📚 Year 9 CIE Engineering: Case Study Practical Drill | 9年级 CIE 工程：案例分析实战演练
In this case study, we set out to design, build and test a model bridge using limited materials—just 50 wooden popsicle sticks and white PVA glue. The challenge mimics real-world engineering where constraints on cost, weight and material force creative problem-solving. This article walks you through the entire engineering design process, from analysing the brief to evaluating the final structure, helping you understand how engineers think and work.
在这个案例研究中，我们将用有限的材料——仅50根冰棍棒和白胶——设计、制作并测试一座模型桥。这个挑战模拟了真实的工程环境，在成本、重量和材料的限制下破解难题。本文将带你走完整整一个工程设计流程，从分析任务书到评估最终结构，帮助你理解工程师的思维方式与工作方法。
1. Understanding the Design Brief and Constraints | 理解设计纲要与约束
The design brief states: “Build a bridge that spans a 500 mm gap and carries the maximum possible load before failure. You may only use 50 popsicle sticks (11.3 mm × 114 mm × 2 mm) and white PVA glue. The bridge must sit freely on two level supports; no fixing to the supports is allowed. The total mass of the bridge must not exceed 200 g.” These constraints force us to balance strength, weight and material usage from the very start.
设计纲要说明：“建造一座跨越 500 毫米间隙的桥梁，在失效前承受尽可能大的载荷。只能使用 50 根冰棍棒（11.3 毫米 × 114 毫米 × 2 毫米）和白乳胶。桥梁必须自由放置在两个水平支座上，不得固定。桥梁总质量不得超过 200 克。”这些约束从一开始就迫使我们权衡强度、重量和材料用量。
A successful solution requires careful interpretation of the brief. The 500 mm span defines the minimum clear distance between supports. The mass limit prevents over-engineering with excessive glue or densely laminated members. Additionally, the time limit of two hours for construction simulates production deadlines, making efficient assembly processes essential.
要成功解题，必须仔细解读纲要。500 毫米跨度规定了支座间的最小净距。质量上限避免了过度使用胶水或过密的层压杆件。此外，两小时的建造时限模拟了生产截止期，因此高效装配流程至关重要。
2. Researching Existing Bridge Types | 研究现有桥梁类型
Before drawing any design, we study real bridges. Beam bridges are the simplest—a horizontal member supported at both ends. They carry loads mainly through bending, which creates tension at the bottom and compression at the top. However, for a given material, a solid beam is often heavy and inefficient over longer spans.
在画任何设计方案前，我们先研究真实的桥梁。梁桥是最简单的——一根水平构件两端支承。它们主要靠弯曲承载，导致底部受拉、顶部受压。但就给定的材料而言，实心梁在较大跨度下通常较重且效率低。
Arch bridges transfer loads along the curve to the abutments, converting vertical loads into compressive forces. This suits materials strong in compression, like stone or our popsicle sticks (wood is stronger in compression along the grain). Truss bridges use triangulated frameworks to convert bending into axial tension and compression in individual members, making efficient use of material. We decide a truss design fits our constraints best because it optimises the strength-to-weight ratio.
拱桥通过曲线将载荷传递到桥台，把竖向载荷转化为压力。这适合抗压强的材料，如石材或我们的冰棍棒（木材顺纹抗压较强）。桁架桥用三角形杆系将弯曲转化为杆件的轴向拉力和压力，材料利用效率极高。我们决定桁架设计最适合我们的约束，因为它让强度‑重量比达到最优。
3. Generating Design Ideas and Sketches | 生成设计方案与草图
We brainstorm three concepts: a simple Warren truss with equilateral triangles, a Pratt truss with verticals and diagonals sloping toward the centre, and a Baltimore truss with additional sub-struts. Each concept is sketched as freehand isometric and orthographic views, with key dimensions labelled. The Pratt truss appears attractive because the longer compression members (top chord) can be built from doubled sticks, while the tension diagonals can remain single sticks.
我们头脑风暴了三种方案：由等边三角形构成的简单华伦桁架、带有竖杆且斜杆向中心倾斜的普拉特桁架，以及带有辅助短柱的巴尔的摩桁架。每个方案都画了徒手等轴测图和正视图，并标注了关键尺寸。普拉特桁架看起来很有吸引力，因为较长的受压构件（上弦）可用双片冰棍棒制成，而受拉斜杆可用单片。
Annotations on the sketch highlight how we intend to reinforce joints with small gusset plates cut from popsicle sticks. By sketching multiple ideas, we avoid locking into a single solution too early and can compare the predicted performance of each design before committing to construction.
