W12x30 Beam to Beam Connection -------------------------------------------------------------------------------------------------------- Connection Template : SP BG Connection ID : BG - N(11) - M(11,12) Design Code: AISC-LRFD Status:: OK -------------------------------------------------------------------------------------------------------- LOADS Members Load Type V2 V3 M33 M22 Axial [Kip] [Kip] [Kip*ft] [Kip*ft] [Kip] -------------------------------------------------------------------------------------------------------- Beam LC-1 Design -0.09 -- -- -- -0.04 LC-2 Design -0.64 -- -- -- -0.09 LC-3 Design 0.01 -- -- -- 0.01 LC-4 Design -3.82 -- -- -- -0.51 LC-5 Design -1.01 -- -- -- -0.17 LC-6 Design -6.98 -- -- -- -0.97 LC-7 Design -4.68 -- -- -- -0.66 LC-8 Design -0.86 -- -- -- -0.14 LC-9 Design -0.65 -- -- -- -0.11 LC-10 Design -4.54 -- -- -- -0.63 -------------------------------------------------------------------------------------------------------- GEOMETRIC CONSIDERATIONS Dimensions Unit Value Min. value Max. value Sta. References -------------------------------------------------------------------------------------------------------- Plate (beam side)

Vertical edge distance [in] 2.00 0.88 -- TablesJ3.4,J3.5 Lemin = edmin + C2 = 0.875[in] + 0[in] = 0.875[in] Tables J3.4, J3.5

Horizontal edge distance [in] 2.00 0.88 -- TablesJ3.4,J3.5 Lemin = edmin + C2 = 0.875[in] + 0[in] = 0.875[in] Tables J3.4, J3.5

Vertical center-to-center spacing (pitch) [in] 3.00 1.67 6.24 Sec.J3.3,Sec.J3.5 smin = 8/3*d = 8/3*0.625[in] = 1.666667[in] Sec. J3.3 IsCorrosionConsideredFalse smax = min(24*tp, 12[in]) = min(24*0.26[in], 12[in]) = 6.24[in] Sec. J3.5 Beam

Vertical edge distance [in] 3.17 0.88 -- TablesJ3.4,J3.5 Lemin = edmin + C2 = 0.875[in] + 0[in] = 0.875[in] Tables J3.4, J3.5

Horizontal edge distance [in] 2.50 0.88 -- TablesJ3.4,J3.5 Lemin = edmin + C2 = 0.875[in] + 0[in] = 0.875[in] Tables J3.4, J3.5 Support

