Elastic Limit, Breaking Stress, and Safety
Breaking stress is the maximum tensile stress sustained before fracture, while an elastic limit bounds recoverable behavior; safe design requires the working stress not to exceed the applicable limit.
Why this shows up in the exam
Crane-rope sizing · Minimum rod diameter · Checking stacked wire loads
Learn the idea
Allowable load is an allowable stress multiplied by the resisting cross-sectional area. A stronger or thicker member can carry more force, but material failure thresholds are stated as stress so geometry must be applied explicitly.
🧠 Memory hook: Limit stress times area gives limit force.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F_max = sigma_limit A — largest load at a specified stress limit
- A_min = F_required/sigma_allowable — minimum resisting area
- factor of safety = sigma_failure/sigma_working — safety ratio when specified
How to approach it
- 1Choose elastic, yield, or breaking limit as stated
- 2Find the maximum section tension
- 3Solve sigma = F/A and apply any safety factor
Common slip-ups that cost marks
- •Confusing breaking stress with breaking force
- •Ignoring the heaviest-loaded upper segment
- •Using radius where area is required
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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