Why use a box girder instead of a W-shape or plate girder?

Box girders are chosen over open sections (W-shapes, plate girders) when torsional rigidity is needed. The closed cell provides a torsional constant J hundreds to thousands of times larger than an equivalent open section. Applications: (1) Curved bridge girders — torsion from curvature is the primary load effect; open sections twist excessively. (2) Eccentric crane runway beams — the crane wheel load is eccentric to the shear center, producing torsion that open sections cannot efficiently resist. (3) Transfer beams supporting offset columns — the eccentric load introduces torsion that would twist an I-shape. (4) Long-span beams with lateral stability concerns — box sections resist LTB naturally because the compression flange is continuously supported by both webs. (5) Architectural exposed steel — the clean rectangular profile is visually preferred. Trade-offs: box girders are more expensive to fabricate (4 plates, internal diaphragms, more welding), heavier for the same flexural capacity (two webs vs one), and more complex to detail connections. The decision is typically driven by torsion — if torsion is > 10% of the design moment, a box section should be considered over an I-shape.

How is torsional capacity calculated for a steel box girder?

Closed box sections resist torsion through Saint-Venant shear flow using the Bredt-Batho formula. Torsional constant: J = 4 x Am^2 / sum(si/ti). Where Am = area enclosed by the median line of the cross-section (width x depth for rectangular box). si = length of each wall segment. ti = thickness of each wall segment. For a 24 in x 48 in box with 1 in flanges and 1/2 in webs: Am = (24-1) x (48-1) = 23 x 47 = 1,081 in^2. sum(si/ti) = (23/0.5) x 2 + (47/1.0) x 2 = 92 + 94 = 186. J = 4 x 1,081^2 / 186 = 4 x 1,168,561 / 186 = 25,128 in^4. For comparison, a W24x76 has J = 3.0 in^4 — the box girder has 8,376 TIMES the torsional stiffness! Torsional shear stress: tau_t = T / (2 x Am x t). For T = 500 kip-ft = 6,000 kip-in: tau_t = 6,000/(2 x 1,081 x 0.5) = 5.55 ksi in webs. This is the beauty of closed sections — even large torsional moments produce modest shear stresses because the shear flow has a long circulation path.

How are box girder flanges checked per AISC 360?

AISC 360-22 Section F7 governs box girder flexure. Flange slenderness determines whether the flange is compact, noncompact, or slender: Compact flange (bf/tf 33.7): use effective width be per AISC F7.2. For a 24 in wide x 1 in thick flange: bf/tf = 24/1 = 24 (< 27), compact. Web slenderness for shear in box sections: the web is checked per AISC G2 with kv = 5.0 (stiffened web). For no tension field action in box sections: Vn = 0.6Fy x Aw x Cv. Box sections cannot develop tension field action because the closed shape prevents the tension diagonal from anchoring. A critical difference from I-girders: box girder flanges must be checked for COMBINED effects — global bending stress PLUS local bending from distortion between diaphragms.

What are internal diaphragms and why are they needed?

Internal diaphragms are transverse stiffening plates inside a box girder that: (1) Maintain cross-sectional shape — without diaphragms, eccentric loads distort the rectangular box into a parallelogram, introducing secondary bending stresses not captured by Bredt-Batho theory. (2) Transfer torsional loads into the section — at supports, the torsional reaction must be transferred from the bearings into the box, requiring a stiff diaphragm. (3) Provide intermediate stability for the compression flange — diaphragms divide the flange into sub-panels, controlling local buckling. Types: support diaphragms (full-depth plates at bearings, designed for full torsional reaction), intermediate diaphragms (at L/3 to L/4 spacing, minimum thickness 3/8 in, may be plate or channel frames), and load diaphragms (at concentrated load points to distribute eccentric load into the section). Per AISC DG3 and AASHTO: diaphragm spacing a <= 2 x depth for compact flange behavior. For a 48 in deep box: max diaphragm spacing = 96 in (8 ft). Access holes are required in diaphragms for welding and inspection — typically 18 in x 24 in minimum with reinforced edges.

How do AISC 360 and EN 1993-1-5 differ for box girder design?

