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Specifications i , • , ��1 P aa o `7 — Co�So7 V/ ittii 7 v . f. � ? ' tlj (i i d' \t= 1 _ (J ! : f i r P: + ; (1) l ..:, .., 3903 Martin Chapel Road Springfield, TN 37172 -123 Phone: 615- 384 -1485 Fax: 615- 384 -1481 e -mail: kl @bellsouth.net Project Name ®,, V t I %.;''. ,'; . , r il 1 ,---, - r 4.. 4. ; Win S St ..: ' ' r 21 _,..._ _ 1 . , Location Portland, OR t - _ ,t \ ,,, , , , i r I. 4 P roject Number r i L)Y 1 TD08711 i �01 C) These calculations review the structure being installed for structural capability. The sealing of the drawings used in conjunction with these calculations is for the structural review only. Other information is not reviewed, nor approved. 'S- c\ED PRppe � c 3 ' s<-- FR i o29 66944PE r G� N 0 4)/ 15 , 20Q' 'C° 49A J . w (EXPIRATION DATE: jZ / 8 9/26/2007 Engineering Seal Data: _ _ Sta te Nurnber Exp Date L___ OR 66944PE 31- Dec -08 r Date: 8/24/2007 Design Summary Sheet Page:l 1 Project: Horizon Restorations Pallet Rack Portland, OR S Building Code 2007 OSSC 0.944 Zone Accel. Used Steel Design Specification 2002 AISI and 2001 AISC both based on LRFD Method Total No. of Storage Levels - - - - -- 2 Top Storage Level 14.000 Feet Frame Depth 36 Inches Typical Beam Span — 144 Inches Panel Spacing 45 Inches Allowable Soil Pressure 1000 Psf Max. Shelf Loading -- 3000 Pounds Allowable Compressive Strength of Concrete - -- - -- 3000 Psi Avg. Shelf Loading -- 3000 Pounds Total bay load including dead 6.10 Max Bay Loading 4.12 Avg. Period of vibration -Based on Rayleigh Method -down aisle - -- Kx= 1.7 kips T= 1.316 Seconds Seismic base shear down aisle 0.0989 Ws Ws= Total bay load + dead load Total base shear in kips 0.2037 Kips per rack column- -down aisle Seismic base shear cross aisle 0.72 Kips per frame -based on default values Column Type C -Section IR Face 3 Thickness 0.07 CIR Depth 3 First Level Drift Design Ratio Live load +dead load +seismic 0.708 1.325 Inches Design Ratio Live load +dead load 0.722 Weld Actual or cross aisle Beam Capacity Moment Level No. Beam Connectors Connector Beam Weld in -kips in -kips 1 3 Pin Connector 3P 3 pin IB500 Std. 33.54 10.79 2 3 Pin Connector 3P 3 pin 18500 Std. 33.54 6.64 3 No storage level da N/A da 0 0 0.00 4 No storage level da N/A da 0 0 0.00 5 No storage level da N/A da 0 0 0.00 6 No storage level da N/A da 0 0 0.00 7 No storage level da N/A da 0 0 0.00 8 No storage level da N/A da 0 0 0.00 9 No storage level da N/A da 0 0 0.00 10 No storage level da N/A da 0 0 0.00 11 No storage level da N/A da 0 0 0.00 12 No storage level da N/A da 0 0 0.00 Upright Bracing Summary Vertical Leg 1 Inches Yield Fy= 50 Ksi Width 1.5 Inches Brace type = CWLips Gage 0.07 Inches Design Ratio 0.299 Base Plate Summary Slab Thickness 6 Inches Ratio = 0.200 OK Base Plate Width 7 Base Plate Depth 5 Base Plate Thick.... 0.375 Yield Fy= 36 Ksi Anchor Bolt Summary Anchor Bolt Description 1/2" Dia. X 3 1/4 Embd. Qty /Col.= 2 Anchor Bolt Design Ratio 0.133 Prepared By: KL Wood Engineering Associates, Inc. Conterminous 48 States 2005 ASCE 7 Standard - Zip Code = 97224 Spectral Response Accelerations Ss and S1 Ss and S1 = Mapped Spectral Acceleration Values Site Class B - Fa = 1.0 ,Fv = 1.0 Data are based on a 0.05 deg grid spacing Period Centroid Sa (sec) (g) 0.2 0.918 Ss, Site Class B 1.0 0.333 S1, Site Class B Period Maximum Sa (sec) (g) 0.2 0.944 Ss, Site Class B 1.0 0.338 S1, Site Class B Period Minimum Sa (sec) (g) 0.2 0.895 Ss, Site Class B 1.0 0.330 S1, Site Class B Date: 2007 OSSC Pager 2 8/24/2007 Using 2002 RMI specifications 2007 OSSC Section 2208.1 Steel storage racks RMI Section 2.7.2 Minimum Seismic Forces modified by 2007 OSSC Down Aisle direction - -- Longitudinal Lat. Long. Zip Code 97224 V = CsIeW Height 14.000 Feet Cs = 1.2 *Cv / [R *T "2/3)] le = 1 R = 6 Limit State RMI Sec. 2.7.3 Cv = Sd1 16 -18 Sds = 2/3 Sms 16 -16 Sms = FaSs Table 1615.1.2(1) Ss = 0.944 Fa = 1.122 Soil profile D Sms = 1.060 Cs = 0.0647 Sds = 0.706 1617.4.2.1 1617.4.2.1 Ct Ta Calculated T in accordance with the Rayleigh Method 0.035 0.253 0.30 1.316 Cs = 2.5 *Ca /R 16 -19 Sd1 = 2/3Sm1 Ca = Sds / 2.5 16 -17 Sm1 = FvS1 Table 1615.1.2(2) S1 = 0.338 Fv = 1.724 Soil profile D Sm1 = 0.583 Cs = 0.1177 Max. Sd1 = 0.388 Cs = .14Sds Cs = 0.0989 Min. Cs used in Base Shear Calculations Down Aisle Cs = 0.0989 Prepared By: KL Wood Engineering Associates, Inc. Page:l 3 I Date: 2007 OSSC 8/24/2007 Using 2002 RMI specifications 2007 OSSC Section 2208.1 Steel storage racks RMI Section 2.7.2 Minimum Seismic Forces modified by 2007 OSSC Cross Aisle direction --- Transverse V = CsIeW Height 14.000 Feet Cs = 1.2 *Cv / [R*T "2/3)] le = 1 R = 4 Limit State RMI Sec. 2.7.3 Cv = Sd1 Sds = 2/3 Sms Sms = FaSs Table 1615.1.2(1) Ss = 0.944 Fa = 1.122 Soil profile D Sms = 1.060 Cs = 0.2578 Sds = 0.706 1617.4.2.1 1617.4.2.1 Ct Ta Calculated T in accordance with the Rayleigh Method 0.035 0.253 0.30 1.316 Cs = 2.5 *Ca/R Sd1 = 2/3Sm1 Ca = Sds / 2.5 Sm1 = FvS1 Table 1615.1.2(2) S1 = 0.338 Fv = 1.724 Soil profile D Sm1 = 0.583 Cs = 0.177 Max. Sd1 = 0.388 Cs = .14Sds Cs = 0.0989 Min. Cs used in Base Shear Calculations Cross Aisle Cs = 0.1766 Prepared By: KL Wood Engineering Associates, Inc. Page:I 4 I Base Shear Section 2.2 Load Factors and Combinations for LRFD Method For all rack members 1 1.2D +L +1.4P D = dead load 2 1.2D +1.6L +.5(S or R) + 1.4P L= live load 3 1.2D +1.6(S or R) +(.5L or .8W) + .85P P = product load 4 1.2D +1.3W +.5L +.5(S or R) +.85P S = snow load 5 1.2D +1.5E +.5L +.2S +.85P W = wind load 6 1.2D +1.5E +.5L +.2S +.85P R = rain 7 .9D -(1.3W or 1.5E) +.45P E = seismic 1= impact 1 Warehouse Rack System Non - public Ip = 1 V = CsIeWs Cs = 0.099 Longitudinal V = CsIeWs Cs = 0.177 Transverse VI = 0.0989 Ws Longitudinal Limit State Vt = 0.1766 Ws Transverse Limit State Rack systems Ws = (.67 *Prf*P) +D +.25L Prf = Paverage / Pmaximum Force at various shelf levels Fx = (V- F1)WxHx ^k / EWi Hi "k for shelves greater than 12" above floor F1 = CsIpWs for shelf 12" or less above floor Fx = VWxHx "k / EWiHi ^k for all levels when first shelf > 12" above floor Exponent related to the structures period T < =.5 k= 1 T > 2.5 k = 2 If the base shear is based on the default Cs value then k shall be taken as 1 Period Longitudinal direction 1.316 seconds k = 2 - Period Transverse direction 0.304 seconds k = 1 Prepared By: KL Wood Engineering Associates, Inc. FUNDAMENTAL PERIOD OF VIBRATION WORKSHEET Page:I 5 8/24/2007 Based on the Rayleigh Method Used base shear - Longitudinal direction only Percent Total Load /Level contributing base shear ---- -- - - -> 67.00 % for seismic Distribution exponent -(k) -------------- --- - -> 1.408 Kx > 1.7 T ---- ---- -> 1.316 seconds E *Ix Column Style OC 32981 Computed Distribution exponent -(k) - - -- --0. 