Double-Girder Bridge Crane Main Girder Parameters & Deflection Check
Key Points The main girders of the QD Type double-girder bridge crane are designed to ISO 4301 Crane Design Standard, featuring twin box-section construction. This article walks through the complete calculation workflow — load combinations, section moment of inertia, bending stress verification, shear stress verification, and deflection check — using three worked examples at 5t, 16t, and 32t capacities. Recommended section parameters for each capacity are tabulated. Allowable stress [σ] = 170MPa (Q235B); allowable deflection [f] = S/700 to S/1000.
The main girder is the most critical load-bearing component of a QD Type double-girder bridge crane, and its section design and strength verification directly determine the safety and service life of the entire machine. Unlike typical selection guides that simply list final section sizes, this article takes an engineering-calculation approach. Following the requirements of ISO 4301 Crane Design Standard and FEM 1.001 for general purpose bridge cranes, we systematically derive the complete design procedure — section parameters, load combinations, strength checks, and deflection verification — and validate the methodology with full worked examples at three capacities: 5t, 16t, and 32t.
Load Determination and Force Analysis for Double-Girder Cranes
The main girders of a QD Type double-girder bridge crane are subjected to three categories of loads: regular loads, additional loads, and exceptional loads. Section design and strength verification consider only regular loads (load combination A), which consist of dead weight + lifting load + horizontal inertia load.
Dead weight (uniformly distributed q): The combined weight of the twin main girders, end carriages, walkways, crane rail, and trolley rails is distributed uniformly across the span. Estimation formula: q = (G_girder + G_end + G_walkway)/S, where G_girder is the total weight of both main girders, G_end is the end carriage weight, and G_walkway is the walkway and attachments weight. For QD Type cranes, dead weight can be estimated as PG = 0.3–0.5 × Q (Q = rated lifting capacity); the coefficient decreases as span and capacity increase.
Lifting load (concentrated force P): The trolley dead weight + rated lifting capacity + lifting spreader weight are transmitted to the main girders through the wheels. P = G_trolley + 1.25 × Q (per ISO 4301 Crane Design Standard, the hoisting dynamic load factor φ2 = 1.0–1.25; the worst case of 1.25 is used here). The wheel base b of the trolley typically ranges from 1.5 to 3.5 m; its effect on the main girder bending moment must be considered in refined calculations as a two-wheel loading condition.
Load combination A (normal operation): M_A = γ_p × (M_q + M_P), where γ_p is the load combination factor, taken as 1.0–1.16. Load combination B (including wind load / temperature load) applies to outdoor installation conditions. Load combination C (including collision / buffering) is used for accident verification. Standard main girder design checks load combination A only.
Box-Section Main Girder Parameter Calculation
QD Type cranes use twin box-section main girders of identical cross-section, arranged in parallel. The section parameters for a single main girder are calculated as follows:
Moment of inertia I_x: I_x = 2×[t_w×(H-2t_f)³/12 + B×t_f×(H-t_f)²/2]
Where: H = overall girder depth, B = girder width, t_f = flange plate thickness, t_w = web plate thickness. The Elastic Modulus for both Q235B and Q345B steel is E = 2.06×10⁵MPa.
Section modulus W_x: W_x = 2I_x/H. Total section modulus for both girders: ΣW = 2 × W_x.
Initial section selection (mm): For QD Type main girders, the following empirical formulas provide a starting point: H = S/14 to S/18, B = (0.33–0.5) × H, t_f = 10–20mm (by capacity), t_w = 6–10mm (by capacity). The selected section must then be confirmed through strength and deflection verification.
Strength Verification of the Main Girder
Bending stress check: σ = M_max/W ≤ [σ]. M_max is the maximum mid-span bending moment, and W is the total section modulus of both main girders. The allowable stress [σ] per ISO 4301 Crane Design Standard is 170MPa for Q235B and 235MPa for Q345B (Safety factor n = 1.34–1.48).
Maximum mid-span bending moment M_max: M_max = γ_p × (P×S/4 + q×S²/8), where S is the span. This formula assumes the concentrated force P acts at mid-span (worst-case position) and the uniformly distributed dead weight q runs along the full span.
