22-Mec-B5 Product Design and Development · May 2015

Question 7 of 7: Materials for a chair and a selection framework

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams, May 2015 — 07-Mec-B5 Product Design and Development. Three hours. Open book; no calculator is permitted. Question 1 must be completed and is worth 40 marks; four of the six remaining questions are chosen, each worth 15 marks, for 100 marks in total. Only the first five questions as they appear in the answer book are marked. The paper states that most questions require an answer in essay format or the use of tables, figures and charts, and that clarity and organisation of the answer are important.

The paper prints 40 + 6 × 15 = 130 marks and a candidate attempts 40 + 4 × 15 = 100 of them. All seven questions are answered below, because this set is a study resource rather than an examination script. The marking scheme printed on the last source page splits Question 1 as 6 / 9 / 9 / 6 / 4 / 6 and gives the part weights for each 15-mark question, and the answers here are proportioned to that split. Because no calculator is allowed, every calculation is arranged so that it can be carried out on paper in one or two lines.

Reference texts for this subject

K. T. Ulrich and S. D. Eppinger, Product Design and Development — the framework text for this exam code: identifying customer needs, target specifications, concept generation, concept selection by Pugh screening and weighted scoring, design for manufacturing, and product development economics.
G. E. Dieter and L. C. Schmidt, Engineering Design — problem definition, decision matrices, design for the environment and life-cycle assessment, standards and codes, and the four components of a complete design.
G. Pahl and W. Beitz, Engineering Design: A Systematic Approach — the systematic conceptual / embodiment / detail sequence and function structures.
G. Boothroyd, P. Dewhurst and W. Knight, Product Design for Manufacture and Assembly — part-count reduction, handling and insertion time, and the design-for-assembly index used in Question 6.
M. F. Ashby, Materials Selection in Mechanical Design — translate, screen, rank and seek supporting information; the property charts and material indices used in Question 7.
S. Kalpakjian and S. R. Schmid, Manufacturing Engineering and Technology — process selection, process capability, tooling cost and economic batch size.
I. Gibson, D. Rosen and B. Stucker, Additive Manufacturing Technologies — process families and design for additive manufacturing, for Question 2.
W. Preiser and K. Smith (eds.), Universal Design Handbook, and the seven Principles of Universal Design (Centre for Universal Design, North Carolina State University, 1997) — the framework Question 1 asks for.
Canadian context: CSA B125.3, Plumbing fittings; CSA B651, Accessible design for the built environment; the National Plumbing Code of Canada; the Accessible Canada Act framework; CSA Group, Standards Council of Canada and Health Canada under the Canada Consumer Product Safety Act.

Check: the exam gives no data of its own — every question asks the candidate to bring a product, a set of numbers and a method. All quantities used below (operating torques, embodied energies, machine rates, process sigmas, material properties) are stated explicitly as design assumptions drawn from the reference texts and from Canadian standards, and each answer is written so that the method stands whatever numbers a marker would prefer.

Question 7: Materials for a chair and a selection framework (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A four-legged stacking side chair for a Canadian school or cafeteria, tested to a 1.3 kN static seat load (325 N per leg) and required to survive commercial cleaning. Three candidate materials, with the properties needed for the indices of part D:

Given data — candidate materials for the chair frame
Material	E (GPa)	ρ (Mg/m³)	σ_y (MPa)	C_m (CAD/kg)
Mild steel tube	210	7.85	250	0.90
Polypropylene, injection moulded	1.5	0.905	32	1.80
Laminated beech plywood	10	0.70	60	1.60

Find. Three candidate materials with their challenges, the effect of the choice on use and on manufacture, and a defensible selection framework applied to the chair with numerical ranking.

Part A — Three materials and their challenges (3 marks)

Mild steel tube. The default for stacking chairs: stiff, strong, tolerant of abuse, cheap per kilogram and joined by processes every fabricator has. Its challenges are corrosion, which forces a plated or powder-coated finish and makes any coating breach a maintenance liability; mass, since steel is nearly eleven times denser than plywood and the chair must be carried and stacked by staff; thermal feel, an unpleasantly cold seat in an unheated hall; noise, because a thin-walled tube frame on a hard floor is loud; and weld distortion, which must be controlled by fixturing if four legs are to sit flat.

Polypropylene, injection moulded. The default for the seat and back, and increasingly for a single-piece chair: tough, unaffected by water and cleaning chemicals, cheap in volume, coloured throughout so scratches do not show, and capable of integral living hinges and snap features. Its challenges are the high tooling cost, which makes it viable only at large volume; low stiffness, so section depth and ribbing must do the work the material cannot; creep under sustained load, which matters for a seat occupied for hours; ultraviolet degradation and embrittlement at low temperature, both relevant to a Canadian setting; and sink marks and warpage that constrain the wall thickness the industrial designer may specify.

