📚 Year 10 Engineering Case Study: Practical Walkthrough | 剑桥IGCSE工程：案例分析实战演练
In Cambridge IGCSE Engineering, case studies test your ability to apply theoretical knowledge to real‑world design problems. This exercise walks you through a typical bridge bracket design challenge, showing how to analyse requirements, select materials, evaluate forces, and justify your choices. Use this as a model to sharpen your own design reasoning.
在剑桥 IGCSE 工程课程中，案例分析考查你把理论知识应用到实际设计问题的能力。本次实战演练将以一个典型的桥梁支架设计任务为例，逐步展示如何分析需求、选择材料、评估受力并论证你的选择。可将本文作为范例，提升你的设计推理能力。
1. Understanding the Design Brief | 理解设计任务书
Read the design brief carefully. You are asked to design a steel bracket that connects a pedestrian guardrail post to a concrete bridge beam. The bracket must resist a horizontal impact load of 1.2 kN applied to the top of the post at a height of 0.8 m above the bracket fixing. It will be exposed to rain, salt spray and temperature variations, so corrosion resistance is important. The client requires a safety factor of at least 2 on yield, and the bracket must not deflect more than L/100 under the design load. The preferred manufacturing method is cutting and welding from hot‑rolled steel plate.
仔细阅读设计任务书。你需要设计一个将人行护栏立柱连接到混凝土桥梁主梁上的钢支架。支架必须承受施加于立柱顶部、距支架固定点 0.8 m 高度处 1.2 kN 的水平冲击载荷。它将暴露在雨水、盐雾和温度变化中，因此耐腐蚀性非常重要。客户要求屈服安全系数至少为 2，并且在设计载荷下支架的挠度不得超过 L/100。首选的制造方法是从热轧钢板切割并焊接。
2. Identifying Loads and Constraints | 识别载荷与约束
The dominant load is a horizontal point force of 1.2 kN acting as a cantilever. Since the bracket is rigidly bolted to the bridge beam, the fixed end must resist the entire bending moment. Secondary loads such as self‑weight and wind are negligible for this initial sizing. The main functional constraint is the allowable stress, derived from the material’s yield strength divided by the safety factor. Geometric constraints give a maximum bracket length of 200 mm and a width limited to 80 mm by the post dimensions.
主要载荷是一个使支架像悬臂梁一样工作的 1.2 kN 水平集中力。由于支架用螺栓刚性固定在桥梁主梁上，固定端必须承受全部弯矩。支架自重和风荷载等次要载荷在初步尺寸确定中可以忽略不计。主要的功能约束是许用应力，它由材料的屈服强度除以安全系数得到。几何约束要求支架最大长度为 200 mm，宽度受立柱尺寸限制不得超过 80 mm。
acket itself can be treated as a horizontal beam element with a fixed support at one end and the force transmitted through the post connection. The critical cross‑section is at the fixed end, where the bending moment is at its maximum.
绘制一个简单的结构模型：一根垂直立柱在距主梁 d = 0.8 m 处施加力 F = 1.2 kN。支架本身可视为一端固定、力通过立柱连接传递的水平梁单元。危险截面位于固定端，该处弯矩达到最大值。
3. Free Body Diagram and Force Analysis | 受力图与力分析
A free body diagram of the bracket shows a fixed support at the left end, with a vertical upward reaction force, a horizontal reaction, and a reaction moment. For the cantilever, the maximum bending moment M at the fixed end is simply:
支架的受力图显示左端为固定支座，有竖直向上的支反力、水平支反力和支反力矩。对于悬臂梁，固定端最大弯矩 M 为：
M = F × d = 1.2 kN × 0.8 m = 0.96 kN·m
Convert this to consistent units: M = 0.96 kN·m = 960 N·m = 960 000 N·mm. The bending stress formula for a rectangular section of width b and height h is:
将其转换为一致的单位：M = 0.96 kN·m = 960 N·m = 960 000 N·mm。对于宽度为 b、高度为 h 的矩形截面，弯曲应力公式为：
σ = M y / I, with y = h/2 and I = b h³ / 12, so σ = 6M / (b h²)
= 15 mm. The section modulus Z = b h² / 6 = 60 × 225 / 6 = 2250 mm³. Then σ = M / Z = 960 is stress far exceeds the yield strength of mild steel (typically 235 MPa for S235 grade).