Key differences: (1) Flange classification — AISC uses bf/tf limits for compact/noncompact/slender. EN 1993-1-5 uses Class 1-4 with different limits: Class 3 limit (elastic) for flange in compression is 42 x epsilon for internal elements vs AISC lambda_r = 1.40 x sqrt(E/Fy) = 33.7. EN is more generous for flange slenderness. (2) Shear buckling — AISC uses Cv coefficient with kv=5.0 for stiffened webs, no tension field for box sections. EN 1993-1-5 uses the rotated stress field method which allows some post-buckling shear resistance. (3) Torsion — AISC addresses torsion indirectly through combined stress checks. EN 1993-1-1 Section 6.2.7 provides explicit torsion + bending interaction equations. (4) Diaphragm design — AISC follows DG3 with empirical spacing rules. EN 1993-1-5 Section 9 provides calculation-based diaphragm stiffness requirements. (5) Effective width for shear lag — EN 1993-1-5 explicitly accounts for shear lag in wide flanges using effective width concepts. AISC mentions shear lag in Commentary but leaves effective width to engineering judgment. In practice, the two codes produce similar designs, with EN being slightly more economical for slender webs and wide flanges.

Steel Box Girder Design — AISC 360 Flexure, Torsion & Shear Reference

Q: What are internal diaphragms and why are they needed?

Internal diaphragms are transverse stiffening plates inside a box girder that: (1) Maintain cross-sectional shape — without diaphragms, eccentric loads distort the rectangular box into a parallelogram, introducing secondary bending stresses not captured by Bredt-Batho theory. (2) Transfer torsional loads into the section — at supports, the torsional reaction must be transferred from the bearings into the box, requiring a stiff diaphragm. (3) Provide intermediate stability for the compression flange — diaphragms divide the flange into sub-panels, controlling local buckling. Types: support diaphragms (full-depth plates at bearings, designed for full torsional reaction), intermediate diaphragms (at L/3 to L/4 spacing, minimum thickness 3/8 in, may be plate or channel frames), and load diaphragms (at concentrated load points to distribute eccentric load into the section). Per AISC DG3 and AASHTO: diaphragm spacing a <= 2 x depth for compact flange behavior. For a 48 in deep box: max diaphragm spacing = 96 in (8 ft). Access holes are required in diaphragms for welding and inspection — typically 18 in x 24 in minimum with reinforced edges.

Q: How do AISC 360 and EN 1993-1-5 differ for box girder design?

Key differences: (1) Flange classification — AISC uses bf/tf limits for compact/noncompact/slender. EN 1993-1-5 uses Class 1-4 with different limits: Class 3 limit (elastic) for flange in compression is 42 x epsilon for internal elements vs AISC lambda_r = 1.40 x sqrt(E/Fy) = 33.7. EN is more generous for flange slenderness. (2) Shear buckling — AISC uses Cv coefficient with kv=5.0 for stiffened webs, no tension field for box sections. EN 1993-1-5 uses the rotated stress field method which allows some post-buckling shear resistance. (3) Torsion — AISC addresses torsion indirectly through combined stress checks. EN 1993-1-1 Section 6.2.7 provides explicit torsion + bending interaction equations. (4) Diaphragm design — AISC follows DG3 with empirical spacing rules. EN 1993-1-5 Section 9 provides calculation-based diaphragm stiffness requirements. (5) Effective width for shear lag — EN 1993-1-5 explicitly accounts for shear lag in wide flanges using effective width concepts. AISC mentions shear lag in Commentary but leaves effective width to engineering judgment. In practice, the two codes produce similar designs, with EN being slightly more economical for slender webs and wide flanges.

A box girder is a closed hollow section fabricated from steel plates, offering torsional rigidity orders of magnitude greater than open sections such as W-shapes or plate girders. Box girders are used in crane runways, curved bridge girders, transfer beams, and any application where torsional loads, eccentric gravity loads, or lateral instability of open sections drive the design. Their analysis involves flexural, shear, torsional, and local buckling checks that are more involved than open-section design, but the payoff is a member that resists twist without continuous lateral bracing.

