Geometry-Coupled Elastic Equilibrium
In statically balanced elastic assemblies, vector equilibrium determines member forces and geometric compatibility relates displacement to member extension, after which each member obeys its constitutive law.
Why this shows up in the exam
Sagging wires with a central load · Inclined two-wire supports · Multi-member elastic assemblies
Learn the idea
When wires are angled or displaced, force balance and geometric compatibility must be solved together. A small sag changes wire direction and length; the tensions must support the load while their elastic extensions must match the geometry of the displaced shape.
🧠 Memory hook: Balance sets tension; geometry sets extension; elasticity connects them.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum vector F = 0 — equilibrium condition for the displaced joint or body
- Delta L approximately y²/(2a) — small-sag extension of one half-span of horizontal projection a
- Delta L = TL/(AY) — constitutive relation closing the force-geometry system
How to approach it
- 1Draw the displaced geometry and free-body diagram
- 2Relate displacement to each member's length change
- 3Combine equilibrium with Delta L = TL/(AY)
Common slip-ups that cost marks
- •Using the vertical load as the tension in an inclined wire
- •Linearizing geometry before identifying the small parameter
- •Solving force balance without compatibility
🌟 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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