Question

For a state of pure shear stress acting on a point shown in the figure, which of the following equations represents the corresponding transformation equation of a shear stress (Tx y)? (Note: use the equations of stress transformation and principal stresses) y Tyx Try 0 x Txy Tyx A) (1 + cos26) B) sin20 C) Txy sin20 Dexy cos20 ОА OB ОС OD

Answer 1

Ques of a vertical plane of given Surface on Troms formation equation shear stuess ie, shear stress at any other plane melined to go with the As we all know, stress is second order tensor first convent it into force by multiply it with area in order to take component of stress in a & direction. Trey shear try using try = Type Condition słyn B hence, we cry ģ A To find try using try = lyn condition pure Cos AB Base Sino= Try (ABYL) COSE try (AB**) o AC (thypotenuse Be perpendiculars Ac (thypotenuse ts thickness of the free Surface (en to the paper Tym. (BC*t) >X tyx.(BC *+) sino Trig (AC *t)

By equating, we get Enlye (AC **) + Тух ( всък) fm в Try (AB*X) COSO Tryl (AC) = Try (AB cose) - Tyn (BC 8m 8) Све Enly = Try (AB tryl Tyr (el IBC Ismo AC g? 0 Try costo Try - * («? 8- sin+ 6) аѕ wе аl Kmous, (са? Ө– sfw19 = cus 0) Try = try &o, csgo

Hence, option (D) is correct, i.e. corresponding transformation equation of shear stress is given by:

$\boldsymbol{\tau _{x'y'}= \tau _{xy}cos2\theta}$