📚 Engineering Case Study in Practice: Bridge Design and Analysis | 工程案例分析实战演练：桥梁设计与分析
In engineering, real-world case studies allow students to apply theoretical knowledge to practical scenarios. This case study examines the design of a pedestrian footbridge, highlighting the iterative nature of engineering design, material selection, and failure analysis. By working through the problem, you will see how decisions are justified and how unforeseen issues are resolved.
在工程中，真实案例研究使学生能够将理论知识应用于实际场景。本案例研究考察了一座人行天桥的设计，突出了工程设计的迭代性质、材料选择和失效分析。通过解决这个问题，您将看到决策如何合理化，以及如何解决不可预见的问题。
1. Case Background | 案例背景
A city council requires a 15 m span footbridge to connect two campus buildings across a busy road. The bridge must be lightweight yet strong, with minimal maintenance due to the coastal location’s corrosive salt spray. Initial concept meetings identified an aluminium alloy truss bridge as a promising solution because of its low density and good extrudability.
某市议会需要一座15米跨径的人行天桥，连接两座校园建筑，跨越一条繁忙道路。桥梁必须轻便且坚固，由于沿海位置的盐雾腐蚀，需尽可能减少维护。初步方案讨论认定铝合金桁架桥是一个有前景的解决方案，因其密度低且挤压成型性能良好。
The site is exposed to wind gusts up to 45 m/s, and the clearance below the bridge must be at least 5 m. Aesthetics are important because the structure will be highly visible, and the total project budget is capped at £150,000. Sustainability targets require a minimum 50-year design life with low embodied carbon.
场地暴露在高达45 m/s的阵风中，桥下净空至少需5米。美学很重要，因为结构非常显眼，项目总预算上限为15万英镑。可持续发展目标要求设计使用寿命至少50年，且隐含碳低。
2. Design Requirements and Constraints | 设计要求与约束
Several key specifications were derived from the client brief and relevant codes (Eurocode 1 and 3):
从客户需求和相关规范（欧洲规范1和3）中得出了几个关键规格：
• Pedestrian live load: 5.0 kN/m² uniformly distributed, plus a point load of 10 kN for occasional maintenance vehicle.
• 行人活荷载：均布5.0 kN/m²，另加偶尔检修车辆的10 kN集中荷载。
• Wind load: design wind speed of 45 m/s applied to the projected area, resulting in a lateral pressure of 1.2 kN/m².
• 风荷载：设计风速45 m/s作用于投影面积，产生1.2 kN/m²的侧向压力。
• Deflection limit: maximum vertical deflection under full live load shall not exceed L/200 (75 mm).
• 挠度限制：满布活载下最大竖向挠度不得超过L/200 (75 mm)。
• Durability: the structure must resist marine corrosion without requiring repainting more than once every 15 years.
• 耐久性：结构必须抵抗海洋腐蚀，重涂周期不得低于15年。
• Aesthetic constraint: a sleek, modern appearance with colour-matched anodised finish.
• 美学限制：外观流畅现代，采用颜色匹配的阳极氧化表面处理。
• Budget: total installed cost ≤ £150,000.
• 预算：总安装成本 ≤ 15万英镑。
• Sustainability: design life 50 years, and the material should be recyclable at end of life.
• 可持续性：设计寿命50年，材料在寿命终止时应可回收。
3. Material Selection Process | 材料选择过程
The design team shortlisted three candidate materials: aluminium alloy 6061-T6, structural steel S355, and a carbon fibre reinforced polymer (CFRP) laminate. A preliminary comparison is shown in the table below.
设计团队筛选出三种候选材料：铝合金6061-T6、结构钢S355和碳纤维增强聚合物（CFRP）层压板。初步比较如下表所示。
| Property | Al 6061-T6 | Steel S355 | CFRP Laminate |
|---|---|---|---|
| Density (kg/m³) | 2700 | 7850 | 1550 |
| Yield strength (MPa) | 275 | 355 | *600 (tensile) |
| Elastic modulus (GPa) | 69 | 210 | 120 (longitudinal) |
| Corrosion resistance | Good (self-passivating) | Poor unless galvanised | Excellent |
| Relative cost per kg | 2.5 | 1.0 | 15.0 |
Aluminium alloy 6061-T6 was initially selected because of its low density, adequate strength, excellent corrosion resistance, and the ability to be extruded into complex truss profiles. Steel was rejected due to weight and maintenance painting costs. CFRP was deemed too expensive for the initial budget, though its long-term potential was noted.
铝合金6061-T6最初被选中，因为它密度低、强度足够、耐腐蚀性优异，并且可以挤压成复杂桁架型材。钢因重量和维护涂装成本而被否决。CFRP因初始预算过高而被认为不合适，但其长期潜力被注意到。
4. Structural Analysis and Load Calculations | 结构分析与载荷计算
The truss bridge was modelled as a simply supported beam for preliminary bending moment calculation. The self-weight of the aluminium deck and truss was estimated at 2.0 kN/m. With a deck width of 2.5 m, the live load is 5.0 × 2.5 = 12.5 kN/m. Thus, the total uniformly distributed load w = 14.5 kN/m.
