Plate girders are normally proportioned to resist bending on the assumption that the moment of inertia of the gross section is effective. The web must be propor-
tioned such that the maximum web depth-thickness ratio h/tdoes not exceed h/t given by (7.32) or (7.33), whichever is applicable.
Ifa/hⱕ1.5,
h 2000
ⱕ (7.32)
t 兹Fyƒ Ifa/h⬎1.5,
h 14,000
ⱕ (7.33)
t 兹Fyƒ(Fyƒ⫹Fr) wherea⫽clear distance between transverse stiffeners, in
t⫽web thickness, in
Fyƒ⫽specified minimum yield stress of steel, ksi
Fr⫽compressive residual stress in flange⫽16.5 ksi for plate girders Web stiffeners are frequently required to achieve an economical design. However, web stiffeners are not required ifh/t⬍260 and adequate shear strength is provided by the web. The criteria for the design of plate girders are given in the AISC LRFD Specification.
Design Flexural Strength. The design flexural strength isbMn, whereb⫽0.90.
If hc/t ⱕ 970兹Fy, determine the nominal flexural strength as indicated in Art.
7.15, for either compact or noncompact shapes. Ifhc/t⬎970兹Fy,Mnis governed by the limit states of tension-flange yielding or compression-flange buckling.
The design strength is the smaller of the values of bMn for yielding of the tension flange, which is
bMn⫽0.90S R R Fxt PG e yt (7.34) and for buckling of the compression flange, which is
bMn⫽0.90S R R Fxc PG e cr (7.35) whereRPG⫽ plate-girder bending-strength reduction factor
⫽ 1⫺0.0005ar(hc/t⫺ 970 /兹Fcr)ⱕ 1.0 Re⫽ hybrid girder factor
⫽ 1⫺0.1(1.3⫹ar)(0.81⫺ m)ⱕ1.0
⫽ 1 for nonhybrid girders
ar⫽ ratio of web area to compression-flange area
m⫽ ratio of web yield stress to flange yield stress or toFcr Fcr⫽ critical compression-flange stress, ksi
Fyt⫽ yield stress of tension flange, ksi
Sxt⫽ section modulus, in3, with respect to the tension flange Sxc⫽ section modulus, in3, with respect to the compression flange The critical stress Fcr is different for different limit states. Its value is computed from the values of parameters that depend on the type of limit state: plate girder coefficient CPG, slenderness parameter , limiting slenderness parameter pfor a compact element, and limiting slenderness parameter, for a noncompact element.
Thus, Fcr may be computed from one of Eqs. (7.34) to (7.36) for the limit states
of lateral-torsional buckling and flange local buckling. The limit state of local buck- ling of web does not apply.
Fcr⫽Fyƒ ⱕ p (7.36)
⫺
1 p
Fcr⫽C Fb yƒ冋 冉 冊册1⫺2 r⫺p ⱕFyƒ p⬍ ⱕ r (7.37)
Fcr⫽CPG/2 ⬎r (7.38)
whereFyƒ⫽specified minimum flange yield stress, ksi
Cb⫽bending coefficient dependent on moment gradient
⫽1.75⫹1.05(M1/M2)⫹0.3(M1/M2)2for lateral-torsional buckling
⫽1 for flange local buckling
CPG⫽286,000 /Cbfor lateral torsional buckling
⫽11,200 for flange local buckling
⫽Lb/rTfor lateral-torsional buckling
⫽bƒ/ 2tƒfor flange local buckling Lb⫽laterally unbraced length of girder, in
rT ⫽radius of gyration, in, of compression flange plus one-sixth the web bƒ⫽flange width, in
tƒ⫽flange thickness, in
p⫽300 /兹Fyƒfor lateral-torsional buckling
⫽65 /兹Fyƒfor flange local buckling
r⫽756 /兹Fyƒfor lateral-torsional buckling
⫽150 /兹Fyƒfor flange local buckling
Design Shear Strength. This is given byvVn, wherev⫽ 0.90. With tension- field action, in which the web is permitted to buckle due to diagonal compression and the web carries stresses in diagonal tension in the panels between vertical stiffeners, the design shear strength is larger than when such action is not permitted.
Tension-field action is not allowed for end panels in nonhybrid plate girders, for all panels in hybrid girders and plate girders with tapered webs, and for panels in which the ratio of panel width to deptha/hexceeds 3.0 or [260(h/t)]2, wheretis the web thickness. For these conditions, the design shear strength is given by
nVn⫽0.90⫻0.6A F Cw yw v⫽0.54A F Cw yw v (7.39) whereAw⫽web area, in2
Fyw⫽specified web yield stress, ksi
Cv⫽ratio of critical web stress, in the linear buckling theory, to the shear yield stress of the web steel
For tension-field action, the design shear strength depends on the ratio of panel width to deptha/h. For h/tⱕ187兹k/Fyw,
vVn⫽0.54A Fw yw (7.40)
Forh/t⬎187兹k/Fyw,
1⫺Cv
vVn⫽0.54A Fw yw冉Cv⫹1.15兹1⫹(a/h)2冊 (7.41) wherek⫽ web buckling coefficient
⫽ 5 ifa/h⬎ 0.3 ora/h⬎[260 / (h/t)]2
⫽ 5⫹5 / (a/h)2 otherwise
Cv⫽ 187兹k/Fyw when 187 ⱕh/tⱕ
兹k/Fyw 234兹k/Fyw h/t
⫽ 44,000 k whenh/t⬎
234兹k/Fyw
(h/t)2 Fy
Web Stiffeners. Transverse stiffeners are required if the web shear strength with- out stiffeners is inadequate, if h/t ⬎418 /兹Fyw, or ifh/t does not meet the re- quirements of Eqs. (7.30) and (7.31). Where stiffeners are required, the spacing of stiffeners should be close enough to maintain the shear within allowable limits.
Also, the moment of inertiaIst, in4, of a transverse stiffener should be at least that computed from
Ist⫽at j3 (7.42)
wherej⫽2.5 / (a/h)2⫺2.
The moment of inertia for a pair of stiffeners should be taken about an axis through the center of the web. For a single stiffener,Istshould be taken about the web face in contact with the stiffener. In addition, for design for tension-field action, the stiffener areaAst, in2, should be at least that computed from
Fyw Vu 2
Ast⫽ Fys 冋0.15Dht(1⫺Cv)uVn⫺18t册ⱖ0 (7.43) whereFys⫽specified yield stress of stiffener, ksi
Vu⫽required shear strength at stiffener, kips, calculated for the factored loads
D ⫽1.0 for a pair of stiffeners
⫽1.8 for a single-angle stiffener
⫽2.4 for a single-plate stiffener
Bending and Shear Interaction. Plate girders should also be proportioned to sat- isfy Eq. (7.43) if they are designed for tension-field action, stiffeners are required, andVu/Mulies between 60 and 133% ofVn/Mn.
Mu Vu
⫹0.625 ⱕ1.24 (7.44)
Mn Vn
whereMn⫽design flexural strength
Mu⫽required flexural strength calculated for the factored loads but may not exceed 0.90Mn
Vn⫽design shear strength
Vu⫽required shear strength calculated for the factored loads but may not exceed 0.90Vn