Week 11 Study Guide — Normal Stress and Strain + Mechanical Properties

Directly supported by notes

These sub-topics are explicitly covered in the lecture slides and tutorial PDFs:

Topic	Direct source coverage
Axial stress $\sigma =P/A$	Slides 4–7 + Tutorial recap 3 + Exercises 1, 4, 5
Axial strain $\epsilon =\Delta L/L_0$	Slides 8–9 + Tutorial recap 4 + Exercises 1, 6
Hooke’s law / Young’s modulus	Slides 11–12 + Tutorial recap 5–6 + Exercise 2
Engineering vs. true stress / strain	Slide 13
Stress–strain diagram (yield, UTS, fracture)	Slide 14 + Tutorial recap 9–10 + Exercise 3
0.2% offset yield method	Slide 16 + Tutorial recap 11 + Exercise 3
Ductility (%EL, %AR)	Slide 15
Factor of safety + allowable stress	Slides 18–19 + Tutorial recap 14 + Exercise 5
Cable car worked example	Slide 20 (Example 5)
Poisson’s ratio	Slides 21–23 + Tutorial recap 16–17 + Exercise 6

The workshop expects you to be able to:

1. Free-body a joint, solve for the axial force, then compute $\sigma =P/A$.
2. Find $\epsilon =\Delta L/L_0$ and read the resulting $L_f$.
3. Compute $E$ from a stress/strain pair or read it as a slope.
4. Read yield, UTS, and the 0.2% offset yield from a plotted $\sigma$–$\epsilon$ curve.
5. Apply a safety factor to size a member or count passengers.
6. Use Poisson’s ratio to predict lateral deformation and cross-sectional change.

Strongly inferred from workshop materials

The lecture also frames (in this order):

• Structural actions (slide 3) — tension, compression, shear, bending, torsion, loading combinations. EGD102 limits itself to axial + shear.
• A worked free-body / equilibrium step in Example 2 (the two-rod lamp).
• The “Force is ALWAYS in newtons” reminder at the top of every unit-sensitive calculation.
• Rule-of-thumb $SF$ ranges by industry (slide 19).
• Typical Poisson’s ratios for common materials (slide 22).

Possible lecture content (not in notes)

May appear in the lecture but is not in the workshop:

• Hooke’s-law assumptions (small strain, homogeneous + isotropic material).
• Resilience and toughness as areas under the $\sigma$–$\epsilon$ curve.
• True stress–strain conversion formulas ${\sigma }_T={\sigma }_{\text{eng}}(1+{\epsilon }_{\text{eng}})$.
• Hardness measures (Brinell, Rockwell, Vickers) as proxies for strength.

Gaps requiring official source check

• Whether the final exam asks for engineering vs. true numerical comparisons or just the qualitative distinction.
• Whether the 0.2% offset is examined symbolically (read off a curve) or numerically (from given gradient + slope).
• Solutions PDF for Tutorial 11 is not provided — exercise answers below are the expected forms but should be cross-checked against the official sheet.

Worked examples

Three notes cover the topic at different depths:

• Lecture summary — slide-by-slide reconstruction with worked Examples 1, 2, 3, 5 and Example 5 continued.
• Cheatsheet — every formula and recipe on one page. Includes the full quiz.
• In-depth analysis — why each formula exists, the physical picture behind necking and Poisson’s ratio, and a full exam-style worked example for the aluminium rod (Exercise 6).

Common mistakes

• Unit slip: mixing kN with mm² gives GPa, not MPa. Convert force to N first.
• Steel $E$ in MPa instead of GPa — off by 1000.
• 0.5% = 0.005, not $0.5$.
• Missing minus sign on Poisson’s ratio: definition has it.
• Rounding people up rather than down when sizing for ${\sigma }_{\text{allow}}$.
• Confusing yield, UTS, and fracture stress — three distinct points on the curve.
• Forgetting trig sign conventions at joints (is the 3 the vertical leg of the 3-4-5?).

Practice questions

Pick from Tutorial 11. Recommended pass:

• Stress + strain: Exercises 1, 2.
• Stress–strain diagram + offset yield: Exercise 3.
• Multi-member free body: Exercise 4 (two-wire bilinear curve).
• Factor of safety / sizing: Exercise 5 (flowerpot).
• Poisson’s ratio: Exercise 6 (aluminium rod) — fully worked in the in-depth note.

Quick answer-form hints:

Exercise	Quantity asked	Hint
1	$\Delta \sigma$, $\epsilon$	$\Delta P=6.5\text{kN}$; $A=\pi d^2/4$; $\epsilon =\Delta L/L_0$
2	$E$	$\sigma =P/A$, $\epsilon =\Delta L/L_0$, then $E=\sigma /\epsilon$
3	$E$, ${\sigma }_{y,\text{offset}}$	Slope of linear part; 0.2% offset line parallel to slope
4	$\Delta L_{AB}$, $\Delta L_{BC}$	Joint equilibrium $\to F$; $\sigma$; pick branch of bilinear curve; $\Delta L=\epsilon L_0$
5	$d_{\min }$	${\sigma }_{\text{allow}}=350/2.5=140\text{MPa}$; $A=F/{\sigma }_{\text{allow}}$; $d=\sqrt{4A/\pi }$
6	$\Delta L$, $\Delta d$	$\sigma =P/A$, ${\epsilon }_{\text{long}}=\sigma /E$, $\Delta L={\epsilon }_{\text{long}}{L}_0$; ${\epsilon }_{\text{lat}}=-\nu {\epsilon }_{\text{long}}$; $\Delta d={\epsilon }_{\text{lat}}{d}_0$

Assessment relevance

• This week feeds Portfolio 10/11 directly.
• Final exam: high probability of a multi-part tensile-test or cable-loading question that walks through stress → strain → modulus → safety factor → diameter change in sequence.
• The Poisson’s-ratio diameter-change step is a common “show all working” item.

Confidence report

• Directly supported: every formula, slide-cited example, and tutorial exercise listed above.
• Inferred: the lecture’s narrative ordering and the framing of structural actions.
• Gap: solutions to Tutorial 11 (no solutions PDF supplied); coverage depth of true-stress numerical conversion.

Source files used

• EGD102-Physics/Lecture11_CTP1.pdf
• EGD102-Physics/Tutorial 11.pdf