Laminated beech plywood. The classic bent-ply chair material: an outstanding stiffness-to-weight ratio, warm to the touch, quiet, renewable, and formable into compound curves that give both strength and appearance in one operation. Its challenges are moisture sensitivity, since a chair that is mopped daily will delaminate unless the adhesive and the edge sealing are right; anisotropy, so the ply layup must be oriented to the load and the designer must think about grain direction; splintering and edge damage in service; variability between veneer batches; and long press cycles that limit output per mould.

Part B — How the material choice affects usage (3 marks)

The material is felt by the user long before it is analysed by the engineer. Mass determines whether a member of staff can stack forty chairs: a steel frame at roughly 6 kg against a plywood frame at 3 kg is the difference between a routine task and an injury risk, and it is why the material index of part D is a stiffness-per-unit-mass measure rather than a stiffness measure. Compliance determines comfort: a completely rigid seat concentrates pressure, whereas a plywood or polypropylene seat pan deflects a few millimetres and spreads it, which is a functional benefit that the stiffness calculation must therefore not over-deliver. Thermal conductivity and surface texture determine whether the chair is pleasant on contact — metal at 15 °C draws heat from the skin far faster than wood at the same temperature. Durability and cleanability determine service life in the real environment: polypropylene shrugs off a bleach solution that will lift a plywood veneer, while plywood tolerates a scuff that would show as a scratch on a painted steel tube. Acoustics matter more than designers expect in a room with a hundred chairs on a hard floor. And end of life is a usage property too: a steel frame is worth money as scrap, a plywood frame is combustible biomass, and a glass-filled polypropylene moulding is difficult to recycle usefully.

Part C — How the material choice affects the manufacturing process (3 marks)

Choosing a material chooses a process family, and with it the tooling cost, the batch economics, the achievable geometry and the factory itself. Steel tube implies cutting, mandrel bending, end forming, welding or brazing, fixturing to control distortion, degreasing, and powder coating with a cure oven: low tooling cost, so it is viable from a few hundred units, but many operations, each with labour and work-in-progress. Polypropylene implies a single injection-moulding operation on a large machine with a steel tool costing tens of thousands of dollars and a lead time of months: almost no labour per part and a cycle of under a minute, but the geometry must obey draft, uniform wall and ejection rules from the first sketch, and any change after tooling is a tool modification. Laminated plywood implies veneer preparation, adhesive application, layup, hot pressing in a matched mould for several minutes, trimming on a router or CNC, sanding and finishing: moderate tooling cost, long cycle, significant skilled labour, and an output limited by press time rather than by machine capacity.

Three consequences follow that a designer must act on. The break-even volume differs by an order of magnitude between the three routes, so the annual volume must be known before the material is chosen, not after. The geometric freedom differs: compound curvature is free in moulding and in bent ply and expensive in tube. And the joining strategy is decided at the same moment — steel welds, polypropylene snaps or is welded ultrasonically but does not glue reliably, and plywood is best joined by mechanical inserts because adhesives are weak across the veneer face.

Part D — A material selection framework applied to the chair (6 marks)

Approach. The framework is Ashby’s four-step method — translate, screen, rank, then seek supporting information — and its power is that step 3 produces a single number per material derived from the mechanics of the actual part.

Translate the requirement into function, constraints, objective and free variables. The function of a chair leg is to carry a compressive and bending load between the seat and the floor: mechanically it is a beam of freely choosable section. The constraints are that it must not deflect more than a specified amount under the 1.3 kN test load (325 N per leg), must not yield or buckle, must survive cleaning and a −5 to +40 °C environment, and must be manufacturable at the planned volume. The objective is to minimise mass, because stacking and carrying dominate the user experience. The free variables are the section dimensions and the material.
Derive the material index from the objective and the stiffness constraint. For a beam of length L and free section carrying a bending stiffness constraint, the mass at fixed stiffness varies as ρ/E^1/2, so the material to maximise is $$M_1 = \frac{E^{1/2}}{\rho} \qquad\text{(light, stiff beam of free section)}$$ and if the governing constraint were strength rather than stiffness the corresponding index would be σ_y^2/3/ρ. Both are evaluated, because a chair leg must satisfy both and the shortlist should be robust to which one binds.
Screen on the hard constraints, then rank on the index. Screening removes anything that cannot survive a wet cleaning regime or the temperature range, and anything whose process is uneconomic at the planned volume. Ranking is then arithmetic, and the results are tabulated immediately below.
Seek supporting information before committing. The index ranks; it does not decide. Plywood’s moisture sensitivity has to be resolved with a phenolic adhesive and a sealed edge, its anisotropy with a layup specified on the drawing, and its supply with a second qualified veneer source. Steel’s corrosion is resolved with powder coating and a specified coating thickness at the weld heat-affected zone. Polypropylene’s creep must be checked against a seat occupied for several hours, not against a short-term modulus.

