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**PLATE GIRDERS Built-up sections with deep thin webs**

susceptible to buckling in shear Dr S R Satish Kumar, IIT Madras

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**Dr S R Satish Kumar, IIT Madras**

Types of Plate Girders Unstiffened Plate Girder Transversely Stiffened Plate Girder Transversely and Longitudinally Stiffened Plate Girder web plate flange plates ITS BS LS Dr S R Satish Kumar, IIT Madras

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**SHEAR RESISTANCE OF STIFFENED GIRDER**

Shear resistance of a web Pre-buckling behaviour (Stage 1) Requirements of equilibrium in an element inside a square web plate subject to a shear stress result in generation of complementary shear stresses This results in element being subjected to principal compression along one diagonal and tension along the other Dr S R Satish Kumar, IIT Madras

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**Shear resistance of a web - 1**

q 45o B D C E Unbuckled Shear panel Dr S R Satish Kumar, IIT Madras

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**BUCKLING OF WEB PLATES IN SHEAR**

cr Shear buckling of a plate Dr S R Satish Kumar, IIT Madras

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**Shear resistance of a web - 2**

As the applied loading is incrementally enhanced, plate will buckle along direction of compressive diagonal - corresponding shear stress in plate is“critical shear stress” Critical shear stress in such a case is given by Boundary conditions assumed to be simply supported Dr S R Satish Kumar, IIT Madras

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**Shear resistance of a web - 3**

shear buckling coefficient (ks) given by c d Dr S R Satish Kumar, IIT Madras

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**Post buckled behaviour (Stage 2)**

Compression diagonal is unable to resist any more loading beyond elastic critical stress Any further increase in shear load is supported by a tensile membrane field, anchored to top and bottom flanges and adjacent stiffener members on either side of web Total state of stress in web plate may be obtained by superimposing post-buckled membrane tensile stresses upon critical shear stress Dr S R Satish Kumar, IIT Madras

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**Anchoring of Tension Field**

Post buckled behaviour - 1 Anchoring of Tension Field Dr S R Satish Kumar, IIT Madras

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**Dr S R Satish Kumar, IIT Madras**

Tension field action Dr S R Satish Kumar, IIT Madras

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**Collapse behaviour (Stage 3)**

When load is further increased, tensile membrane stress continues to exert an increasing pull on flanges Eventually resultant stress obtained by combining the buckling stress and membrane stress reaches yield value for web - can be determined by Von-Mises yield criterion Dr S R Satish Kumar, IIT Madras

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**Tensile membrane stress at yield**

Collapse behaviour - 1 Collapse of the panel Tensile membrane stress at yield Dr S R Satish Kumar, IIT Madras

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**Three phases of tension field action**

Pre-buckling post-buckling collapse Dr S R Satish Kumar, IIT Madras

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**ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS**

Transverse stiffeners play important role by increasing web buckling stress by supporting tension field after web buckling by preventing tendency of flanges to get pulled towards each other Stiffeners should possess sufficient rigidity to ensure that they remain straight, while restricting buckling to individual web panels 14 Dr S R Satish Kumar, IIT Madras

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**ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS - 1**

Force imposed on transverse stiffeners by tension field 15 Dr S R Satish Kumar, IIT Madras

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**GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS**

Generally located in compression zones of girder Main function - to increase buckling resistance of web When it is subject predominantly to shear would develop a collapse mechanism, provided stiffeners remained rigid up to failure Once one of sub panels has buckled, post buckling tension field develops over whole depth of web panel and influence of stiffeners may be neglected 16 Dr S R Satish Kumar, IIT Madras

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**GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS – 1**

Longitudinal and Transverse stiffeners Dr S R Satish Kumar, IIT Madras

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IS 800: 2007 8.4 Shear The factored design shear force, V, in a beam due to external actions shall satisfy V Vd Vd = design strength calculated as , Vd = Vn / γm0 8.4.1 The nominal plastic shear resistance under pure shear is given by: Vn = Vp Av = shear area Cont… Dr S R Satish Kumar, IIT Madras

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**IS 800: 2007 8.4.2 Resistance to Shear Buckling for an unstiffened web**

for a stiffened web Simple Post-Critical Method The nominal shear strength is Vn = Vcr Vcr = d twb b = shear stress corresponding to buckling, b) Tension Field Method V n = V tf Dr S R Satish Kumar, IIT Madras

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**8.4.2.2 Shear Buckling Design Methods**

a) Simple Post-Critical Method -The nominal shear strength is Vn = Vcr Vcr = d twb b = shear stress corresponding to buckling, determined as follows: a) When w < 0.8 b) When 0.8 < w < 1.25 c) When w 1.25 b =0.9 fyw/(3w2) Cont… 0.8 1.25 w b Dr S R Satish Kumar, IIT Madras

