Case Study in Action: Designing a Model Bridge | 案例分析实战：设计一座模型桥

📚 Case Study in Action: Designing a Model Bridge | 案例分析实战：设计一座模型桥

This case study puts you in the role of a Year 10 engineer tasked with designing, building, and testing a simple model bridge to carry a 5 kg mass across a 600 mm gap. You will follow a structured engineering design process: from capturing requirements and researching existing solutions, through sketching concepts, selecting materials, calculating key forces, to manufacturing a prototype and evaluating its performance. The goal is to show how theory meets practice in a classroom engineering project, and to prepare you for the real challenges Edexcel Engineering assessments can present.

本案例将你带入一名十年级工程师的角色，任务是为跨越 600 mm 间隙设计、制作并测试一座能承载 5 kg 质量的简易模型桥。你将遵循结构化的工程设计流程：从捕获需求与调研现有方案，到绘制概念草图、选择材料、计算关键受力，再到制造原型并评估其性能。目标是展示在课堂工程项目中理论如何与实践结合，并帮助你为爱德思工程考试中可能出现的真实挑战做好准备。

1. Understanding the Design Brief | 理解设计任务书

Every engineering project starts with a clear brief. Ours states: “Design and construct a model bridge to support a central 5 kg mass over a 600 mm clear span. The bridge must be fabricated from standard 6 mm × 6 mm balsa wood sticks and PVA glue. Maximum allowed self-weight of the bridge is 150 g. It should be stable, safe to load, and visually tidy. The cost of materials and manufacturing time must be kept to a realistic minimum.” This brief gives us constraints for span, load, materials, weight, aesthetics, and cost — all of which we must balance in our design.

每个工程项目都始于清晰的任务书。我们的任务书写道：“设计和制作一座模型桥，跨越 600 mm 净跨距并支撑中央 5 kg 质量。桥必须用标准 6 mm × 6 mm 轻木条与白乳胶制成。桥的最大允许自重为 150 g。结构应稳定、安全加载且外观整洁。材料成本和制造时间必须保持在合理的最低水平。”该任务书给出了跨距、载荷、材料、自重、美学和成本等约束条件——我们必须在设计中平衡这些因素。

2. Research and Existing Solutions | 调研与现有解决方案

Engineers never design from a blank sheet of paper. We first study real bridges and model-scale precedents. Truss bridges (Warren, Pratt, Howe) offer high strength-to-weight ratios. A Warren truss uses equilateral triangles to convert bending loads into axial tension and compression in the members, which suits our lightweight balsa material. Arch bridges direct force along the curve into abutments, but are harder to make with straight sticks. Beam bridges are simple but less material-efficient. For our brief, a through Warren truss with a slight camber appears optimal: the triangulated web resists the bending moment under the central load, and the use of twin parallel trusses connected by lateral bracing improves stability against twisting.

工程师从不凭空设计。我们首先研究真实桥梁和模型级先例。桁架桥（沃伦式、普拉特式、豪威式）能提供高比强度。沃伦桁架使用等边三角形将弯曲载荷转化为杆件的轴向拉压力，这很适合我们的轻木材料。拱桥将力沿曲线导向桥台，但用直木条制作较难。梁桥虽简单却材料效率较低。针对我们的任务书，一座带有轻微预拱的下承式沃伦桁架看似最优：三角形腹板抵抗中央载荷下的弯矩，而由横向支撑连接的双平行桁架则提高抗扭稳定性。

3. Concept Design and Sketching | 概念设计与草图绘制

We produce freehand sketches of three distinct concepts: (A) a simple rectangular Warren truss with top and bottom chords and V-shaped web members, (B) a bowstring truss with curved top chord, and (C) a double-layer space frame. Concept A is chosen for further development because it is straightforward to manufacture with straight members, gives predictable force paths, and allows easy integration of a central loading platform. The sketch defines a span of 600 mm, height 80 mm, with 7 equilateral panels each of side length ~100 mm. Two such trusses stand 70 mm apart, united by horizontal struts and cross-bracing.

