Twenty minutes or less.

5-minute version

Two big blocks. One sentence each.

• Stress-strain curve — identify yield / UTS / fracture; toughness is the whole area, resilience is the elastic triangle $\frac{1}{2}{\sigma }_y{ϵ}_y$.
• Shear — cut the body, identify the shear plane, $\tau =V/A$; for design ${\tau }_{allow}={\tau }_{fail}/SF$; for stiffness $G=\tau /\gamma =E/[2(1+\nu )]$.

Open the cheatsheet quiz, do 3 easy questions, close it. You’re prepped.

20-minute prep plan

Time	Action
0-5 min	Skim the cheatsheet tables — focus on the axial-vs-shear analogy.
5-10 min	Re-do Example 3 (punched disk sizing) and Example 6 (polymer block $G$) from the lecture reconstruction, covering the worked answer.
10-15 min	Take the cheatsheet quiz. Don’t worry about the score.
15-20 min	Read the matching “common mistakes” + worked example in the in-depth note.

What to revise first

Most students slip on two specific things this week:

1. Counting cut planes wrong. Single vs double shear changes $V$ by a factor of 2. Always start with the FBD of the fastener.
2. Picking the wrong shear area. For a disk punched through a hole, the shear surface is the cylindrical edge $\pi dt$, not the disk face $\pi d^2/4$. Same for an embedded rod ($\pi d\ell$).

Key formulas

$${\tau }_{avg}=\frac{V}{A}{\tau }_{allow}=\frac{{\tau }_{fail}}{SF}{A}_{\min }=\frac{V}{{\tau }_{allow}}$$ $$\gamma =\frac{\pi }{2}-{\theta }^{\prime }\text{(small: }\gamma \approx \delta /h\text{)}\tau =G\gamma G=\frac{E}{2(1+\nu )}$$ $$u_r=\frac{1}{2}{\sigma }_y{ϵ}_y\text{Toughness}={\int }_0^{{ϵ}_f}\sigma dϵ$$

Likely workshop tasks

Note: there is no Tutorial 12 PDF — slide 23 of the lecture deck directs students to Mastering Physics (Shear Stress and Strain, Material Properties) and to the workshop class for Portfolio 11. So the workshop session itself will likely be Portfolio 11 work, not a separate tutorial problem set.

Expect tasks of these shapes (based on the lecture worked examples):

Task type	What the setup usually looks like
Stress-strain curve labelling	Sketch a curve, mark ${\sigma }_y$, ${\sigma }_{UTS}$, ${\sigma }_{failure}$, the resilience triangle, and the toughness area
Resilience / toughness calculation	Compute $u_r=\frac{1}{2}{\sigma }_y{ϵ}_y$ or area under a piecewise curve
Strain hardening	Given new ${\sigma }_y$ and original $E$, find new ${ϵ}_y$ and new $u_r$
Direct shear stress	Glued / bolted / pinned joint — compute $V$, then $\tau$, identify single vs double
Connection sizing	Find min thickness, area, or embedment length using ${\tau }_{allow}$
Shear strain	Compute ${\gamma }_{xy}$ at a corner from a deformed-rectangle sketch
Shear modulus	Block test ($\delta$, $h$, $P$, area) $\to$ $G$; or use $G=E/[2(1+\nu )]$

Mistakes to avoid

• Mixing up ${\tau }_{allow}$ and ${\tau }_{fail}$ — always divide by $SF$ in design.
• Using degrees instead of radians for $\gamma$ in $G=\tau /\gamma$ or in $\sin \gamma \approx \gamma$.
• Calling the disk face $\pi d^2/4$ the shear area (it’s the cylindrical edge $\pi dt$).
• Mistaking a normal strain (compression of a side) for a shear strain at a corner.
• Forgetting that $E$ doesn’t change after strain hardening — only ${\sigma }_y$ does.

Mini self-test

Try these without notes. Five minutes total.

1. A pin in double shear must carry $F=16$ kN. Allowable shear stress ${\tau }_{allow}=80$ MPa. What is the minimum pin cross-sectional area $A$?
2. A polymer block 200 mm tall has its top displaced 1 mm sideways. Given $\tau =40$ kPa on the shear surface, find $G$.
3. Aluminium has $E=70$ GPa, $\nu =0.33$. Predict $G$ and compare to the handbook value $G=25$ GPa.

Answers:

Question	Answer
1	$V=F/2=8$ kN per plane. $A=V/{\tau }_{allow}=8000/(80\times 10^6)=1.0\times 10^{-4}$ m² $=100$ mm²
2	$\gamma \approx 1/200=5\times 10^{-3}$ rad. $G=\tau /\gamma =40,000/0.005=8$ MPa
3	$G=70/[2(1+0.33)]=70/2.66\approx 26.3$ GPa; handbook $25$ GPa — within $\sim 5\%$

Done checklist

• Read the cheatsheet tables.
• Two worked examples from the lecture reconstruction, copied out longhand.
• Cheatsheet quiz attempted.
• Mini self-test attempted.
• Materials ready for Portfolio 11 in the workshop.

That’s it. Close the laptop.

Source files used

• EGD102-Physics/Lecture12_CTP1.pdf