尝试一个初始尺寸：b = 60 mm，h = 15 mm。截面模量 Z = b h² / 6 = 60 × 225 / 6 = 2250 mm³。于是 σ = M / Z = 960 000 N·mm / 2250 mm³ ≈ 426.7 N·mm⁻² (MPa)。这个应力远超普通低碳钢的屈服强度（S235 等级典型值为 235 MPa）。
the section depth. Let b = 60 mm, h = 25 mm. Then Z = 60 × 625 / 6 = 6250 mm³, and σ = 960 promising working stress value, but we must also check deflection and material selection.
我们必须加大截面高度。设 b = 60 mm，h = 25 mm。则 Z = 60 × 625 / 6 = 6250 mm³，σ = 960 000 / 6250 = 153.6 MPa。这是一个有希望的工作应力值，但我们还需要校核挠度和材料选择。
4. Material Selection and Properties | 材料选择与性能
Selecting the right material is crucial for safety, durability and cost. The table below compares three candidate metals commonly used in structural brackets.
选择合适的材料对安全性、耐用性和成本至关重要。下表比较了三种常用于结构支架的候选金属。
| Material | Yield Strength σy (MPa) | Elastic Modulus E (GPa) | Density (kg/m³) | Corrosion Resistance | Relative Cost |
|---|---|---|---|---|---|
| S235 Structural Steel | 235 | 210 | 7850 | Poor (needs coating) | 1.0 |
| S355 High‑Strength Steel | 355 | 210 | 7850 | Poor (needs coating) | 1.2 |
| 304 Stainless Steel | 215 | 193 | 8000 | Excellent | 3.5 |
The working stress of 153.6 MPa is well below the yield of S355, giving a healthy margin, but S235 with a 2‑fold safety factor gives an allowable stress of only 117.5 MPa, which is insufficient. Stainless steel 304 offers superb corrosion resistance but its slightly lower yield and much higher cost make it less attractive for this non‑visible structural part if a protective coating can be applied.
工作应力 153.6 MPa 远低于 S355 的屈服强度，提供了充裕的裕度，但 S235 钢在 2 倍安全系数下许用应力仅为 117.5 MPa，不满足要求。304 不锈钢具有出色的耐腐蚀性，但其屈服强度略低且成本高得多，如果可以使用保护涂层，这种不锈钢对这个非外观结构件来说吸引力较低。
Therefore, the preliminary choice is S355 hot‑rolled steel with a zinc‑rich epoxy corrosion protection system. S355 provides an allowable stress σallow = 355 / 2 = 177.5 MPa > 153.6 MPa, satisfying the yield criterion.
因此，初步选择 S355 热轧钢并采用富锌环氧防腐系统。S355 的许用应力为 σallow = 355 / 2 = 177.5 MPa > 153.6 MPa，满足屈服准则。
5. Safety Factor and Design Calculations | 安全系数与设计计算
With b = 60 mm and h = 25 mm, re‑examine the actual maximum bending stress. Compute the second moment of area I:
使用 b = 60 mm 和 h = 25 mm，重新核算实际的最大弯曲应力。计算截面惯性矩 I：
I = b h³ / 12 = 60 × 25³ / 12 = 60 × 15 625 / 12 = 78 125 mm⁴
The maximum bending stress is σmax = M (h/2) / I = 960 000 N·mm × 12.5 mm / 78 125 mm⁴ = 12 000 000 / 78 125 = 153.6 MPa, as before.
最大弯曲应力为 σmax = M (h/2) / I = 960 000 N·mm × 12.5 mm / 78 125 mm⁴ = 12 000 000 / 78 125 = 153.6 MPa，与之前相同。
Now check the deflection at the post attachment point. For a cantilever beam with a point load at the free end, the maximum deflection δ is:
现在校核立柱连接点处的挠度。对于自由端承受集中载荷的悬臂梁，最大挠度 δ 为：
δ = F L³ / (3 E I)
re L = 800 mm (the distance from the fixed end to the point load). Using E = 210 GPa = 210 000 N/mm² for steel:
此处 L = 800 mm（固定端到集中载荷的距离）。钢材的 E = 210 GPa = 210 000 N/mm²：
δ = (1200 N) × (800 mm)³ / (3 × 210 000 N/mm² × 78 125 mm⁴)
Compute numerator: 1200 × 512 000 000 = 6.144 × 10¹¹ N·mm³. Denominator: 3 × 210 000 × 78 = 8 mm. The current design fails the stiffness criterion even though strength is adequate.
