Intermediate transverse stiffeners at regular spacing along the web of a plate girder are used to increase the buckling capacity of the web. Stiffeners provided at support points require a different design approach and these are considered in the next section. The design of intermediate transverse stiffeners in box girders adheres to similar requirements. In general, transverse stiffener cross-sections are made of hot-rolled sections and are either flats or bulb flats, angles or T-sections. The latter are used where the depth of the stiffener needs to be great enough to permit longitudinal stiffeners to pass through cut-outs in them. Longitudinal stiffeners would normally be either bulb flats or angles and would be welded to the transverse stiffeners. It is an important principle that the main longitudinal load-carrying elements, e.g. the longitudinal stiffeners, are continuous to avoid eccentricities in the longitudinal load path.
As mentioned above, the Eurocode requires stiffeners to be spaced at between one and three times the web depth. While BS 5400 Part 3 imposes no such restriction it is a sensible range for normal design application. If the stiffener spacing were any closer it is likely that increased fabrication cost would more than offset the savings in web material achieved through using a thinner web and if more widely spaced the enhancement to web buckling capacity would be limited.
Transverse stiffeners have two main functions in terms of the web capacity. First, they will increase the out-of-plane buckling resistance of the web by acting as a nodal line
preventing out-of-plane deformation. Second, they provide anchorage for tension field forces thereby enhancing ultimate web shear strength. They can also carry limited direct loading from the deck into the web (not relevant for composite plate girders) and can also help to prevent the flange buckling into the web.
The Eurocode and BS 5400 differ in their design approach. The Eurocode provides an inertia requirement (a stiffness) to prevent buckling of the web distorting the stiffener out of the plane of the web and a column (strut) requirement to ensure that the stiffener can carry the resolved tension field force. In contrast, BS 5400 converts the web buckling loading, via a critical buckling equivalence, into an equivalent compressive loading and bases the stiffener design on the ultimate collapse of an eccentrically loaded strut. There is evidence that the latter approach is over-conservative in its representation of a lateral beam load as a compressive column load because of the P-A effect the latter introduces in the non-linear response of the column. Non-linear analyses carried out by the second author of this chapter suggest that a simple beam model with a beam spanning between the flanges, loaded by a uniform load which is a function of the in-plane stress state in the web, provides an accurate design alternative. This leads to the use of a beam column model when the other load components are included.
Looking first at the Eurocode 3 Part 1.1 design method, the equations for the inertia of the stiffener are given in terms of the web depth, web thickness and stiffener spacing and are also dependent on the panel aspect ratio. The strut approach uses the resolved tension field force NS acting at the centre line of the web. It is therefore an eccentric load if the stiffener is only on one side of the web plate as is the norm for intermediate stiffeners. The stiffener and an associated width of web plate (15etw on either side of the stiffener section) are designed as a strut section using the column rules in the code. The load applied to this section is:
where Tbb is the shear buckling resistance without any allowance for tension field and is the design value of the shear force.
In BS 5400 Part 3, the effective strut is defined as the stiffener section comprised of the stiffener together with a total effective width of web equal to 32 times the web thickness. A strut equation combining moment and axial load is provided and used in combination with the column design curve in the code which is a function of the l/r of the effective section where l is the length of the stiffener.
There are a number of load components applied to the stiffener which include the resolved tension field force, the axial force representing through equivalence the destabilising influence of web panel buckling, any moment applied through U-frame action and compressive loads from direct loading to the flange or through cross-frames and due to any curvature of the flange. The approach is too complex to present in detail here, but the first two load actions will be described.
The tension field force, which acts at the mid-plane of the web, is defined as Ftw which is the smaller of:
where is the length of the transverse stiffener, t is the average shear stress present in the web and t0 is a reference shear buckling stress:
but is equal to zero if the square root term is negative.
The term a is the panel length, b is the panel width (web depth between flanges) and o is the average longitudinal stress in the panel (+ve if compressive). The equation references web panel width because the same transverse stiffener design equations are used in the design of transverse stiffeners in longitudinally stiffened webs.
Again the approach is not dissimilar to that of the Eurocode where the force results from the increased web capacity above a certain critical buckling stress. The axial force representing the destabilising action, acting at the centroid of the effective strut, is given by:
where amax is the maximum transverse stiffener spacing to satisfy the web design (can be taken as a), is a numerical parameter which is a function of the strut slenderness with a maximum value of 0.4 for very slender struts, and represents the destabilising stresses present in the web (with an allowance for web longitudinal stiffeners if present).
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