Plate Girder Design: Web Panels, Transverse Stiffeners, and Shear Buckling

When span lengths and load magnitudes exceed what standard rolled wide-flange sections can supply, engineers turn to plate girders — built-up I-sections fabricated by welding flanges to a web plate. The web can be made as deep and as thin as needed to place steel where it is most effective, but that freedom introduces a new design problem: thin webs buckle in shear at stresses well below steel’s shear yield strength. Managing that instability is the central challenge of plate girder design.

Web Slenderness and Shear Buckling Regimes

The web slenderness ratio h/t_w, where h is the clear web height and t_w is the web thickness, governs which shear resistance model applies. AISC 360 Chapter G defines three regimes:

Regime	h/tw limit	Behavior	Shear factor Cv1
Shear yielding	≤ 2.24√(E/Fy)	Web yields before buckling	1.0
Inelastic shear buckling	≤ kvE/Fy thresholds	Partial post-buckling reserve	Cv1 < 1.0
Elastic shear buckling	Very thin webs	Buckles elastically, relies on TFA	Cv2 per G2.2

For A36 steel (F_y = 36 ksi) the shear yielding limit is h/t_w ≤ 63.4. Most plate girders in bridge and industrial work operate well above this limit, entering the buckling regime and requiring explicit treatment of post-buckling capacity.

Tension Field Action

After a thin web panel buckles in shear, it does not lose all load-carrying ability. The buckled web panel acts like a diagonal tension brace: the compression diagonal has buckled and carries no stress, but the tension diagonal continues to develop axial force anchored to the transverse stiffeners and flanges on either side. This redistribution mechanism is called tension field action (TFA). The flanges and stiffeners frame the web panel like the chords and verticals of a Pratt truss, while the inclined tension band traverses the web diagonally.

AISC 360 Section G2.2 accounts for tension field action through the factor C_v2, which captures the fraction of shear yield strength recoverable after web buckling. The nominal shear capacity with TFA is:

V_n = 0.6F_yA_w[C_v2 + (1 − C_v2) / (1.15√(1 + (a/h)²))]

where A_w = ht_w is the web area and a is the stiffener spacing. Tension field action increases the usable shear capacity of slender webs by 20 to 60 percent over the elastic buckling load alone, making it highly valuable in girder design. End panels adjacent to supports and panels containing large holes cannot develop TFA and are limited to the elastic buckling capacity without the post-buckling term.

Transverse Stiffener Design

Transverse intermediate stiffeners serve two purposes: they raise the elastic shear buckling load of each web panel, and they anchor the tension field. Stiffener design steps under AISC 360 G2.2:

1. Select stiffener spacing a to achieve the target k_v = 5 + 5/(a/h)². Closer spacing raises k_v and thus the buckling load.
2. Check moment of inertia of the stiffener about the web face: I_st ≥ I_st1 for the buckling demand and I_st2 for the tension field anchoring demand. I_st2 is the more stringent requirement for slender, highly loaded webs.
3. Check area: The stiffener gross area must satisfy A_st ≥ F_yw/(2F_yst) × (0.15D_sht_w(1 − C_v2)V_u/V_n − 18t_w²) ≥ 0, where D_s is 1.0 for one-sided stiffeners and 1.8 for pairs.
4. Weld the stiffener to the web for the force demand; weld termination near tension flanges requires a gap of 4t_w to avoid fatigue-inducing weld root notches.

Bearing Stiffeners at Supports and Point Loads

Transverse stiffeners at supports and under concentrated loads are bearing stiffeners, not intermediate stiffeners. They transfer concentrated vertical force directly into the web and must be designed as columns buckling about an axis parallel to the web, with an effective length of 0.75h. The column cross-section includes the stiffener plates plus a width of web (12t_w for interior stiffeners). Bearing stiffeners run the full height of the web and are tightly fit or welded to both flanges to transfer load without web crippling.

Flange Local Buckling and Flexure

Plate girder flanges are wide and often thin to maximize moment of inertia economically. AISC 360 Table B4.1b limits the flange width-to-thickness ratio b_f/(2t_f) to λ_pf = 0.38√(E/F_y) for a compact flange. Non-compact flanges (up to λ_rf = 1.0√(E/F_y)) experience reduced flexural capacity interpolated between M_p and 0.7F_yS_x. Slender flanges beyond λ_rf are rarely specified in new plate girder design but may appear in assessments of older girders.

The combination of a tension-field web and compact or non-compact flanges gives plate girders their efficiency: a deep web places the flanges far apart for maximum moment arm, the web sheds shear into a post-buckling tension field, and transverse stiffeners stitch it all together. Correctly sizing those elements requires iterating web depth, web thickness, stiffener spacing, and flange dimensions together rather than optimizing each independently.