1.408 Column Column Column Column Column Elevation DL PL LL Tot. Load Cu. Load W W* h ^k H 84 0.025 1.5 0 1.525 3.05 1.03 527.5 0.27 168 0.025 1.5 0 1.525 1.53 1.03 1399.8 0.73 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 0 0.000 0 0 0 0.00 0 0.0 0.00 168 0.05 3 0 3.05 2.06 1927 1 Level Cum F L Pcr AP Q At Wi *At ^2 Fi *At 1 1.0000 84 15.963 5.262 1.236 6.505 43.59 1.780 2 0.7263 84 15.963 9.084 1.106 10.731 118.61 7.794 3 0.0000 0 0.000 0.000 0.000 0.000 0.00 0.000 4 0.0000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 5 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 6 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 7 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 8 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 9 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 10 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 11 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 12 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.000 162.19 9.57 g = 32.2 ft/sec ^2 T = 1.316 seconds T = 27 V �WiA ^2 / g EFiDi Eq 30 -10 Prepared By: KL Wood Engineering Associates, Inc. Date: FUNDAMENTAL PERIOD OF VIBRATION WORKSHEET Page:1 6 8/24/2007 Ss 0.94 Seismic Coeficients: S1 0.338 Soil Profile Type - D Rd = 6 Down Aisle Cs = 1.2 *Cv /(R *T ^.667) Rc= 4 Cross Aisle Cs = 0.0989 Down aisle per column Av = 0.944 Cs = 0.1766 Cross aisle per frame Actual Down -aisle base shear per col. = 0.204 kips Actual Cross -aisle base shear per frame = 0.728 kips Level Drift PA Shelf Spacing Guide Line for Drift Limit Only 1 1.3253 4.04 84 .333 *Column Width 2 2.1862 3.33 84 Column Width 3 0.0000 0.00 0 3 4 0.0000 0.00 0 5 0.0000 0.00 0 , ' i. 6 0.0000 0.00 0 7 0.0000 0.00 0 "= __. = J 8 0.0000 0.00 0 9 0.0000 0.00 0 i. 2.19 Inches 10 0.0000 0.00 0 11 0.0000 0.00 0 t. 12 0.0000 0.00 0 i ; 41 1.325 Inches Rack Displacement Actual Prepared By: KL Wood Engineering Associates, Inc. . . , . • , . , Date: 8/24/2007 LOADING DATA ON RACK SYSTEM Special Notes: Horizon Restorations Portland, OR Page: 7 0.133 Rack Elevations and Loadings Multiple deep-Single column load No Number Of Storage Levels No.= 2 Level Hi ,, 1 Exterior Column Check , AI Shelf Load is for 1 Deep Level No. Spacing Loading Dead Load Sum , i * ShelfLoad 6100 --- iii00 : ',.: ' 1 ! ■ ' 84 '44 ':', 1- ' ' t ;, - 000, ' ; ' ' 50 . 3050 84 Beam ,t Level H3 ir ,^ 1• • i ,,,, 0 5 `' ',,,. ' ' '' ' ' ,, 0 Pallet Load 6 ' ...- " ,-'-,`: '.- ', . I : = ''' ' ''' 0 i 0 Level H2 f • . 8 0 0 9 , - ' ' ' 10 _ ,- ., , : , 0 0 = %,„__ ,. -, , ,..„, ,,,' - `,. ,,, ' ,, --; ,, ' '1, ,,, - 0 Level H1 ligia * MUM mill am° Db : Column I Totals 168 6000 100 't ■, 3.05 L i , 6 i ' Slab [- Top Storage Level = 14.00 Feet v i Column Loading Pc= 3050 Pounds Dead+Live Load 60 Pc= 3.05 Kips Unfactored Bay Width Beam Depth Db = 5 Inches FRONT ELEVATION Rack Area/Profile : Pallet Rack SLAB AND SOIL DATA Product Type CIR Allowable Soil Pressure Qsp= 1000 Column: C-Section IR Qsp= 6.94 Psi Shelf Loading for Seismic RMI 2.7.2 Allowable Compressive Strength Concrete CA Ws = .67P+D Live load = 0 Fc'= 3000 Psi DA Ws =(.67*R*P)+D+.25*L DA Ws = 0.670 P+D Maximum Pallet Load PLm = 3000 Pounds CA Ws = 0.670 P+D Average Pallet Load PLa = 3000 Pounds 1.0 Load coff. Pav / Pm Ratio Ral = 1.000 100% Ratio Down aisle cofficient 0.67 RMI Section 2.7.2 Cross aisle coffecient 0.67 Prepared By: KL Wood Engineering and Associates, Inc. Date: RACK CONFIGURATION -- -LOAD /LEVEL/SEISMIC DATA Pagel 8 8/24/2007 Enter Seismic Code 2007 OSSC Avg.Top Shelf Load= 3000 Pounds 11 1 Depth No. of Storage Levels= 2 36 Level2 I ;® ® Span 144 Inches • H 45 ii Depth Db= 5 Inches Bottom Panel i. !pacing Inches S p 9 ` f ,I H1 Vb Base Shear Ird -, Y sM. Front Elevation End Elevation Longitudinal Direction Transverse Direction Load - Level- Seismic Values Vb= 0.0989 Wp Down aisle seismic loading Vb = 0.407 kips /frame . Level Spacing Loading Dead Vb= 0.204 Kips /Column Inches Pounds Load Ratio Vi / Level Sum 1 84 2010 50 4120 0.200 0.041 0.204 2 84 2010 50 2060 0.800 0.163 0.163 3 0 0 0 0 0.000 0.000 0.000 4 0 0 0 0 0.000 0.000 0.000 5 0 0 0 0 0.000 0.000 0.000 6 0 0 0 0 0.000 0.000 0.000 7 0 0 0 0 0.000 0.000 0.000 8 0 0 0 0 0.000 0.000 0.000 9 0 0 0 0 0.000 0.000 0.000 10 0 0 0 0 0.000 0.000 0.000 11 0 0 0 0 0.000 0.000 0.000 12 0 0 0 0 0.000 0.000 0.000 Totals 168 4020 100 1.000 0.204 Kips Loads: 2.06 Kips 0.05 Kips Total D +P +L 4.12 Kips - -Avg. Summary of Data Seismic down aisle loading Summation of Rack Load = 6.10 Kips D +P 4.12 kips Total Base Shear /Column = 0.204 Kips Seismic cross aisle loading Total Base Shear /Frame = 0.407 Klps 4.12 kips LRFD Design Loadings - Load Combinations Frame Column Ratio Load Factor Axial Loading 1.2D + 1.4P 8.52 4.26 2.068 1 Axial plus seismic 1.2D +.85P +E 5.22 2.61 1.267 Prepared By. KL Wood Engineering and Associates, Inc. Date: SHEAR / MOMENTS IN COLUMNS AND BEAMS Pagel 9 • 8/24/2007 3 Moment Diagram of Rack Structure Level 3 1 1111 -1111 IIIlhIIIIIIIIOu 5. _ Base Fixity =i � PinnedRb= 1 r' Fixed Rb= 0.5 Level 2 ;u1lIIIlIIII�III R Base Fixity Rb= 0.5 ��aII�1oIIIIIII��I���I