a) A thin aluminium plate with a modulus of elasticity E=72GPa and Poisson's ratio v=0.3 is loaded in a biaxial stress state (see Figure Q.1a). A strain gauge is fixed to the plate at an angle phi =21 deg . i. If the stress sigma _(x) is 86.4MPa and the strain measurement by the gauge is 946 times 10^(-6), what is the maximum in-plane shear st solutionspile.com

Question

a) A thin aluminium plate with a modulus of elasticity

E=72GPa

and Poisson's ratio

v=0.3

is loaded in a biaxial stress state (see Figure Q.1a). A strain gauge is fixed to the plate at an angle

\phi =21\deg

. i. If the stress

\sigma _(x)

is

86.4MPa

and the strain measurement by the gauge is

946\times 10^(-6)

, what is the maximum in-plane shear stress

(\tau _(max))_(xy)

and the maximum in-plane shear strain

(\gamma _(max))_(xy)

in the xy plane? ii. What is the maximum shear strain

(\gamma _(max))_(xz)

in the

xz

plane and the maximum shear strain

(\gamma _(max))_(yz)

in the

yz

plane? Figure Q.1a

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