor f = mm (ca1) mm mm (ca2 ) (ca4 ) Plate details Depth of end plate Dp = Width of end plate Bp = Thickness of end plate tp = Material strength & grade Grade of bolt = Tensile Strength of bolt futa = Characteristic strength of Concrete (cylinder) fc ' = Yield strength of plate fyp = 1325 12 250 250 2000 560.0 95 1055 N/mm 2 N/mm2 8.8 grade 200.0 mm 20.0 mm 250.0 mm 40.0 N/mm 2 0.75 265.0 2 / 14
  • 3.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 CONNECTION CAPACITY CHECKS SUMMARY TENSION LOAD Remarks 2.5ca1>hef, Blow-out strength check is not required SHEAR LOAD INTERACTION OF TENSILE AND SHEAR LOADING Interaction for single anchor (Nua/fNn+Vua/fVn) = <= 1.2 SAFE Interaction for group of anchors (Nuag/fNng+Vuag/fVng) = <= 1.2 SAFE PLATE End plate thickness required = < tp SAFE 0.096 Concrete pryout strength of group of anchors 157.16 50.0 0.318 SAFE Concrete pryout strength of an anchor 128.58 12.50 0.097 SAFE Concrete breakout strength for group of anchors 253.80 50.00 0.197 SAFE 0.050 25.00 78.6 SAFE SAFE 0.095 SAFE Concrete breakout strength of an anchor 251.93 12.50 SAFE Steel strength for group of anchors 527.79 50.00 0.095 SAFE Steel strength of an anchor 131.95 Checks Design values Utilization Ratio Capacity(kN) Load(kN) Status Concrete side-face blowout strength of anchor Pullout strength of an anchor Concrete breakout strength of an anchor 0.08 Concrete side-face blowout strength for group of anchor Pullout strength for group of anchors Concrete breakout strength for group of anchors N.A. Steel strength for group of anchors 10.1 N.A. 263.88 0.08 N.A MAXIMUM UTILIZATION RATIO SAFE 10.10 0.16 20.2 12.50 0.58 20.20 10.10 SAFE 0.08 SAFE SAFE 0.26 SAFE 0.25 20.20 10.10 20.2 N.A Steel strength of an anchor Concrete breakout strength for group of anchors near concrete edge 260.59 131.95 SAFE 0.08 Capacity(kN) Load(kN) Status Design values Utilization Ratio Checks 263.89 64.29 131.94 0.32 15.12 20.0 SAFE 3 / 14
  • 4.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 MAXIMUM FORCES IN ANCHORS Shear force Torsion due to horizontal eccentricity in shear Me = V*ev' = Shear force anchor due to moment Vh = Me*r/εr 2 = Vertical shear due to Fm FVm = Fm * cosO O = = Horizontal shear due to Fm FHm = Fm * sin O = Shear force per anchor due to vertical force Vv = 50/4 = Total Shear force per anchor Vua = Shear force for group of anchors Vuag = Tension force Bearing strength of concrete = 0.85fcfc' = Force equilibrium for the design bearing stress T+N = C Considering the moment equilibrium M = T(D-Dp/2)+C(Dp-X/2) 0.85fc'fcbpX(D-X/2)-Fy(D-Dp/2) = M 20.4*200*X(250-X/2)-0*(250-250/2) = 50* 0.1+0*0+0 2.04X^2-1020X+5000 = a = b = c = X1 = -(-1020)+(-1020^2-4*2.04*5000)^0.5/(2*2.04) = X2 = -(-1020)-(-1020^2-4*2.04*5000)^0.5/(2*2.04) = Length of compressive stress block X = mm Compression force resisted by concrete C = kN Tension force transfer to anchors T = kN (Assumed to be transfer to anchors located above the C.G. of end plate) Nos of anchors row effective in tension nrt = (2 ) / 2 = -1020 2.04 5000 0 495.05 4.95 0.0 kN.m kN 12.5 kN 56.3 4.95 20.2 20.2 1.0 12.5 kN 50.0 kN KN 0.00 KN Assuming the shear transfer to anchors as below MPa 20.4 0.00 0.0 4 / 14