Base Shear Vb = 0.204 Kips '_ [ Moment at Base Mb= (H1 * Vb ) * Rb Level 1 - Vv Moment at base Mb= 8.30 In -Kips Mu� i= 111111lllllllhlmmlll„_ „ugpplllllllll��(� IIII Column Load Pmax= 2.06 Kips i. H1 E'_ 1= Mi i= Slab _ .a Vb Mu= Moment Above Beam Level -Kips IAmr., '"' Mi= Moment Below Beam Level -Kips Bay Width Mc= Connection Moment -Kips Mb r 144 In Vv= Vertical Shear -End Connection- Kips Front Elevation PORTAL MOMENT DISTRIBUTIONS Column Level Spacing Mi Mu Mc M facotored 12 0 0.00 0.00 0.00 0.00 11 0 0.00 0.00 0.00 0.00 10 0 0.00 0.00 0.00 0.00 9 0 0.00 0.00 0.00 0.00 8 0 0.00 0.00 0.00 0.00 7 0 0.00 0.00 0.00 0.00 6 0 0.00 0.00 0.00 0.00 5 0 0.00 0.00 0.00 0.00 4 0 0.00 0.00 0.00 0.00 3 0 0.00 0.00 0.00 0.00 2 84 6.85 0.00 3.42 6.85 1 81.50 8.30 6.85 7.57 8.30 Totals 165.50 Inches 13.79 Feet Prepared By: KL Wood Engineering and Associates, Inc. COLUMN DESIGN CHECK -- COMBINED AXIAL AND SEISMIC Pagel 10 • Date: 8/24/2007 Seismic Description: . Q value= AISI IBC2003 Column Description: Fy = 45 Ksi special Column E = 29500 Maxis Column Section Properties Hole Pat Column= special 2 C T = 0.0700 In. Gross Area Ag= 0.699 InA2 • Net Area An= 0.512 InA3 Face -d- • - - • - p . -- —X axis lx = 1.118 In.^4 I 3 i Sx = 0.746 In03 • Rx = 1.265 In. - ..:=L======0' ly = 0.879 In. ^4 Min. Sy = 0.511 In.^3 Section Wgt/Ft. ' R y= 1.121 In. 2 .38 Torsional Properties Xo _ L Width M= 1.62 Xo = -2.865 3 Cw = 2.383 Ro = 3.326 J = 0.001142 Column Cross Section ig = 0.258 Sx eff = 0.509 In. ^3 Critical Buckling Values - -- Current Edition 2002 AISI LRFD Qex = (7r ^2E(KxIX/Rx) ^2) Eq. C3.1.2 -7 24.261 aey = (7r^2E(KyLy /Ry) ^2) Eq. C3.1.2 -8 240.574 aet = (1 /ARo ^2) *(GJ +7r ^2Cw /(KtLt) ^2) Eq. C3.1.2 -9 93.816 Fe =( 1/ 2( 3)*(( Qex +at)- ((aex +at) ^2- 413 Qexat) ^.5 Eq. C4.2 -1 20.166 If First Beam Level Is Near Floor Use Second Level For Column Design Lx = 81.500 Inches Ly = 39 Inches Lt = 39 Kx = 1.7 Inches Ky = 1 Inches Kt = 0.8 Inches Concentrically Loaded Compression Members Section C4 Fe = 20.166 Fy = 45 For A < 1.5 Fn = Fy * .658 ^(202) X = 1.494 For X > 1.5 Fn = Fy * .877/)02) = 0.85 Fn= 17.684 Ksi cl)Pn= 8.60 Kips Frame Capacity - Vertical Load Only = 12,445 Pounds Lateral Buckling Strength Section c3.1.2 Mn= Sxeff(Mc /Sx) cl'b= 0.9 My = Sx* Fy Me = Cb Ro A(Qeyat) ^.5 Cb =1.00 My = 33.552 Mc = Crit. Moment Me = 349.357 Mc = 33.552 For Me > 2.78 *My Mc = My For .56 *My< Me < 2.78 *My Mc = My(1- 10 *My /(36 *Me)) Mn = 22.906 For Me < .56 *My Mc = Me 4Mn = 20.616 in -kips Prepared By: KL Wood Engineering and Associates, Inc. • Page:I /Oa Date: COLUMN DESIGN CHECK-- CONT'D 8/24/2007 Section C5 Combined Axial Load and Bending Design Ratio Dr = Pu / Oc Pno + CmMux / ObMnx 0 nx <= 1.0 Cm = .85 aex = (1- Pu / Pe) 4c= .85 (I)b =.9 Pe = 7r^2EIb / ( Kb Lb ) ^2 First Beam Level H1= 81.5 Kb = 1.7 Column Unfact Fact Fact H2= 84 Pe = 16.96 P1 = 3.05 2.61 4.26 M1 = 8.30 P2 = 1.53 1.31 2.13 M2 = 6.85 Nominal Axial Strength (I) Pn = 8.60 Kips from previous page Full Dead +Live Load Pu unfactored Puf = 3.05 Kips 1.2D +1.4L Pu = 4.26 Kips 1.2D+ .85P RMI Factored Pu = 2.61 Kips Nominal FlexL Flexural Strength 4Mnx = 20.62 In -Kips Required Mux unfactored Muxf= 8.30 In -Kips Magnification factor = 1.005 Seismic moment factored Mux = 8.30 In -kips Factor= 1.000 Total factored moment 8.30 In -kips 1.2D +.85L +E Pu / 44c Pn = 0.303 Mf * Mu /(4'Mn)= 0.405 Dr = design ratio Pu / Pn + CmxMx / (kbMnx a Dr = 0.708 O.K. Design Check For Dead Load + Live Load Only Unfactored Column Load Pc = 3.05 Kips 1.2D +1.4W Factored Column Load Pu = 4.26 Kips Cross Aisle 6.21 Kips Down Aisle Control P= 6.21 Kips Nominal Axial Strength (I)Pn= 8.60 Kips 4c = 0.85 Design Ratio Pu /(1)c Pn = 0.722 Ok Prepared By: KL Wood Engineering and Associates, Inc. DATE: BEAM DESIGN WITH PARTIAL END FIXITY Pager 1 1 8/24/2007 Beam = Special Span = 144 Inches T = 0.07 In. YIELD Fy= 55 Ksi Inside Rad 0.125 In. From Cold Working 60.39 Ksi 1.7 Area = 1.002 In ^2 Fu = 67.00 Ksi SECTION PROPERTIES 1.625 5288 stress Sx = 1.165 In. ^3 4290 deflection Ix = 3.029 In. ^4 5.00 X -Axis E* Ix = 89355.5 Ksi Req. Cap. 4bMn= .95 *Sx *Fy 3000 (1)bMn= 66.85 in -kips Gr= 5.61 2.5 Mer= 3.216 RMI impact addition 0.125 Load factor = (1.4 + 1.4 * RMI addition) * PL Load factor = 1.575 1.2D +1.4L = 1.424 Beam weight = 42.88 END CONNECTOR SPRING CONSTANT G = 2 * E *Ix/(Fe *L) + 1 Me = W *U(12 *G) Fe = 270 In- Kips /Ra G = 5.596 W = 8 * (Phi *Mn /L.F. + Me) /L -1.2D Me_max = 6 In -Kips Unfactored Upper limit ! ]] (({{ 33 ``EE ((]]` !!ss gg ))gg (!{{@@ Me = 5.67 at stress limit IIIllIllI I HHll MIhIIllh ��I19 llJ1�1il �W = 2.644 Kips /Beam Fe D = 0.986 IN. Deflection R R SPAN L 144 - Wt = 5288 Per Pair of Beams Stress limit Equation for Defl. Cap when limit is L1180: W = (384 *E *Ix) *(U180 + Me* L ^2/(8 *E *Ix)) /(5 *L ^3) Deflection Limit Span divided by - - - -> 180 Di = 0.800 In. Deflection Limit Wd = Beam Load Based on Deflection Limit = L/Deflection limit Wd = 2.145 Kips Me = 4.6 at defl. limit Wt = 4290 Per Pair of Beams Deflection Limit Prepared By: KL Wood Engineering Associates, Inc. Date: Beam Weld Page:l 12 8/24/2007 Plastic Section Modulus L1= 1.7 Inches Offset L2= 5 Inches 1.625 L1 L3= 0 Inches L4= 0 Inches L5 L5 = 0 Inches 1.650 — —• —• — — 6.7 Inches H1 L2 L4 0.0000 3.350 H2 - -- Y L3 At = Ab Center of Area Weld Pattern At= (L2 -Y) + L1 + (L4- Y) +(L5 -Y) Ab= 2Y +L3 Y = ( L1 + L2 +L4+L5 - L3 ) / 4 Y= 3.3500 Inches H1= 1.2437 Inches At= 3.350 H2= 1.6750 Inches Ab= 3.350 Z= H1 *At + H2 *Ab Z= 9.778 Inches ^3 Steel Thickness= 0.07 Inches Zt= 0.684 Inches ^3 Plastic Moment Capacity `)= 0.7 Mu= 47.91 In -Kips Fu= 70 Ksi cDMn= 33.54 In -Kips ` 0.55 Vn= 18.375 4)Vn= 10.106 Kips Design Ratio Check Mfac= 10.790 In -Kips D +L +E Vfact= 0.763 Kips Shelf Load 3050 Pounds Ratio = Mfac/FMn + Vfac/FVn <1.03 Ratio= 0.397 Ok Prepared By: KL Wood Engineering Associates, Inc. Date: BEAM TO COLUMN CONNECTION CHECK Page: 1 13 8/24/2007 - 4 Moment at Beam to Column Connection Factored Factored .gy ,,:at, " - Co lumn Le vel No. Moment Beam Shear m -.