Shear Modulus and Shear Deformation
For small simple shear, shear modulus G is tangential stress divided by shear strain, with shear strain approximately lateral displacement divided by the perpendicular thickness.
Why this shows up in the exam
Sheared slabs and riveted blocks · Torsional material characterization · Comparing sideways deformation
Learn the idea
Shear modulus relates tangential stress to angular or lateral shear strain. Pushing the top of a fixed slab sideways turns a rectangle into a slight parallelogram; thickness sets how a given sideways shift becomes an angle.
🧠 Memory hook: Side force over face area, divided by sideways shift over height.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- G = (F/A)/gamma — definition of shear modulus
- gamma approximately theta approximately Delta x/h — small-angle shear strain
- Delta x = Fh/(AG) — top-face displacement of a uniformly sheared slab
How to approach it
- 1Identify the tangential force and loaded face
- 2Find the perpendicular separation of faces
- 3Apply small-angle shear strain and check dimensions
Common slip-ups that cost marks
- •Using the wrong loaded face area
- •Confusing shear angle with rigid-body rotation
- •Using length parallel to displacement as the thickness
🌟 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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