我们绘制了三个不同构思的自由手绘草图：（A）一个由上下弦杆和 V 形腹杆构成的简洁矩形沃伦桁架，（B）一座上弦弯曲的系杆拱桥，（C）一个双层空间框架。方案 A 被选定深入开发，因为它用直杆易于制造、传力路径可预测，且易于集成中央加载平台。草图定义了跨距 600 mm，高 80 mm，7 个等边节间，每边长约 100 mm。两片这样的桁架相距 70 mm 竖立，由水平横撑和交叉支撑连接为一体。

4. Force Analysis and Simple Calculations | 受力分析与简单计算

We model the bridge as a simply supported beam under a central point load. The 5 kg mass provides a force F = m × g = 5 × 9.81 ≈ 49 N (let’s use g = 10 m/s² for simplicity, so F = 50 N). The reaction force at each support is R = F / 2 = 25 N. The maximum bending moment in the centre is M = (F × L) / 4 = (50 N × 0.6 m) / 4 = 7.5 N·m. The truss resists this by developing compression in the top chord and tension in the bottom chord. In a Warren truss of height h = 0.08 m, the axial force in the mid-span chords is approximately M / h = 7.5 / 0.08 ≈ 93.75 N. Web members take alternating tension and compression. Balsa wood can typically withstand about 10 N/mm² in tension but only about 5 N/mm² in compression before buckling. A 6 mm × 6 mm stick has a cross-sectional area A = 36 mm², so its tensile capacity is around 10 × 36 = 360 N, and compressive capacity (considering short length and low slenderness) about 5 × 36 = 180 N. Our calculated 93.75 N is well within these limits for both tension and compression, confirming the structural feasibility at the ultimate load.

我们将桥模拟为受中央集中载荷的简支梁。5 kg 质量提供的力 F = m × g = 5 × 9.81 ≈ 49 N（为简化取 g = 10 m/s²，则 F = 50 N）。每个支座反力为 R = F / 2 = 25 N。跨中最大弯矩 M = (F × L) / 4 = (50 N × 0.6 m) / 4 = 7.5 N·m。桁架通过上弦受压、下弦受拉来抵抗此弯矩。在高度 h = 0.08 m 的沃伦桁架中，跨中弦杆的轴向力约为 M / h = 7.5 / 0.08 ≈ 93.75 N。腹杆交替承受拉压。轻木典型抗拉强度约 10 N/mm²，但因屈曲抗压强度仅约 5 N/mm²。一根 6 mm × 6 mm 木条横截面积 A = 36 mm²，其抗拉承载力约为 10 × 36 = 360 N，抗压承载力（考虑短长度和低长细比）约 5 × 36 = 180 N。我们计算的 93.75 N 远低于这些拉压极限，确认了在极限载荷下的结构可行性。

5. Detailed Design and Working Drawings | 详细设计与施工图纸

The chosen concept is refined into a technical drawing with front elevation, plan, and end view. All dimensions are in millimetres. The overall length is 650 mm (to allow a small overhang at supports), width 70 mm, height 80 mm. Top and bottom chords each run full length. Web members are cut from the same 6 mm × 6 mm stock and glued at nodes. A central loading hook is formed by a small eyelet glued between the two trusses. The drawing includes a parts list: 2 × 650 mm chords (×2 trusses = 4 total), 12 × 100 mm web members (×2 = 24), and various lateral bracing sticks. A cutting schedule is prepared to minimise waste. Total estimated wood length is about 8.5 m, giving a self-weight of roughly 8.5 × (density 160 kg/m³ × 36 × 10⁻⁶ m²) ≈ 49 g, which is well below the 150 g limit.

选定的构思被细化为带有前视图、俯视图和端视图的技术图纸。所有尺寸以毫米为单位。总长 650 mm（两端留有少量悬挑），宽 70 mm，高 80 mm。上下弦杆各自全长贯通。腹杆用同规格 6 mm × 6 mm 木料截切并胶接于节点。一个中央加载钩由胶合在两片桁架之间的小环眼构成。图纸包含材料清单：2 根 650 mm 弦杆（共 2 片桁架 = 4 根）、12 根 100 mm 腹杆（×2 = 24 根）以及若干横向支撑条。制定了切割排料表以减少浪费。估计总木料长度约 8.5 m，自重约为 8.5 ×（密度 160 kg/m³ × 36 × 10⁻⁶ m²）≈ 49 g，远低于 150 g 的限制。

6. Material Selection and Justification | 材料选择与论证

Balsa wood is specified for its excellent strength-to-weight ratio and ease of cutting and gluing with PVA. However, balsa is anisotropic — properties differ along the grain versus across it. We orient all chord and web members with grain parallel to the member axis to maximise tensile and compressive strength. PVA glue is chosen because it forms a bond stronger than the balsa itself, dries clear, and is safe for classroom use. Alternative adhesives like cyanoacrylate (superglue) were rejected due to brittleness and health risks. Small sandpaper strips and a craft knife are the only allowed tools, which aligns with Edexcel’s emphasis on safe, accessible manufacturing processes.