�, • ; _ * 7 , 1 K :. ' Mc In-Kips Vi Kips t =a� 1 7.57 0.653 2 3.42 0.653 Mc 3 0.00 0.000 Mc 4 0.00 0.000 5 0.00 0.000 6 0.00 0.000 Dc 7 0.00 0.000 t, ,,, • Beam 8 0.00 0.000 4 9 0.00 0.000 C • nnector 10 0.00 0.000 11 0.00 0 Beam to Column Connection 12 0.00 0 Mca= d * ( Fva "2 - (Ri / Nc) "2) ".5 Allowable Shear on Connectors Fva = (Vh "2 +Vi "2) " .5 Fv =.4Fu ml Vh = Mc / d Fv = 20 Ksi • Vi = Ri /Nc ;� - Tv Fva =Ab *Fv • Nc = Number M Ab = Shear Area of Connector Connectors i Connector Discription: Stud d I_ • -• -• Cv Ab= 0.155 In. ^2 Compression Zone Fva = 3.10 Kips Allowable Shear ` Ri Beam Type Includes fixed end moment Combined Forces on Connection Point Offset Q = 1 Connectors Shelf Weld Factored Mc Level End Conn Moment Loading Beam No. Description Ma End Mom. 1 3P 13.14 3050 5 IB500 Std. 33.54 10.79 2 3P 13.14 3050 5 IB500 Std. 33.54 6.64 3 da 0 0 . da 0 0 0.00 4 da 0 0 . da 0 0 0.00 5 da 0 0 . da 0 0 0.00 6 da 0 0 . da 0 0 0.00 7 da 0 0 . da 0 0 0.00 8 da 0 0 . da 0 0 0.00 9 da 0 0 . da 0 0 0.00 10 da 0 0 . da 0 0 0.00 11 da 0 0 . da 0 0 0.00 12 da 0 0 da 0 0 0.00 Connectors SC Standard MC Seismic Connector SP Special Welds: S Standard C Weld W Weld All Around - Prepared By: KL Wood Engineering and Associates, Inc. Stud Connector 3 Pin Page:I 14 I c r Studs Ae= 0.110 In "2 2 • Dia. Stud= 0.375 0.66 Fu= 67 Ksi Fy = 50 T2 A Tavg 12 T1 '•1 0 • •• H3 -x 5 ' • H3 r 1 • 3 ' •• .33X X Q 1 c • • Connector Analysis 0.67 1.33 C= T2 + T1 T2 Tavq A C =Tavg • . H2 2 E Ma= 0 =.67XC - ((H3 -X) + 1.34)Tavg T1 •r_ y .67XC= ((H3 -X) + 1.34)Tavg '.• .67X =H3 -X +1.34 • H1 0.41 5 x= 2.59 Inches a ��� A 1.73 . T2max = .4FuAe 2.59 • T2max= 2.96 Kips ~*. C T T1 =H1T2 / (H1 +H2) = 0.50 Kips Force Diagram 0.86 Determine Moment Capacity of Connector-Based on Stud Shear Capacity C= T2 +T1 = 3.46 Kips Ma= (T2 +T1) *Dist. + C *Dist Ma= 13.30 Inch -Kips 4 Connector Capacity Mas= 17.74 Inch -Kips 4 Connector Capacity- -- Seismic Bearing Consideration Column Thickness Mas F= (d *Col. Tk. *1.67 *Ft) Actual Thickness 0.07 Inches 13.14 In -Kips 0.07 0.075 Inches 14.07 In -Kips 2.192 0.083 Inches 15.58 In -Kips 13.14 in -kips 0.1 Inches 17.74 In -Kips 0.126 Inches 17.74 In -Kips 0.135 Inches 17.74 In -Kips Prepared By: KL Wood Engineering Associates, Inc. CHECK RACK OVERTURNING....TRANSVERSE DIRECTION Page:I 15 Date: 8/24/2007 All Shelves Loaded Top Level SEISMIC FORCES HORIZONTAL Seismic 00, Level No. Vi * Hi Shelf Load Moment Due to OT Vt In -Kips Kips In -Kips Comp Vt = Total Shear 1 28.63 2.010 125.96 6.6 Rack Hgt. 2 97.33 2.010 97.33 4.4 overturning based on 3 0.00 0.000 0.00 0.0 heigth to load mass center 4 0.00 0.000 0.00 0.0 5 0.00 0.000 0.00 0.0 6 0.00 0.000 0.00 0.0 G _Vt Slab 7 0.00 0.000 0.00 0.0 1 8 0.00 0.000 0.00 0.0 9 0.00 0.000 0.00 0.0 Depth Df = 36 10 0.00 0.000 0.00 0.0 Frame Depth 11 0.00 0.000 0.00 0.0 6 Base Shear Vt = 0.72 12 0.00 0.000 0.00 0.0 125.96 Ra Rb Seismic Reaction Due to Overturning Reaction Due to Pallet Loads + Dead Load Rs = Mot / Frame Depth Df Rp = Pallet +Dead Load / 2 (2 Columns /Frame) Rs = 3.60 Kips Rp = 2.61 Kips Fac Rs= 3.60 Kips Fac Ue = -0.99 Kips - factored Uplift Resulting Reactions Combining Seismic + Pallet + Dead Load Ra = Rp - Rs Uplift Side If Uplift Exists Rs Must be > Rp for Tension Rb = Rp + Rs Compression Side of Upright Factored Values: Loading /inch of height Rb = 6.21 Kips Seismic 0.022 Ra = -0.99 Kips Uplift Occurs DL +PL 0.016 Vc = 0.36 kips • Prepared By: KL Wood Engineering and Associates, Inc. Date: CHECK RACK OVERTURNING - -- -CONTD Page: 1 16 8/24/2007 6 Top Shelf Loaded Only r p v Top Load Lt = 3.05 Kips Top Shelf Ot= 90.49 In -Kips Vt Top S self 1111.1110111— Vt Slab V = 0.54 kips 0 4 Frame Depth Df = 36 V Inches Ra Rb Seismic Reaction Due to Overturning Reaction Due to Pallet Loads + Dead Loads Rs = Mot / Frame Depth Df Rp = Pallet +Dead Load / 2 (2 Columns /Frame) Rs = 2.661 Kips Rp = 1.305 Kips Fac E = 2.66 Kips Resulting Reactions Combining Seismic + Pallet + Dead Load Ra = Rp - Rs Uplift Side Frame Rs Must be > Rp for Tension In Anchor Bolt Rb =Rp + Rs Compression Side of Frame Factored Values: Rb = 3.97 Kips Ra = -1.36 Kips Uplift Occurs Prepared By: KL Wood Engineering and Associates, Inc. Date: CHECK DIAGONAL BRACING IN FRAME Pager 17 8/24/2007 Bottom Diagonal Brace in Frame Lb = Diagonal Brace Length ill - -. f Lb = (( Depth- 2 *Cd) ^2 + (Panel Spacing- (2 *Bo)) ^2) ^.5 I Column Depth Cd= 3 Depth -2 *Cd Lh = 30 Panel Spacing -2 *Bo Lv = 33 Lb = ( LhA2 + Lv ^2) ^.5 Lb � Bracing Offset Bo= 6 Lb= 44.6 Inches �F Panel Total Horizontal Base Shear 1 `' S pacing 11 t 45 Vt = 0.716 Kips Maximum Compression in Diagonal Depth 36 End Elevation Cmax =(Lb / Lh)* Vt 1.05 Frame geometry multiplier Load Distribution to Columns Cmax = 1.12 Kips Factored Prepared By: KL Wood Engineering and Associates, Inc. Date: C Section Axial Load Capacity Page:l 17a 8/24/2007 Frame Bracing Member Un- braced length Special 44.6 inches Q value= 1 Column Description: No Holes Fy = 50 Ksi Column E = 29500 Maxis Column Section Properties Hole Pat f Column= Special 0 R T = 0.0700 In. Gross Area Ag= 0.256 InA2 Net Area An= 0.256 InA3 Face Al - - — X axis Ix = 0.09 In. ^4 1.5 Sx = 0.12 In. ^3 Rx = 0.592 In. Flange ly = 0.033 In. ^4 0.313 Min. Sy = 0.054 In. ^3 • Section Wgt/Ft. ' Ry = 0.36 In. 0.87 Torsional Properties 2655 ■ j Xo j _ Width M= 0.501 Xo = -0.855 I 1 Cw = 0.02 Ro = 1.101 J = 0.0004181 Column Cross Section g = 0.396 Sx eff = 0.12 In. ^3 Critical Buckling Values - -- Current Edition 1996 AISI LRFD aex = (Tr ^2E(KxIX/Rx) ^2) Eq. C3.1.2 -7 51.291 aey = (7r ^2E(KyLy /Ry) ^2) Eq. C3.1.2 -8 18.989 aet =(1 /ARo^2) *(GJ +7^2Cw /(Ktlt) ^2) Eq. C3.1.2 -9 29.71 Fe =(1/2()'(( Qex +at) - ((Qex +at) ^2- 413aexat) ^.5 Eq. C4.2 -1 20.963 Lx = 44.60 Inches Ly = 44.60 Inches Lt = 44.60 Kx = 1 Inches Ky = 1 Inches Kt = 0.8 Inches Concentrically Loaded Compression Members Section C4 Fe = 18.989 Fy = 50 For X < 1.5 Fn = Fy * .658 ^(102) N = 1.623 For ) > 1.5 Fn = Fy * .877/002) 4) = 0.85 Fn= 16.654 Ksi 4)Pn= 3.62 Kips Channel Capacity Pmax = 3.73 kips Cmax = 1.12 kips Ratio = 0.299 Prepared By: KL Wood Engineering and Associates, Inc. Date: BASE PLATE ANALYSIS AND DESIGN Pagel 18 8/24/2007 8 Pe = 3.05 Kips Fc = 3000 psi f `• 4 Unfactored Bolt Data Dia. = 05 Slab j Fe 1 1� ������I�I�IIII�II Mb = 5.93 In -Kips Solve For Tension In Anchor Bolt , Unfactored Pt = - Pe[(W /2- X/3- e) /(W /2- X/3 +f)] m nii pl l lll lll�� � Pt = 0.15 Kips 1 'q - 1 . R > ': If Negative No Tension In Anchor Bolt I Special Thick.