1Moment frame Prof Schierle 1Moment frameMoment frame Prof Schierle 2Eight-story steel moment frameBased on former UBC requirementsLive load 50 psfLive load reduction R = 0.08 (A-150)whereR = LL reduction in percentA = tributary areaReduction shall not exceed:40% for members supporting a single level60% for other members90100Total DL+LL50 x 0.4 = 2050 x 0.6 = 30LL7070DL2020Partitions1010FramingColumnBeamGravity load33Floor/ceiling3737Concrete slabMoment frame Prof Schierle 39095Total DL+LL50 x 0.4 = 2050 x 0.5 = 25LL7070DL2020Partitions1010FramingColumnBeamGravity load33Floor/ceiling3737Concrete slabEight-story steel moment frameAssume ASCE 7 & IBC requirementsLive load 50 psfLive load reduction for tributary are > 600 sq. ft.Reduction shall not be less than:50% for members supporting one level40% for members supporting two or more levels2Moment frame Prof Schierle 4AssumeAverage wind pressure P = 30 psfGravity loadBeams = 95 psfColumns = 90 psfDesign ground floor beams and columnsUniform beam load w = 95 psf x 30’/1000 w = 2.85 klfUniform column load (distributed on beam) w = 90 psf x 30’/1000 w = 2.7 klfBase shear V = 30 psf x 30’ x 7.5 x 12’/1000 V = 81 kOverturn momentsGround floor M0M0 = 30 psf x 30’ x (7.5x12)2 /2 / 1000 M0 = 3,645 k’First floor M1M1= 30 psf x 30’(6.5 x12)2 /2 / 1000 M1= 2,738 k’Moment frame Prof Schierle 5Column bending162k’027x6 = 162k’b & c 194k’3x302/24 = 11313.5x6 = 81k’a & d MMgravity= wL2/24Mlateral = Vc h/2Col.Column axial force (n = # of stories)648k8x2.7x30 = 6480b & c 365k8x2.7x15 = 3243645/90 = 41ka & d PPgravity= nwLtributaryPlateral= M0/BCol.Combined axial + bending ( P= P + M Bx) 1006k162k’x12”x0.184 = 358648kb & c 793k194k’x12”x0.184 = 428365ka & d PM Bx (Bx assumes M in k-in)PCol.0.184 > 0.1831083 > 1006W14x193b & c 0.184 = 0.184812 > 793W14x145a & dBxestimate vs. BxPallowablevs. PUseCol.Column design (assume KL = 1.2x12’ = 14’)27.0k30 x 81 / 90b & c 13.5k15 x 81 / 90a & dVcVc = LtribV/BColumnColumn shearMoment frame Prof Schierle 60.184 > 0.1831083 > 1006W14x193b & c 0.184 = 0.184812 > 793W14x145a & dBxestimate vs. BxPallowablevs. PUseCol.3Moment frame Prof Schierle 7Beam designFrom previous page: Uniform beam load w = 2.85 klfOverturn momentsGround floor M0M0 = 3,645 k’First floor M1M1 = 2,738 k’Column a &d axial load N0= M0/ B = 3645 / 90 N0= 41 kN1= M1/ B = 2738 / 90 N1= 30 kBeam shearV = N0 -N1V = 11 kBeam bendingMlateral = V L/2 = 11 x30/2 Mlateral = 165 k’Mgravity = wL2/12 = 2.85x302/12 Mgravity = 214 k’M = 165+214  M = 379 k’Section modulus requiredSx= M / Fb= 379 k’ x 12” / 22 ksi Sx= 207 in3Use W18x119Note: W18 beam has optimal ratio L/d = 20Moment frame Prof Schierle 8RequiredSx≥ 207UseW18x119Sx= 231Moment frame Prof Schierle 9Column bending76k’012.6x6 = 76k’b & c 139k’2.7x302/24 = 1016.3x6 = 38k’a & d