LD Single-Girder Bridge Crane Main Girder Deflection
Key Point Box-section design calculations for the LD-type single-girder bridge crane main girder: mid-span bending moment Mmax=qL²/8+φ₂QL/4, section moment of inertia Ix=(BH³-bh³)/12, bending stress σ=M/Wx≤[σ] (Q235B: 160 MPa, Q345B: 230 MPa), mid-span deflection f=5qL⁴/384EI+φ₂QL³/48EI≤L/700 (A3~A4). This article presents the complete calculation procedure using three standard capacity groups — 5t, 10t, and 16t — covering end carriage bolt verification, wheel load calculations, and camber setting methods.
The LD-type electric single-girder bridge crane — commonly referred to as the LD single-girder overhead crane — is the most widely used light-duty lifting device in factory workshops and industrial facilities. It consists of a main girder, end carriages, an electric hoist, and the electrical system. The main girder features a box-section design with a built-in I-beam that serves as the travel rail for the electric hoist. Both ends of the girder are suspended from the crane runway girders via end carriages and wheels. The structural design of the main girder directly determines the crane's load capacity, operating performance, and service life. This article provides a systematic engineering approach to LD main girder design, covering bending moment analysis, section design, strength and stiffness verification, and pre-camber setting — with complete worked examples for the three most common capacities: 5t, 10t, and 16t.
For selection parameters and pricing information on LD-type single-girder cranes, refer to the single-girder crane pricing FAQ and the LD-type electric single-girder bridge crane selection guide. For hoisting mechanism calculations, see electric hoist hoisting mechanism engineering calculations.
LD-type electric single-girder bridge crane structural diagram
Section Property Calculations
1.1 LD Main Girder Section Configuration
The LD main girder is a composite structure consisting of a box section with a built-in I-beam: the box is formed by welding the top flange plate, bottom flange plate, and two side web plates, with the I-beam rail welded to the bottom flange (alternatively, a rolled H-beam with a welded bottom flange plate may be used). The electric hoist travels along the lower flange of the I-beam.
1.2 Box-Section Geometric Properties
Ix = (B·H³ – b·h³) / 12 (moment of inertia, mm⁴)
Wx = Ix / (H/2) = (B·H³ – b·h³) / (6H) (section modulus, mm³)
A = B·H – b·h (cross-sectional area, mm²)
qG = A × 7850 × 9.81 × 10⁻⁶ (main girder dead weight, N/m)
Where: B — overall section width, H — overall section height, b = B − 2δw (internal cavity width), h = H − δtop − δbottom (internal cavity height)
1.3 Common I-Beam Rail Models
| Lifting Capacity(t) | I-Beam Model | h×b×d(mm) | flange thickness(mm) | Ix(cm⁴) |
|---|---|---|---|---|
| 1~2 | I20a | 200×100×7.0 | 11.4 | 2370 |
| 3~5 | I25a | 250×116×8.0 | 13.0 | 5020 |
| 10 | I28a | 280×122×8.5 | 13.7 | 7110 |
| 16 | I32a | 320×130×9.5 | 15.0 | 11100 |
| 20 | I36a | 360×136×10.0 | 15.8 | 15800 |
Strength and Stiffness Calculations
2.1 Load Determination
The main girder is simplified as a simply supported beam (supported at the end carriages). Loads include: the dead weight of the main girder (including the I-Beam rail, walkway/platform, and busbar support brackets), the dead weight of the electric hoist and lifting spreader, and the rated lifting capacity (including the dynamic load factor). The primary load combination in the vertical plane is GG + φ₂·(Q + q). The horizontal plane must be checked for crane bridge acceleration/braking inertia forces, approximately 0.1·(GG + Q).
2.2 Maximum Bending Moment at Mid-Span
Mmax = MG + MQ
MG = qG·L²/8 (dead-weight bending moment, N·m)
MQ = φ2·(Q + qhoist)·L/4 (maximum when the hoist is at mid-span, N·m)
L — LD Type span (center-to-center distance between end carriages), m
φ₂ — hoisting dynamic load factor: 1.1–1.2 for CD1 Type; 1.05–1.15 for MD1 two-speed
2.3 Bending Stress
σvertical = Mmax / Wx ≤ [σ]
[σ] — 160 MPa for Q235B (≈S235JR); 230 MPa for Q345B (≈S355J2) (load combination A)
Load combination B (test condition): [σ] may be increased by a factor of 1.33
2.4 Shear Stress Check
Vmax = qG·L/2 + φ₂·(Q + qhoist)/2 (maximum shear at support)
τmax = Vmax / (2·hw·δw) (shared by both web plates)
[τ] — 95 MPa for Q235B; 140 MPa for Q345B
2.5 Deflection Check
ftotal = fG + fQ ≤ [f]
fG = 5·qG·L⁴ / (384·E·Ix)
fQ = φ₂·(Q + qhoist)·L³ / (48·E·Ix)
[f] — A3 to A4: L/700; A5: L/800; A6 and above: L/1000
E = 2.06 × 10⁵ MPa (Elastic Modulus of steel)
Design Calculation Examples
Example 1: 5t LD Type, 16.5 m Span, Q235B, A4 Duty
Given: Q = 50,000 N, qhoist = 3,500 N, L = 16.5 m, φ₂ = 1.15
Initial section: B = 400 mm, H = 550 mm, δtop = δbottom = 8 mm, δweb = 5 mm
Ix = 5.23 × 10⁸ mm⁴, Wx = 1.90 × 10⁶ mm³, qG,total ≈ 1,600 N/m
MG = 54,450 N·m, MQ = 253,528 N·m, Mmax = 307,978 N·m
σ = 162.1 MPa ≈ [σ] = 160 MPa (acceptable when the I-Beam's load-sharing contribution is included)
fG = 14.2 mm, fQ = 52.5 mm, ftotal = 66.7 mm > [f] = 23.6 mm
With a preset camber of fcamber = 30 mm (≈ L/550), effective deflection = 66.7 − 30 = 36.7 mm — still insufficient.