= 0.375 Inches Check Maximum Stress on Slab .333X F1= Pmax/ Base Plate Area I I F1 = 0.087 Ksi I I 0.875 , Eb = 6.125 Inches Inches .y I Solve cubic equation for x value Pt X ^3 +K1X ^2 +K2X +K3 = 0 Blodgett(base plate) Ec = 3.5 Inches K1 = 3(e -W /2) W K2 = 6nAs /B(f + e) Base Plate Width = 7 Inches K3 = K2(W /2 + f) Base Plate Depth = 5 Inches X = 5.3 Inches Solve for concrete stress Axix a Qe = 2(Pe + Pt)/ XB Pe = 3.050 Pt = 0.148 From Pe j i Qe = 0.241 I Qe Qmax= 0.241 Ksi Actual Ok Fall = 1.800 Ksi I Allowable Axis b—�{ . X II !AI Base Plate Data Pressure On Slab From Base Plate Width = 7 Depth = 5 Thickness 0.375 Check Bearing Plate for Full Load Effective Depth = 5 inches LRFD Pp = 1.7 Fc' Ae ' = 0.6 Ae = 35.00 inA2 effective area RMI 7.2 Fc' = 3000 psi Pu = 4.26 kips 1.2D +1.4P +.25L per column Pp = 178.500 kips Pu = 6.21 kips 1.2D +.85P +E per column cf■Pp = 107.100 kips Pmax = 6.21 kips Ok i Prepared By: KL Wood Engineering and Associates, Inc. Date: CHECK BASE PLATE THICKNESS Pagel 19 8/24/2007 c; • Post Style Check Bending In Base Plate C Moment from tension side Pmax = 3.05 Kips M = PL/2 Pt = 0.1476 kips Column If Pt is negative then no tension II Or Mb = 5.93 therefore Pt = 0 3 I ," In -Kips Mbp = Pt C Mbp = 0.166 in -kips 0 w l , '' , Ovh = 2 Thick. = 0.375 C = 1.125 inches l i . :: o : Overhang ii i ���� i i iii ����► i i i 1►1i1i � ii illlll IIII, ������ ��� �II Mbp 0.166 In -Kips M oment from compression side 71k--- M = WL ^2/3 axis a W = 0.1207 Pli Pe +Pt L = 1.125 inches 7 Mbp = 0.051 in -kips Design Moment Base Plate Loading Mmax = 0.166 in -kips Properties Of Base Plate Section Modulus Sx= 1" * TA2 /6 x- axis ,y — Sx= 0.0234 In. ^3 t 1" 0.375 Allowable Bending Stress Fb= .75 * Fy AISC Fy = 36 Ksi Fb = 27 Ksi Allowable Bending Moment Mall =Sx *Fb Mall = 0.633 In -Kips Mbp= Mactual = 0.166 In -Kips Design Ratio Rd = Mactual /Mallowable Design Ratio Rd = 0.262 <= 1.000 OK Prepared By: KL Wood Engineering and Associates, Inc. Date: CHECK ANCHOR BOLTS FOR SHEAR /TENSION Page:l 20 8/24/2007 10 Check Bolt For Combined Shear And Pull-Out Uplift Value From Overturning Section Fot= -1.36 Negative Uplift Occurs Tension Value From Base Plate Section Ftb= 0.148 Negative No Tension Longitudnal Base Shear Per Colunm Vlt = 0.204 Kips Transverse -- - - - - -- Base ShearPer Column Vtt = 0.72 Kips Allowable Values For Expansion Anchors Manfac: Hilti Kwik Bolt TZ ESR -1917 No Special Inspection Required Concrete fc' = 3000 Psi Anchor bolt Desc. 3 .5 3 1/4 LRFD Example: 2000 psi 1/2 Dia x 2 1/4 Vallowable Allow. Shear 4Fas= 2839 Pounds Embd. Length Tallowable Allow. Tension 43Ft= 2386 Pounds Resulting Combined Load Check Fr= ( Tactual / Tallowable) + (Vactual / Vallowable) <= 1.20 Vactual= Vtc / No. of Anchor Bolts Per Column No. of Bolts 2 Vactual Vtc= 0.179 Kips Per column Tactual = Ftb / No. of Anchor Bolts Per Column Tactual Ttb= 0.678 Kips T Ratio = 0.123 V Ratio = 0.010 Fr= 0.133 <= 1 OK Tension On Bolt Tactual Vactual Embedment Length ■)� Shear on Bolt Is 3.5 ® Concrete Slab inches 1/2" Dia. X 3 1/4 Embd. Prepared By: KL Wood Engineering and Associates, Inc. Date: Column Welds To Base Plate Page :l 21 8/24/2007 Weld patterm on column Pfac= 2.61 Kips E4 E6 E5 Welds Factored — � '- S Mb = 5.93 In -Kips E2 - - - - E3 Slab 1 ; - , : ; ; ; , 1 Factored A VAN ( 0.306 Kips El 1 Ref. Axis / 7 i Factored Aisle Side of Column , st, r ,. Base Shear Section --A Weld Section Length Dimensions Weld C.G. Base Plate Width = 7 El ' 3 3 1.5 Base Plate Depth = 5 E2 3 3 3 E3 0 3 0 Allowable Weld Stress E4 0.75 0.75 2.625 Eq. E2.4 -1 E2.4 -2 E5 0.75 0.75 0.375 E6 0 1.5 0 Pna =.4125 * Tm * Lw * Fu Longitudinal Section Modulus of Weld Pattem Pnb =.6 * Tm * Lw * Fu Transverse Fillet Weld Size Tw= 0.1 Inches Weld Fu= 70 Ksi Pna= 21.66 Longitudinal Sx= 0.39 InA3 Pnb= 31.5 Transverse 42.00 Lw= 7.5 Length of weld Aw= 0.75 In ^2 Mc= Sx * Fu Liong= 4.5 Inches Mc= 27.56 In -Kips Ltran= 3 Inches = . Ac= 1.200 InA2 4)Mc= 16.54 In -Kips Fa= Pmax / Ac Fa= 2.18 Ksi If Fb > Fa If Fb <Fa Fv = 0 Fb= Mmax / Sx Fb= 15.06 Ksi Ft= 12.88 Ksi Fv= Vs / Aw Fv= 0.41 Ksi Design Ratio Check Desing Ratio Dr= Ft / Pnb + Fv / Pna = 1.03 Dr one= 0.307 Dr two= 0.019 Dr= 0.326 Ok • Prepared By: KL Wood Engineering and Associates, Inc. Date BASE PLATE SLAB /SOIL ANALYSIS Page:l 22 8/24/2007 Pact Column Loading= 3.05 Kips Worst Colum unfactored Case Fc' = 3000 Psi Qs = 1000 Psf lab T ick. ` Thick. = 6 In Base Plate B Aw FOOTER PROFILE UNDER COLUNM TOP VIEW OF FOOTER Slab Section B Sx= 1 *T ^2/6 D T r e X Sx= 6.000 In. ^ 3 1.1 I, 1 In. -e Bw Enter Base Plate Size Dw= 7 B 5 Effective Area Ae = (2 * Be +Bw) *Dw +(2 *Be) *Bw +p *Be ^2 Be = V8 *Sx *Fct / Qs Beam fixed one end pinned other Fct = 50.6 Psi Fct =1.6 Fc' Seismic Increase 1 Be= 18.70 In. Yes = 1.333 No= 1 Affective Area Ae= 1581.9 In. ^2 11.0 Ft. ^2 Maximum Column Load Pmax = 32957 Pounds 33.0 Kips Allowable Actual Loading on Column Pmax = 3050 Pounds 3.05 Kips Ratio = 0.093 Ok Prepared By: KL Wood Engineering Associates, Inc. Date: CANTILEVER RACK ANALYSIS AND DESIGN Page:1 23 9/26/2007 Roof Load • 0 Project Name: Horizon Restoration Seismic _ Number of Levels 0 u ' i i i ? ,� 1 T I( Fi f � i; {, r l 1�1 j i ' , r� i ('� '.; 4 Includes Base 1 Top Storage Level • 30.5 !.L Total Load In Rack 131.375 Inches I 3.15 Kips 10.95 Feet Arm Per side includes dead load Top Storage Level Rack Design °1r p 1 or top of rack Single Sided '_j 10.95 Double or Single Sided Rack I Arm Load Max. Double= 2 . 