  • 5.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Nos of anchors efective for tension nt = 2 * 1 = Tension force on an anchor due to bending T1 = 20.2/ 2 T1 = kN Direct tension force in each anchor T2 = = kN Total tension in each anchor, Nua = T1+T2 = kN Tension force transfer to group of anchors Nuag = = kN STEEL STRENGTH OF ANCHORS As per ACI 318-05 D5.1 Nominal strength of a single anchor in tension Nsa = Ase * futa = 314.16*560/1000 = As per ACI 318-05 D4.4 a(i) f = f Nsa = >Nua SAFE ( ) Nominal strength of group of anchors in tension Nsag = nt * Ase * futa = 2*314.16*560/1000 = f Nsag = > Nuag SAFE ( ) CONCERE BREAKOUT STRENGTH OF ANCHOR Single Anchor min(ca3,1.5hef) mm min((ca1+(nr-1)p), 1.5hef) mm min(ca2, 1.5hef) min((ca4 +(nc-1)g), 1.5hef) mm mm As per ACI 318-05 D5.2 Nominal concrte breakout strength of an Ncb = ANc/ANco * yed,N * yc,N * ycp,N* Nb anchor in tension 225 95 225 2.0 10.1 Nua*nt 20.2 0.75 175.9 0 / 4 0.0 10.1 kN 131.9 kN 10.1 351.9 kN 263.9 kN 20.2 225 CAPACITY AGAINST TENSION LOADING 5 / 14
  • 6.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Basic concrete breakout strength of an anchor Nb = kc sqrt(fc ' ) hef 1.5 in cracked concrete For cast-in anchors kc = Actual anchor embedment depth h1 = ca,min = mm ca,max = mm Max(Cmax/1.5,max spacing/3) h2 = mm Effective anchor embedment depth hef = If 1.5*h1>Cmax = h2 or h1 = Nb = 10* sqrt(40) *150^1.5 Nb = Modification factor for edge effects yed,N = 0.7 + 0.3 (ca,min/1.5hef) for ca,min <1.5hef = for ca,min >1.5hef yed,N = Modification factor to account for cracking yc,N = Modification factor to account for post-install ycp,N = For cast-in anchors anchors Projected concerte failure area of an anchor ANco = 9 hef 2 (not limited by edge distance or spacing) = 9 *150^2 = Projected concerte failure area of an anchor = (225+95) * (225+225) < ANco ( limited by edge distance or spacing) = ANc = Nominal concrte breakout strength of an Ncb = (144000/202500) * 0.83*1.25*1*116.19 anchor in tension = f Ncb = >Nua SAFE ( ) Group of anchors Basic concrete breakout strength of an anchor Nb = kc sqrt(fc ' ) hef 1.5 in cracked concrete For cast-in anchors kc = Actual anchor embedment depth h1 = ca,min = mm ca,max = mm Max(Cmax/1.5,max spacing/3) h2 Effective anchor embedment depth hef = If 1.5*h1>Cmax = h2 or h1 = Nb = 10* sqrt(40) *150^1.5 = 116.2 10.0 150.0 mm 150.0 mm 95 225 0.83 1.25 1.00 202500.0 mm2 116.2 kN 1.0 10.1 144000.0 mm2 144000.0 mm 2 85.7 kN kN 150 mm 150.0 mm 64.3 kN 150.0 mm 150 95 225 10.0 6 / 14