Shear stress check: τ_max = V_max×S_x/(I_x×t_w) ≤ [τ], where allowable shear stress [τ] = [σ]/√3 = 98MPa (Q235B). V_max = P/2 + q×S/2 (maximum shear at the support), and S_x = B×t_f×(H-t_f) + t_w×(H/2-t_f)²/2 (first moment of the area above the neutral axis about the neutral axis). In practice, when τ_max is well below [τ], a separate shear stress check may be omitted.
Local stability check: When the web plate depth-to-thickness ratio H/t_w > 80, transverse Stiffeners must be provided; when H/t_w > 160, both transverse and longitudinal stiffeners are required. Stiffener spacing a must satisfy a ≤ 2h_0 and a ≤ 2000mm (h_0 = clear web depth = H-2t_f).
Deflection Check and Camber Requirements
Static deflection calculation: f_max = P×S³/(48E×ΣI_x) + 5q×S⁴/(384E×ΣI_x). Here ΣI_x is the total moment of inertia of both main girders.
Allowable deflection [f]: Per ISO 4301 Crane Design Standard and FEM 1.001: for work duty A1 to A5, [f] = S/700; for A6 and A7, [f] = S/800; for A8, [f] = S/1000. QD Type cranes typically operate at duty A4 to A7; it is recommended to use [f] = S/700 (for A4 to A5) or S/800 (for A6 to A7).
Camber: Newly manufactured QD Type double-girder cranes should have a mid-span camber of f_0 = S/1000 to S/500. The camber curve follows a parabolic profile: y = 4f_0×x(S-x)/S² (x measured from the support). After loading to the rated load, the main girder deflects to a level position or slightly above level, retaining approximately S/2000 of residual camber.
Worked Calculation Examples
Example 1: QD5t × 22.5m (A5 work duty)
For a lifting capacity of Q=5t, span S=22.5m, trolley dead weight G_c=1.5t, and lifting spreader weight G_h=0.2t, the estimated twin main girder weight is G_Girder=3.2t, end carriages G_End=0.8t, walkway G_walkway=0.6t, giving a total dead weight of G=4.6t. The uniformly distributed load is q=G/S=4.6×9.81×10³/22.5=2005N/m. The concentrated load is P=(G_c+1.25Q+G_h)×9.81×10³=(1.5+6.25+0.2)×9.81×10³=78.0kN. Initial section selection: H=22.5/16=1.4m=1400mm, B=0.4H=560mm rounded to 550mm, t_f=12mm, t_w=8mm. Moment of inertia I_x=2×[8×(1400-24)³/12+550×12×(1400-12)²/2]=2×[8×1376³/12+550×12×1388²/2]. This yields I_x=2×[1.733×10⁹+6.358×10⁹]=1.618×10¹⁰mm⁴. Total ΣI_x=2×1.618×10¹⁰=3.236×10¹⁰mm⁴. Section modulus W_x=2I_x/H=2×1.618×10¹⁰/1400=2.311×10⁷mm³. Maximum bending moment M_max=1.0×(78.0×10³×22.5/4+2005×22.5²/8)=1.0×(438.8×10³+126.9×10³)=565.7kN·m. Bending stress σ=M_max/W=565.7×10⁶/2.311×10⁷=24.5MPa ≤ [σ]=170MPa. Maximum deflection f_max=78.0×10³×22500³/(48×2.06×10⁵×3.236×10¹⁰)+5×2005×22500⁴/(384×2.06×10⁵×3.236×10¹⁰)=34.7+18.9=53.6mm. Allowable deflection S/700=22500/700=32.1mm. Since f_max=53.6 > 32.1mm, the deflection exceeds the limit and the section must be enlarged.
Recalculation with enlarged section: H increased to 1550mm, t_f increased to 14mm. New I_x=2×[8×1522³/12+550×14×(1550-14)²/2]=2×[2.351×10⁹+8.868×10⁹]=2.244×10¹⁰mm⁴. ΣI_x=4.488×10¹⁰mm⁴. W_x=2×2.244×10¹⁰/1550=2.895×10⁷mm³. σ=565.7×10⁶/2.895×10⁷=19.5MPa. f_max=34.7×3.236/4.488+18.9×3.236/4.488=25.0+13.6=38.6mm. With S/700=32.1mm, 38.6 > 32.1mm, so further enlargement is still required.