桁架桥初步被视为简支梁进行弯矩计算。铝合金桥面和桁架的自重估计为2.0 kN/m。桥面宽2.5米，活载为5.0 × 2.5 = 12.5 kN/m。因此，总均布荷载 w = 14.5 kN/m。
Maximum bending moment Mmax = wL² / 8 = 14.5 × 15² / 8 = 407.8 kNm
For a hollow box-section chord with moment of inertia I = 1.2×10-4 m4 and extreme fibre distance y = 0.15 m, the bending stress σ is:
对于一个中空箱型截面弦杆，惯性矩 I = 1.2×10-4 m4，最远纤维距离 y = 0.15 m，弯曲应力 σ 为：
σ = M y / I = 407.8×103 × 0.15 / (1.2×10-4) = 509.75 MPa
This stress exceeds the yield strength of 6061-T6 (275 MPa), indicating a grossly inadequate section. The design was immediately revised to use a deeper truss with a 0.5 m height and a larger built-up I-section (I = 4.8×10-4 m4). The recalculated stress dropped to 127 MPa, providing a safety factor of 2.16 against yield.
该应力超过了6061-T6的屈服强度（275 MPa），表明截面严重不足。设计立即修改为采用0.5 m高的较深桁架和更大的组合工字形截面（I = 4.8×10-4 m4）。重新计算的应力降至127 MPa，对屈服的安全系数为2.16。
5. Failure Mode and Effects Analysis (FMEA) | 失效模式与影响分析
Even with the revised design, an FMEA was conducted to identify potential failure risks. The critical failure modes are summarised below.
即使修改了设计，仍进行了失效模式与影响分析（FMEA）以识别潜在失效风险。关键失效模式总结如下。
| Failure mode | Effect | Severity (1-10) | Cause | Occurrence (1-10) | Detection (1-10) | RPN |
|---|---|---|---|---|---|---|
| Fatigue crack at weld toe | Progressive failure, possible collapse | 9 | Cyclic loading + stress concentration | 6 | 4 | 216 |
| Galvanic corrosion at bolted joint | Loss of section, reduced strength | 7 | Dissimilar metal contact with salt spray | 5 | 5 | 175 |
| Local buckling of thin-walled member | Sudden instability | 8 | Inadequate stiffening + high compression | 3 | 6 | 144 |
RPN = Severity × Occurrence × Detection. The fatigue crack at the welded node had the highest RPN and became the focus of subsequent prototyping. During a 1/5-scale model test with cyclic loads simulating wind and pedestrian traffic, a 2 mm crack was indeed observed at a weld toe after 200,000 cycles, confirming the FMEA prediction.
RPN（风险优先级数）= 严重度 × 发生率 × 检测度。焊接节点处的疲劳裂纹具有最高的RPN，并成为后续原型制作的重点。在使用模拟风和行人交通的循环荷载进行1/5比例模型测试时，经过20万次循环后，在焊趾处果然观察到了一条2毫米的裂纹，证实了FMEA的预测。
6. Manufacturing Process Considerations | 制造工艺考虑
The original plan was to weld aluminium truss connections using TIG welding. However, welding 6061-T6 severely reduces the strength in the heat-affected zone (HAZ), where the yield strength can drop by 40–50%. This explained the low fatigue life. Alternatives were urgently needed.
原计划采用钨极氩弧焊（TIG）焊接铝合金桁架连接。然而，焊接6061-T6会严重降低热影响区（HAZ）的强度，屈服强度可下降40–50%。这解释了低疲劳寿命的原因。迫切需要替代方案。
• Bolted connections: using stainless steel bolts with insulating washers could avoid galvanic corrosion, but they add weight and create stress concentrations at bolt holes.
• 螺栓连接：使用不锈钢螺栓配绝缘垫圈可以避免电化学腐蚀，但会增加重量并在螺栓孔处产生应力集中。
• Adhesive bonding: epoxy adhesives can distribute stress evenly and seal against moisture, but long-term durability under UV and cyclic loading was uncertain.
• 胶接：环氧胶粘剂可均匀分布应力并密封防潮，但在紫外线和循环荷载下的长期耐久性不确定。
• Redesigning with CFRP pultruded profiles: the manufacturing would shift from welding to adhesive bonding of tailored joints, completely eliminating the HAZ problem. This became the leading redesign option.
• 改用CFRP拉挤型材重新设计：制造将从焊接转向定制接头的胶接，完全消除热影响区问题。这成为主要的重新设计方案。
7. Cost-Benefit Analysis | 成本效益分析
A whole-life cost comparison was made between the aluminium bolted truss and a CFRP-adhesive truss, assuming a 50-year service life and a 5% discount rate.
在铝合金螺栓桁架和CFRP胶接桁架之间进行了全寿命成本比较，假设50年使用寿命和5%的折现率。
| Cost item | Aluminium bolted truss | CFRP bonded truss |
|---|---|---|
| Material + fabrication initial cost | £95,000 | £130,000 |
| Installation | £20,000 | £18,000 (lighter) |
| Maintenance (inspections + recoating) | £30,000 (every 15 years × 3) | £5,000 (minimal) |
| Replacement of corroded parts | £15,000 | £0 |
| Present value total | £144,500 | £149,500 |
Although the CFRP option had a slightly higher total present cost, it offered a much lower risk of unexpected fatigue failure, reduced whole-life carbon due to less maintenance traffic, and better client perception of innovation. The client approved the CFRP redesign with the condition that a rigorous testing programme validates the bonded joints.
尽管CFRP方案的总现价成本略高，但它显著降低了意外疲劳失效的风险，减少了因维护交通产生的全寿命碳排放，并提升了客户对创新的感知。客户批准了CFRP重新设计，条件是要有严格的测试计划验证胶接接头。
8. Prototyping and Testing Plan | 原型制作与测试计划
A comprehensive testing plan was designed to verify the CFRP truss before full-scale manufacture:
设计了一个
Published by TutorHao | Year 13 工程 Revision Series | aleveler.com
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