Weld size [1/16in] 5 4 -- p. 10-101 wmin = ceil((5/8)*tp/(1[in])*16) = ceil((5/8)*0.394[in]/(1[in])*16) = 4 p. 10-101 -------------------------------------------------------------------------------------------------------- DESIGN CHECK Verification Unit Capacity Demand Ctrl EQ Ratio References -------------------------------------------------------------------------------------------------------- Plate (beam side) Bolts shear [Kip] 10.54 7.04 LC-6 0.67 Tables (7-1..14) (n>=10)and(n<=12)and(IsStandardHole)(3>=10)and(3<=12)and(True)False BoltFactor = 1 p. 10-102 Rn = *Fnv*Ab = 0.75*48[Kip/in2]*0.307[in2] = 11.052[Kip] Eq. J3-1 Rn = C*Rn*BoltFactor = 0.953874*11.052[Kip]*1 = 10.542214[Kip] Tables (7-1..14) Flexure with the Von-Mises shear reduction [Kip*ft] 26.48 3.56 LC-6 0.13 p. 10-103 Ag = Lp*tp = 10[in]*0.394[in] = 3.94[in2] Sec. D3-1 fv = V/Ag = -6.977531[Kip]/3.94[in2] = -1.770947[Kip/in2] p. 10-103 Fcr = (max(0, (*Fy)2 - 3*fv2))1/2 = (max(0, (0.9*36[Kip/in2])2 - 3*-1.770947[Kip/ in2]2))1/2 = 32.254476[Kip/in2] p. 10-103 Zx = tp*L2/4 = 0.394[in]*10[in]2/4 = 9.85[in3] T. 17-27 Mn = Fcr*Z = 32.254476[Kip/in2]*9.85[in3] = 26.475549[Kip*ft] p. 10-103 Bolt bearing under shear load [Kip] 30.65 6.98 LC-6 0.23 Eq. J3-6, p. 7-18 Lc-end = max(0.0, Le - dh/2) = max(0.0, 2[in] - 0.6875[in]/2) = 1.65625[in] Sec. J4.10 Lc-spa = max(0.0, s - dh) = max(0.0, 3[in] - 0.6875[in]) = 2.3125[in] Sec. J4.10 rn1 = min(k1*Lc-end*tp*Fu, k2*d*tp*Fu) = min(1.5*1.65625[in]*0.394[in]*58[Kip/ in2], 3*0.625[in]*0.394[in]*58[Kip/in2]) = 42.8475[Kip] Eq. J3-6 rn2 = min(k1*Lc-spa*tp*Fu, k2*d*tp*Fu) = min(1.5*2.3125[in]*0.394[in]*58[Kip/ in2], 3*0.625[in]*0.394[in]*58[Kip/in2]) = 42.8475[Kip] Eq. J3-6 Rn = *C*min(rn1, rn2) = 0.75*0.953874*min(42.8475[Kip], 42.8475[Kip]) = 30.653333[Kip] p. 7-18 Shear yielding [Kip] 85.10 6.98 LC-6 0.08 Eq. J4-3 Ag = Lp*tp = 10[in]*0.394[in] = 3.94[in2] Sec. D3-1 Rn = *0.60*Fy*Ag = 1*0.60*36[Kip/in2]*3.94[in2] = 85.104[Kip] Eq. J4-3 Shear rupture [Kip] 79.70 6.98 LC-6 0.09 Eq. J4-4