草图中的注释标明了如何用从冰棍棒剪下的小节点板加固节点。通过绘制多个方案，我们避免过早锁定单一解法，在动手建造前可以对各个设计的预期表现进行比较。
4. Forces and Loads in Structures | 结构中的力与载荷
The primary forces in our bridge are tension, compression and shear. When a load is applied at the mid-span, the top chord experiences compression and the bottom chord undergoes tension. The web members (diagonals and verticals) distribute the shear force. A basic free-body diagram shows that for a point load P at the centre, the reaction at each support is P/2. The maximum bending moment occurs at the centre and equals (P × L)/4, where L is the span.
我们桥梁中的主要力是拉力、压力和剪切力。当载荷作用在跨中时，上弦杆受压，下弦杆受拉。腹杆（斜杆和竖杆）传递剪力。从基本的隔离体图可知，当集中载荷 P 作用在中心时，每个支反力为 P/2。最大弯矩出现在跨中，等于 (P × L)/4，L 为跨径。
Mₘₐₓ = (P × L) ÷ 4
We can estimate the stress in a member using σ = F / A. If a bottom chord stick has a cross‑sectional area of about 22.6 mm² and carries a tensile load of 50 N, the tensile stress is roughly 2.2 MPa—well within the tensile strength of wood along the grain (typically 30–70 MPa). Understanding these numbers helps us avoid overestimating the material’s capacity.
我们可以用 σ = F / A 估算构件的应力。如果一根下弦杆的截面积约为 22.6 平方毫米，承受 50 牛顿的拉力，那么拉应力约为 2.2 兆帕，远低于木材顺纹抗拉强度（通常为 30–70 兆帕）。理解这些数字能避免我们高估材料的能力。
5. Material Selection and Properties | 材料选择与性能
Our only materials are birchwood popsicle sticks and PVA glue. Although seemingly simple, they have defined engineering properties. Key data are summarised below.
我们仅有的材料是桦木冰棍棒和白乳胶。看似简单，它们却有明确的工程性能。关键数据汇总如下。
| Property | 性能 | Popsicle Stick (birch) | 冰棍棒（桦木） | PVA Glue | 白乳胶 |
|---|---|---|
| Density (kg/m³) | 密度 | ~600 | ~1,100 |
| Tensile strength (MPa) | 抗拉强度 | 30–70 along grain | 顺纹 | ~2 (after curing) | 固化后 |
| Compressive strength (MPa) | 抗压强度 | ~40 along grain | 顺纹 | ~5 |
| Modulus of elasticity (GPa) | 弹性模量 | ~10 | ~0.5 |
The glue is weaker than the wood, so joint strength is critical. Using gusset plates and double-lap joints increases the bonded area, reducing the shear stress in the glue line. Selecting the right orientation of wood grain also matters: sticks should be arranged so that the grain runs along the member axis for maximum strength.
胶水强度低于木材，因此节点强度很关键。使用节点板和双搭接接头可以增加粘合面积，降低胶层中的剪应力。选择正确的木纹方向同样重要：冰棍棒的木纹应沿着杆件轴线方向，以获得最大强度。
6. Modelling and Prototyping | 建模与原型制作
We begin by constructing a half-scale balsa wood model to validate the truss geometry. Mistakes are cheaper at small scale. This physical model reveals that the bottom chord tends to buckle laterally if left unbraced. Consequently, we add lateral bracing between the two parallel trusses of the bridge. A full-size prototype is then built from 10 sticks to test joint techniques before committing the final 50 sticks.
我们先做一个比例缩小的轻木模型，以验证桁架几何。在小尺度上犯错代价更低。这个实物模型揭示，如果缺少侧向支撑，下弦杆容易发生侧向屈曲。因此，我们在桥的两个平行桁架间增加了横向系杆。然后，用 10 根冰棍棒搭建全尺寸原型，以测试节点制作工艺，然后再动用手头 50 根材料建造最终模型。
For the final prototype, we use a jig to maintain alignment and apply glue sparingly with a small brush. Excess glue adds dead weight without increasing strength. Each joint is clamped for 15 minutes. The top and bottom chords are laminated from two sticks each, offsetting the joints to avoid weak points. This laminated technique is a design decision that trades extra mass for increased bending stiffness.