This reference covers box girder behavior, AISC 360-22 design provisions, flange and web design, torsional stiffness, diaphragm requirements, typical proportions, comparison with plate girders and W-shapes, worked examples, common mistakes, and frequently asked questions.

Box girder structural behavior

Box girders resist loads through four interacting mechanisms: bending, shear, torsion, and cross-sectional distortion.

Bending

Under vertical loads, the top and bottom flanges carry bending as axial compression and tension. For a symmetric rectangular box, I_x = (bd^3 - (b-2tw)(d-2tf)^3)/12. Because the section is closed, the compression flange is continuously supported by the webs on both sides, so lateral-torsional buckling (LTB) is rarely a governing limit state -- a major advantage over I-shaped members.

Shear

Shear is carried by the web plates. The total shear stress in each web is the sum of flexural and torsional contributions: tau_total = tau_flexure + tau_torsion. On one web these add; on the other they subtract. The critical web is the one where both contributions are in the same direction. This additive nature must be accounted for in both the web shear check and the web-to-flange weld design.

Torsion

Closed sections resist torsion through Saint-Venant shear flow circulating around the perimeter. Warping torsion is negligible because the closed cell prevents differential flange movement. The Bredt-Batho formula gives J = 4*A_m^2 / sum(s_i/t_i), where A_m is the area enclosed by the median line. The resulting J is typically hundreds or thousands of times larger than for an equivalent open section.

Distortion

Under eccentric loading, the rectangular cross-section distorts out of its original shape, producing stresses not captured by Bredt-Batho analysis. Distortional effects are resisted by internal diaphragms. For thin-walled boxes with large width-to-depth ratios, distortional analysis using the beam-on-elastic-foundation (BEF) analogy or FEA may be necessary.

Types of box girders

Single-cell box girder

The most common configuration: four plates forming a single rectangular or trapezoidal cell. Simple to fabricate and analyze. Typical for building transfer beams, crane girders, and short-to-medium span bridge girders. The Bredt-Batho torsional constant applies directly.

Multi-cell box girder

Two or more cells separated by internal web plates. Used for wider bridge girders, where a single cell would have an unacceptably wide flange. The torsional constant is the sum of individual cell contributions. Intermediate webs reduce the effective flange width for local buckling checks. Design is more complex because the shear flow distribution between cells must be solved using compatibility equations.

Composite box girder

A steel box with a reinforced concrete deck acting compositely through shear studs. The concrete deck serves as the top flange, significantly increasing flexural capacity and stiffness. Common in bridge applications (AASHTO LRFD Section 6.11). The concrete also contributes to the enclosed area for torsional resistance, but the shear lag across the wide deck slab must be considered using an effective width.

Non-composite box girder

A pure steel box without composite action. Both flanges are steel plates. Used in building structures, crane runways, and situations where composite construction is not practical.

Trapezoidal box girder

Webs are inclined rather than vertical, producing a wider bottom flange and narrower top flange. Used in bridge aesthetics and to optimize structural depth at supports. Sloped webs complicate fabrication but can reduce the bottom flange width needed for compact section behavior.

AISC 360-22 and AREMA design provisions

AISC 360-22 Section F7 -- flexural strength of box sections

Section F7 governs the flexural strength of square and rectangular HSS and box-shaped members. Key provisions:

Compact sections (F7.1): The nominal moment capacity Mn = Mp = Fy _ Z, where Z is the plastic section modulus, when both flanges and webs meet compact limits. For the flange: b/t <= 1.12 _ sqrt(E/Fy). For the web: h/tw <= 2.42 * sqrt(E/Fy).
Noncompact sections (F7.2): When the flange exceeds the compact limit but remains below the noncompact limit (b/t <= 1.40 _ sqrt(E/Fy)), Mn is linearly interpolated between Mp and 0.7 _ Fy * Sx.
Slender sections (F7.3): When b/t exceeds the noncompact limit, Mn is based on the effective section modulus using reduced effective flange widths per Section E7.
Lateral-torsional buckling (F7.4): LTB is explicitly recognized as typically not governing for box sections. The high torsional constant J means the LTB limit state is reached only at very large unbraced lengths. For most practical cases, LTB does not control.