  • 7.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 min(ca3, 1.5hef) mm (nrt-1)p = mm min((ca1+(nr-1)p-(nrt-1)p), 1.5hef) mm min(ca2, 1.5hef) (nc-1)g min(ca4, 1.5hef) mm mm mm Modification factor for eccentrically loaded anchor group yec,N = 1/(1 + (2e'N / 3hef)) Modification factor for edge effects = 0.7 + 0.3 (ca,min/1.5hef) for ca,min <1.5hef = for ca,min >1.5hef yed,N = Modification factor to account for cracking yc,N = Modification factor to account for post-install ycp,N = For cast-in anchors anchors Projected concerte failure area of an anchor ANco = 9 hef 2 (Not limited by edge distance or spacing) = 9 *150^2 = Projected concerte failure area of group of = (95+0+225) * (225+100+225) (Limited by edge distance or spacing) = < nt ANco ANc = ( mm 2 ) Nominal concrte breakout strength for Ncbg = ANc/Anco yec,N* yed,N * yc,N * ycp,N* Nb group of anchors in tension = (176000/202500) * 1*0.83*1.25*1* 116.19 = f Ncbg = > Nuag SAFE ( ) PULLOUT STRENGTH OF ANCHOR As per ACI 318-05 D5.3 Nominal pullout strength of an anchor Npn = yc,P * Np in tension Pullout strength in tension of an Np = Abrg * 8* fc ' headed bolt or headed bolt 225 100 225 95 225 1.00 1.0 78.6 kN 0.83 1.25 1.00 202500.0 mm 2 176000.0 mm2 20.2 176000.0 mm2 405000 104.8 kN 0 7 / 14
  • 8.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Bearing area of the head of bolt or anchor Abrg = pi() * (30^2 - 20^2 )/ 4 bolt = Pullout strength in tension of an Np = 392.7 * 8 * 40 headed bolt or headed bolt = Modification factor to account for cracking yc,P = Single Anchor Nominal pullout strength of an anchor Npn = 1.4* 125.66 = f Npn = >Nua SAFE ( ) Group of anchors Nominal pullout strength of group of anchor Npng = 2 * 175.92 = f Npng = > Nuag SAFE ( ) CONCRETE SIDE-FACE BLOWOUT STRENGTH OF ANCHOR Single anchor As per ACI 318-05 D5.4 Nominal side-face blowout strength of an anchor Nsb = 13 ca1 sqrt(Abrg) sqrt(fc') ca1 = mm Abrg = Perpendicular distance to ca1 ca2 = mm If ca2 < 3ca1, Nsb shall be multiplied by a factor (1+ca2/ca1)/4 (1+ca2/ca1)/4 = Nominal side-face blowout strength of an anchor Nsb = 13 * 95 * sqrt(392.7) * sqrt(40)*1 = Nominal side-face blowout strength of an anchor Nsb = anchor in tension f Nsb = >Nua SAFE ( ) 2.5ca1>hef, Blow-out strength check is not required 392.70 mm2 125.66 kN 1.40 175.92 kN 131.9 kN 10.1 351.8 kN 263.9 kN 20.2 95 1.0 392.70 392.70 mm2 1325.0 154.8 kN N.A. kN N.A. kN 10.1 8 / 14
  • 9.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Group of anchors For multiplie headed anchors Nsbg = (1+s/6ca1) Nsb Spacing of outer anchors along the edge s = Nominal side-face blowout strength of Nsbg = (1+100/(6*95))*154.78 group of anchors in tension Nominal side-face blowout strength of Nsbg = group of anchors in tension 2.5ca1>hef, Blow-out strength check is not required f Nsbg = > Nuag SAFE ( ) STEEL STRENGTH OF ANCHOR As per ACI 318-05 D 6.1 Nominal strength of an anchor in shear Vsa = Ase * futa = 314.16*560/100 = f Vsa = > Vua SAFE ( ) Nominal strength of anchor group in shear Vsag = n * Ase * futa 4*314.16*560/1000 = f Vsag = > Vuag SAFE ( ) Nominal strength of anchor group f Vsag = f* nc * Ase * futa in shear (for no. of columns of anchors) = BREAKOUT STRENGTH OF ANCHOR Single anchor As per ACI 318-05 D 6.2 Nominal breakout strength of an anchor for shear force perpendicular to the edge Vcb = AVc/AVco * yed,V * yc,V * Vb Basic concrete breakout strength of an anchor Vb = 0.6 (le/da) 0.2 sqrt(da)sqrt(fc ' ) ca1 1.5 in cracked concrete le = min.( hef, 8da) = Actual edge distance ca1 = 100.0 mm 175.9 kN 131.9 kN 181.9 kN N.A. kN N.A. kN 12.5 703.7 kN 527.8 kN 50.0 263.9 kN 150.0 mm 1055.0 mm CAPACITY AGAINST VERTICAL SHEAR LOADING 20.2 9 / 14