对于最终原型，我们采用定位夹具保持对齐，并用小刷子薄涂胶水。多余的胶水只会增加自重而不增强度。每个节点夹紧 15 分钟。上下弦杆各由两根冰棍棒叠合而成，并错开接头以避免薄弱点。这种叠合技术是在增加质量与提高弯曲刚度之间做出的设计权衡。
7. Structural Testing and Data Collection | 结构测试与数据收集
Testing is carried out by placing the bridge on two sturdy supports exactly 500 mm apart. A loading bucket is hung from the centre of the bottom chord, and sand is added slowly until failure. We record the mass of sand (converted to force in newtons) and observe the failure mode. The bridge fails at 18.2 kg (≈ 178 N), with a loud crack in the top chord near the mid-span—a classic compression buckling failure.
测试时，将桥梁放置在相距恰好 500 毫米的两个稳固支座上。在下弦杆中心悬挂装载桶，缓慢加沙直至破坏。我们记录沙的质量（换算成牛顿力）并观察破坏模式。桥梁在 18.2 公斤（约 178 牛顿）时失效，跨中附近上弦杆发出一声脆响——典型的受压屈曲破坏。
We also measure deflection at several load steps using a ruler. Plotting load versus deflection gives a graph that is almost linear until just before failure, indicating elastic behaviour. The collected data are organised in a table:
我们还用直尺测量了几个加载步的挠度。绘制载荷-挠度图，图形近似线性直到临近破坏，这表明呈弹性行为。收集的数据整理在表格中：
| Load (N) | 载荷 | Deflection (mm) | 挠度 |
|---|---|
| 0 | 0 |
| 50 | 2.1 |
| 100 | 4.3 |
| 150 | 6.8 |
| 178 | 10.5 (failure) | 破坏 |
Documenting data accurately allows us to compare our results with theoretical predictions and with other teams’ bridges.
准确记录数据让我们能够将结果与理论预测以及其他团队的桥梁进行对比。
8. Evaluating and Improving the Design | 评估与改进设计
Analysing the failure reveals that the top chord buckled because the unbraced length between vertical supports was too large. Euler’s buckling formula tells us that the critical buckling load is inversely proportional to the square of the effective length. To improve, we could add intermediate struts to reduce the unsupported length, or increase the second moment of area of the top chord by using a T-section instead of a flat laminate. Another improvement is to stagger the joints in the bottom chord to avoid stress concentration.
分析失效情况发现，上弦杆屈曲是因为竖杆之间的无支撑长度过大。欧拉屈曲公式告诉我们，临界屈曲载荷与有效长度的平方成反比。为了改进，我们可以增加中间撑杆以缩短无支撑长度，或者通过采用 T 形截面而不是扁平叠层来增大上弦杆的截面惯性矩。另一个改进措施是错开下弦杆的接头以避免应力集中。
We also note that the glue joints at the ends held perfectly, confirming that our gusset plate strategy worked. The mass of the bridge was 187 g, just under the limit, so we had 13 g spare for additional stiffeners. These observations form the basis of a second design iteration.
我们还注意到端部胶接节点完好无损，说明节点板策略是奏效的。桥梁总质量为 187 克，刚好低于上限，因此我们还有 13 克的余量可用于增加加劲肋。这些观察为第二轮设计迭代夯实了基础。
9. Manufacturing and Assembly Process | 制造与装配流程
In a manufacturing context, producing multiple identical trusses requires standardised processes. We document a production plan: cut eight 100 mm long sticks for verticals, twenty 120 mm sticks for diagonals, and prepare 16 gusset plates. Using a cutting template ensures consistency. The assembly sequence matters: first build the two truss frames flat, allow glue to cure, then join them with lateral cross-braces. This sequence minimises the risk of misalignment.
在制造语境中，生产多个相同的桁架需要标准化流程。我们记录了生产计划：切割 8 根 100 毫米长的竖杆、20 根 120 毫米长的斜杆，并准备 16 块节点板。使用切割模板可确保一致性。装配顺序很要紧：先平放制作两个桁架框，待胶水固化后，再用横向剪刀撑将它们连在一起。此顺序能最大限度地减少错位风险。
We also reflect on safety: always wear safety glasses when cutting sticks, and work in a well-ventilated area when using glue. In a factory, these would be formalised into risk assessments and standard operating procedures.