AISC 360-22 Section G4 -- shear in box sections

Section G4 covers shear strength of round and rectangular HSS and box sections. The nominal shear strength is:

Vn = 0.6 * Fy * Aw * Cv2

where Aw = 2 _ h _ tw (both webs contribute) and Cv2 is the shear buckling coefficient. For h/tw <= 2.24 * sqrt(E/Fy) = 53.9 (for Fy = 50 ksi), Cv2 = 1.0 and shear yielding governs. For slender webs, Cv2 is reduced per Table G4-1.

Note: tension field action is not permitted for box sections per AISC 360 Section G4.1. The closed section prevents the diagonal tension field from developing in the same way as an open plate girder. This is a significant difference from plate girder shear design.

AISC 360-22 Section H3 -- combined torsion with other forces

Section H3 addresses members subject to torsion combined with flexure, shear, and axial force. The interaction equation for round and rectangular HSS under combined torsion and flexure is:

(M_u / phi*M_n)^2 + (T_u / phi*T_n)^2 <= 1.0

where T*n = F_cr * C, and C is the torsional function depending on the section geometry. For closed sections, C is effectively 0.6 _ Fy _ J / (2 _ A_m) for yielding in pure torsion.

AISC Design Guide 9 -- torsional analysis

AISC Design Guide 9 provides procedures for computing torsional stresses and rotations. For box girders, Chapter 4 confirms that warping normal stresses are negligible and provides formulas for common loading conditions on closed members.

AREMA provisions

For railway bridge box girders, AREMA Manual Chapter 15 provides additional requirements: more stringent flange slenderness limits, mandatory bearing diaphragms at every support, fatigue categories for web-to-flange welds, and minimum web thickness for corrosion allowance.

Flange design

Longitudinal stiffeners

Wide compression flanges may require longitudinal stiffeners (flat bars or tees welded to the inside face of the flange) to prevent local buckling. They divide the flange into narrower sub-panels with lower b/t ratios. The required moment of inertia per AISC Section E7.2 is:

I_st >= 0.75 * t_f^3 * b_sub

where b_sub is the sub-panel width between stiffeners or between a stiffener and the web.

Effective width

When b/t > 1.49 _ sqrt(E/Fy) = 35.9 (for Fy = 50 ksi), the effective width is reduced per AISC Section E7. The effective section modulus is computed using the reduced flange width, and Mn = Fy _ S_eff. For bridge box girders, AASHTO LRFD Section 6.11 provides a different effective width formula that accounts for shear lag.

Web design

Shear buckling

Box girder webs are subject to shear buckling, but tension field action is not available (AISC G4.1). The web shear capacity relies entirely on pre-buckling strength: phiV_n = phi * 0.6FyAwCv2. For stocky webs (h/tw <= 2.24*sqrt(E/Fy)), Cv2 = 1.0. For slender webs, Cv2 is reduced per Table G4-1. Transverse stiffeners can increase the buckling coefficient but cannot develop tension field action.

Transverse stiffeners

Transverse stiffeners increase web shear buckling resistance by subdividing the web panel. Design requirements per AISC Section G2.3: I_st >= btw^3j (j = 2.5/(a/h)^2 - 2 >= 0.5), width b_s >= h/30 and b_s >= b_f/6, thickness t_s >= b_s/15. In box girders, stiffeners are typically in pairs (one per web) and may be connected by internal cross-frames.

Torsional stiffness and warping

Saint-Venant torsional constant J

For a single-cell rectangular box: J = 4A_m^2 / sum(s_i/t_i), where A_m = h_mb_m. For a box with outside depth d, width b, flange thickness tf, and web thickness tw: h_m = d - tf, b_m = b - tw, sum(s_i/t_i) = 2b_m/tf + 2h_m/tw.

Warping constant

For a single-cell box, Cw is approximately zero. The closed shear flow prevents differential flange warping. In contrast, an open I-section has Cw values in the thousands of in^6.