  • 10.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 min(ha, 1.5ca1) mm min(ca2, 1.5ca1) min((nc-1)g+ca4, 1.5ca1) mm mm ca2max = mm ca2min = mm ha = s = mm Minimum free edge distance ef = Min(ha,ca2min) = Effective anchor edge distance ca1 = if ef< 1.5ca1= max(ca2/1.5,ha/1.5,S/3 or Ca1) = Vb = 0.6 * (150/20)^0.2 * sqrt(20) * sqrt(40) * 1055^1.5 Vb = Modification factor for edge effects yed,V = 0.7 + 0.3 (ca2/1.5ca1) for ca2 <1.5ca1 = for ca2 >1.5ca1 yed,V = Modification factor to account for cracking yc,V = Projected concrete failure area of an anchor AVco = 4.5 ca1 2 (Not limited by corner influence, spacing, or member thickness) = 4.5 *1055 ^ 2 AVco = Projected concrete failure area of an anchor = (1325 + 1582.5) * 500 (Limited by corner influence, spacing, or member thickness) = < Avc0 AVc = Nominal concrete breakout strength of an Vcb = (1453750/5008612.5) * 0.95*1.4*870.14 anchor for shear force = f Vcb = > Vua SAFE ( ) 2000 1325 500 1582.5 500.0 mm 100.0 870.1 kN 1055.0 mm 1325.0 500.0 mm mm2 mm 2 5008612.5 1453750.0 1.0 0.95 1.40 mm 2 335.9 kN 251.9 kN 1453750.0 12.5 10 / 14
  • 11.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Group of anchors min(ha, 1.5ca1) mm min(ca2, 1.5ca1) (nc-1)g min(ca4, 1.5ca1) mm mm mm Basic concrete breakout strength of an anchor Vb = 0.6 (le/do) 0.2 sqrt(d0)sqrt(fc ' ) ca1 1.5 in cracked concrete Where, le = min.( hef, 8d0) = Actual edge distance ca1 = ca2max = ca2min = ha = s = Minimum free edge distance ef = Min(ha,ca2min) = Effective anchor edge distance ca1 = if ef< 1.5ca1= max(ca2/1.5,ha/1.5,S/3 or Ca1) = Vb = 0.6 * (150/20)^0.2 * sqrt(20) * sqrt(40) * 1055^1.5 Vb = Modification factor for eccentrically loaded yec,V = 1/(1 + (2e'V / 3ca1)) anchor group = Modification factor for edge effects yed,V = 0.7 + 0.3 (ca2/1.5ca1) for ca2 <1.5ca1 = for ca2 >1.5ca1 yed,V = ca2,min = mm Modification factor to account for cracking yc,V = Projected concrete failure area of an anchor, AVco = 4.5 ca1 2 (Not limited by corner influence, spacing, or member thickness) = 4.5 *1055 ^ 2 AVco = Projected concrete failure area for groups of AVc = (1325 + 100+ 1582.5) * 500 < nc AVc (Limited by corner influence, spacing, or member thickness) = = mm 2 AVc = 2000 1582.5 500 1325 100 150.0 mm mm 2 1055.0 mm 500.0 mm 870.1 0.95 1.40 1055.0 mm mm 1325 mm 500.0 mm mm2 1503750.0 5008612.5 kN 1.0 1.0 mm 2 10017225 1503750.0 150.0 mm 11 / 14
