📚 Pre-U AQA Engineering: Case Study Practical Exercises | Pre-U AQA 工程：案例分析实战演练
In the Pre-U AQA Engineering syllabus, the ability to deconstruct complex, real-world problems and apply technical knowledge is core to success. This article presents a hands-on case study — an integrated pedestrian footbridge with solar panels and structural health monitoring — to walk you through the systematic engineering approach expected at this level. You will practise problem scoping, detailed analysis, sustainability assessment and ethical considerations, all reinforced by calculations and design choices.
在 Pre-U AQA 工程课程中，解构复杂的现实问题并应用技术知识是取得成功的核心能力。本文通过一个集成太阳能板和结构健康监测的人行天桥案例，带你实战演练该阶段所需的系统化工程方法。你将逐步实践问题界定、详细分析、可持续性评估和伦理考量，并通过计算和设计决策巩固所学。
1. Introducing the Integrated Footbridge Case | 综合人行天桥案例介绍
Our client, a city council, requires a new pedestrian bridge spanning a 30 m dual carriageway. The bridge must be durable, safe, and incorporate renewable energy to power LED lighting and a monitoring system. This project merges structural, electrical, and systems engineering. We shall assume a design life of 50 years in a temperate climate, with moderate traffic loading and exposure to wind gusts up to 40 m/s.
我们的客户——某市议会，需要一座跨越 30 米双车道的行人天桥。该桥须耐久、安全，并整合可再生能源为 LED 照明和监测系统供电。此项目融合结构、电气与系统工程。假设该项目设计寿命为 50 年，地处温带，承受中等行人荷载及高达 40 m/s 的阵风。
2. Problem Statement & Design Brief | 问题陈述与设计概要
The bridge must convey pedestrians and cyclists, support a maximum deck load of 5 kN/m², and exhibit a natural frequency above 3 Hz to prevent uncomfortable vibrations. It needs a photovoltaic (PV) system meeting an average daily lighting load of 2 kWh. A health monitoring system must record strain and temperature data, transmitting alerts to maintenance crews.
该桥须承载行人和骑行者，承受上限 5 kN/m² 的桥面荷载，且固有频率须高于 3 Hz 以避免不适振动。需要一套光伏系统满足日均 2 kWh 的照明负荷。结构健康监测系统应记录应变与温度数据，并向维护人员发送警报。
3. Stakeholder Analysis | 利益相关者分析
Primary stakeholders include the municipal authority (budget holder and owner), daily users (safety and comfort), and maintenance teams (access and longevity). Secondary stakeholders include nearby residents (visual impact and night‑time light pollution) and utility companies that may need to relocate underground services. Each stakeholder’s needs must be prioritised using a weighted matrix.
主要利益相关者包括市政当局（预算持有者与所有者）、日常使用者（安全与舒适）、以及维护团队（可达性与耐久性）。次要利益相关者包括邻近居民（视觉影响与夜间光污染）、以及可能需迁移地下设施的公用事业公司。必须使用加权矩阵对每项需求排序。
4. Design Specifications & Constraints | 设计规范与约束条件
A clear specification sets measurable targets. Below we list essential parameters that directly influence concept generation and analysis. All requirements must align with relevant British Standards (BS EN 1991‑1‑1, BS EN 1993‑1‑1).
明确的规范设定了可测量的目标。下表列出了直接影响概念生成和分析的关键参数。所有要求必须符合相关英国标准 (BS EN 1991‑1‑1, BS EN 1993‑1‑1)。
| Specification / 规范 | Value / 数值 | Rationale / 依据 |
|---|---|---|
| Span length | 30 m | Clear width of carriageway |
| Deck live load | 5 kN/m² | Crowd loading as per BS EN 1991‑2 |
| Min. natural frequency | 3 Hz | Avoid pedestrian-induced resonance |
| Design wind speed | 40 m/s | 50-year return period gust |
| PV daily energy output | 2 kWh | Lighting and sensor power demand |
With these, we can begin generating feasible concepts and evaluating them against criteria such as cost, weight, and sustainability.
有了这些规范，我们便可开始生成可行概念，并根据成本、重量和可持续性等标准加以评估。
5. Concept Generation & Selection | 概念生成与选择
Two primary structural concepts emerge: (a) a steel truss bridge with a photovoltaic canopy, and (b) an aluminium arch bridge with integrated PV film on the deck. A decision matrix scores each on mass, aesthetics, ease of monitoring integration, and embodied carbon. The steel truss scores highly due to proven behaviour, ease of sensor embedding, and lower unit cost, although its maintenance (painting) is higher. The aluminium arch is lighter but more expensive and harder to fit standard monitoring brackets.