Enlarge section: increase H from 550 to 650 mm → ftotal,new = 39.9 mm; with a 35 mm camber, effective deflection = 4.9 mm.
Example 2: 10t LD Type, 19.5 m Span, Q345B, A5 Duty
B = 450 mm, H = 750 mm, δ = 10 mm, δweb = 6 mm
Ix = 1.45 × 10⁹ mm⁴, Wx = 3.87 × 10⁶ mm³, qG,total ≈ 2,500 N/m
Mmax = 687,253 N·m, σ = 177.6 MPa ≤ 230 MPa
ftotal = 75.7 mm > [f] = 24.4 mm
With a preset camber of 55 mm, effective deflection = 75.7 − 55 = 20.7 mm < 24.4 mm — acceptable.
Example 3: 16t LD Type, 22.5 m Span, Q345B, A5 Duty
B = 500 mm, H = 900 mm, δ = 12 mm, δweb = 6 mm
Ix = 3.01 × 10⁹ mm⁴, Wx = 6.69 × 10⁶ mm³, qG,total ≈ 3,500 N/m
Mmax = 1,262,953 N·m, σ = 188.8 MPa ≤ 230 MPa
ftotal = 97.7 mm > [f] = 28.1 mm
With a preset camber of 70 mm, effective deflection = 97.7 − 70 = 27.7 mm < 28.1 mm — marginal.
Recommend increasing H to 1,000 mm for a greater safety margin.
End Carriage Connections and Wheel Load Calculations
The main girder of the LD type single-girder crane is connected to the end carriages at both ends using high-strength bolts, which primarily withstand shear forces at the connections. Each end carriage is typically equipped with two wheels (one driving wheel and one driven wheel). The shear force at the connection is calculated as V=qG·L/2+φ₂·(Q+qhoist)/2, and the maximum wheel load per wheel is Pmax=V/2×ψ (where ψ=1.1~1.2 is the load distribution coefficient). Taking a 10t LD type crane as an example: V=82675N, Pmax≈47.5kN per wheel, which is well below the allowable limits for P38/P43 rails, meaning the LD type imposes relatively low wheel loads on the factory building's crane runway girders.
Recommended Main Girder Cross-Sections
| Lifting Capacity(t) | recommended H(mm) | height-to-span ratio | B(mm) | Web platethickness(mm) | flange plate thickness(mm) |
|---|---|---|---|---|---|
| 5 | 500~700 | 1/20~1/24 | 350~400 | 5 | 8 |
| 10 | 650~900 | 1/18~1/22 | 400~500 | 6 | 10 |
| 16 | 800~1100 | 1/16~1/20 | 450~550 | 6~8 | 12 |
| 20 | 900~1200 | 1/16~1/18 | 500~600 | 6~8 | 12~14 |
Related Standards
• GB/T 6974.7-2008 — Cranes — Terminology — Part 7: Floating Cranes
• ISO 12480-2:2008 — Cranes — Safe Use — Part 2: Mobile Cranes
• ISO 12480-5:2012 — Cranes — Safe Use — Part 5: Bridge and Gantry Cranes
LD Type Crane Main Girder: Common Questions & Answers
Q: Why is camber required on the LD type main girder, and what value is recommended?
A: Concentrated loads account for 75%–85% of total deflection. Since factory-building clearance limits prevent unlimited section enlargement, a pre-camber of L/600 to L/400 is standard practice to compensate. The camber is achieved by profiling the web plate during cutting. Kelude sets the pre-camber based on deflection calculated at 1.25 times the rated load and supplies a camber measurement record with each crane.
Q: Is a 5 mm web plate too thin?
A: Shear stress in the LD type web plate typically ranges from 30 to 50 MPa, well below the allowable value of 95 MPa for Q235B (≈S235JR). The governing factor is local stability: hw/δw ≤ 180 for Q235. If this ratio is exceeded, longitudinal stiffeners must be added.
Q: What is the acceptance standard for main girder camber?
A: ISO 4306 specifies an unloaded camber of L/2000 to L/1000, with a residual camber of no less than L/2000 after three years of service. Inspection is performed using a level instrument or the wire-pull method. Kelude supplies a measurement record with every crane.
Q: Should the I-beam rail be welded or rolled as a single piece?
A: For cranes up to 5 t, a welded I-beam fabrication is used. Above 10 t, a rolled I-beam or a thickened lower flange is recommended to minimize weld seams and extend fatigue life. Kelude selects the fabrication route based on rated load.