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IS 800: 2007 λw = non -dimensional web slenderness ratio for shear buckling stress, given by The elastic critical shear stress of the web, cr is given by: kv = 5.35 when transverse stiffeners are provided only at supports = /(c/d) for c/d < 1.0 = /(c/d)2 for c/d 1.0 Cont… Dr S R Satish Kumar, IIT Madras

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IS 800: 2007 b) Tension Field Method - the nominal shear resistance, Vn, should be Vn=Vtf Vnp fv = yield strength of the tension field obtained from =1.5 b sin 2 = inclination of the tension field The width of the tension field, wtf, is given by: wtf = d cos – (c-sc-st) sin sc st c wtf Dr S R Satish Kumar, IIT Madras

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**(web connection by flanges along one longitudinal edge only)**

IS 800: 2007 8.6 Design of Beams and Plate Girders with Solid Webs 8.6.1 Minimum Web Thickness Serviceability Requirement a) when transverse stiffeners are not provided (web connection by flanges along both longitudinal edges) (web connection by flanges along one longitudinal edge only) b) when transverse stiffeners only are provided; when c d ii) when 0.74 d < c < d iii) when c < 0.74 d Cont… Dr S R Satish Kumar, IIT Madras

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**(0.1 d from compression flange) i) when c > d**

c) when transverse and longitudinal stiffeners are provided at one level only (0.1 d from compression flange) i) when c > d ii) when 0.74 d < c < d iii) when c < 0.74 d d) when a second longitudinal stiffener (located at neutral axis is provided ) Cont… Dr S R Satish Kumar, IIT Madras

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**Design Procedure Initial Sizing**

Taking L/d as 15, calculate min. d and provide suitably Afreqrd. = BM/ (fy/mo)d ; using bf = 0.3d select flange plate Also calculate Nf = axial force in the flange Check that flange criteria gives a plastic section b = (bf – tw)/2 and b/ tf < 7.9 Web thickness for serviceability 67 < d/ tw < 200 choose such that tw > d/200 Check for flange buckling into web Assuming c >1.5d , d/ tw < 3452 Dr S R Satish Kumar, IIT Madras

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**Design Procedure Check for shear capacity of web**

V < Vd = Vn/ mo; Vn = A (fyw /3) or Vcr Check for calculating resistance to shear buckling d/ tw > 67 (kv/5.35) use kv for c/d > 1 8) Simple post-critical method Vcr = d tw b where b = (w) and w = (cr ) 9) If V < Vcr/ mo then safe else tension field calculation reqrd. 10) Vn = Vtf = (fv and ); also calculate Mfv = (Nf ) If V < Vn/ mo safe ! else revise design Dr S R Satish Kumar, IIT Madras

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**IS 800: 2007 Design Procedure 8.7 Stiffener design**

a) Intermediate Transverse Web Stiffener To improve the buckling strength of slender web due to shear. b) Load Carrying Stiffener To prevent local buckling of the web due to concentrated loading. c) Bearing Stiffener To prevent local crushing of the web due to concentrated loading . d) Torsion Stiffener To provide torsional restraint to beams and girders at supports. e) Diagonal Stiffener To provide local reinforcement to a web under shear and bearing. f) Tension Stiffener To transmit tensile forces applied to a web through a flange. Dr S R Satish Kumar, IIT Madras

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**Design Procedure Rtf c bs tq**

11) End panel design – check as a beam between flanges Rtf = Hq/2 Av = c t and Vtf = Av (fy /3) > Rtf 12) Mtf = Hqd/10 MR = tc3/12*fyd / (c/2) > Mtf 13) Intermediate Transverse Stiffener Design i) decide to provide stiffener on one side or both sides ii) choose tq > tw ; outstand bs < 14tq also < b 14) check for minimum stiffness Cl p91 for c = 1.5d, c > 2 d giving I prov. = (bs-tw/2)3 tq/12 > 0.75dtw3 Rtf c bs tq Dr S R Satish Kumar, IIT Madras

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**Design Procedure bs tq 15) Check for Buckling Cl.8.7.2.5 p91**

Stiffener force, Fq = V - Vcr/mo Fqd Buckling Resist. Pq with 20tw on either side Cl p90 Calculate Ixx and A, rxx = (Ixx/A) Leff = 0.7d, = Leff/rxx, Find fc Pq = fc A > Fq 16) Connection to web Cl p92 shear = tw2 / 8bs kN/mm choose appropriate weld size 19) Check for Intermediate Stiffener under Load Cl p91 bs tq Dr S R Satish Kumar, IIT Madras

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