产生两种主要结构概念：(a) 带光伏顶棚的钢桁架桥，以及 (b) 桥面集成光伏膜材的铝拱桥。决策矩阵按质量、美观、监测集成难度和隐含碳打分。钢桁架因受力特性成熟、传感器嵌入方便、单价较低而得分更高，尽管维护（涂装）成本较高。铝拱桥更轻，但成本更高且难以安装标准监测支架。
6. Structural Analysis: Forces & Materials | 结构分析：受力与材料
We model the main beam as simply supported with a uniformly distributed load. For a deck width of 3 m, the load per unit length w = 5 kN/m² × 3 m = 15 kN/m. The maximum bending moment at mid‑span is M_max = wL² / 8 Substituting w = 15 kN/m and L = 30 m gives M_max = 15 × 30² / 8 = 1687.5 kNm. Selecting structural steel S355, we apply a safety factor of 1.65 to yield stress (355 MPa), giving an allowable stress σ_allow = 215 MPa. The required elastic section modulus Z_req = M_max / σ_allow = 1687.5 × 10⁶ Nmm / 215 N/mm² ≈ 7.85 × 10⁶ mm³
我们将主梁简化为简支梁承受均布荷载。桥面宽 3 m，单位长度荷载 w = 5 kN/m² × 3 m = 15 kN/m。跨中最大弯矩为 M_max = wL² / 8 代入 w = 15 kN/m 和 L = 30 m，得 M_max = 15 × 30² / 8 = 1687.5 kNm。选用结构钢 S355，对屈服应力（355 MPa）取安全系数 1.65，得许用应力 σ_allow = 215 MPa。所需弹性截面模量 Z_req = M_max / σ_allow = 1687.5 × 10⁶ Nmm / 215 N/mm² ≈ 7.85 × 10⁶ mm³
Checking standard steel I‑beams, a 762×267 UKB section provides Z = 8.52 × 10⁶ mm³, satisfying the requirement. A deflection check under live load alone confirms δ_max = 5wL⁴ / 384EI < L/360, well within serviceability limits. The natural frequency is estimated using f = (π / 2L²) √(EI / m), yielding approximately 3.2 Hz, which meets the specification.
核查标准工字钢截面，762×267 UKB 型钢提供 Z = 8.52 × 10⁶ mm³，满足要求。仅对活载进行挠度验算，δ_max = 5wL⁴ / 384EI < L/360，远在正常使用极限之内。固有频率用 f = (π / 2L²) √(EI / m) 估算，约为 3.2 Hz，符合规范。
7. Thermal & Wind Loading Considerations | 热效应与风荷载考量
A 30 m steel beam will expand in summer heat. Using a linear thermal expansion coefficient α = 12 × 10⁻⁶ /°C for steel and a temperature rise ΔT = 40 °C, the free elongation is ΔL = α L₀ ΔT = 12 × 10⁻⁶ × 30 m × 40°C = 0.0144 m (14.4 mm) We accommodate this with sliding bearings at one end. Wind load is estimated using the pressure equation P = 0.5 ρ C_d V². For air density ρ = 1.25 kg/m³, drag coefficient C_d = 1.3 for the truss, and velocity V = 40 m/s, the pressure is approximately 1.3 kN/m². Multiplied by the projected area of the truss (roughly 60 m²), the total wind force is about 78 kN, which is resisted by bracing and foundation design.
30 m 长的钢梁在夏季升温时会产生膨胀。钢的热膨胀系数 α = 12 × 10⁻⁶ /°C，温升 ΔT = 40 °C，自由伸长量为 ΔL = α L₀ ΔT = 12 × 10⁻⁶ × 30 m × 40°C = 0.0144 m (14.4 mm) 我们在一端设置滑动支座以适应此形变。风荷载按压力公式 P = 0.5 ρ C_d V² 估算，空气密度 ρ = 1.25 kg/m³，桁架气流阻力系数 C_d = 1.3，风速 V = 40 m/s，压力约 1.3 kN/m²。乘以桁架投影面积（约 60 m²），总风力约为 78 kN，由支撑和基础设计抵抗。
8. Photovoltaic & Electrical System Design | 光伏与电气系统设计
The daily lighting demand is 2 kWh. Assuming 4 peak sun hours per day, the required PV array power is 2 kWh / 4 h = 0.5 kW. With 400 W panels, two panels suffice (0.8 kW), allowing for cloudy days. A 24 V battery system stores surplus energy; capacity chosen for 2 days autonomy: 2 kWh × 2 / 24 V ≈ 167 Ah. A charge controller prevents overcharging, and an inverter supplies 230 V AC for LED drivers. Sensor nodes (strain gauges, thermocouples) draw 5 W continuously, easily met by the battery. The control system uses an Arduino‑based datalogger transmitting via LoRaWAN.
日间照明需求为 2 kWh。假定每天 4 个峰值日照小时，所需光伏阵列功率为 2 kWh / 4 h = 0.5 kW。选用 400 W 组件，两块即可（0.8 kW），留有阴天余量。24 V 电池组存储富余电能；按 2 天自持容量选取：2 kWh × 2 / 24 V ≈ 167 Ah。充电控制器防止过充，逆变器为 LED 驱动器提供 230 V 交流电。传感器节点（应变计、热电偶）持续功耗 5 W，电池轻松满足。控制系统采用 Arduino 数据记录器，通过 LoRaWAN 传输数据。
9. Sustainability & Lifecycle Assessment | 可持续性与生命周期评估
We compare embodied carbon of the steel truss (2.8 tCO₂e per ton of steel) versus the aluminium arch (11 tCO₂e per ton). With 18 tonnes of steel, total embodied carbon is about 50 tCO₂e, while an equivalent aluminium structure (12 t) generates 132
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