Lh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 Le = L - n*Lh = 10[in] - 3*0.75[in] = 7.75[in] DG4 Eq. 3-13 Anv = Le*tp = 7.75[in]*0.394[in] = 3.0535[in2] Sec. J4-2 Rn = *0.60*Fu*Anv = 0.75*0.60*58[Kip/in2]*3.0535[in2] = 79.69635[Kip] Eq. J4-4 Block shear [Kip] 78.91 6.98 LC-6 0.09 Eq. J4-5 dhh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 dhv = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 Ant = (Leh - dhh/2)*tp = (2[in] - 0.75[in]/2)*0.394[in] = 0.64025[in2] Sec. J4-3 Agv = (Lev + (n - 1)*s)*tp = (2[in] + (3 - 1)*3[in])*0.394[in] = 3.152[in2] Sec. J4-3 Anv = (Lev + (n - 1)*(s - dhv) - dhv/2)*tp = (2[in] + (3 - 1)*(3[in] - 0.75[in]) - 0.75[in]/2)*0.394[in] = 2.41325[in2] Sec. J4-3 IsStressUniformTrue Ubs = 1 Sec. J4-3 Rn = *min(0.6*Fu*Anv + Ubs*Fu*Ant, 0.6*Fy*Agv + Ubs*Fu*Ant) = 0.75* min(0.6*58[Kip/in2]*2.41325[in2] + 1*58[Kip/in2]*0.64025[in2], 0.6*36[Kip/in2]*3.152[in2] + 1*58[Kip/in2]* 0.64025[in2]) = 78.913275[Kip] Eq. J4-5 Flexural rupture [Kip] 58.57 6.98 LC-6 0.12 p. 9-6 Lh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 Znet = tp/4*(L2 - s2*n*(n2 - 1)*Lh/L) = 0.394[in]/4*(10[in]2 - 3[in]2*3*(32 - 1)* 0.75[in]/10[in]) = 8.2543[in3] [4] Rn = *Fu*Znet/e = 0.75*58[Kip/in2]*8.2543[in3]/6.13[in] = 58.57456[Kip] p. 9-6 Bolt bearing under axial load [Kip] 37.65 0.01 LC-3 0.00 Eq. J3-6, p. 7-18 Lc-end = max(0.0, Le - dh/2) = max(0.0, 2[in] - 0.6875[in]/2) = 1.65625[in] Sec. J4.10 Lc-spa = max(0.0, s - dh) = max(0.0, 5.5[in] - 0.6875[in]) = 4.8125[in] Sec. J4.10 rn1 = min(k1*Lc-end*tp*Fu, k2*d*tp*Fu) = min(1.5*1.65625[in]*0.394[in]*58[Kip/ in2], 3*0.625[in]*0.394[in]*58[Kip/in2]) = 42.8475[Kip] Eq. J3-6 rn2 = min(k1*Lc-spa*tp*Fu, k2*d*tp*Fu) = min(1.5*4.8125[in]*0.394[in]*58[Kip/ in2], 3*0.625[in]*0.394[in]*58[Kip/in2]) = 42.8475[Kip] Eq. J3-6 Rn = *C*min(rn1, rn2) = 0.75*1.171561*min(42.8475[Kip], 42.8475[Kip]) = 37.648833[Kip] p. 7-18 Yielding strength due to axial load [Kip] 127.66 0.01 LC-3 0.00 Eq. J4-1 Ag = Lp*tp = 10[in]*0.394[in] = 3.94[in2] Sec. D3-1 Rn = *Fy*Ag = 0.9*36[Kip/in2]*3.94[in2] = 127.66[Kip] Eq. J4-1 Rupture due to axial load [Kip] 132.83 0.01 LC-3 0.00 Eq. J4-2 Ag = Lp*tp = 10[in]*0.394[in] = 3.94[in2] Sec. D3-1 IsBoltedConnectionTrue Lh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 An = (l - n*Lh)*tp = (10[in] - 3*0.75[in])*0.394[in] = 3.0535[in2] Sec. D3-2 Ae = min(0.85*Ag, An) = min(0.85*3.94[in2], 3.0535[in2]) = 3.0535[in2] Sec. J4-1 Rn = *Fu*Ae = 0.75*58[Kip/in2]*3.0535[in2] = 132.83[Kip] Eq. J4-2 Tear out under axial load [Kip] 102.66 0.01 LC-3 0.00 Eq. J4-5 dhh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 dhv = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 n>13>1True Agv = 2*(L + (nc - 1)*g)*tp = 2*(2[in] + (1 - 1)*5.5[in])*0.394[in] = 1.576[in2] Sec. J4-3 Anv = 2*(L + (nc - 1)*g - dhh*(nc - 0.5))*tp = 2*(2[in] + (1 - 1)*5.5[in] - 0.75[in]*(1 - 0.5))*0.394[in] = 1.2805[in2] Sec. J4-3 Ant = (s - dhv)*(n - 1)*tp = (3[in] - 0.75[in])*(3 - 1)*0.394[in] = 1.773[in2] Sec. J4-3 IsStressUniformTrue Ubs = 1 Sec. J4-3 Rn = *min(0.6*Fu*Anv + Ubs*Fu*Ant, 0.6*Fy*Agv + Ubs*Fu*Ant) = 0.75* min(0.6*58[Kip/in2]*1.2805[in2] + 1*58[Kip/in2]*1.773[in2], 0.6*36[Kip/in2]*1.576[in2] + 1*58[Kip/in2]* 1.773[in2]) = 102.66[Kip] Eq. J4-5 Plate (support side) Weld capacity [Kip] 163.59 7.04 LC-6 0.04 Tables 8-4 .. 8-11 e = 0 p. 10-135 Rn = 2 * (*C*C1*D*L) = 2 * (0.75*1.903331[Kip/in]*1*5*11.46[in]) = 163.59[Kip] Tables 8-4 .. 8-11