Torsional rotation

For a simply supported box of span L under uniform torque t: theta_max = tL^2/(8G*J), where G = 11,200 ksi. Rotation is typically very small because J is large -- torsional rotation is rarely a serviceability concern.

Diaphragm and cross-frame requirements

Purpose of diaphragms

Internal diaphragms serve three functions: (1) maintain cross-sectional shape under eccentric loads, preventing rhombic distortion; (2) distribute concentrated loads to both webs; (3) provide torsional rigidity at supports.

Types of internal diaphragms

Full-depth solid plate: Welded to all four walls. Used at bearings and heavy concentrated loads. Maximum stiffness.
Ring diaphragms: A rectangular frame inside the box without the central portion. Lighter; adequate for intermediate locations.
K-frame and X-frame cross-bracing: Angles or plates forming a truss. Lightest option for intermediate diaphragms.

Spacing requirements

AASHTO LRFD Section 6.7.4: intermediate diaphragm spacing <= 1.5 times box depth for bridges. Full-depth solid diaphragms required at bearings and concentrated load points. For buildings, AISC 360 has no explicit rule; engineering judgment suggests maximum spacing of 2d to 3d with bearing diaphragms at all supports.

Bearing diaphragm design

Bearing diaphragms transfer the full reaction into both webs. The plate is checked for shear (spanning between flanges), bearing against the bottom flange, and weld capacity connecting the diaphragm to all four walls.

Typical proportions

The following table provides typical proportioning guidelines for steel box girders in building and bridge applications:

Parameter	Building girders	Bridge girders	Crane girders
Depth-to-span ratio (d/L)	1/20 to 1/30	1/20 to 1/35	1/12 to 1/20
Width-to-depth ratio (b/d)	0.4 to 0.7	0.4 to 0.8	0.3 to 0.5
Web slenderness (h/tw)	40 to 80	60 to 150	30 to 60
Flange slenderness (b_f/t_f)	12 to 30	15 to 40	10 to 20
Diaphragm spacing	1.5d to 3d	1.0d to 1.5d	1.0d to 1.5d
Minimum web thickness	5/16 in.	3/8 in. (corrosion)	3/8 in.
Top flange width	b_f/2 to b_f	b_f (full width)	b_f/2 (rail width)

Key observations:

Crane girders are proportioned deeper and stockier to control deflections under moving loads.
Bridge girders can use thinner webs because AASHTO permits transverse stiffeners and the loads are more uniform.
The width-to-depth ratio of 0.4 to 0.8 balances torsional stiffness against fabrication cost and access for internal welding.

Comparison with plate girders and W-shapes

Property	W-shape	Plate girder	Box girder
Torsional constant J	Very small (0.5 to 20 in^4)	Very small (1 to 50 in^4)	Very large (100 to 10,000 in^4)
Warping constant Cw	Large (500 to 50,000 in^6)	Large	Approximately zero
LTB susceptibility	High -- requires lateral bracing	High -- requires lateral bracing	Low -- closed section resists twist
Tension field action	Not applicable	Available (AISC G2.2)	Not available (AISC G4.1)
Fabrication complexity	Rolled -- minimal	Moderate (welded plates)	High (closed section, internal welds)
Internal inspection	Open -- easy	Open -- easy	Closed -- limited access
Cost per pound	Low	Moderate	High (50-100% premium over plate girder)
Optimal use case	Typical beams, columns	Long-span transfer beams	Curved girders, crane runways, torsion-critical
Maximum practical depth	~44 in. (W44)	Unlimited (typically 48-120 in.)	Unlimited (typically 24-120 in.)

When to choose a box girder: significant torsion (eccentric loads, curved alignment), impractical lateral bracing, serviceability limits on twist, or fatigue under torsional cycling. When a plate girder is better: negligible torsion, cost-driven project, straight spans with available bracing, or when internal inspection access is required.

Worked example -- box girder section capacity check

Given: Simply supported box girder, span = 60 ft. Factored uniform load = 4.0 kip/ft. Concentrated factored torque T_u = 200 kip-ft at midspan. Section: 36 in. deep x 20 in. wide, t_f = 0.75 in., t_w = 0.50 in., Fy = 50 ksi.

