Dr S R Satish Kumar, IIT Madras1 PLATE GIRDERS Built-up sections with deep thin webs susceptible to buckling in shear

Dr S R Satish Kumar, IIT Madras 1

PLATE GIRDERS

Built-up sections with deep thin webssusceptible to buckling in shear


Types of Plate Girders• Unstiffened Plate Girder

• Transversely Stiffened Plate Girder

• Transversely and Longitudinally Stiffened Plate Girder

web plate flange plates

ITSBS

LS


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


Shear resistance of a web - 1

Aq

q

45o

B

DC

q

E

q

Unbuckled Shear panel


Shear buckling of a plate

BUCKLING OF WEB PLATES IN SHEAR

cr



– 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

2

d

t

2112

E2skcrq



• shear buckling coefficient (ks) given by

panelswideforeid

cwhere

c

dks ..,1435.5

2

stiffenerstransversespaced

closelywithwebsforeid

cwhere

c

dks ..,1435.5

2

c

d


• 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


Post buckled behaviour - 1

Anchoring of Tension Field


Tension field actionTension field action


• 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


Collapse behaviour - 1

Collapse of the panel

Tensile membrane stress at yield


Three phases of tension field actionThree phases of tension field action

Pre-buckling post-buckling collapse


ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERSULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS

Transverse stiffeners play important role by increasing web buckling stressby supporting tension field after web bucklingby 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


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

Force imposed on transverse stiffeners by tension field


GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERSGENERAL 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


GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS – 1

Longitudinal and Transverse stiffeners


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…

3ywv

p

fAV


8.4.2 Resistance to Shear Bucklingfor an unstiffened web

for a stiffened web

a) Simple Post-Critical Method The nominal shear strength is

Vn = Vcr Vcr = d twb

b = shear stress corresponding to buckling,

b) Tension Field Method

The nominal shear strength is

V n = V tf

67wt

d

yf/250

vk


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…

3/ywb f

3/8.0625.01 ywwb f

0.8 1.25 w

b


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…

)3( ,ecryww f

22

2

/112 w

vcr

td

Ek


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

5.0222 3 bywv ff

c

d1tan

ctf

Ms

wy

fr

5.0

sin

2

202 //125.0 myffffyffffr ftbNftbM

sin9.0 vwtfbwtf ftwtdV

sc

stc

wtf


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

Cont…

180wt

d

90wt

d

wwt

d 200

wwt

c 200

wwt

d 270


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…

wwt

d 250

wwt

c 250

wwt

d 340

wwt

d 400


Design Procedure

Initial Sizing1) Taking L/d as 15, calculate min. d and provide suitably

2) Afreqrd. = BM/ (fy/mo)d ; using bf = 0.3d 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 < 200choose such that tw > d/200

5) Check for flange buckling into web

Assuming c >1.5d , d/ tw < 3452


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


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.


Design Procedure

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.8.7.2.4 p91for c = 1.5d, c > 2 d giving

I prov. = (bs-tw/2)3 tq/12 > 0.75dtw3

)/1(.25.1 dpcrdpq VVVH Rtf

c

bs

tq


Design Procedure

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.8.7.1.5

p90Calculate Ixx and A, rxx = (Ixx/A)Leff = 0.7d, = Leff/rxx, Find fcPq = fc A > Fq

16) Connection to web Cl.8.7.2.6 p92

shear = tw2 / 8bs kN/mm choose appropriate weld size

19) Check for Intermediate Stiffener under Load Cl.8.7.2.5 p91

1

ys

s

xd

x

qd

xq

M

M

F

F

F

FF

bs

tq

Documents

Dr S R Satish Kumar, IIT Madras1 PLATE GIRDERS Built-up sections with deep thin webs susceptible to buckling in shear