PLATE GIRDERS Builtup sections with deep thin webs

PLATE GIRDERS Built-up sections with deep thin webs susceptible to buckling in shear Dr S R Satish Kumar, IIT Madras 1

Types of Plate Girders • Unstiffened Plate Girder flange plates web plate • Transversely Stiffened Plate Girder ITS BS • Transversely and Longitudinally Stiffened Plate Girder LS Dr S R Satish Kumar, IIT Madras 2

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 3

Shear resistance of a web - 1 q A B q q E 45 o D q C Unbuckled Shear panel Dr S R Satish Kumar, IIT Madras 4

BUCKLING OF WEB PLATES IN SHEAR cr Shear buckling of a plate Dr S R Satish Kumar, IIT Madras 5

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 6

Shear resistance of a web - 3 • shear buckling coefficient (ks) given by d Dr S R Satish Kumar, IIT Madras c 7

• 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 8

Post buckled behaviour - 1 Anchoring of Tension Field Dr S R Satish Kumar, IIT Madras 9

Tension field action Dr S R Satish Kumar, IIT Madras 10

• 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 11

Collapse behaviour - 1 Tensile membrane stress at yield Collapse of the panel Dr S R Satish Kumar, IIT Madras 12

Three phases of tension field action Pre-buckling Dr S R Satish Kumar, IIT Madras post-buckling collapse 13

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

ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS - 1 Force imposed on transverse stiffeners by tension field Dr S R Satish Kumar, IIT Madras 15 15

GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS v Generally located in compression zones of girder v Main function - to increase buckling resistance of web v When it is subject predominantly to shear would develop a collapse mechanism, provided stiffeners remained rigid up to failure v 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 Dr S R Satish Kumar, IIT Madras 16 16

GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS – 1 Longitudinal and Transverse stiffeners Dr S R Satish Kumar, IIT Madras 17

8. 4 Shear The factored design shear force, V, in a beam due to external actions shall satisfy V Vd = design strength calculated as , Vd = Vn / γm 0 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 18

8. 4. 2 Resistance to Shear Buckling for an unstiffened web for a stiffened web a) Simple Post-Critical Method The nominal shear strength is Vn = Vcr = d tw b b = shear stress corresponding to buckling, b) Tension Field Method The nominal shear strength is V n = V tf Dr S R Satish Kumar, IIT Madras 19

8. 4. 2. 2 Shear Buckling Design Methods a) Simple Post-Critical Method -The nominal shear strength is Vn = Vcr = d tw b b = shear stress corresponding to buckling, determined as follows: a) When w < 0. 8 b) When 0. 8 < w < 1. 25 b c) When w 1. 25 b =0. 9 fyw/( 3 w 2) Cont… Dr S R Satish Kumar, IIT Madras 0. 8 1. 25 w 20

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 = 4. 0 +5. 35 /(c/d)2 for c/d < 1. 0 = 5. 35+4. 0 /(c/d)2 for c/d 1. 0 Cont… Dr S R Satish Kumar, IIT Madras 21

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 wtf Dr S R Satish Kumar, IIT Madras c st 22

8. 6 Design of Beams and Plate Girders with Solid Webs 8. 6. 1 Minimum Web Thickness 8. 6. 1. 1 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; i) when c d ii) when 0. 74 d < c < d iii) when c < 0. 74 d Dr S R Satish Kumar, IIT Madras Cont… 23

c) when transverse and longitudinal stiffeners are provided level only (0. 1 d from compression flange) at one 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 24

Design Procedure Initial Sizing 1) Taking L/d as 15, calculate min. d and provide suitably 2) Afreqrd. = BM/ (fy/ mo)d ; using bf = 0. 3 d select flange plate Also calculate Nf = axial force in the flange 3) Check that flange criteria gives a plastic section b = (bf – tw)/2 and b/ tf < 7. 9 4) Web thickness for serviceability 67 < d/ tw < 200 choose such that tw > d/200 5) Check for flange buckling into web Assuming c >1. 5 d , d/ tw < 345 2 Dr S R Satish Kumar, IIT Madras 25

Design Procedure 6) Check for shear capacity of web V < Vd = Vn/ mo; Vn = A (fyw / 3) or Vcr 7) 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 26

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 27

Design Procedure 11) End panel design – check as a beam between flanges Rtf = Hq/2 Rtf Av = c t and Vtf = Av (fy / 3) > Rtf 12) c Mtf = Hqd/10 MR = tc 3/12*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 < 14 tq also < b 14) check for minimum stiffness for c = 1. 5 d, c > 2 d giving Cl. 8. 7. 2. 4 p 91 I prov. = (bs-tw/2)3 tq/12 > 0. 75 dtw 3 Dr S R Satish Kumar, IIT Madras bs tq 28

Design Procedure 15) Check for Buckling Cl. 8. 7. 2. 5 p 91 Stiffener force, Fq = V - Vcr/ mo Fqd Buckling Resist. Pq with 20 tw on either side Cl. 8. 7. 1. 5 p 90 Calculate Ixx and A, rxx = (Ixx/A) Leff = 0. 7 d, = Leff/rxx, Find fc Pq = fc A > Fq bs 16) tq Cl. 8. 7. 2. 6 p 92 Connection to web shear = tw 2 / 8 bs k. N/mm choose appropriate weld size 19) Check for Intermediate Stiffener under Load Cl. 8. 7. 2. 5 p 91 Dr S R Satish Kumar, IIT Madras 29