Step 1 -- Section properties:

I_x = (20 * 36^3 - 19.0 * 34.5^3) / 12 = 12,739 in^4
S_x = 12,739 / 18 = 707.7 in^3
Z_x = 20 * 0.75 * 35.25 + 2 * 0.25 * 0.50 * 34.5^2 = 826.3 in^3
A_w = 2 * 34.5 * 0.50 = 34.5 in^2 (both webs)
A_m = 35.25 * 19.5 = 687.4 in^2 (enclosed area)

Step 2 -- Torsional constant:

sum(s_i/t_i) = 2 * 19.5/0.75 + 2 * 35.25/0.50 = 193.0
J = 4 * 687.4^2 / 193.0 = 9,793 in^4  (vs. W36x150: J = 9.69 in^4)

Step 3 -- Flexure (AISC F7): Flange b/t = 26.0 < 27.0 (compact). Web h/tw = 69.0 > 58.3 (noncompact but < 90.5). Using F7.2 interpolation: phi*M_n = 2,687 kip-ft. Demand M_u = 1,800 kip-ft. Ratio = 0.67 -- OK.

Step 4 -- Shear (AISC G4): h/tw = 69.0 > 53.9, so Cv2 = (53.9/69.0)^2 = 0.609. phi*V_n = 0.90 * 0.6 _ 50 _ 34.5 * 0.609 = 567 kips. Demand V_u = 120 kips. Ratio = 0.21 -- OK. Note: tension field action not permitted.

Step 5 -- Torsion: q = 2,400/(2*687.4) = 1.75 kip/in. Web shear tau = 3.49 ksi, flange tau = 2.33 ksi. Both well below 30 ksi.

Step 6 -- Combined (AISC H3): (M_u/phiM_n)^2 + (T_u/phiT_n)^2 = 0.67^2 + 0.017 = 0.466 < 1.0 -- OK. All checks pass with reserve capacity.

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.

Quick 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 0.6 _ Fy = 0.6 _ 50 = 30 ksi.

Code comparison

Aspect	AISC 360-22	EN 1993-1-5	AS 4100	AASHTO LRFD
Flexure	Section F7 (box shapes)	Section 4 + EN 1993-1-5	Clause 5.6 (closed sections)	Section 6.10 / 6.11
Torsion	Section H3 (combined)	EN 1993-1-1 Section 6.2.7	Clause 5.12	Section 6.11.1
Shear flow	Bredt-Batho	Bredt formula	Bredt formula	Bredt formula
Plate buckling	Chapter E7 (Q-factor)	EN 1993-1-5 Section 4	Clause 6.2 (effective width)	Section 6.11.3
Diaphragm requirements	DG Box girder (no code rule)	EN 1993-1-5 Annex A	No specific clause	Section 6.7.4
Tension field action	Not permitted for boxes	Available with stiffeners	Available with stiffeners	Not typical for boxes

Key clause references

AISC 360-22 Section F7 -- Flexural strength of square and rectangular HSS and box-shaped members
AISC 360-22 Section G4 -- Shear strength of round and rectangular HSS and box sections
AISC 360-22 Section H3.1 -- Combined torsion, flexure, shear, and axial force
AISC 360-22 Section E7 -- Effective width of slender elements
AISC Design Guide 9 -- Torsional Analysis of Structural Steel Members
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
AASHTO LRFD Section 6.7.4 -- Diaphragms and cross-frames
AASHTO LRFD Section 6.11 -- Box girder flexural design

