📚 Case Study Practical Drill for CIE Engineering | CIE 工程案例分析实战演练
In CIE Engineering (Year 12), case study questions often require you to analyse a real-world product or system by applying principles from materials, mechanics, manufacturing and sustainability. This article provides a step-by-step drill based on an outdoor bench support structure, building your skills to tackle such extended response questions confidently.
在 CIE 工程（Year 12）考试中，案例分析题常要求你分析真实的产品或系统，综合运用材料、力学、制造和可持续性等工程原理。本文以户外长凳支撑结构为例，提供分步实战演练，帮助你建立信心，从容应对此类开放性大题。
1. Understanding the Case Context | 理解案例背景
Read the scenario carefully: a park bench consists of two cantilever steel beams supporting a wooden seat. Each beam protrudes 0.8 m from a wall, and the design load is two adults (total 2000 N) uniformly distributed. Your task is to evaluate the structure’s adequacy and suggest improvements.
仔细阅读题目描述：公园长凳由两根悬臂钢梁支撑木制座板，每根梁从墙体伸出 0.8 m，设计载荷为两名成人（总重 2000 N）均匀分布。你的任务是评估该结构是否满足要求并提出改进建议。
2. Key Engineering Parameters | 关键工程参数
Extract and list the given data: load per beam = 1000 N, length L = 0.8 m, beam cross-section 50 mm × 100 mm, material mild steel with yield strength σ_yield = 250 MPa, and Young’s modulus E = 210 GPa. These parameters form the basis for all subsequent calculations and decisions.
提取并列出给定数据：单梁载荷 1000 N，长度 L = 0.8 m，梁截面 50 mm × 100 mm，材料低碳钢，屈服强度 σ_yield = 250 MPa，杨氏模量 E = 210 GPa。这些参数是所有后续计算和决策的基础。
3. Material Selection Analysis | 材料选择分析
Mild steel offers high strength, good weldability and low cost, making it suitable for structural applications. However, outdoor exposure leads to corrosion, requiring protective coatings. Aluminium alloys are lighter and naturally corrosion-resistant but have a lower elastic modulus and cost more. Stainless steel provides excellent durability but at significantly higher expense.
低碳钢具有高强度、良好的焊接性和低廉的成本，适合结构应用。但户外暴露会导致腐蚀，需要防护涂层。铝合金更轻且天然耐腐蚀，但弹性模量较低且价格更高。不锈钢耐久性极佳，但成本高昂。
| Material | Yield Strength (MPa) | Density (kg/m³) | Corrosion Resistance | Relative Cost |
|---|---|---|---|---|
| Mild Steel | 250 | 7850 | Poor (requires coating) | Low |
| Aluminium Alloy | ~270 (7075-T6) | 2800 | Good | Medium |
| Stainless Steel | ~205-520 | ~8000 | Excellent | High |
4. Manufacturing Process Evaluation | 制造工艺评估
The cantilever beam can be fabricated by cutting steel plate to size or by using a standard hot-rolled section. Mounting brackets are then welded on, and bolt holes are drilled. To prevent rust, the surface is prepared by shot blasting and then finished with hot-dip galvanising or powder coating.
悬臂梁可通过将钢板切割至尺寸或使用标准热轧型材来制造。然后焊接安装支架，并钻出螺栓孔。为防止生锈，先对表面进行喷丸处理，再进行热浸镀锌或粉末涂装。
5. Structural Mechanics Calculations | 结构力学计算
First, determine the maximum bending moment. For a uniformly distributed load w on a cantilever, the formula is:
首先，确定最大弯矩。对于悬臂梁上的均布载荷 w，公式为：
Mₘₐₓ = wL²/2
where w = 1000 N / 0.8 m = 1250 N/m. So Mₘₐₓ = (1250 N/m) × (0.8 m)² / 2 = 1250 × 0.64 / 2 = 400 N·m.
其中 w = 1000 N / 0.8 m = 1250 N/m。因此 Mₘₐₓ = (1250 N/m) × (0.8 m)² / 2 = 1250 × 0.64 / 2 = 400 N·m。
Next, calculate the section modulus S for a rectangular cross-section:
接下来，计算矩形截面的截面模量 S：
S = b h²/6
where b = 0.05 m, h = 0.1 m. S = (0.05 m) × (0.1 m)² / 6 = 0.05 × 0.01 / 6 = 8.333 × 10⁻⁵ m³.
其中 b = 0.05 m，h = 0.1 m。S = (0.05 m) × (0.1 m)² / 6 = 0.05 × 0.01 / 6 = 8.333 × 10⁻⁵ m³。
Finally, the maximum bending stress:
最后，最大弯曲应力：
σₘₐₓ = Mₘₐₓ / S = 400 N·m / (8.333 × 10⁻⁵ m³) = 4.8 × 10⁶ Pa = 4.8 MPa
6. Interpreting Results and Safety Factors | 结果解读与安全系数
The calculated bending stress of 4.8 MPa is far below the yield strength of 250 MPa, giving a safety factor of 250 / 4.8 ≈ 52. While a high safety factor ensures reliability, it often indicates over-engineering – unnecessary material usage, increased weight and higher cost. For static outdoor structures, a safety factor of 3–5 is typically adequate.