  • 12.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Nominal concrete breakout strength for Vcbg = AVc/AVco * yec,V* yed,V * yc,V * Vb group of anchors in a single row for shear force = (1503750/5008612.5) * 1*0.95*1.4* 870.14 = f Vcbg = > nc*Vua SAFE ( ) Group of anchors min(ha, 1.5ca1) mm min(ca2, 1.5ca1) (nc-1)g min(ca4, 1.5ca1) mm mm mm Basic concrete breakout strength of an anchor Vb = 0.6 (le/do)0.2 sqrt(d0)sqrt(fc ' ) ca1 1.5 in cracked concrete Where, le = min.( hef, 8d0) = Actual edge distance ca1 = ca2max = ca2min = ha s Effective anchor edge distance ca1 = if ef< 1.5ca1= max(ca2/1.5,ha/1.5,S/3 or Ca1) = Vb = 0.6 * (150/20)^0.2 * sqrt(20) * sqrt(40) * 1205^1.5 Vb = Modification factor for eccentrically loaded yec,V = 1/(1 + (2e'V / 3ca1)) anchor group = Modification factor for edge effects yed,V = 0.7 + 0.3 (ca2/1.5ca1) for ca2 <1.5ca1 = for ca2 >1.5ca1 yed,V = Modification factor to account for cracking yc,V = 1807.5 100 1325 mm 500 347.5 kN 150.0 mm 500.0 260.6 kN 25.0 2000 mm 150.0 kN 1205.0 mm 1.00 1.0 1205.0 mm 1.40 0.92 1325 mm mm 1062.2 12 / 14
  • 13.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Projected concrete failure area of an anchor, AVco = 4.5 ca1 2 (Not limited by corner influence, spacing, or member thickness) = 4.5 *1205 ^ 2 AVco = Projected concrete failure area for groups of = (1325 + 100+ 1807.5) * 500 < n Avco (Limited by corner influence, spacing, or member thickness) = = mm 2 AVc = Nominal concrete breakout strength for Vcbg = AVc/AVco * yec,V* yed,V * yc,V * Vb group of anchors for shear force = (1616250/6534112.5) * 1*0.92*1.4* 1062.16 = f Vcbg = > Vuag SAFE ( ) CONRETE PRYOUT STRENGTH OF ANCHOR Single anchor As per ACI 318-05 D 6.3 Nominal pryout strength of an anchor Vcp = kcp * Ncb kcp = Nominal concrte breakout strength of an anchor Ncb = Nominal pryout strength of an anchor Vcp = 2* 85.72 = f Vcp = > Vua SAFE ( ) Group of anchors Nominal concrte breakout strength for Ncbg = Nominal pryout strength for group of anchor Vcpg = kcp * Ncbg = 2* 104.77 = f Vcpg = > Vuag SAFE ( ) INTERACTION OF TENSILE AND SHEAR FORCES Lowest design strength in tension f Nn = min. ( 131.95, 64.29, 131.94, N.A. ) of an anchor = > Nua SAFE ( ) 338.4 kN 253.80 kN mm 2 mm2 6534112.5 12.5 104.8 kN 50.0 2.0 85.7 kN 209.5 kN 157.2 kN 50.0 171.4 kN 128.6 kN 64.3 kN 10.1 26136450 1616250.0 1616250.0 mm 2 13 / 14
  • 14.
    Checked by Connectionid Designed by Date 20-Sep-14 SUBJECT ANCHOR BOLT DESIGN PROJECT REFERENCE A ACI 318M-11 Lowest design strength in tension f Nng = min. ( 263.89, 78.58, 263.88, N.A. ) of group of anchors = > Nuag SAFE ( ) Lowest design strength in shear f Vn = min. ( 131.95, 251.93, 128.58 ) of an anchor = > Vua SAFE ( ) Lowest design strength in shear f Vng = min. ( 527.79, 253.8, 157.16 ) of group of anchors = > Vuag SAFE ( ) Inetraction check for single anchor Nua Vua = (10.1 / 64.29) + (12.5/ 128.58) f Nn f Vn = <= 1.2 SAFE Inetraction check for group of anchors Nuag Vuag = ((20.2 / 78.58) + (50/ 157.16) f Nng f Vng = <= 1.2 SAFE END PLATE THICKNESS Edge distance = mm Number of bolts in tension side nf = Tension in group of anchors T1 = Nua*nf = kN Moment on plate due to tension Mt = T1*ev = kNm Thickness of end plate required = SQRT(6*M2/(Bp*fyp)) = SQRT((6*2.02*10^6/(200*265)) = mm > SAFE ( ) 20.2 12.5 50.0 100 78.6 kN 128.6 kN 157.2 kN + + 0.58 tp 20.2 0.25 20.0 2.02 15.12 treq2 2 14 / 14