Common mistakes

Neglecting distortional warping. For thin-walled boxes under eccentric load, the cross-section distorts, producing stresses not captured by Bredt-Batho. BEF analysis or FEA may be needed for b/t > 40.
Omitting diaphragms at load application points. Concentrated loads on a 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 web-to-flange weld. Flexural shear flow and torsional shear flow are additive on one web. The critical weld must resist q_flexure + q_torsion, not flexural shear alone. This can double the weld demand on heavily loaded girders.
Using open-section LTB formulas. W-shape LTB equations (AISC F2) do not apply to box sections. Box sections use F7, where LTB rarely governs. Applying F2 to a box is conservative but incorrect.
Assuming tension field action is available. AISC G4 explicitly does not permit TFA for box sections. Using plate girder shear equations with TFA for a box is unconservative and violates the code.
Ignoring shear lag in wide flanges. For b > L/10, flexural stress is non-uniform across the flange. Shear lag reduces effective width, particularly for short spans. AASHTO and EN 1993-1-5 require explicit checks.
Not providing access holes in diaphragms. Solid diaphragms block inspection and maintenance access. Provide 12-18 in. diameter access holes with reinforcement as needed.
Welding stiffeners to the tension flange. Transverse welds on the tension flange create fatigue-sensitive details. Stiffeners should be stopped short of the tension flange per AREMA and good practice.

FAQ

When should I use a box girder instead of a plate girder?

Use a box girder when torsional loads are significant (eccentric loads, curved alignment, crane lateral forces), when lateral bracing is impractical, or when the girder must resist twist under service loads without excessive rotation. If the member is primarily a flexural element with negligible torsion and lateral bracing is available, a plate girder is more economical.

Does lateral-torsional buckling apply to box girders?

In theory, yes. In practice, almost never. AISC Section F7 provides an LTB check for box sections, but the high torsional constant J means the LTB capacity is much larger than the yield moment for typical unbraced lengths. For most practical box girders, LTB does not govern and the section capacity is controlled by yielding or local buckling.

Can I use tension field action for box girder web shear design?

No. AISC 360-22 Section G4 does not permit tension field action for round and rectangular HSS or box sections. The web shear capacity is limited to the pre-buckling strength (phiVn = phi * 0.6Fy*Aw*Cv2). This means box girder webs may need to be thicker or more closely stiffened than equivalent plate girder webs for the same shear demand.

How do I calculate the torsional constant J for a multi-cell box?

For a multi-cell box, use the Bredt-Batho method with compatibility equations. Set up simultaneous equations requiring that the twist rate is the same for all cells and that the shear flow is continuous around each cell. For a two-cell box, this results in a 2x2 system of equations. Most structural analysis textbooks provide the derivation. Alternatively, use the property calculator built into engineering software or the formula for thin-walled multi-cell sections.

What is the minimum web thickness for a box girder?

AISC 360 does not specify a minimum web thickness for box girders beyond the slenderness limits in Section F7. However, practical minimums apply: 5/16 in. for building structures (handling and welding considerations), 3/8 in. for bridge girders (corrosion allowance per AASHTO), and 3/8 in. to 1/2 in. for crane girders (fatigue and wear). AREMA requires a minimum of 3/8 in. for railway bridges.

How far apart should internal diaphragms be spaced?

AASHTO LRFD Section 6.7.4 recommends a maximum spacing of 1.5 times the box depth for bridge girders. For building structures, engineering judgment suggests 1.5d to 3d. Always provide full-depth solid diaphragms at supports, concentrated load points, and changes in cross-section. The first diaphragm from the support should be within 1.5d.

Do box girders need to be composite with a concrete deck?

Not necessarily. Composite construction increases flexural capacity and stiffness significantly, but non-composite steel box girders are common in crane runways, transfer beams, and building structures where composite action is impractical. In bridge applications, composite box girders are standard because the concrete deck also serves as the riding surface and distributes loads laterally.

How do I handle fatigue in box girder web-to-flange welds?

The web-to-flange weld is typically a longitudinal fillet weld, which is a Category B detail per AISC 360 Appendix 3. The stress range at this weld is the sum of the flexural shear stress and the torsional shear stress. For crane girders and bridge girders under repeated loading, compute the stress range at the critical web and compare with the allowable fatigue stress range for the appropriate detail category and number of cycles.

Run this calculation

Related references

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 (AISC 360-22, AASHTO LRFD, EN 1993, AS 4100) and project specification before use. Box girder design involves complex interactions between flexure, shear, torsion, and local buckling that may require project-specific finite element analysis. The site operator disclaims liability for any loss arising from the use of this information.