Portal Method Prof Schierle 1Portal MethodPortal Method Prof Schierle 2Portal MethodAssumes:• Moment resistant joints• Lateral load• Not gravity loadPortal Method Prof Schierle 3Portal MethodThe Portal Method for approximate analysisof moment frames is based on the following assumptions:• Lateral forces resisted by frame action• Inflection points at mid-height of columns• Inflection points at mid-span of beams• Column shear is based on tributary area• Overturn is resisted by exterior columns only1 Single moment frame (portal)2 Multistory moment frame3 Moment frame subject to total shear V4 Column shear is proportional to tributary area:Va = (V/B) L1/2Vb = (V/B) (L1+L2)/2Vc = (V/B) (L2+L3)/2Vd = (V/B) L3/25 Column moment = shear x height to inflection pointMa = Va h/2Mb = Vb h/2Mc = Vc h/2Md = Vd h/2Portal Method Prof Schierle 4Column axial force N:Overturn moment generates column axial force1 Exterior columns resist most overturn2 Portal method assumes exterior columns resist all overturnColumn axial force = overturn / building width N = M / B3 Overturn moments per level are the sum offorces above the level times lever arm of eachforce to inflection point at respective level: M2 = F2 h2/2 (level 2)M1 = F2 (h2+h1/2) + F1 h1/2 (level 1)Column axial force per level:N2 = M2 / B (level 2)N1 = M1 / B (level 1)Portal Method Prof Schierle 51 Beam shear at any level is column axial forcebelow beam minus column axial force above beam Level 1 beam shear:V = N1 - N2Roof beam:V = N2 - 0 = N22 Beam bending moment is beam shear timesdistance to beam inflection point3 The beam inflection point is assumed at mid-span.Hence beam bending is:M = V L/2Beam axial force is negligible and assumed 0Portal Method Prof Schierle 6Analyze 1st floor columns and beamsColumn shear and bendingBase shearV = F1+F2 = 8+12 V = 20 kColumn shearVa = (L1/2) (V/B) = 15’x20/80 Va = 3.75 kVb = (L1+L2)/2 (V/B)Vb = (20+30)/2 (20/80) Vb = 6.25 kColumn bendingMa = Va h/2 = 3.75 x 14/2 Ma = 26 k’Mb = Vb h/2 = 6.25 x 14/2 Mb = 44 k’Example: two-story buildingAssume:L1 = 30’L2 = 20’B = 30+20+30 B = 80’h = h1 = h2 h = 14’F1 = 8 kF2 = 12 kPortal Method Prof Schierle 7Beam shear and bendingOverturn momentsM1 = F2 (h2+h1/2)+F1 h1/2M1 = 12 (14+7)+8x7 M1 = 308 k’M2 = F2 h2/2 = 12x7 M2 = 84 k’Column axial load 1stfloorN1 = M1/B = 308/80 N1 = 3.9 kColumn axial load 2ndfloorN2 = M2/B = 84/80 N2 = 1.1 kBeam shearV1 = N1–N2 = 3.9-1.1 V1 = 2.8 kBeam bendingM1 = V1 L1/2 = 2.8x30/2 M1 = 42 k’ M2 = V1 L2/2 = 2.8x20/2 M2 = 28 k’Example: two-story buildingAssume:L1 = 30’L2 = 20’B = 30+20+30 B = 80’h = h1 = h2 h = 14’F1 = 8kF2 = 12kPortal Method Prof Schierle 8Unite d’habitation 1952MarseilleArchitect: Le CorbusiersPortal supportPortal Method Prof Schierle 9Terragni: Casa Fascio Como, 1936Concrete PortalPortal Method Prof Schierle 10Panos Koulermos: Hellas Research Foundation, Crete Concrete PortalsPortal Method Prof Schierle 11Frank Lloyd Wright: Storer House, 1923Masonry PortalsMinor lateral resistancePortal Method Prof Schierle 12Ocean view condos VeniceSteel PortalsPortal Method Prof Schierle 13Mies Van der Rohe: Crown Hall IIT, ChicagoSteel PortalPortal Method Prof Schierle 14USC buildingSteel PortalsPortal Method Prof Schierle 15exit