Steel Box Girder Design — Engineering Reference

A box girder is a closed hollow section fabricated from plates, offering superior torsional rigidity compared to open sections like W-shapes. Box girders are used for crane runways, curved bridge girders, transfer beams, and long-span applications where torsional loads are significant. Their design involves flexural, shear, torsional, and local buckling checks that are more involved than open-section design.

Torsional properties — Bredt-Batho theory

For a single-cell closed section, the Saint-Venant torsional constant J is calculated using the Bredt-Batho formula:

J = 4 * A_m^2 / sum(s_i / t_i)

where A_m is the area enclosed by the median line of the walls, s_i is the length of each wall segment, and t_i is its thickness.

Worked example — torsional constant for a rectangular box

Given: Box girder with outside dimensions 24 in. deep x 16 in. wide. Top and bottom flanges: t_f = 1.0 in. Web plates: t_w = 0.625 in.

Step 1 — Median line dimensions:

• Height between flange centers: h_m = 24 - 1.0 = 23.0 in.
• Width between web centers: b_m = 16 - 0.625 = 15.375 in.
• Enclosed area: Am = h_m * bm = 23.0 * 15.375 = 353.6 in.^2

Step 2 — Perimeter integral:

• Two flanges: 2 * (15.375 / 1.0) = 30.75
• Two webs: 2 * (23.0 / 0.625) = 73.6
• sum(s_i / t_i) = 30.75 + 73.6 = 104.35

Step 3 — Torsional constant: J = 4 _ 353.6^2 / 104.35 = 4 _ 125,033 / 104.35 = 4,794 in.^4

For comparison, a W24x76 open section has J = 2.68 in.^4. The box section provides roughly 1,800 times more torsional stiffness per unit torque.

Step 4 — Shear flow under applied torque T = 150 kip-ft = 1,800 kip-in.: q = T / (2 _ A_m) = 1,800 / (2 _ 353.6) = 2.54 kip/in.

Step 5 — Shear stress in web: tau_w = q / t_w = 2.54 / 0.625 = 4.07 ksi

Shear stress in flange: tau_f = q / t_f = 2.54 / 1.0 = 2.54 ksi

Both are well below the shear yield stress of 0.60 _ Fy = 0.60 _ 50 = 30 ksi.

Flexural design considerations

Box girders are typically compact in flexure because both flanges are stiffened by the webs. However, wide flanges can be slender. The compression flange width-to-thickness ratio must be checked:

b/t <= 1.49 _ sqrt(E / Fy) = 1.49 _ sqrt(29000 / 50) = 35.9

For our example: b/t = 15.375 / 1.0 = 15.4 — compact.

Lateral-torsional buckling is rarely a concern for box girders because the closed section has very high warping and torsional stiffness. AISC 360 Section F7 governs flexure of box sections and recognizes that LTB is typically not the controlling limit state.

Diaphragm design

Internal diaphragms (transverse stiffeners or full-depth plates inside the box) are required to maintain the cross-sectional shape under load. Without diaphragms, the box distorts under eccentric loading, reducing torsional efficiency. AASHTO LRFD Section 6.7.4 provides guidance:

• Diaphragm spacing should not exceed 1.5 times the box depth for bridge applications.
• At bearing locations and points of concentrated load, full-depth diaphragms (bearing diaphragms) are required.
• Intermediate diaphragms can be plates, cross-frames, or K-frames inside the box.

Code comparison

Key clause references

• AISC 360-22 Section F7 — Flexural strength of square and rectangular HSS and box-shaped members
• AISC 360-22 Section H3.1 — Combined torsion, flexure, shear, and axial force
• AISC 360-22 Section G4 — Shear strength of hollow tubular sections
• EN 1993-1-1 Section 6.2.7 — Torsion design
• EN 1993-1-5 Section 4 — Plate buckling for stiffened and unstiffened plates
• AS 4100 Clause 5.12 — Members subject to combined actions including torsion

Topic-specific pitfalls

• Neglecting distortional warping — for thin-walled boxes under eccentric load, the cross-section can distort. This produces additional stresses not captured by simple Bredt-Batho shear flow. Full BEF (beam on elastic foundation) analysis or FEA may be needed for large thin-walled boxes.
• Omitting diaphragms at load application points — concentrated loads applied to a box girder flange without a diaphragm cause local flange bending and web crippling. Always provide a bearing stiffener or full-depth diaphragm at each point load.
• Undersizing weld between web and flange — the horizontal shear flow from flexure plus the torsional shear flow are additive on one web and subtractive on the other. The critical web weld must resist q_flexure + q_torsion, not just the flexural shear alone.
• Using open-section LTB formulas — W-shape LTB equations from AISC Chapter F2 do not apply to box sections. Box sections use Section F7, which typically shows that LTB does not govern due to the very high J value.

Run this calculation

• Section Properties Database
• Beam Calculator

Related references

• How to Verify Calculations
• Plate Girder Design
• Steel Crane Girder
• Torsion Design
• Stiffener Design
• steel beam capacity calculator

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.