我们还反思了安全事项：切割冰棍棒时始终佩戴护目镜，使用胶水时在通风良好的场所作业。在工厂里，这些会被规范为风险评估和标准操作程序。
10. Cost and Sustainability Considerations | 成本与可持续性考量
Each popsicle stick costs about £0.02, making the material cost for 50 sticks just £1.00. A 250 ml bottle of PVA glue costs £2.50 but uses only 10 ml, so approximately £0.10. The total direct material cost is around £1.10. However, labour time (2 hours) and tools (cutting mat, knife, clamps) add indirect costs. In industry, a detailed cost breakdown is essential for pricing a product competitively.
每根冰棍棒成本约 0.02 英镑，50 根的材料费仅为 1.00 英镑。一瓶 250 毫升的白乳胶售价 2.50 英镑，但只用了 10 毫升，成本约 0.10 英镑。直接材料总成本约 1.10 英镑。然而，人工时间（2 小时）和工具（切割垫、刀、夹具）会增加间接成本。在工业中，要定出有竞争力的产品价格，就必须进行详细的成本分解。
Sustainability is also considered. Birchwood is renewable and biodegradable, but the adhesive is a synthetic polymer derived from petroleum. Engineers are increasingly seeking bio-based adhesives to lower the environmental footprint. The low mass of the bridge also reduces transport emissions if it were a real product.
可持续性也同样考虑在内。桦木是可再生、可生物降解的，但粘合剂是源于石油的合成聚合物。工程师们正在越来越多地寻找生物基粘合剂以降低环境足迹。若这是一件真实产品，桥梁质量较轻也能减少运输环节的排放。
11. Engineering Documentation | 工程文档
An engineering project is incomplete without proper documentation. We create a dimensioned orthographic drawing of the final truss, showing front view, top view and a section through a joint. The drawing includes a title block with the designer’s name, date, scale and material list. A cutting list is also prepared so that someone else could manufacture the bridge without additional instructions.
没有规范文档的工程项目是不完整的。我们为最终桁架绘制了带尺寸标注的正视图，包括正视图、俯视图和一个节点剖面图。图纸含有包含设计者姓名、日期、比例和材料清单的标题栏。我们还准备了截料表，这样无需额外指令，旁人也能把桥造出来。
Written instructions describe the assembly steps, curing times and quality checks. Good documentation ensures repeatability and is a hallmark of professional engineering practice. We also store test data and evaluation notes in a design portfolio, which can be used to support claims in a design competition or report.
书面说明描述了装配步骤、固化时间及质量检查。良好的文档保障了可重复性，是专业工程实践的标志。我们还将测试数据和评估笔记保存在设计档案夹中，可用于支持设计比赛或报告中的论述。
12. Reflecting on the Engineering Process | 反思工程设计流程
The case study demonstrates that engineering is not just about building—it is a cycle of analysing, designing, prototyping, testing and refining. Constraints forced us to make trade-offs: stronger joints meant more glue and mass; a lighter structure meant higher stresses. By following a structured process, we turned a heap of popsicle sticks into a bridge that held over 178 N, which is a load-to-weight ratio of about 97—meaning it supported 97 times its own weight.
本案例研究表明，工程远不止于建造——它是一个分析、设计、原型制作、测试和改进的循环。约束迫使我们权衡取舍：更强的节点意味着更多的胶水和质量；更轻的结构意味着更高的应力。通过遵循结构化的流程，我们将一堆冰棍棒变成了一座承载超过 178 牛顿的桥，荷重比约为 97——即它支撑了约自身重量 97 倍的载荷。
Every failure, such as the top chord buckling, taught us something new about materials and forces. The next iteration would be even better. This is the heart of engineering: learning from failure to create more reliable, efficient and innovative designs. We encourage you to try your own case study—choose a simple structure, set constraints, document everything, and improve. That is how real engineers change the world.
每次失效，例如上弦杆屈曲，都让我们对材料和力有了新的认识。下一轮迭代会更好。这正是工程的核心：从失败中汲取教训，创造出更可靠、更高效、更具创新性的设计。我们鼓励你尝试自己的案例研究——选择一个简单结构，设定约束，记录一切，然后改进。真正的工程师就是这样改变世界的。
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