Plate Girders

• Customization: The designer can specify the web depth, web thickness, flange width, and flange thickness independently to precisely match the required moment and shear capacities at every point along the span.
• Efficiency: Material is placed exactly where it is needed. For example, thicker or wider flanges can be used at midspan where bending moments are highest, while thinner flanges are used near supports. The web can be kept extremely thin to save weight.
• Long Spans: Plate girders can span distances far beyond the capability of standard rolled sections (e.g., up to 200 feet or more).

The design of a plate girder typically follows a logical sequence:

1. Determine Required Maximum Bending Moment and Shear Force: Based on the structural analysis of loads.
2. Proportion the Web Depth and Thickness: Often starting with a span-to-depth ratio rule of thumb, keeping the web as thin as practically possible.
3. Proportion the Flanges: Designed to carry the required bending moment assuming the web provides little to no contribution.
4. Check Web Slenderness and Flexural Strength: Verify if the web is slender and apply appropriate reductions (like $R_{pg}$) to the moment capacity.
5. Check Shear Strength: If the unstiffened thin web is insufficient for the shear force, transverse stiffeners are added.
6. Design Transverse Stiffeners: Evaluate if Tension Field Action (TFA) is needed and design stiffener spacing and size accordingly.
7. Design Bearing Stiffeners: Placed at supports and under heavy concentrated loads to prevent local web crippling.
8. Design the Flange-to-Web Welds: Calculate the horizontal shear flow and size continuous fillet welds appropriately.
9. Check Serviceability: Ensure deflections are within acceptable limits.

The fundamental challenge of plate girder design is the impact of slender webs on performance and design. To minimize weight and material cost, the primary objective is to make the web as deep as possible (to maximize the moment arm between the flanges, minimizing flange area) and as thin as possible.

This makes the web highly susceptible to local buckling under bending (flexure) and shear long before the material reaches its yield strength.

Because the web is typically slender, it will buckle locally under the compressive stresses caused by the primary bending moment before the flanges can reach their full yield stress. AISC specifications account for this by either:

• Reducing the allowable flexural strength of the compression flange: A bending strength reduction factor ($R_{pg}$) is applied to limit the maximum stress in the flange, acknowledging that the buckled web is shedding compressive stress to the stiffer flange.
• Ignoring a portion of the web in compression (Effective Width Method): Only a small effective width of the web adjacent to the compression flange is considered active, and the section properties ($I$, $S$) are recalculated based on this reduced area.

The most significant unique behavior of plate girders is how they resist shear. A very thin, deep web is terrible at resisting shear forces without buckling.

Pre-Buckling Shear Initially, the thin web resists shear through a pure shear stress state (which can be resolved into principal diagonal tension and compression stresses acting at $45^\circ$). However, because the web is thin, it will buckle diagonally under the principal compressive stress at a relatively low load.

Post-Buckling Strength: Tension Field Action (TFA) If transverse stiffeners are provided at appropriate intervals along the span, the web does not fail immediately after it buckles. Instead, a new, highly stable load-carrying mechanism develops called Tension Field Action (TFA).

Once the web buckles diagonally in compression (forming wrinkles), it completely loses its ability to carry any more compressive stress. However, it can still carry diagonal tensile stress across the wrinkles. The web essentially acts like a series of diagonal tension ties (like the cables in a bridge). The transverse stiffeners act as vertical compression struts. The top and bottom flanges act as chords. The plate girder literally transforms its internal load path into a Pratt truss!

Because plate girder webs are so thin, they almost always require stiffening. There are three primary types of stiffeners used:

1. Bearing Stiffeners (AISC J10): Required at unframed ends (supports) and at locations of heavy concentrated loads. They prevent local web yielding and crippling under direct compression. Usually placed in pairs and designed as a fictitious column.
2. Intermediate Transverse Stiffeners (AISC G2): Placed vertically at intervals along the span to increase the shear buckling strength of the web and to enable Tension Field Action (TFA). Act as vertical compression struts.
3. Longitudinal Stiffeners: Rarely used in building construction, but common in massive bridge girders. Placed horizontally along the web (usually in the compression zone) to significantly increase the bending buckling strength of the web.

The flanges must be welded to the web to form the I-shape using continuous fillet welds (or CJP groove welds). The size of the weld is governed by the horizontal shear flow ($q$) at the interface.

The required weld size must resist this horizontal shear flow in addition to any local vertical wheel loads (e.g., in a crane girder). Furthermore, plate girders subjected to many loading cycles (bridges, cranes) must have these continuous welds rigorously checked for fatigue, which often dictates a much larger weld size than required for static strength.