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, and 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. Box girders are used in crane runways, curved bridge girders, transfer beams in buildings, and any application where torsional loads or lateral instability of open sections drive the design.

This reference covers box girder behavior, AISC 360-22 design provisions, flange and web design, torsional stiffness, diaphragm requirements, typical proportions, and worked examples.

Torsional Behavior of Closed Sections

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.

The critical advantage of a box girder is its torsional stiffness. For an open section (W-shape), the torsional constant J is approximately sum(bt^3/3), dominated by the flange and web thicknesses cubed. For a W24x76: J = 1.43 in^4.

For a closed box section of the same depth and width, the torsional constant is:

J_box = 4 * A_o^2 / sum(b/t)

where A_o is the enclosed area of the box (measured to the mid-thickness of the plates), and sum(b/t) is the sum of the width-to-thickness ratios of the four walls.

For a box girder 24 in. deep x 18 in. wide, with 5/8 in. web and 1 in. flanges:

A_o = (18 - 1) x (24 - 0.625) = 17 x 23.375 = 397.4 in^2 sum(b/t) = 2 x (17/0.625) + 2 x (23.375/1.0) = 2 x 27.2 + 2 x 23.375 = 54.4 + 46.75 = 101.15 J_box = 4 x 397.4^2 / 101.15 = 4 x 157,915 / 101.15 = 6,244 in^4

J_box = 6,244 in^4 compared to J_W24x76 = 1.43 in^4 -- the box section is over 4,000 times stiffer in torsion. This is why box girders are the section of choice for torsion-dominated applications.

Shear Flow in Box Girders

Under torsion, shear flows around the closed perimeter of the box:

q = T / (2 * A_o)
tau = q / t = T / (2 * A_o * t)

where T is the applied torque and t is the wall thickness. The shear flow is constant around the perimeter (pure torsion). The shear stress varies inversely with wall thickness -- thinner webs have higher shear stress.

The angle of twist per unit length:

theta = T / (4 * G * A_o^2) * sum(b/t)

where G = shear modulus = 11,200 ksi for steel.

Worked example -- torsional shear stress:

Box girder as above, T = 200 kip-ft = 2,400 kip-in.

q = 2,400 / (2 x 397.4) = 3.02 kip/in (constant shear flow around the perimeter).

Shear stress in the web (t = 5/8 in.): tau_web = 3.02 / 0.625 = 4.83 ksi. Shear stress in the flange (t = 1.0 in.): tau_flange = 3.02 / 1.0 = 3.02 ksi.

The allowable shear stress per AISC 360 Section G2 for the web: phi_v x 0.60 x Fy = 0.90 x 0.60 x 50 = 27.0 ksi. tau_web = 4.83 ksi << 27.0 ksi. OK.

Angle of twist: theta = 2,400 / (4 x 11,200 x 397.4^2) x 101.15 theta = 2,400 / (4 x 11,200 x 157,915) x 101.15 theta = 2,400 / (7.075 x 10^9) x 101.15 theta = 3.392 x 10^-7 rad/in = 2.033 x 10^-5 rad/ft = 1.165 x 10^-3 degrees/ft

Over a 40 ft span, total rotation = 40 x 1.165 x 10^-3 = 0.047 degrees -- negligible. This is the hallmark of closed section torsional stiffness.

Flange and Web Slenderness Limits (AISC 360 Table B4.1)

Box girder flanges are classified as stiffened compression elements (both longitudinal edges supported by the webs). The width-to-thickness limit for a non-slender flange:

lambda_r = 1.40 * sqrt(E / Fy)  (uniform compression, Case 10)

For Fy = 50 ksi: lambda_r = 1.40 x sqrt(29,000/50) = 1.40 x 24.08 = 33.7.

For a flange with b/t <= 33.7, the section is compact and the full plastic moment can be developed. For 33.7 < b/t <= 56.8 (the non-slender limit, 5.70 x sqrt(E/Fy) for stiffened elements), the section is non-slender and the yield moment can still be reached but plastic moment redistribution is limited.

Box girder webs are stiffened by the flanges at both longitudinal edges. For a doubly-symmetric box section in pure flexure, the web slenderness limit is:

lambda_r = 5.70 * sqrt(E / Fy)  (Case 15, webs in flexural compression)

For Fy = 50 ksi: lambda_r = 5.70 x 24.08 = 137.3. For a web with h/tw <= 137.3, the web is non-slender.

Stiffener Design for Box Girders

Box girders require internal diaphragms at regular intervals to maintain the cross-sectional shape under torsion and to distribute concentrated loads. Without diaphragms, the cross-section distorts (breathes) under asymmetric loading, reducing torsional stiffness and introducing warping stresses.

Diaphragm Spacing

Per AASHTO LRFD Bridge Design Specifications Section 6.7.4 (commonly referenced for building box girders as well): diaphragm spacing should not exceed 2.5 times the box depth. For a 24 in. deep box girder, diaphragms should be placed at no more than 60 in. (5 ft) intervals.

Diaphragms are typically 3/8 in. to 1/2 in. thick plates with a manhole cutout for access (in larger girders). The diaphragm is fillet-welded to all four walls of the box.

Longitudinal Stiffeners

For deep box girders (depth > 40 in.), longitudinal stiffeners on the web and compression flange may be required to prevent local buckling. The stiffeners divide the plate into smaller sub-panels, increasing the buckling coefficient k and allowing a higher slenderness limit. Per AISC 360 Section F13.3, the stiffener must satisfy:

I_st >= a * t_w^3 * (2.5 / (a/h)^2 - 2)  >= 0.375 * a * t_w^3

where I_st is the moment of inertia of the stiffener about an axis at the base of the stiffener (parallel to the web), a is the stiffener spacing, and h is the web depth.