轻木被指定使用，因其优异的比强度以及易于用白乳胶切割和粘接。然而轻木是各向异性的——顺纹与横纹特性不同。我们将所有弦杆和腹杆的纹理方向与杆件轴线平行，以最大化抗拉和抗压强度。白乳胶被选用是因为它能形成比轻木本身更强的粘接，干后透明，且适合课堂使用。氰基丙烯酸酯（快干胶）等替代粘合剂因其脆性和健康风险而被排除。小砂纸条和一把美工刀是唯一允许的工具，这与爱德思强调的安全、可操作的制造工艺相符。

7. Manufacturing Process and Quality Control | 制造工艺与质量控制

We begin by cutting all members to length using a cutting jig to ensure repeatability. A full-scale template is printed and placed under a sheet of baking paper to prevent glue from sticking to the bench. The bottom chord is pinned to the template; then vertical and diagonal web members are positioned, tack-glued, and left to set. The top chord is added last. After both trusses are assembled, they are propped vertically and lateral cross-braces are installed between corresponding nodes. A central wood block with a wire loop is glued as the loading point. Quality control checks include verifying symmetry, measuring the 600 mm span, inspecting glue joints for gaps, and weighing the bridge before testing. Any excess glue is wiped away to avoid unnecessary mass.

我们首先使用切割夹具将所有杆件裁切至规定长度，以确保重复精度。打印一张全尺寸模板，并垫在烘焙纸下以防胶水粘到桌面上。下弦杆用大头针固定在模板上；然后放置竖杆和斜腹杆，点胶并静置固化。最后加上上弦杆。两片桁架分别组装完成后，将它们竖直支撑，并在对应节点间安装横向交叉支撑。中央一块木块与金属丝环胶合作为加载点。质量控制检查包括验证对称性、测量 600 mm 跨距、检查胶接缝隙并称重。多余的胶水全部擦除以避免不必要质量。

8. Testing and Data Collection | 测试与数据采集

The bridge is set up on two level supports with a 600 mm gap. A mass hanger is suspended from the central hook, and slotted masses are added gradually in 0.5 kg increments. We record the load at which first audible cracking or visible buckling occurs. A typical outcome might be that the bridge holds 5 kg safely, and failure initiates at around 7.5 kg in the top chord near the centre due to compression buckling. We also note any deflection by measuring the vertical displacement at mid-span with a ruler for each load increment. Data is plotted in a load-deflection graph. The test demonstrates that the structure behaves linearly at first, then shows non-linear deformation as buckling progresses, finally failing abruptly once a critical member snaps.

桥被架设在两个水平支座上，跨距 600 mm。一个砝码挂钩悬挂在中央钩上，以 0.5 kg 的增量逐步添加砝码。我们记录首次出现可听见的断裂声或可见屈曲时的载荷。一个典型结果可能是桥安全承载 5 kg，而破坏起始于约 7.5 kg 时中央附近的上弦杆因受压屈曲。我们还用直尺测量每级载荷下跨中的竖向位移，观察挠度。数据绘制成载荷-挠度图。测试表明结构最初呈线性响应，随着屈曲发展呈现非线性变形，在某一关键杆件折断时最终突然失效。

9. Evaluation Against the Design Brief | 对照设计任务书的评估

The bridge met the core requirement by supporting the 5 kg mass without collapse. Self-weight was 48 g, well within the 150 g cap, demonstrating efficient use of material. The cost of balsa and glue was approximately £2.40, and total manufacturing time was around 3 hours — both acceptable for a classroom project. Aesthetics were decent, with clean joints and symmetrical trusses. However, the failure mode was sudden buckling of the top chord, suggesting local weaknesses. Also, the design relies on perfect glue joints, which are hard to achieve consistently in a classroom setting. The evaluation reveals that while the design is fundamentally sound, robustness and repeatability could be improved.