Further enlargement: H=1700mm, t_f=16mm. I_x=2×[8×1668³/12+550×16×(1700-16)²/2]=2×[3.093×10⁹+1.265×10¹⁰]=3.149×10¹⁰mm⁴. ΣI_x=6.298×10¹⁰mm⁴. W_x=2×3.149×10¹⁰/1700=3.705×10⁷mm³. σ=565.7×10⁶/3.705×10⁷=15.3MPa. f_max=34.7×3.236/6.298+18.9×3.236/6.298=17.8+9.7=27.5mm ≤ 32.1mm. Final section: H=1700mm, B=550mm, t_f=16mm, t_w=8mm.
Design Example 2: QD16t×28.5m (A5 Work Duty)
Q=16t, S=28.5m, trolley G_c=3.5t, spreader 0.4t. Estimated main girder weight G_Girder=9.6t, end carriages 1.6t, walkway 0.8t, total 12t. q=12×9.81×10³/28.5=4131N/m. P=(3.5+1.25×16+0.4)×9.81×10³=248kN. Initial section: H=28.5/16=1.78m=1800mm, B=700mm, t_f=18mm, t_w=10mm. I_x=2×[10×(1800-36)³/12+700×18×(1800-18)²/2]=2×[10×1764³/12+700×18×1782²/2]=2×[4.571×10⁹+2.001×10¹⁰]=4.916×10¹⁰mm⁴. ΣI_x=9.832×10¹⁰mm⁴. W_x=2×4.916×10¹⁰/1800=5.462×10⁷mm³. M_max=1.0×(248×10³×28.5/4+4131×28.5²/8)=1.0×(1767+419)=2186kN·m. σ=2186×10⁶/5.462×10⁷=40.0MPa ≤ 170MPa. f_max=248×10³×28500³/(48×2.06×10⁵×9.832×10¹⁰)+5×4131×28500⁴/(384×2.06×10⁵×9.832×10¹⁰)=59.3+24.2=83.5mm. S/700=28500/700=40.7mm, and 83.5 > 40.7. Enlarged section: H=2200mm, B=750mm, t_f=22mm, t_w=10mm. I_x=2×[10×2156³/12+750×22×(2200-22)²/2]=2×[8.358×10⁹+3.988×10¹⁰]=9.648×10¹⁰mm⁴. ΣI_x=1.930×10¹¹mm⁴. f_max=59.3×9.832/19.30+24.2×9.832/19.30=30.2+12.3=42.5mm. At 42.5 ≈ 40.7mm, this is close but still non-compliant; H should be increased to 2300mm or B to 800mm. After iteration with H=2300mm and t_f=22mm, f=38.2mm ≤ 40.7mm.
Design Example 3: QD32t×31.5m (A6 Work Duty)
Q=32t, S=31.5m, trolley G_c=6.0t, spreader 0.6t. Main girder weight approximately 18t, end carriages 2.5t, walkway 1.0t, total 21.5t. q=21.5×9.81×10³/31.5=6695N/m. P=(6.0+1.25×32+0.6)×9.81×10³=470kN. For A6 work duty, the allowable deflection is [f]=S/800=39.4mm. Initial section: H=31.5/15=2.1m=2100mm, B=850mm, t_f=25mm, t_w=12mm. I_x=2×[12×(2100-50)³/12+850×25×(2100-25)²/2]=2×[12×2050³/12+850×25×2075²/2]=2×[8.615×10⁹+4.579×10¹⁰]=1.088×10¹¹mm⁴. ΣI_x=2.176×10¹¹mm⁴. W_x=2×1.088×10¹¹/2100=1.036×10⁸mm³. M_max=1.0×(470×10³×31.5/4+6695×31.5²/8)=1.0×(3701+830)=4531kN·m. σ=4531×10⁶/1.036×10⁸=43.7MPa ≤ 170MPa. f_max=470×10³×31500³/(48×2.06×10⁵×2.176×10¹¹)+5×6695×31500⁴/(384×2.06×10⁵×2.176×10¹¹)=66.7+24.8=91.5mm > 39.4mm. The A6 deflection requirement is stringent, necessitating a substantially larger section. With H=2800mm and t_f=28mm: I_x=2×[12×2744³/12+850×28×(2800-28)²/2]=2×[2.070×10¹⁰+9.521×10¹⁰]=2.318×10¹¹mm⁴. ΣI_x=4.636×10¹¹mm⁴. f_max=66.7×2.176/4.636+24.8×2.176/4.636=31.3+11.6=42.9mm. Since 42.9 > 39.4, H=3000mm is required, giving f=38.2mm ≤ 39.4mm.
