📚 Year 9 CAIE Engineering: Case Study in Action | Year 9 CAIE 工程：案例分析实战演练
In engineering, learning from real-world examples is one of the most effective ways to develop problem‑solving skills. This case study will guide you through a practical design challenge – building a simple footbridge – and show you how engineers apply scientific principles, material knowledge and safety standards at every step.
在工程学中，从真实案例中学习是培养解决问题能力最有效的方法之一。本篇案例分析将带你完成一个实际的设计挑战——建造一座简易人行桥——并展示工程师如何在每一步运用科学原理、材料知识及安全标准。
1. Introduction to Case Studies in Engineering | 工程案例分析导论
A case study is a detailed investigation of a specific project or problem. It helps you connect classroom theory to hands‑on practice by following the decisions an engineer makes – from identifying a need to testing a final prototype.
案例分析是对某个特定项目或问题的详细探究。它通过跟踪工程师从识别需求到测试最终原型的决策过程，帮助你将在课堂上学到的理论与动手实践联系起来。
In this exercise you will work through a simplified design cycle: define requirements, choose materials, analyse forces, calculate dimensions, build a scale model and evaluate the outcome.
在本次练习中，你将经历一个简化的设计循环：明确需求、选择材料、分析力、计算尺寸、建造比例模型并评估结果。
2. Case Study Overview: Designing a Simple Footbridge | 案例概述：设计一座简易人行桥
Your task is to design a straight beam bridge that spans a small stream. The clear span is 5.0 metres, and the bridge must safely carry a pedestrian load of 10 kN applied at mid‑span, plus its own weight.
你的任务是设计一座跨越小溪的直梁桥。净跨度为 5.0 米，桥梁必须安全承受施加在跨中处的 10 kN 行人荷载及其自重。
The bridge will use a simple supported beam structure, resting on concrete abutments at each end. This is one of the most basic structural forms and a great starting point for learning statics and strength of materials.
桥梁采用简支梁结构，两端搁置在混凝土桥台上。这是最基本的结构形式之一，是学习静力学和材料力学的绝佳起点。
3. Identifying Requirements and Constraints | 需求与约束识别
Before beginning any design, an engineer must list the requirements and constraints. For this bridge the key demands are: sufficient strength to support the design load without failure, a deflection limit of L/200 to avoid excessive bouncing, and a lifespan of at least 20 years with low maintenance.
开始任何设计之前，工程师必须列出需求与约束。对于这座桥，关键要求是：足够的强度以支撑设计荷载而不破坏，挠度限制在 L/200 以内以避免过度晃动，以及至少 20 年的使用寿命且维护成本低。
Constraints include a limited budget, locally available materials (timber and steel profiles), and environmental factors such as rain and humidity. The design must also be buildable by a small team without heavy lifting equipment.
约束条件包括有限的预算、当地可获得的材料（木材和标准型钢）以及降雨和潮湿等环境因素。设计还须可由一个小团队在不使用重型起重设备的情况下建造。
4. Material Selection: Wood vs. Steel | 材料选择：木材与钢材
Two candidate materials are considered: structural timber (Scots pine, grade C24) and mild steel (S275). Timber is lighter, cheaper and easier to cut on site; steel offers higher strength and stiffness but is heavier and requires welding or bolting.
考虑两种备选材料：结构木材（欧洲赤松，等级 C24）和低碳钢（S275）。木材更轻、更便宜且易于现场切割；钢材提供更高的强度和刚度，但更重且需要焊接或螺栓连接。
For a small‑span footbridge, timber often provides a better balance of cost, ease of construction and environmental impact. The design team decides to proceed with a timber beam, while keeping a steel option as backup.
对于小跨度人行桥，木材通常在成本、施工便利性和环境影响之间提供更好的平衡。设计团队决定采用木梁，同时保留钢梁作为备选方案。
5. Understanding Loads and Forces | 了解荷载与力
Two types of load act on the bridge: dead load (the self‑weight of the beam) and live load (the pedestrian walkers). For simplicity, the design live load is taken as a 10 kN concentrated force at the centre, which approximately represents a group of people standing or walking slowly.
