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Elasticity

December 8, 2016
Published By : Pratik Kataria
Categorised in:

(1) Stress = $F/A$

(2) i. Tensile strain: $E/A$ = ${Mg}/{πr^2}$
ii. Volume = ${A dP}/{A}$ = $dP$

iii. Shearing: $F/A$ (tangential)

(3) Strain: ${\text"Change in dimension"}/{\text"Original dimension"}$

(4) i. Longitudinal: $l/L$
ii. Volume: – ${dv}/{V}$

iii. Shearing: tanθ

(5) Elastic constants:

i. Young’s Modulus: $Y = {FL}/{Al}$

ii. Bulk Modulus: $k = V {dP}/{dV}$

iii. Modulus of Rigidity: $η = F/{A tanθ}$ = ${F}/{Aθ}$

(6) Lateral Strain: $d/D$

(7) Poisson’s Ratio: ${\text"lateral strain"}/{\text"longitudinal strain"}$ = ${dl}/{DL}$

(8) $W = 1/2 \text"load x extension"$ = $1/2 Fl$


(9)
Strain Energy/ Unit volume = $U = 1/2 F/A l/L$ i.e. 1/2 (stress) (strain)
$U = 1/2 Y (strain)^2$ = $1/2 {(stress)^2}/{Y}$

(10) Apparant weight = $V g [ρ_b – {a ρ_l}/{100}]$

${\text"Apparant weight"}/{\text"Original weight"}$ = ${ρ_b – {ρ_l}/{100}}/{ρ_b}$ = ${V_g}/{V ρ_b g}$