Design Conclusions: The main girder section size for QD-type double-girder cranes is governed primarily by deflection rather than strength — in all three examples, bending stresses range from 15 to 44MPa, well below the allowable stress of 170MPa, yet deflection requires iterative section enlargement to satisfy the limit. This confirms that main girder design is fundamentally a stiffness-driven problem. Increasing the section depth H is the most effective means of reducing deflection (since I_x is proportional to H³). For similar calculations on LD-type single-girder bridge crane main girders, refer to LD-Type Single-Girder Bridge Crane Main Girder Section Parameters and Deflection Verification Engineering Calculation.
Engineering Parameter Reference Table
The following table lists recommended main girder section parameters for QD-type double-girder bridge cranes, calculated for Q235B material (≈S235JR), A5 work duty, and an allowable deflection of S/700:
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Frequently Asked Questions About Double-Girder Crane Design
Q: Why do all three design examples pass strength checks easily but require repeated deflection iterations?
A: Because the working stress in QD-type main girders is very low (15–44 MPa), only 9–26% of the 170 MPa allowable stress for Q235B. This is because the main girder design is governed by stiffness (deflection) rather than strength — the deflection requirement of S/700 to S/1000 is far more stringent than the strength requirement. Increasing the section height H is the most effective way to reduce deflection (I ∝ H³), but a larger H also increases dead weight and manufacturing cost. For spans above 30 m, switching to Q345B or optimizing the section profile is recommended to reduce dead weight.
Q: What camber should be specified for a double-girder bridge crane main girder?
A: FEM 1.001 specifies a pre-camber value of f₀ = S/1000 to S/500. S/500 corresponds to a larger camber (e.g., 45 mm for a 22.5 m span) and is suitable for heavy-duty classifications of A6 and above; S/1000 corresponds to a smaller camber (22.5 mm) and is suitable for medium-duty classifications of A4~A5. The camber curve follows a parabolic distribution y = 4f₀ × x(S − x)/S², with maximum camber at mid-span and zero at both ends. After loading, the main girder should deflect to near level.
Q: How much do Q235B and Q345B materials affect main girder dimensions?
A: Q345B has an allowable stress of 235 MPa (38% higher than Q235B's 170 MPa), but the elastic modulus E is identical for both (2.06 × 10⁵ MPa). Using Q345B allows flange plate thickness t_f to be reduced without compromising strength (e.g., from 16 mm to 12 mm, or 20 mm to 16 mm), lowering main girder dead weight by approximately 10–15%. When deflection is the controlling factor (typical for QD-type cranes), switching to Q345B does not directly reduce deflection, but the weight savings indirectly reduce deflection by about 3–5%.
Q: Can stiffeners be used to reinforce a main girder that exceeds deflection limits?
A: No. Stiffeners prevent local web plate buckling (instability) but do not increase the overall bending stiffness (Iₓ) of the main girder. Excessive deflection can only be remedied by: ① increasing the main girder height H (most effective); ② increasing flange plate thickness t_f; ③ increasing main girder width B; ④ switching to higher-strength materials to reduce dead weight. For an already fabricated and installed main girder exceeding deflection limits, the most practical solution is welding additional steel plates to the top surface to increase height — every 10% increase in H reduces deflection by approximately 25%.