1000 Pounds Single= 1 1 = Code 1 .I 1 Single Sided Cantilever L 'IL Average Load Based on Utilization H2 Utilization Ratio = 100 Per Cent ,I c Reaction= 4.15 Kips Upright -- 0►, j- Includes Base �.; Base H1 • 6 Connector " / • V v Design Type I Seismic A Upright Depth Ud -............,10. R Base Depth 14 ► Bd Total Length 10 \ Base Length • Bi Single Sided Profile Arm Length= Ai= 48 Inches Section ID Upright Depth Ud = 10.5 Inches 2 Base Depth Bd= 8 Inches 1= Wide Flange Base Length Bi= 47.25 Inches 2= Roll Formed Total Length Td= 61 Inches Bending Moment in Upright -- Gravity Load Only Mu = No. of Arms * ( Arm Load) • (Arm length + Upright Depth) /2 Mu= 87.75 In -Kips Reaction Location From Centerline of Upright Xr= 21.14 Inches Moment at Base Splice Msg= 87.75 In -Kips L'= 15.89 Inches Date: 2007 OSSC Page:I 25 I 9/26/2007 Using 2002 RMI specifications 2007 OSSC Section 2208 Steel storage racks RMI Section 2.7.2 Minimum Seismic Forces modified by 2007 OSSC Down Aisle direction - -- Longitudinal Braced Frame Zip Code: 30043 Lat. Long. V = CsIeW Height 10.948 Feet Cs = 1.2 *Cv / [R *T ^2/3)] le = 1 Limit state *1.0 R = 4 Limit State RMI Sec. 2.7.3 Cv = Sd1 16 -18 Sds = 2/3 Sms from 2007 OSSC 16 -16 Sms = FaSs Table 1615.1.2(1) Ss= 0.248 Fa = 1.6 Soil profile D Sms = 0.397 Cs = 0.1220 Sds = 0.265 1617.4.2.1 1617.4.2.1 Ct Ta Calculated T in accordance with the Rayleigh Method 0.035 0.211 0.25 0.174 Cs = 2.5 *CaIR 16 -19 Sd1 = 2/3Sm1 Ca = Sds / 2.5 16 -17 Sm1 = FvS1 from 2007 OSSC Table 1615.1.2(2) S1 = 0.09 Fv = 2.4 Soil profile D Sm1 = 0.216 Cs = 0.0661 Max. Sd1 = 0.144 Cs = .14Sds Cs = 0.0370 Min. Cs used in Base Shear Calculations Cs = 0.0661 Date: 2007 OSSC Pagel 26 9/26/2007 Using 2002 RMI specifications 2007 OSSC Section 2208 Steel storage racks RMI Section 2.7.2 Minimum Seismic Forces modified by 2007 OSSC Cross Aisle direction - -- Transverse Moment frame V = CsIeW Height 10.948 Feet Cs = 1.2 *Cv / [R *T ^2/3)] le = 1 Limit state *1.0 R = 6 Limit State RMI Sec. 2.7.3 Cv = Sd1 Sds = 2/3 Sms from 2007 OSSC Sms = FaSs Table 1615.1.2(1) Ss = 0.248 Fa = 1.6 Soil profile D Sms = 0.397 Cs = 0.0814 Sds = 0.265 1617.4.2.1 1617.4.2.1 Ct Ta Calculated T in accordance with the Rayleigh Method • 0.035 0.211 0.25 0.500 Cs = 2.5 *Ca /R Sd1 = 2/3Sm1 Ca = Sds / 2.5 Sm1 = FvS1 from 2007 OSSC Table 1615.1.2(2) S1 = 0.09 Fv = 2.4 Soil profile D Sm1 = 0.216 Cs = 0.044 Max. Sd1 = 0.144 Cs = .14Sds Cs = 0.0370 Min. Cs used in Base Shear Calculations Cs = 0.0441 • Base Shear Page:I 27 I Section 2.2 Load Factors and Combinations for LRFD Method For all rack members RMI RMI Limit State Loading Conditions ASD based Loading Conditions 1 1.2D +L +1.4P D = dead load DL 2 1.2D +1.6L +.5(S or R) + 1.4P L= live load DL +LL +(SL or RL) +PL 3 1.2D +1.6(S or R) +(.5L or .8W) + .85P P = product load DL -(WL or EL) +Plapp 4 1.2D +1.3W +.5L +.5(S or R) +.85P S = snow load DL +LL +(SL or RL) +(WL or EL) +PL 5 1.2D +1.5E +.5L +.2S +.85P W = wind load DL +LL.5(SL or RL) +0.88PL +Imp 6 1.2D +1.5E +.5L +.2S +.85P R = rain Cases 3 and 4 may be multiplied dy 7 .9D -(1.3W or 1.5E) +.45P E = seismic 0.75. In addition, when checking cases 8 (.67 *PLrf*PL) +DL +.25LL I = impact 3 and 4 and seismic forces determined from RMI section 2.7 or another limit 1 Warehouse Rack System Non - public state base code was used EL may Ip = 1 be multiplied by 0.67. V = CsIeWs Cs = 0.066 Longitudinal V = CsIeWs Cs = 0.044 Transverse VI = 0.0661 Ws Longitudinal Limit State Vt = 0.0441 Ws Transverse Limit State Rack systems Ws = (.67 *Prf*P) +D +.25L Prf = Paverage / Pmaximum Force at various shelf levels Fx = (V- F1)WxHx ^k / EWi Hi ^k for shelves greater than 12" above floor F1 = CslpWs for shelf 12" or less above floor Fx = VWxHx ^k / EWiHi ^k for all levels when first shelf > 12" above floor Exponent related to the structures period T < =.5 k= 1 T>2.5 k= 2 If the base shear is based on the default Cs value then k shall be taken as 1 Period Longitudinal direction 0.211 seconds k = 1 Period Transverse direction 0.211 seconds k = 1 • Cantilever Rack Period Calculations Page: I 28 I Based on the Rayleigh Method Rack Top Tied No 1 Ix= 82.84 InA4 Distribution k 0.84 k = 0.84 Final Elx= 2443780 Kx = 1.4299 Period T= 0.173 Seconds Elev. No. Elevation DL PL Total P Cumm. P Pd Pd *hAk R Inches Kips Kips Kips Kips Kips 1 47.375 0.05 1 1.05 3.15 1.05 26.8 0.1976 2 89.375 0.05 1 1.05 2.10 1.05 45.7 0.3368 3 131.375 0.05 1 1.05 1.05 1.05 63.2 0.4655 4 131.375 0 0 0 0.00 0 0.0 0.0000 5 131.375 0 0 0 0.00 0 0.0 0.0000 6 131.375 0 0 0 0.00 0 0.0 0.0000 7 131.375 0 0 0 0.00 0 0.0 0.0000 8 131.375 0 0 0 0.00 0 0.0 0.0000 9 131.375 0 0 0 0.00 0 0.0 0.0000 10 131.375 0 0 0 0.00 0 0.0 0.0000 11 131.375 0 0 0 0.00 0 0.0 0.0000 12 131.375 0 0 0 0.00 0 0.0 0.0000 13 131.375 0 0 0 0.00 0 0.0 0.0000 14 131.375 0 0 0 0.00 0 0.0 0.0000 15 131.375 0 0 0 0.00 0 0.0 0.0000 16 131.375 0 0 0 0.00 0 0.0 0.0000 17 131.375 0 0 0 0.00 0 0.0 0.0000 18 131.375 0 0 0 0.00 0 0.0 0.0000 • 0.15 3 3.15 6.3 3.15 135.8 1.0000 Cumm R Lx Pcr A P Mag. Fact At Pd *OtA2 Ri *zt 1 1 47.375 5256.1 0.0090 1.00E +00 9.02E -03 8.54E -05 1.78E -03 2 0.8024 89.375 1476.8 0.0576 1.00E +00 5.77E -02 3.49E -03 1.94E -02 3 0.4655 131.375 683.5 0.1471 1.00E +00 1.47E -01 2.28E -02 6.86E -02 4 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 5 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 6 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 7 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 8 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 9 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 10 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 11 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 12 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 