Part D — ranking the candidates on the material indices (E in GPa, ρ in Mg/m³, σ_y in MPa)
Material	M₁ = E^1/2/ρ	M₂ = σ_y^2/3/ρ	M₃ = E^1/2/(C_mρ)	Rank on M₁
Laminated beech plywood	4.52	21.9	2.82	1
Aluminium 6061-T6 (added on screening)	3.10	14.3	0.91	2
Mild steel tube	1.85	5.06	2.05	3
Polypropylene, moulded	1.35	11.1	0.75	4

Working one entry to show the arithmetic, for plywood

$$M_1 = \frac{\sqrt{10}}{0.70} = \frac{3.162}{0.70} = \boxed{4.52}$$

against 1.85 for steel. The interpretation is direct: a steel leg of the same bending stiffness weighs 4.52/1.85 = 2.45 times as much as a plywood one, and a polypropylene leg 3.34 times as much. Plywood also leads on M₂, so the ranking does not depend on whether stiffness or strength binds, and it leads on the cost-corrected index M₃ as well — a result that surprises people who assume steel is always the cheap answer, and which holds because the mass saving outruns the price per kilogram.

Figure 7.1 — The four candidates on a modulus–density chart with the E^1/2/ρ guideline. Materials above and to the left of the dashed line have a higher index; laminated plywood sits furthest above it.

The trap worth naming, because it decides this question. The index depends on the mechanical idealisation, not on the part’s name. A chair leg is a beam of free section and ranks on E^1/2/ρ. A chair seat pan is a panel of fixed area and free thickness, and ranks on E^1/3/ρ — a different exponent that reorders the shortlist: on the panel index polypropylene scores 1.26 against steel’s 0.76, reversing their positions from the beam index where steel led 1.85 to 1.35. Using the beam exponent on a panel flatters the metals enough to select the wrong material for the seat. The correct outcome for the whole chair is therefore a hybrid: a laminated plywood or steel-tube frame ranked on the beam index, with a moulded polypropylene seat pan ranked on the panel index — which is exactly what almost every mass-produced stacking chair is, and the framework arrives at it rather than assuming it.

Question 7 — results
Quantity	Value
Beam index M₁ = E^1/2/ρ (plywood / aluminium / steel / PP)	4.52 / 3.10 / 1.85 / 1.35
Strength index M₂ = σ_y^2/3/ρ	21.9 / 14.3 / 5.06 / 11.1
Cost-corrected index M₃ = E^1/2/(C_mρ) (plywood / steel / PP)	2.82 / 2.05 / 0.75
Relative leg mass at equal bending stiffness (steel / PP vs plywood)	2.45 × / 3.34 ×
Panel index E^1/3/ρ for the seat pan (plywood / PP / steel)	3.08 / 1.26 / 0.76
Load per leg at the 1.3 kN seat test	325 N
Selection	Plywood or steel-tube frame with a moulded polypropylene seat pan

Topic. Systematic material selection: translate, screen, rank, seek supporting information; material indices and the dependence of the exponent on the mechanical idealisation.

Key relations. Light stiff beam of free section, M = E^1/2/ρ; light strong beam, M = σ_y^2/3/ρ; light stiff panel of free thickness, M = E^1/3/ρ; light stiff tie, M = E/ρ; cost-corrected index, divide by C_mρ. On a log–log modulus–density chart each index is a straight guideline of slope equal to the reciprocal of the exponent.

Why this works. The index falls out of eliminating the free geometric variable between the constraint equation and the objective. For a beam of free section the stiffness constraint fixes EI, and with I proportional to the square of the area the area needed varies as E^−1/2; the mass, ρ times area times length, therefore varies as ρ/E^1/2, and minimising mass means maximising its reciprocal. The same elimination on a panel, whose second moment goes as the cube of thickness, gives the exponent 1/3. This is why the index is a property of the problem and not of the material, and why quoting “specific stiffness” E/ρ for everything is wrong: that is the tie index, and it applies only to a member loaded purely in tension.

Common pitfall. Using one exponent for the whole product. Reading a seat pan as a beam promotes steel above polypropylene and selects the wrong material; the fix is to state the idealisation explicitly for each element before evaluating anything. A second pitfall is stopping at the ranking — the index says nothing about moisture, creep, ultraviolet exposure or supply, and step 4 exists because the top-ranked material is regularly eliminated there.

Source. Ashby, Materials Selection in Mechanical Design, ch. 5–6 (materials selection: the basics, and case studies) and the modulus–density chart of ch. 4; Dieter & Schmidt, Engineering Design, ch. 11 (materials selection); Kalpakjian & Schmid, ch. 40 (process selection and economics).

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