Beam Bolt bearing under shear load [Kip] 20.23 6.98 LC-6 0.34 Eq. J3-6, p. 7-18 Lc-end = max(0.0, Le - dh/2) = max(0.0, 3.17[in] - 0.6875[in]/2) = 2.82625[in] Sec. J4.10 Lc-spa = max(0.0, s - dh) = max(0.0, 3[in] - 0.6875[in]) = 2.3125[in] Sec. J4.10 rn1 = min(k1*Lc-end*tp*Fu, k2*d*tp*Fu) = min(1.5*2.82625[in]*0.26[in]*58[Kip/ in2], 3*0.625[in]*0.26[in]*58[Kip/in2]) = 28.274999[Kip] Eq. J3-6 rn2 = min(k1*Lc-spa*tp*Fu, k2*d*tp*Fu) = min(1.5*2.3125[in]*0.26[in]*58[Kip/ in2], 3*0.625[in]*0.26[in]*58[Kip/in2]) = 28.274999[Kip] Eq. J3-6 Rn = *C*min(rn1, rn2) = 0.75*0.953874*min(28.274999[Kip], 28.274999[Kip]) = 20.228087[Kip] p. 7-18 Shear yielding [Kip] 69.30 6.98 LC-6 0.10 Eq. J4-3 Ag = Lp*tp = 12.34[in]*0.26[in] = 3.2084[in2] Sec. D3-1 Rn = *0.60*Fy*Ag = 1*0.60*36[Kip/in2]*3.2084[in2] = 69.301438[Kip] Eq. J4-3 Shear rupture [Kip] 68.47 6.98 LC-6 0.10 Eq. J4-4 Lh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 Le = L - n*Lh = 12.34[in] - 3*0.75[in] = 10.09[in] DG4 Eq. 3-13 Anv = Le*tp = 10.09[in]*0.26[in] = 2.6234[in2] Sec. J4-2 Rn = *0.60*Fu*Anv = 0.75*0.60*58[Kip/in2]*2.6234[in2] = 68.470739[Kip] Eq. J4-4 Bolt bearing under axial load [Kip] 63.62 0.01 LC-3 0.00 Eq. J3-6 Lc-end = max(0.0, Le - dh/2) = max(0.0, 2.5[in] - 0.6875[in]/2) = 2.15625[in] Sec. J4.10 Lc-spa = max(0.0, s - dh) = max(0.0, 5.5[in] - 0.6875[in]) = 4.8125[in] Sec. J4.10 Rn = *(min(k1*Lc-end, k2*d) + min(k1*Lc-spa, k2*d)*(n - 1))*tp*Fu* nc = 0.75*(min(1.5*2.15625[in], 3*0.625[in]) + min(1.5*4.8125[in], 3*0.625[in])*(1 - 1))* 0.26[in]*58[Kip/in2]*3 = 63.618748[Kip] Eq. J3-6 Yielding strength due to axial load [Kip] 284.80 0.01 LC-3 0.00 Eq. D2-1 Rn = *Fy*Ag = 0.9*36[Kip/in2]*8.79[in2] = 284.8[Kip] Eq. D2-1 Rupture due to axial load [Kip] 226.63 0.01 LC-3 0.00 Eq. J4-2 IsBoltedConnectionTrue Lh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 An = Ag - nh*tp*Lh = 8.79[in2] - 3*0.26[in]*0.75[in] = 8.205[in2] Sec. D3-2 U = 1 - x/l = 1 - 1.095072[in]/3[in] = 0.634976 Table D3.1 Ae = U*An = 0.634976*8.205[in2] = 5.209978[in2] Sec. D3-3 Rn = *Fu*Ae = 0.75*58[Kip/in2]*5.209978[in2] = 226.63[Kip] Eq. J4-2 Tear out under axial load [Kip] 71.95 0.01 LC-3 0.00 Eq. J4-5 dhh = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 dhv = dh + 1/16[in] = 0.6875[in] + 1/16[in] = 0.75[in] Sec. D3-2 n>13>1True Agv = 2*(L + (nc - 1)*g)*tp = 2*(2.5[in] + (1 - 1)*5.5[in])*0.26[in] = 1.3[in2] Sec. J4-3 Anv = 2*(L + (nc - 1)*g - dhh*(nc - 0.5))*tp = 2*(2.5[in] + (1 - 1)*5.5[in] - 0.75[in]*(1 - 0.5))*0.26[in] = 1.105[in2] Sec. J4-3 Ant = (s - dhv)*(n - 1)*tp = (3[in] - 0.75[in])*(3 - 1)*0.26[in] = 1.17[in2] Sec. J4-3 IsStressUniformTrue Ubs = 1 Sec. J4-3 Rn = *min(0.6*Fu*Anv + Ubs*Fu*Ant, 0.6*Fy*Agv + Ubs*Fu*Ant) = 0.75* min(0.6*58[Kip/in2]*1.105[in2] + 1*58[Kip/in2]*1.17[in2], 0.6*36[Kip/in2]*1.3[in2] + 1*58[Kip/in2]* 1.17[in2]) = 71.954997[Kip] Eq. J4-5 Support Welds rupture [Kip/ft] 108.58 4.80 LC-6 0.04 p. 9-5 e = 0 p. 10-135 Dmin = P/(*C*C1*L) = 3.522084[Kip]/(0.75*1.903331[Kip/in]*1*11.46[in]) = 0.215298 tables 8-4..11 Ru = 0.6*FEXX*(2)1/2/2*Dmin/16[in] = 0.6*70[Kip/in2]*(2)1/2/2*0.215298/16[in] = 4.795511[Kip/ ft] p. 9-5 Rn = 0.6*Fu*tp = 0.6*58[Kip/in2]*0.26[in] = 108.58[Kip/ft] p. 9-5