MMgravity= wL2/24Mlateral = Vc h/2Col.Column axial force (n = # of stories above)324k4x2.7x30 = 3240b & c 171k4x2.7x15 = 162794/90 = 9ka & d PPgravity= nwLtributaryPlateral= M/BCol.Combined axial load + bending ( P= P + M Bx) 494k76k’x12”x0.186 = 170324kb & c 481k139k’x12”x0.186 = 310171ka & d PM Bx (Bx assumes M in k-in)PCol.0.186 > 0.185497 > 494W14x90b & c 0.186 > 0.185546 > 481W14x99a & dBxestimate vs. BxPallowablevs. PUseCol.Column design (assume KL = 1.2x12’ = 14’)12.6k30 x 38 / 90b & c 6.3k15 x 38 / 90a & dVcVc = LtribV/BColumn shearLevel 4 ColumnsShear V = 30x30x3.5x12/1000 V = 38 kOverturn moment M4=30psfx30’x(3.5x12)2/2x1000 M = 794 k’ Column shear432104Moment frame Prof Schierle 100.186 > 0.185497 > 494W14x90b & c 0.186 > 0.185546 > 508W14x99a & dBxestimate vs. BxPallowablevs. PUseCol.Moment frame Prof Schierle 110.186 > 0.185497 = 494W14x90b & c Bxestimate vs. BxPallowablevs. PUseCol.0.184 > 0.1831083 > 1006W14x193b & c 0.184 = 0.184812 > 793W14x145a & dBxestimate vs. BxPallowablevs. PUseCol.Ground floor columns Level 4 columns103x12 = 1236 #193-90 = 103 #1236 #b & c 46x12 = 552 #145-99 = 46 #552 #a & dweight/columnweight/footweightCol.DL difference between Level 4 and ground floor0.186 > 0.185546 > 508W14x99a & dCompare columns 43210Moment frame Prof Schierle 12Crown Zellerbach buildingSan FranciscoArchitect: SOM & Hertzka and KnowlesEngineer: H J BrunnierThe 19-story building has an external core and column-free, moment frame, office wingSize: 201x69’ Height: 309’Story height: 13.7’Height/width ratio 4.48A Column B Spandrel beam C Girder D Joist @ 7’E Gusset plateF Fire proofing8’ deep mat footing5Moment frame Prof Schierle 13Crown Zellerbach building San Francisco 1959Size: 201x69’ post spacing = 22’ x 66’Height: 309’ 19 storiesStory height: 13.7’ Ground + top mechanical floors: h ~ 20’Beam Post Fb= 30 ksiDL = 70 psf 70 psf Wing pressure p = 30 psfLL 25 psf 20 psfDL+LL 95 psf 90 psfPortal designBeam load bw = 95 psf x 22’/1000 bw = 2.1 klfPost load pw = 90 psf x 22’/1000 pw = 1.98 klfBase shearV = 30 psf x 22’ x (309-10’)/1000 V = 197 k2ndfloor shear V2= 30 psf x 22’ x((309-26.85’)/1000 V2= 186 kOverturn moment M = 197 x(309-10’)/2 M = 29,452 k’2ndfloor overturn M2= 186 x (309-26.85)/2 M2= 26,240 k’Beam shear V = (M-M2)/B=(29,452-26,240)/66’ V = 49 kLateral M = V B/2 = 49x66/2 M = 1,617 k’Gravity M = wL2/12 = 2.1x662/12 M = 762 k’Total M = 1617+762) x12” M = 28,548 k”Req. S = M/Fb= 28,548./30 ksi S = 952 in3Use W40x244 S = 983 > 952Lateral post load P = M/B = 29,452 / 66’ P = 446 kGravity post load @ ground floorP = 19x1.98 klf x 69’/2 P = 1298 kPost shear V = 197k/2 V = 98.5 kPost bending M = 98.5 x 10’x12” M = 11.820 k”Try bending factor Bx = 0.174Total post load P = 446 +1298+11,820x0.174 P = 3,801 kUse W14x550 , Bx= 0.174 P = 3,856 > 3,801Moment frame