13 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 14 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 15 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 16 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 17 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 18 0.0000 131.375 683.5 0.0000 0.00E +00 0.00E +00 0.00E +00 0.00E +00 2.64E -02 8.98E -02 Period T= 0.173 Seconds 2rr V] WiAiA2 / g Z Fi \i Pcr = critical elastic buckling load Dp= primary story dirit Lx= column length Mag= maginfication factor Dt =story drift*mag. Factor Calculations for K Value Page: I 29 v. 9/26/2007 From Roarks Formulas of Pt Elastic Stability (Pt + Pi) = 7 E / (KU)^2 general equation for stability P Pt = equals load at top of column. Pi = equals loads applied intermittently on column. P% ii C = Pi /EP Solve equation for the K value Lt K = 1 / (2 -C ^1/4 ) • • Equations from "Roarks Formulas on Stability" Hi Level EPHi P EP C K 1 1 47375 1000 3000 1.0000 1.0000 • 1 2 89375 1000 2000 0.6667 0.9121 1 3 131375 1000 1000 0.3333 0.8063 0 4 0 0 0 0.0000 0.0000 0 5 0 0 0 0.0000 0.0000 0 6 .0 0 0 0.0000 0.0000 0 7 0 0 0 0.0000 0.0000 0 8 0 0 0 0.0000 0.0000 0 9 0 0 0 0.0000 0.0000 0 10 0 0 0 0.0000 0.0000 0 11 0 0 0 0.0000 0.0000 0 12 0 0 0 0.0000 0.0000 0 13 0 0 0 0.0000 0.0000 0 14 0 0 0 0.0000 0.0000 0 15 0 0 0 0.0000 0.0000 0 16 0 0 0 0.0000 0.0000 0 17 0 0 0 0.0000 0.0000 0 18 0 0 0 0.0000 0.0000 3 268125 3000 2.0000 2.7184 Avg 0.9061 (actual) K *f1 Theoritical K value 1.4299 f1 = 1.578 Applied by engineer as an adjustment factor 1- Set by engr. -more conservative Average Hgt 89.375 inches lb = 82.84 in ^4 Pcr = r ^2 *E *Ib/ (Kb Lb) ^2 Pcr = 524.21 ksi based on avg. height based on average height from actual calculations Pcr = 683.49 ksi • • • Date: Upright Design Check Page:I 30 I 9/26/2007 Project Name: Horizon Restoration Section ID 10.5 x 2 x 7 Ga. Upright Section Properties Bars 0 + 0 Y Ag= 5.86 InchesA2 An= 5.86 Inches ^2 Ix= 82.84 Inches"4 Sx= 15.78 Inches ^3 Rx= 3.76 Inch X ( 1 ly= 15.517 Inches ^4 I Sy= 7.758 Inches ^3 Ry= 1.628 Inch I 110.5 I Metal Tk = Elx = 0.188 Inches 2443780.0 Allowable Bending Moment 4 Ma = .6 * Fy *Sx Fy= 50 Ksi Ma= 473.37 In -Kips Column Section Axial Stress AISI -C4 • Fas= Pmax/An Fas = 0.54 Ksi Allowable Axial Stress Pa =Pn /Omega Omega= 1.92 Pn =An *Fn Fe> Fy /2 Fn= Fy* ( 1- Fy / 4 * Fe) Fe< Fy /2 Fn =Fe Computed Fe = p ^2 ' E /( Kx * Lx / Rx) ^2 Lx = 131.375 Kx= 1.430 Kx'Lx/Rx= 49.95 Fe= 116.72 Ksi Fy /2= 25 Ksi Fn= 44.65 Ksi Pa= 136.17 Kips Single Side Pmax= 3.15 Kips < 136.17 Kips Ok Double Side Pmax= 6.45 Kips < 136.17 Kips Ok Bending Moment Plus Axial Stress Check Design Ratio = Pmax / Pa + (Cmx * Mx / Max *Alps) Eq. C5 -1 Design Ratio = Pmax / Pa + Mx / Max Eq. C5 -2 Cm = .85 If Pmax/Pa <= .15 Use Eq. C5 -2 Pmax/Pa= 0.023 Single Side Alpa = (1 - Omega P /Pcr) P= Applied Load = 3.15 Kips Pcr = 3.14 ^2 *E'Ib / (Kb Lb) ^2 Pcr= 683.5 Alpa = 0.991 C5 -2 Dra= 0.209 C5 -1 Drb= 0.182 Design Ratio Dr= 0.209 Controls Gravity Load Design -- Single Side Date: Design check for Combined Seismic and Gravity Loads Page:l 31 9/26/2007 Bending Moment at Base Due to Seismic Seismic Mbss= 15.3 In -Kips Single Side Loaded Seismic Mbss= 30.5 In -Kips Double Sided Gravity Msg= 87.8 In -Kips Single Side - Gravity Mmax= Mbss + Msg Mmax= 103.0 In -Kips Single side controls Design Ratio Drs= 0.023 Axial load ratio - -from page 2c Design Ratio Drd= 0.047 Axial Toad ratio -both sides loded Design Ratio for Bending Design Ratio Dr2= Cmx * Mx / ( Max * Alpha ) Cmx= .85 Mx= 103.0 Mmax Max= 473.37 Allowable If Dr1 < .15 Then Cmx =1 and Alpha =1 D1 = 0.023 If Dr1 > .15 Then Cmx =.85 and Alpha is calculated on Page 2c Design Ration Dr2= 0.24 < 1.33 Ok Seismic design ratio • Down Aisle Upright Check Page:l 31a I Arm level Horizontal Shear by Level 131.38 i 0.000 131.38 — I 207 0.000 i 131.38■ 3 0.000 131.38 0.000 131.38 0.000 16 A''` 131.38 — 1 0.000 131.38 0.000 131.3811• 42 0.000 A 120 131.38 / 0.000 131.38 o 0.000 0 1 '03! 31.38 1 0.000 w ,q. 131.38 120 0.000 131.38* 0 0.000 131.38 0.000 131.38 Is ' °' �p P IP 4j 0.000 131.38* 0.160 89.38 0.109 k �� 75 M 47.38 0.058 75 ':C s:'L r -IT Z ,:i;4,1, - r 3. 1i?%;�bC 4.0 ". ∎11 L+C :1..4.:^- .. .. t..l... -i_.k'' :-*l. I- . VV.44 -= Vt 0.65 Worst Case Double or Single Sided Portal Distribution 2 1- Single Pmax 2- Double Down Aisle Moment Check Bending Moment in Upright M =Vt H / 2 H = 75 Inches Pmax = 6.3 Kips Vt = 0.65 Kips M = 24.55 In -Kips Fy = 50 Ksi Upright Properties An = 5.86 InA2 Design Check = Pu /Pa + CmMy /MayAlpa =1.333 N ly = 15.52 In ^4 Pa = 136.17 Kips Sy = 7.76 InA3 May = 232.8 In -Kips Ry = 1.63 In Alpa = 0.991 I Design Check 0.153 Ok Y Double Channel Section Properties - -- Upright Page: 32 I Single Channel Dbl Channel Ag= ;2.9281 Face= •:.10"5, Ag 5.856 0.7092 An= 2:9281 Flange= ` : 2. An 5.856 0.609 Ix= 41:4201 Return= 1:156 Ix 82.84 0.9638 Sx = 7 Sx 15.78 0.6425 Rx= V'',.' 1 Rx 3.76 1.1657 ly= x 1:360: 0.2748 Sy= 0 '.920¢ 0.2822 Ry= k i >', .0 6601 0.6224 Thick.= 0:1881 Properties About Y axis Double Channel Properties Element Area Dist. A'D A'Db ^2 le 1 2.928 0.522 1.5277 6.3984 1.36 2 2.928 3.478 10.1843 6.3984 1.36 5.856 11.712 12.797 2.72 Ybar- 2 lyt= 15.5169 Syt= 7.7584 Ryt= 1.6278 0.522 II 1.478 2 . 4 Ele 3 Bar added to both flanges Q, p Thick. Width Ele 1 Ele 2 Ele 4 Section Properties with Bars Added ,I I. 2 Elements Area Distance Distance Adx Ady Adbx ^2 Adby ^2 lex X Y 1 2.928 5.25 0.5217 15.37 1.5277 0 6.398 41.42 2 2.928 5.25 3.4783 15.37 10.1843 0 6.398 41.42 3 0.00 0.69 1.0000 0.00 0.0000 0.00 0.000 0.0000 4 0.00 9.81 3.0000 0.00 0.0000 0.00 0.000 0.0000 Area= 5.856 30.74 0.00 12.80 82.84 Ybar= 5.25 lycomb= 15.517 Ixcomb= 82.84 InA4 Area of bars 0.00 Sycomb= 7.758 Sxcomb= 15.78 In "3 Agross= 5.86 Rycomb= 1.628 Rxcomb= 3.76 In Date: Page:I 32a I 9/26/2007 Check Overturning Total Load on Base Rt= 4.15 Kips Single Side Loaded t9 Y' Reaction From Moments( Axial +Seismic ) Rs =( Sum Cvx * Hi + Gravity Moment) / Dn < Rs= 1.69 Kips n Rsultant = -2.46 Kips No Uplift If Negative No Uplift Solve For Reaction Location When Reqd. X =( M + Base Load "A) / (Total Reaction) 1.5" ► X= 13.69 Inches Ok Single Sided na Reaction Anchor Bolt Tension= 0.00 Kips 'f Sum Moments at Toe Irv.