Flexural Design per AISC 360 Section F7

For box sections in flexure, AISC 360 Section F7 applies (HSS and box-shaped members). The nominal flexural strength is:

Yielding: Mn = Mp = Fy x Zx (compact sections)
Flange local buckling: Mn = Mp - (Mp - Fy x Sx) x (lambda - lambda_pf) / (lambda_rf - lambda_pf) (non-compact flanges)
Web local buckling: Mn = Fy x Seff (slender webs, effective section properties)

Lateral-torsional buckling is generally not a limit state for box sections in bending because the closed shape provides enormous lateral stiffness. The LTB limit only applies when the unbraced length exceeds:

L_p = 0.13 * E * r_y * sqrt(J * A) / (M_p)

which for typical box girders corresponds to unbraced lengths exceeding 60-100 ft -- far beyond practical framing.

Worked Example -- Box Girder Flexural Capacity

Given: Box girder 24 in. deep x 18 in. wide, 1 in. flanges (A572 Gr 50), 5/8 in. webs (A36), Fy = 50 ksi (flanges control). Span = 40 ft simply supported.

Section properties:

Ix = (18 x 24^3 - (18 - 0.625) x (24 - 2)^3) / 12 = (18 x 13,824 - 17.375 x 10,648) / 12 = (248,832 - 185,031) / 12 = 5,317 in^4
Sx = Ix / (d/2) = 5,317 / 12 = 443 in^3
Zx = approximate plastic modulus for box: 2 x [bf x tf x (d - tf) + (d/2 - tf) x tw x (d/2 - tf)/2] x 2 = approximately 530 in^3

Flange slenderness: b/t = (18 - 0.625) / 1.0 = 17.375 / 1.0 = 17.4. lambda_pf = 1.12 x sqrt(E/Fy) = 1.12 x 24.08 = 27.0. 17.4 < 27.0 -- flange is compact.

Web slenderness: h/tw = (24 - 2 x 1.0) / 0.625 = 22 / 0.625 = 35.2. lambda_pw = 2.42 x sqrt(E/Fy) = 2.42 x 24.08 = 58.3. 35.2 < 58.3 -- web is compact.

Since both elements are compact: Mn = Mp = Fy x Zx = 50 x 530 = 26,500 kip-in = 2,208 kip-ft.

phi Mn = 0.90 x 2,208 = 1,988 kip-ft.

For a simply supported span of 40 ft, the maximum factored uniform load w_u = 8 x phi Mn / L^2 = 8 x 1,988 / 1,600 = 9.94 klf. This corresponds to a total service load of approximately 6.6 klf (at a load factor of 1.5 average) -- suitable for heavy industrial loads.

Shear Design

For box girders, shear is distributed between the two webs. Each web resists V_u / 2. The AISC 360 Section G2 shear check applies to each web individually.

For the example box girder (web 5/8 in. x 22 in. deep between flanges): Aw = 22 x 0.625 = 13.75 in^2 per web. Cv = 1.0 (h/tw = 35.2 < 1.10 x sqrt(kv E / Fy) = 1.10 x sqrt(5.34 x 29,000 / 50) = 61.2) Vn = 0.6 x Fy x Aw x Cv = 0.6 x 50 x 13.75 x 1.0 = 412.5 kip per web. phi Vn = 0.90 x 412.5 = 371 kip per web. Total: 742 kip. This far exceeds the shear demand from the flexural capacity.

Weld Design for Box Girders

The longitudinal welds connecting the webs to the flanges must transfer the shear flow between the web and flange. The shear flow at the web-flange junction is:

q_weld = V * Q / I

where Q = first moment of area of the flange about the neutral axis.

For V = phi Vn / 2 = 371 kip (design shear per web): Q_flange = 18 x 1.0 x (12 - 0.5) = 18 x 11.5 = 207 in^3. q_weld = 371 x 207 / 5,317 = 14.4 kip/in

This shear flow must be resisted by the fillet welds on both sides of each web. With fillet welds on both sides: demand per weld = 14.4 / 2 = 7.2 kip/in.

Required fillet size: 7.2 / 5.57 (per 1/4 in. fillet capacity) = 1.29 x 1/4 in. = 0.32 in. Use 3/8 in. fillet weld (8.35 kip/in capacity > 7.2 kip/in). OK.

Corrosion Protection for Interior Spaces

A critical practical concern: the interior of a box girder is a confined space. Moisture condensation inside the box can cause hidden corrosion that is invisible from the outside. Design measures:

Seal welds at all plate junctions to prevent water ingress.
Drain holes at low points (typically 1/2 in. diameter at 5 ft spacing along the bottom flange).
Vent holes near the top to allow air circulation.
Interior coating: Shop-applied primer on all interior surfaces before final welding and closure.
For exterior box girders (bridges, crane runways exposed to weather): hot-dip galvanize the entire girder or specify ASTM A588 weathering steel with adequate detailing for drainage.

Common Applications

Application	Typical Dimensions	Key Design Driver
Crane runway girder	24-48 in. deep, 18-30 in. wide	Torsion from eccentric crane wheel loads + fatigue
Curved bridge girder	48-96 in. deep, 36-60 in. wide	Torsion from curvature + lateral flange bending
Transfer girder (building)	36-60 in. deep, 24-36 in. wide	High shear + concentrated column loads above
Equipment support beam	18-36 in. deep, 12-24 in. wide	Vibration + fatigue from rotating equipment
Architectural exposed box beam	12-24 in. deep, 12-18 in. wide	AESS finish requirements + limited depth

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Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. Box girder design must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) for the specific project. The site operator disclaims liability for any loss arising from the use of this information. Results are PRELIMINARY -- NOT FOR CONSTRUCTION.