DRAFT IS:800

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PLATE GIRDERS
Built-up sections with deep thin webs susceptible
to buckling in shear
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Types of Plate Girders

• Unstiffened Plate Girder
• Transversely Stiffened Plate Girder
• Transversely and Longitudinally Stiffened Plate
  Girder

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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

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Shear resistance of a web - 1
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BUCKLING OF WEB PLATES IN SHEAR
Shear buckling of a plate
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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
  iscritical shear stress
• Critical shear stress in such a case is given by
• Boundary conditions assumed to be simply supported

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Shear resistance of a web - 3

• shear buckling coefficient (ks) given by

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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

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• Post buckled behaviour - 1

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Tension field action
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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

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• Collapse behaviour - 1

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Three phases of tension field action
Pre-buckling post-buckling
collapse
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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

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ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS -
1
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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 

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GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED
GIRDERS 1
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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 / ?m0 8.4.1 The
nominal plastic shear resistance under pure shear
is given by Vn Vp Av shear
area Cont
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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 tw?b
• ?b shear stress corresponding to
  buckling,
• b) Tension Field Method
• The nominal shear strength is
• V n V tf

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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 tw?b
• ?b shear stress corresponding to buckling,
  determined as follows
• a) When ?w lt 0.8
• b) When 0.8 lt ?w lt 1.25
• c) When ?w ?1.25
• ?b 0.9 fyw/(?3?w2)
• Cont

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IS 800 2007
?w 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 lt 1.0 5.354.0
/(c/d)2 for c/d ? 1.0 Cont
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IS 800 2007
b) Tension Field Method - the nominal shear
resistance, Vn, should be VnVtf ?
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 ?
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IS 800 2007

• 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
• when c ? d
• ii) when 0.74 d lt c lt d
• iii) when c lt 0.74 d
• Cont

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c) when transverse and longitudinal stiffeners
are provided at one level only (0.1 d from
compression flange) i) when c gt d ii)
when 0.74 d lt c lt d iii) when c lt 0.74
d d) when a second longitudinal
stiffener (located at neutral axis is provided )
Cont
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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 lt 7.9?
• Web thickness for serviceability 67? lt d/ tw lt
  200?
• choose such that tw gt d/200?
• Check for flange buckling into web
• Assuming c gt1.5d , d/ tw lt 345?2

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Design Procedure

• Check for shear capacity of web
• V lt Vd Vn/ ?mo Vn A (fyw /?3) or Vcr
• Check for calculating resistance to shear
  buckling
• d/ tw gt 67? ?(kv/5.35) use kv for c/d gt 1
• 8) Simple post-critical method
• Vcr d tw ?b where ?b ?(?w) and ?w
  ?(?cr )
• 9) If V lt Vcr/ ?mo then safe else tension field
  calculation reqrd.
• 10) Vn Vtf ?(fv and ?) also calculate Mfv
  ?(Nf )
• If V lt Vn/ ?mo safe ! else revise design

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Design Procedure
IS 800 2007

• 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.

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Design Procedure

• 11) End panel design check as a beam between
  flanges
• Rtf Hq/2
• Av c t and Vtf Av (fy /?3) gt Rtf
• 12) Mtf Hqd/10
• MR tc3/12fyd / (c/2) gt Mtf
• 13) Intermediate Transverse Stiffener
  Design
• i) decide to provide stiffener on one side or
  both sides
• ii) choose tq gt tw outstand bs lt 14tq?
  also lt b
• 14) check for minimum stiffness Cl.8.7.2.4
  p91
• for c 1.5d, c gt ?2 d giving
• I prov. (bs-tw/2)3 tq/12 gt 0.75dtw3

Rtf
c
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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 p90
• Calculate Ixx and A, rxx ?(Ixx/A)
• Leff 0.7d, ? Leff/rxx, Find fc
• Pq fc A gt 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