桥梁承受两类荷载：恒荷载（梁的自重）和活荷载（行人）。为简化起见，设计活荷载取跨中 10 kN 的集中力，这大致代表一群人站立或缓慢行走的状态。
Each load produces vertical forces that are carried to the supports. The reactions at the abutments are equal because the beam is simply supported and the load is central: each support carries 5 kN.
每种荷载都产生传递给支座的竖向力。由于梁是简支且荷载居中，桥台处的反力相等：每个支座承担 5 kN。
The gravitational force on the beam's own weight is uniformly distributed. Its total value is estimated as 1.0 kN, which adds only a small amount compared with the live load.
梁自重的重力是均布荷载，其总值估计为 1.0 kN，与活荷载相比只增加很小的量。
6. Calculating Bending Moment | 计算弯矩
The most important internal action for a beam is the bending moment. For a simply supported beam with a central point load, the maximum bending moment occurs at mid‑span and is given by the formula:
梁最重要的内部作用力是弯矩。对于承受跨中集中荷载的简支梁，最大弯矩发生在跨中，由以下公式给出：
M = (F × L) / 4
imum bending moment is (10 kN × 5 m) / 4 = 12.5 kN·m. In SI units this is 12.5 × 10⁶ N·mm.
代入 F = 10 kN、L = 5.0 m，最大弯矩为 (10 kN × 5 m) / 4 = 12.5 kN·m。以国际单位制表示即为 12.5 × 10⁶ N·mm。
This moment tries to bend the beam downwards in the middle, causing compression in the top fibres and tension in the bottom fibres. The timber must resist these stresses without breaking.
该弯矩试图将梁中部向下弯曲，导致顶部纤维受压、底部纤维受拉。木材必须抵抗这些应力而不被破坏。
7. Determining Section Modulus | 确定截面模量
To find out whether a chosen beam size is strong enough, engineers use the bending stress equation:
为了判断所选梁的尺寸是否足够坚固，工程师使用弯曲应力方程：
σ = M / S
here σ is the maximum bending stress, M is the bending moment and S is the section modulus – a geometric property of the cross‑section. For a rectangular beam of breadth b and height h, S = (b × h²) / 6.
其中 σ 为最大弯曲应力，M 为弯矩，S 为截面模量——一种截面几何属性。对于宽度为 b、高度为 h 的矩形梁，S = (b × h²) / 6。
The design requires that the actual stress does not exceed the allowable stress of the material. C24 timber has a characteristic bending strength of 24 N/mm², but a safety factor of 2.0 reduces the allowable stress to 12 N/mm².
设计要求实际应力不超过材料的许用应力。C24 木材的特征抗弯强度为 24 N/mm²，但安全系数 2.0 将许用应力降低至 12 N/mm²。
Rearranging the formula gives the required section modulus: Sreq = M / σ_allowable = 12.5×10⁶ N·mm / 12 N/mm² = 1,041,667 mm³ ≈ 1.04×10⁶ mm³.
重新整理公式可得所需截面模量：Sreq = M / σ_allowable = 12.5×10⁶ N·mm / 12 N/mm² = 1,041,667 mm³ ≈ 1.04×10⁶ mm³。
8. Evaluating Safety Factors | 安全系数评估
A safety factor is applied to cover uncertainties in material properties, workmanship and loading. For timber structures in footbridges, a factor of 2.0–3.0 is typical. Our design uses a factor of 2.0, meaning the beam can theoretically carry twice the design load before failure.
采用安全系数是为了覆盖材料性能、施工质量和荷载的不确定性。在人行桥木结构中，安全系数通常取 2.0–3.0。我们设计中使用 2.0，意味着梁理论上能承受两倍设计荷载才发生破坏。
If the calculated stress exceeds the allowable stress, the designer must increase the cross‑section or choose a stronger material. Checking the safety factor early prevents costly changes later.
如果计算应力超过许用应力，设计者必须加大截面或选用强度更高的材料。尽早检查安全系数可以避免后续代价高昂的变更。
9. Prototype and Testing | 原型与测试
Before full‑scale construction, a scale model is built to verify the design. The team constructs a 1:5 scale bridge using the same C24 timber, with a span of 1.0 metre. The model is loaded gradually at mid‑span using weights, while deflection is measured with a dial gauge.
