Plate girders may have either a box or an I shape. Main components are plates or plates and angles, arranged so that the cross section is either singly or doubly symmetrical. Generally, the elements are connected by continuous fillet welds. In existing construction, the connection may have been made with rivets or bolts through plates and angles. Fig. 7.33 depicts typical I-shape girders.
Plate girders are commonly used for long spans where they cost less than rolled W shapes or where members are required with greater depths or thinner webs than those available with rolled W shapes. The AISC LRFD ‘‘Specification for Structural Steel for Buildings’’ distinguished between a plate girder and a beam in that a plate
twice the distance from the neutral axis to (1) the inside face of the compression
flange when it is welded to the web or (2) the nearest line of fasteners to the
compression flange when the web-flange connection is bolted.
ASD Procedure for Plate Girders
Allowable stresses for tension, compression, bending, and shear are the same for plate girders as those given in Arts. 7.18 to 7.20, except where stiffeners are used.
But reductions in allowable stress are required under some conditions, and there are limitations on the proportions of girder components.
Web Depth-Thickness Limits. The ratio of the clear distance h between flanges, in, to web thickness t, in, is limited by
General Design Method. Plate girders may be proportioned to resist bending on the assumption that the moment of inertia of the gross cross section is effective.
No deductions need be made for fastener holes, unless the holes reduce the gross area of either flange by more than 15%. When they do, the excess should be deducted.
Hybrid girders, which have higher-strength steel in the flanges than in the web, may also be proportioned by the moment of inertia of the gross section when they are not subjected to an axial force greater than 15% of the product of yield stress of the flange steel and the area of the gross section. At any given section, the flanges must have the same cross-sectional area and be made of the same grade of steel.
Bearing Stiffeners. These are required on girder webs at unframed ends. They may also be needed at concentrated loads, including supports. Set in pairs, bearing stiffeners may be angles or plates placed on opposite sides of the web, usually normal to the bending axis. Angles are attached with one leg against the web. Plates are welded perpendicular to the web. The stiffeners should have close bearing against the flanges through which they receive their loads, and should extend nearly to the edges of the flanges.
These stiffeners are designed as columns, with allowable stresses as given in Art. 7.19. The column section is assumed to consist of a pair of stiffeners and a strip of girder web with width 25 times web thickness for interior stiffeners and 12 times web thickness at ends. In computing the effective slenderness ratio Kl/ r, use an effective length Kl of at least 0.75 the length of the stiffeners.
Intermediate Stiffeners. With properly spaced transverse stiffeners strong enough to act as compression members, a plate-girder web can carry loads far in excess of its buckling load. The girders acts, in effect, like a Pratt truss, with the stiffeners as struts and the web forming fields of diagonal tension. The following formulas for stiffeners are based on this behavior. Like bearing stiffeners, intermediate stiffeners are placed to project normal to the web and the bending axis, but they may consist of a single angle or plate. They may be stopped short of the tension flange a distance up to 4 times the web thickness. If the compression flange is a rectangular plate, single stiffeners must be attached to it to prevent the plate from twisting.
When lateral bracing is attached to stiffeners, they must be connected to the compression flange to transmit at least 1% of the total flange stress, except when the flange consists only of angles.
The total shear force, kips, divided by the web area, in2, for any panel between stiffeners should not exceed the allowable shear Fv given by Eqs. (7.29a) and (7.29b).
Except for hybrid girders, when Cv is less than unity:
Stiffeners for an end panel or for any panel containing large holes and for adjacent panels should be so spaced that the largest average web shear ƒv in the panel does not exceed the allowable shear given in Eq. (7.29b).
Intermediate stiffeners are not required when h/ t is less than 260 and ƒv is less than the allowable stress given by Eq. (7.29b). When these criteria are not satisfied, stiffeners should be spaced so that the applicable allowable shear, Eq. (7.29a) or (7.29b), is not exceeded, and in addition, so that a/h is not more than [260/ (h/ t)]2 or 3.
Solution of the preceding formulas for stiffener spacing requires assumptions of dimensions and trials. The calculations can be facilitated by using tables in the AISC ‘‘Manual of Steel Construction.’’ Also, Fig. 7.34 permits rapid selection of the most efficient stiffener arrangement, for webs of A36 steel. Similar charts can be drawn for other steels.
If the tension field concept is to apply to plate girder design, care is necessary to ensure that the intermediate stiffeners function as struts. When these stiffeners are spaced to satisfy Eq. (7.29a), their gross area, in2 (total area if in pairs) should be at least
Also, the compressive stresses in the web should be checked (see Art. 7.22).
LRFD Procedure for Plate Girders
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/ t does not exceed h/ t given by (7.32) or (7.33), whichever is applicable.