-------------------------------------------------------------------------------------------------------- Critical strength ratio 0.67 -------------------------------------------------------------------------------------------------------- NOTATION Ab: Nominal bolt area Ae: Effective net area Ag: Gross area Agv: Gross area subject to shear An: Net area Ant: Net area subject to tension Anv: Net area subjected to shear Rn: Available shear strength per bolt BoltFactor: Bolt capacity factor C: Bolt group coefficient c: Coped length C1: Electrode strength coefficient C2: Edge distance increment C: Weld group coefficient d: Nominal bolt diameter dh: Nominal hole dimension dhh: Horizontal hole dimension dhv: Vertical hole dimension D: Number of sixteenths of an inch in the weld size Dmin: Number of sixteenths of an inch in the minimum weld size e: Load eccentricity FEXX: Electrode classification number Fnv: Nominal shear stress Fu: Specified minimum tensile strength fv: Required shear stress Fy: Specified minimum yield stress g: Transversal gage between bolts ho: Reduced beam depth IsBoltedConnection: Is bolted connection IsCorrosionConsidered: Is corrosion considered IsStandardHole: Is standard hole (STD) IsStressUniform: Is the stress uniform k1: Bearing factor k2: Bearing factor l: Length L: Length Lc-end: Clear distance Le: Effective length Le: Edge distance Leh: Horizontal edge distance Lemin: Minimum edge distance Lev: Vertical edge distance Lh: Hole dimension for tension and shear net area Lp: Plate length L: Length of weld : Slenderness edmin: Minimum edge distance n: Bolts rows number nc: Number of bolt columns nh: Holes number P: Required axial force : Design factors

Fcr: Design or allowable flexural stress buckling Mn: Design or allowable strength Rn: Design or allowable strength rn1: Nominal strength of one bolt rn2: Nominal strength of one bolt Rn: Nominal strength Ru: Required strength smax: Maximum spacing smin: Minimum spacing s: Longitudinal bolt spacing Lc-spa: Distance between adjacent holes edges tp: Thickness of the connected material tp: Plate thickness tpmax: Maximum plate thickness tw: Web thickness U: Shear lag factor Ubs: Stress index V: Shear load wmin: Minimum weld size required x: Connection eccentricity Z: Plastic modulus Znet: Net plastic section modulus Zx: Plastic section modulus about the x-axis REFERENCES [4]: AISC 2005, Design Examples Version 13.0, pp. IIA-63, IIA_86, IIA-98