分子：1200 × 512 000 000 = 6.144 × 10¹¹ N·mm³。分母：3 × 210 000 × 78 125 = 4.921875 × 10¹⁰ N·mm²。因此 δ ≈ 12.48 mm。容许挠度为 L/100 = 800/100 = 8 mm。尽管强度足够，但当前设计在刚度准则上不合格。
is most effective. Try h = 30 mm while keeping b = 60 mm. Then I = 60 × 30³ / 12 = 60 × 27 000 / 12 = 135 000 mm⁴. The new stress σ = 960 000 × 15 / 135 000 = 106.7 MPa, and deflection δ = 6.144e11 / (3 × 210 000 × 135 hin the 177.5 MPa allowance. Final chosen dimensions: b = 60 mm, h = 30 mm, length 200 mm.
为增加刚度，我们必须显著增大 I。增大高度 h 最有效。尝试 h = 30 mm，保持 b = 60 mm。则 I = 60 × 30³ / 12 = 60 × 27 000 / 12 = 135 000 mm⁴。新的应力 σ = 960 000 × 15 / 135 000 = 106.7 MPa，挠度 δ = 6.144e11 / (3 × 210 000 × 135 000) = 6.144e11 / 8.505e10 ≈ 7.22 mm。该值低于 8 mm 的限值，且应力仍远低于 177.5 MPa 的许用值。最终选定的尺寸为：b = 60 mm，h = 30 mm，长度 200 mm。
6. Manufacturing Processes and Tolerances | 制造工艺与公差
The bracket will be flame‑cut or plasma‑cut from an S355 hot‑ onal tolerance of ±0.5 mm. The edges will be ground smooth to avoid stress raisers. A full‑ h welding procedure specification (WPS) to be approved. General tolerances follow ISO 2768‑m (medium). After welding, the component will be shot‑blasted and coated with a zinc‑epoxy primer to resist corrosion.
该支架将从 30 mm 厚的 S355 热轧钢板上用火焰切割或等离子切割下料。用于 M16 螺栓的孔将钻制，位置公差为 ±0.5 mm。边缘将被磨平以避免应力集中。支架将通过全熔透对接焊缝与底板连接，焊接工艺规程 (WPS) 需经批准。通用公差遵循 ISO 2768‑m（中等）标准。焊接后，构件将进行喷砂处理并涂覆锌环氧底漆以抵抗腐蚀。
We must also consider the heat‑affected zone (HAZ) near the weld. S355 retains good toughness after welding, but a post‑weld heat treatment may be required if the thickness exceeds certain limits. For a 30 mm plate, stress relieving at 600 °C for 1 hour per 25 mm of thickness is advisable to reduce residual stresses.
我们还必须考虑靠近焊缝的热影响区 (HAZ)。S355 在焊接后保持良好的韧性，但如果厚度超过一定限值，可能需要进行焊后热处理。对于 30 mm 厚的板材，建议在 600 °C 下以每 25 mm 厚度保温 1 小时的工艺进行消应力处理，以减少残余应力。
7. Sketching and CAD Modelling Considerations | 草图和 CAD 建模考量
Produce a fully dimensioned orthographic drawing showing the front, side and plan views. Mark the critical dimensions: overall length 200 mm, width 60 mm, plate thickness 30 mm, hole positions for two M16 bolts at 100 mm centres, and the weld symbol joining the bracket to the base plate. Surface finish symbols should indicate ground edges (Ra 3.2 µm) and the corrosion protection coating.
绘制一张完整标注尺寸的正投影图，显示主视图、侧视图和俯视图。标注关键尺寸：总长 200 mm，宽度 60 mm，板厚 30 mm，两个 M16 螺栓孔的中心距为 100 mm，以及将支架连接到底板的焊缝符号。表面粗糙度符号应标明磨光边缘 (Ra 3.2 µm) 和防腐涂层。
In a CAD system (such as SolidWorks or Fusion 360), model the bracket as a single solid part. Apply the S355 material from the library, then run a static finite element analysis (FEA) with a fixed constraint on the bolt holes and a remote force of 1.2 kN at the post attachment point. The FEA will visualise stress distribution and confirm the hand calculations. Always cross‑check the FEA mesh convergence and compare the maximum von Mises stress with the allowable stress.