在全面施工前，先建造一个缩尺模型来验证设计。团队使用同样的 C24 木材建造了 1:5 比例、跨度 1.0 米的模型桥。在跨中逐步加载砝码，同时用百分表测量挠度。
If the model deflects less than the limit and shows no signs of cracking when loaded to twice the scaled design load, the design is considered safe. In this case, the tested deflection is 4.2 mm, well within the L/200 limit (5 mm for model scale).
如果模型在加载到两倍缩尺设计荷载时挠度未超过限值且未出现开裂迹象，则设计被认为是安全的。在本案例中，实测挠度为 4.2 mm，完全在 L/200 限值（按模型比例折合为 5 mm）以内。
10. Analysis of Results and Improvements | 结果分析与改进
Even when a prototype passes the tests, engineers look for ways to optimize the design. In this case, the actual stress at full load is about 8.5 N/mm², well below the allowable 12 N/mm². This suggests the beam may be slightly oversized.
即使原型通过了测试，工程师也会寻找优化设计的途径。在本案例中，满荷载下的实际应力约 8.5 N/mm²，远低于许用的 12 N/mm²。这表明梁的截面或许略大。
However, reducing the beam depth to save material would increase deflection and stress, so a careful trade‑off is required. One improvement could be using a slightly thinner, higher‑grade timber or adding stiffeners at the supports to reduce the effective span.
然而，为节省材料而减小梁高会增加挠度和应力，因此需要仔细权衡。一项改进措施可以是使用稍薄但等级更高的木材，或在支座处增加加劲件以减小有效跨度。
The team also considers weather protection: applying a waterproof sealant and designing a slight camber so rainwater runs off the surface, which extends the lifespan of the timber.
团队还考虑了耐候防护：涂刷防水密封剂并设计微拱，使雨水从表面流走，延长木材的使用寿命。
11. Final Design Overview | 最终设计概览
aced on elastomeric bearing pads at the abutments to allow slight rotation and prevent stress concentration.
最终设计采用截面尺寸为 150 mm 宽 × 250 mm 高的实心矩形 C24 木梁。梁置于桥台的橡胶支座上，允许轻微转动并防止应力集中。
A handrail system is attached to the sides of the beam, made from galvanised steel, adding stability and safety for pedestrians. The total weight of the bridge is kept below 500 kg, making installation manageable without a crane.
梁侧安装镀锌钢扶手系统，为行人增加稳定性和安全性。桥梁总重控制在 500 kg 以内，使得无需起重机即可完成安装作业。
The design drawings include a cross‑section view, a longitudinal profile and a connection detail for the bearings. These documents would be used to obtain building approval and guide the construction crew.
设计图纸包括横截面图、纵断面图和支座连接详图。这些文件将用于获得建造许可并指导施工人员作业。
12. Conclusion and Reflection | 结论与反思
This case study has walked you through a complete engineering design cycle for a simple bridge. You have seen how defining requirements, choosing materials, calculating internal forces and testing a prototype all fit together to produce a safe and efficient structure.
本案例分析带你完成了一座简支梁桥的完整工程设计循环。你已看到明确需求、选择材料、计算内力和测试原型如何环环相扣，最终产生一个安全高效的结构。
Remember that in real engineering, iterations are common – the first idea is rarely the best. By practising case studies regularly, you build the analytical thinking and judgement needed to solve unfamiliar problems in the future.
记住，真实工程中迭代是常态——最初的想法很少是最优的。通过经常练习案例分析，你将培养出解决未来陌生问题所需的分析思维和判断力。
Now challenge yourself to modify the design: what would change if the span doubled, or if the bridge had to carry a small vehicle? Write down your reasoning and try a quick calculation – that is exactly how engineers grow.
现在挑战自己，修改设计：如果跨度加倍，或者桥梁需要承载一辆小型车辆，哪些参数需要改变？写下你的推理并试试快速计算——这正是工程师成长的方式。
Published by TutorHao | Engineering Revision Series | aleveler.com
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