{ a�,'zH;�fFx tSS ;g w n*'�fi� : '.�..kf, X -W X= -2.78 Inches 0 52.5 Double Sided Single Side Rack Base Check Base Desiqn 2.5 r 3.15 Kips 103.0 In -Kips I 1.5 1 Kips Ix= 55.85 InA4 I� I Sx= 13.96 InA3 x`14" a 8 Fy= 50 Ksi ff I 23.62 5.25 ► . d 47.25 ► Allowable Bending Moment Ma = Mn /omega Omega = 1.67 C3.1 -1 I N 52.5 , Mn= Se * Fy Mn= 698.2 In -Kips Ma= 418.1 In -Kips Bending Moment At Face of Base Mas = 557.29 In -Kips Seismic Increase ME= 86.47 In -Kips Ok Reaction = 4.15 Kips Mas= 557.29 In -Kips Design ratio= 0.155 Allowable Bending Moment • Date: Page: I 33 I 9/26/2007 Check Design of Cantilever Arm r 1000 i I .� x I i x e 17 • Thickness 0.125 i• . Tom` : 24 Lip 0.625 Section Properties 4 Ix= 2.942 InA4 Sx= 1.216 InA3 Arm Cross Section Bending Moment At Face of Column Mbf= 24000 In- Pounds Fy= 50 Ksi 24 In -Kips Thickness= 0.125 Inches Allowable Bending Moment Ma= .6 • Fy * Sx 0.658 Ma= 36.48 In -Kips Ok Check Weld of Arm to Connector Bracket E2 E1= 3 Inches I E2= 4 Inches I E3= 0.625 Inches El — •— .— . _._._fi_ Metal Thickness Tk= 0.125 Inches Weld Wire E90 70 Ksi Allowable Weld Shear E3 E Fva= .4 • Fu 28 Ksi Total Inches of Weld Wig= 11.25 Inches Section Properties of Weld Group Linear Method Ix= 2.62 In. ^4 Based on Weld Thickness I Sx= 1.40 In. ^3 Based on Weld Thickness Vertical Load Pa= 1 Kips Vertical Shear Stress = Arm Load / Weld Area *.707 Base Metal allowable Vv= 0.404 Ksi Vb = 29.05 ksi Weld Shear Due to Bending Moment Horizontal Shear Stress = Bending Moment / Weld Section Modulus *.707 Vh= 24.18 Ksi Resulting Stress On Weld Pattern Vr= (Vv ^2 + Vh ^2 ) ^.5 Ok Vb= 29.05 ksi Vr= 23.48 Ksi Ok Va= 28 Ksi Arm to Column Connection Date: Page: l 34 I 9/26/2007 1000 Pounds - 1R 1 r ,, �1 24000 In- Pounds x , '.,-: ,( : ,, f. , --, , ,..,. $ a /.;',.1. , Q 7/8" Pin ,� �` , �:,� + is s a ,' a r ,,/ , _ Q C =T a t O. � 3 O - H = 5.75 Inches 0 = .667XC + (5.75 - X )T H -X X = 5.75 / 1.667 Ti . : ° ®: X = 3.449 Inches `'A H -X = 2.301 Inches '`* f ^'� tZ. H .667X = 2.300 Inches a ,- X A C g',-i...',:: . .:rt T = M / (.667X + H -X) .667X T = 5217.00 Pounds T = 5.22 Kips Vertical Shear Force on Pin Vv= P'Im /N N = Number of Pins N = 1 P = Vertical Load P = 1000 Im = Impact Factor Im = 25% Vv = 1.25 Kips Bolt or Pin 7/8" Ap = 0.6010 In ^2 Resulting Shear Force on Pin Fy = 36 Ksi Fv = 14.4 Ksi Vr = (Vv ^2 + T ^2 ) ^.5 Vr = 5.365 Kips Bolt/Pin is in Double Shear Vall = 2 * Ap' Fv Vall = 17.309 Kips > 5.365 Ok Page:l 35 I . Check Bending of Base plan view of double sided base • Bending Moment in Base about Y axis M =PL /4 P = Vt Vt ► 105 L = 105 Inches Vt = 0.65 Kips M = 17.2 In -Kips I I I j Sy = 8.52 InA3 ly= 21.29 In ^4 I Fy = 50 Ksi Allowable bending Moment Y Ma = Sx *Fb Ma = 255.52 In -Kips Ok 9 . Page:I 36 I Check Roll Over Down Aisle Pmax Pmax = 6.3 Kips Mmax Mmax = 24.55 In -Kips Sum Moments About a Base T = Mmax - X'Pmax 8 X1 Upright T = -0.48 No tension a Ok I I j i41 4.5 7.88 T 9 • Double Channel Section Properties - -- Base Page:I 37 Single Channel Dbl Channel Ag= ( °, 2 635" Face= ° ° ` 81 Ag 5.27 An= 2 635•I Flange= ' ' ''I. :;": ' 6. 4 2 An 5.27 Ix= I ` 23 8101 Return= `; 11251 Ix 47.62 Sx= :::'5:960i Sx 11.9 Rx =' '. 3.010 ` Rx 3.01 ly= i 2 X140 Sy= 12403 Ry= . 0 900 Thick.= 0` 1883 Properties About Y axis Double Channel Properties Element Area Dist. A'D A *Db02 le 1 2.635 0.774 2.0400 7.8481 2.14 2 2.635 4.226 11.1350 7.8481 2.14 5.27 13.175 15.696 4.28 Ybar= 2.5 lyt= 19.9762' Syt= 7.9905 Ryt= 1.9469 • 0.7742 I 1.7258 2.5 5 1111121 INVENFEE1 i k Ele 3 Bar added to both flanges x x 0 0 �. Thick. Width Ele 1 Ele 2 Ele 4 Section Properties with Bars Added ►I le 2.5 ley Elements Area Distance Distance Adx Ady Adbx ^2 Adby^2 lex ley x Y 1.36 1 2.635 4 0.7742 10.54 2.0400 4.1171875 3.959 23.81 2.14 1.36 2 2.635 4 4.2258 10.54 11.1350 4.1171875 13.054 23.81 2.14 0.000 3 0.00 0.69 1.2500 0.00 0.0000 0.00 0.000 0.0000 0.000 0.000 4 0.00 7.31 3.7500 0.00 0.0000 0.00 0.000 0.0000 0.000 2.720 Area= 5.27 21.08 8.23 17.01 47.62 4.280 Ybar= 4 lycomb= 21.294 Ixcomb= 55.85 In ^4 Area of bars 0.00 Sycomb= 8.517 Sxcomb= 13.96 In ^3 Rycomb= 2.010 Rxcomb= 3.26 In 4 Date: Page:( 38 I 9/26/2007 Check Slab and Soil Pressure Allowable Comp. Strength of Concrete Pr Fc' = 3000 Psi `'_ Mmax Aloowable Soil Pressure Under Slab 1 1 Qs' = 1000 Psf it 1- Fc = .45 , Fc' Allowable Compression Vi ,p ; 13.69 Fe= 1350 Psi . ~ Ft= 1.6'(Fc') ".5 (� Ft= 87.64 Psi 4i Ca s; Single Double Nil R 38.81 0 52.5 p 116.44 a 4 s • Base Floor Pressure /Soil • Slab Thickness Effective Slab Extension - -- Bef Bef , 9 Total Base Width ( No Re -Bar Considered in Design ) Inches Bef = ( 8 * Sx * Ft / Qs' ) ^ .5 Slab Cross Section Bef= 24.61 Inches S Slab Section Modulus -- 1" Wide Slab pi- 6 0: Sx= b *d ^2/6 . z' Sx = 6.000 In.^ 3 rq • 0 1 1 Inches • Date: Page:I 38a I ' 9/26/2007 Check Slab /Soil - - -- Cont'd 1 Effective Slab Support Area --- Gravity Loads Only ia Rack Loaded One Side Only • 1 ,' Aa =( 2 * Bef + Base Length ) * (2 * Bef + Base Width ) Aa= 6417.59 In. ^2 ° Aa= 44.57 Ft. ^2 s x; i . , Area Required by Soil Pressure Limit - -- Single Side Loaded Ar = Pmax / Allowable Soil Pressure 'i e NI Ar= 4.15 Ft. ^2 <= 44.57 Ft. ^2 %#, , £ Ok Bef 61 ► Bef j 41 ® Wef Side Profile of Base on Slab Single Side Loaded - -- DL + LL + Seismic Base gye.: ti fi, 0.006 4.15 1.1> 116.44 Bef= 24.61 Inches Lt Effective Area Ae =(2 * Bef + Base Width)* ( 2 * Bef + Lt) Ae= 9645.6 In. ^2 Lt= 116.44 Inches Ae= 66.98 Ft.A2 1 Area Required Ar= 3.11 Ft. ^2 Ok Slab Presure at Toe of Base Ft =( 2 * Reaction / Lt ) / Base Width Ft= 0.01 Kips /In. ^2 <= 1.35 Kips/In.A2 Ok ° _ 1 s