在 CAD 系统（如 SolidWorks 或 Fusion 360）中，将支架建模为单个实体零件。从材料库中赋予 S355 材料，然后运行静力有限元分析 (FEA)，在螺栓孔上施加固定约束，并在立柱连接点施加 1.2 kN 的远端力。FEA 将可视化应力分布，并验证手工计算结果。务必检查 FEA 网格收敛性，并将最大 von Mises 应力与许用应力进行比较。
8. Cost, Sustainability, and Lifecycle | 成本、可持续性和生命周期
e direct material cost for an S355 plate of 200 mm × 60 mm × 30 mm is low. Adding the zinc‑epoxy coating, welding consumables, drilling and shot‑blasting brings the estimated unit production cost to about £ es as much and require specialised welding, so S355 with coating is the economical choice.
一块尺寸为 200 mm × 60 mm × 30 mm 的 S355 钢板直接材料成本较低。加上锌环氧涂层、焊接耗材、钻孔和喷砂，对于 500 件批量，每个支架的预估生产成本约为 £12。不锈钢的成本几乎是它的 3 倍，且需要专门的焊接技术，因此带有涂层的 S355 是经济的选择。
From a sustainability perspective, steel is 100% recyclable at end of life. The zinc‑epoxy coating can be designed for a 25‑year service life with minimal maintenance, reducing lifecycle environmental impact. The bracket’s design avoids over‑engineering, using just enough material to meet strength and stiffness targets, which saves raw material and energy during manufacturing.
从可持续性角度看，钢材在其寿命终止时可 100% 回收。锌环氧涂层可设计为具有 25 年的使用寿命，且维护量极小，从而降低生命周期环境影响。该支架的设计避免了过度工程化，仅使用刚好满足强度和刚度目标的材料，在制造过程中节省了原材料和能源。
9. Test and Evaluation Plan | 测试与评估计划
A physical prototype should be subjected to a static load test. Apply a gradually increasing horizontal load at the post connection point up to 1.5 times the design load (1.8 kN) and measure the deflection with a dial gauge. The deflection under 1.2 kN must remain below 8 mm, and there must be no permanent set after unloading. Strain gauges near the fixed end can verify that the maximum stress does not exceed 177.5 MPa.
应对物理样机进行静载荷测试。在立柱连接点施加逐步增加的水平载荷，直至设计载荷的 1.5 倍 (1.8 kN)，并用百分表测量挠度。在 1.2 kN 载荷下，挠度必须保持在 8 mm 以下，并且卸载后不得有任何永久变形。靠近固定端的应变片可以验证最大应力不超过 177.5 MPa。
Additionally, a salt spray test (ASTM B117) should be performed on a coated sample to confirm that the corrosion protection meets the 25‑year durability requirement. If FEA was used in design, correlation between test and simulation validates the model for future similar brackets.
此外，应对一个带有涂层的试样进行盐雾试验 (ASTM B117)，以确认防腐系统满足 25 年的耐久性要求。如果在设计中使用了 FEA，试验与模拟之间的相关性可验证模型，以便将来用于类似的支架设计。
10. Justifying the Final Design | 论证最终设计方案
The final design – an S355 steel bracket 200 mm long, 60 mm wide and 30 mm thick – ≈ 3.33, but using allowable stress of 177.5 MPa gives an actual factor of 177.5/106.7=1.66? .5 MPa, and 106.7 MPa is well below it, so the design is safe). The deflection of 7.22 mm is below the 8 mm limit. The zinc‑xy coating provides corrosion protection, and the manufacturing method uses standard, cost‑ safety, performance, economy and sustainability, making it a robust engineering solution.
最终设计——一个长 200 mm、宽 60 mm、厚 30 mm 的 S355 钢支架——满足所有功能要求。它能抵抗 1.2 kN 的冲击，屈服安全系数为 3.33（355/106.7 ≈ 3.33，超过 2.0）。挠度 7
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