该桥满足了核心要求，在未倒塌的情况下承载了 5 kg 质量。自重为 48 g，远低于 150 g 的上限，展示了高效的材料利用。轻木和胶水成本约为 2.40 英镑，总制造时间约 3 小时——对于课堂项目均可接受。美观程度不错，胶接整洁，桁架对称。然而，破坏模式是上弦杆的突然屈曲，表明存在局部弱点。此外，设计依赖完美的胶接节点，而这在课堂环境中难以始终如一地实现。评估揭示出设计虽然基本合理，但稳健性和可重复性仍可改进。

10. Reflections and Future Improvements | 反思与未来改进

After testing, we review the design to identify modifications. One improvement would be to double up the top chord in the central two panels by laminating two sticks together, boosting buckling resistance without adding excessive mass. Another would be to incorporate gusset plates at critical nodes using thin card triangles glued over the joints, as they distribute stress and reduce the chance of glue failure. We could also experiment with a slightly taller truss — say 100 mm — to reduce chord forces further, although this must be balanced against self-weight. From a process viewpoint, using a calibrated digital scale rather than manual mass loading would yield more precise failure data. At Year 10 level, this reflection step mirrors the real-world engineering practice of iterative improvement.

测试之后，我们审视设计以确定修改方案。一个改进是将中央两个节间的上弦杆加叠一层，即用两根木条叠层粘合，以提高抗屈曲能力而不增添过多质量。另一个是在关键节点处使用薄纸板三角形角板胶于接头之上，以分散应力并降低胶接失效几率。我们也可以尝试稍高桁架——比如 100 mm——以进一步减小弦杆内力，但这需与自重取得平衡。从流程角度，使用校准的数字秤代替手动加载会得到更精确的破坏数据。在十年级阶段，这一反思步骤映照出现实工程中迭代改进的实践。

11. Sustainability and Ethical Considerations | 可持续性与伦理考虑

Good engineers consider the wider impact of their designs. Balsa is a fast-growing, renewable timber, which gives it a low carbon footprint compared with plastics or metals. Our design uses minimal wood offcuts, and the bridge can be dismantled after testing for recycling or composting. PVA glue is water-based and less toxic than solvent-based alternatives. Socially, the project is inclusive, requiring only low-cost, non-hazardous materials that are accessible to all schools. These aspects align with the Edexcel Engineering specification’s emphasis on sustainability and responsible resource use, encouraging students to think beyond just technical performance.

优秀的工程师会考虑其设计的更广泛影响。轻木是一种速生可再生的木材，与塑料或金属相比碳足迹较低。我们的设计用材最少，废料很少，测试后桥可以拆解进行回收或堆肥。白乳胶是水性的，毒性低于溶剂型替代品。社会方面，该项目具有包容性，仅需低成本、无危险的材料，所有学校都能获得。这些方面与爱德思工程课程大纲对可持续性和负责任资源使用的强调相吻合，鼓励学生从技术性能之外进行思考。

12. Linking to Edexcel Assessment Criteria | 联系爱德思评估标准

In Edexcel Engineering, case study exercises like this assess your ability to analyse a problem, develop a design proposal, select and justify materials, use mathematical and scientific principles, manufacture a prototype, test and evaluate outcomes, and suggest improvements. Explicitly showing your working in calculations, annotated sketches, and clear evaluation tables earns high marks. For example, the simple stress calculation earlier matches the “apply engineering principles” criterion, while the testing graph links to “analyse and interpret data.” By documenting each stage carefully, you demonstrate a complete engineering cycle — a key expectation at this level.

在爱德思工程课程中，类似这样的案例演练将评估你分析问题、制定设计方案、选择并论证材料、运用数学和科学原理、制造原型、测试与评价成果以及提出改进建议的能力。清晰展示计算过程、附带注释的草图和明确的评价表格能赢得高分。例如，前面的简单应力计算符合“应用工程原理”的标准，而测试图表则与“分析和解读数据”相关联。通过仔细记录每个阶段，你展示了一个完整的工程循环——这是该级别的一个关键期望。

Published by TutorHao | Engineering Revision Series | aleveler.com

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