计算出的弯曲应力 4.8 MPa 远低于屈服强度 250 MPa，安全系数约为 52。虽然高安全系数确保了可靠性，但通常也表明存在过度设计——材料浪费、重量增加、成本上升。对于静态户外结构，安全系数为 3–5 通常就已足够。
7. Failure Mode and Effect Analysis (FMEA) | 失效模式与影响分析
Potential failure modes include plastic yielding (unlikely under normal load), fatigue cracking from repeated dynamic loading if the bench is used vigorously, corrosion thinning the cross-section, and bolt shear failure at the wall connection. FMEA helps rank these risks by severity, occurrence, and detectability, guiding design improvements.
潜在失效模式包括塑性屈服（正常载荷下可能性极低）、因频繁晃动使用导致的疲劳裂纹、腐蚀使截面变薄，以及墙面连接处螺栓的剪切破坏。FMEA 通过严重度、发生频率和可检测度对风险进行分级，从而指导设计改进。
8. Quality Control and Testing | 质量控制与测试
Essential quality control measures: verifying dimensions with calipers and gauges, non-destructive testing of welds using ultrasonic or dye-penetrant methods, measuring coating thickness with an eddy-current gauge, and applying a proof load (e.g., 1.5 times the design load) to confirm structural integrity. These steps ensure compliance with specifications and safety standards.
基本质量控制措施包括：用卡规和量规检验尺寸，采用超声波或渗透法对焊缝进行无损检测，用涡流测厚仪测量涂层厚度，并施加验证载荷（例如设计载荷的 1.5 倍）以确认结构完整性。这些步骤确保产品符合规范和安全标准。
9. Sustainability and Environmental Impact | 可持续性与环境影响
Mild steel is highly recyclable; using recycled steel significantly reduces the carbon footprint. However, galvanising involves zinc and acid baths that can harm the environment if not managed responsibly. A lighter design, or switching to aluminium (also easily recycled), can lower raw material use and emissions. Life-cycle assessment (LCA) should inform final material and process choices.
低碳钢回收率很高，使用回收钢可显著降低碳足迹。然而，镀锌过程涉及锌和酸浴，若管理不当会对环境造成危害。采用更轻的设计或改用铝材（同样易于回收）可减少原材料消耗和排放。生命周期评估（LCA）应作为材料和工艺选择的依据。
10. Cost–Benefit Considerations | 成本效益考量
Steel has low material cost but requires ongoing maintenance for corrosion protection. Aluminium has a higher initial cost but lower lifetime maintenance. A thorough cost–benefit analysis must account for the bench’s expected service life, maintenance intervals, and end-of-life recycling value. The optimal choice balances upfront expenditure with long-term durability.
钢材的材料成本低，但腐蚀防护需要持续维护。铝合金初始成本较高，但全寿命维护成本较低。全面的成本效益分析必须考虑长凳的预期使用寿命、维护周期和报废回收价值。最优选择要在前期投入与长期耐久性之间取得平衡。
11. Design Improvement Proposals | 设计改进建议
To save weight and material while keeping a sensible safety factor (e.g., 4), the beam cross-section could be reduced to 40 mm × 80 mm. Recalculating: S = 0.04 × 0.08² / 6 ≈ 4.27 × 10⁻⁵ m³, σ = 400 / 4.27 × 10⁻⁵ ≈ 9.37 MPa, safety factor ~ 26.7, still very safe. A hollow circular section (e.g., Ø80 × 5 mm) might further enhance torsional stiffness and aesthetic appeal.
为节省重量和材料，同时保持合理的安全系数（如 4），可将梁截面减小至 40 mm × 80 mm。重新计算：S = 0.04 × 0.08² / 6 ≈ 4.27 × 10⁻⁵ m³，σ = 400 / 4.27 × 10⁻⁵ ≈ 9.37 MPa，安全系数约为 26.7，仍然十分安全。采用空心圆管（如 Ø80 × 5 mm）还可进一步提升扭转刚度和美观度。
12. Summary and Exam Tips | 总结与备考建议
In CIE Engineering case studies, adopt a structured method: read the scenario to identify key parameters, apply relevant mechanics and material concepts, present calculations clearly, discuss manufacturability, quality, sustainability and cost, and finally propose justified improvements. Always anchor your answer in the specification and use precise engineering terminology.
在 CIE 工程案例分析中，要采用条理化的方法：阅读情景，识别关键参数；应用相关的力学与材料概念；清晰展示计算过程；讨论可制造性、质量、可持续性与成本；最后提出合理的改进建议。始终将答案扎根于课程规范，并使用准确的工程术语。
Published by TutorHao | Engineering Revision Series | aleveler.com
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