A 6-mm-thick rectangular alloy bar is subjected to a tensile load P by pins at A and B as shown in Figure P3.4/5. The width of the bar is w = 30 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: εx = 900 με and εy = −275 με.

Question

A 6-mm-thick rectangular alloy bar is subjected to a tensile load P by pins at A and B as shown in Figure P3.4/5. The width of the bar is w = 30 mm. Strain gages bonded to the specimen measure the following strains in the longitudinal (x) and transverse (y) directions: [latex]\varepsilon_{x}=900 \mu \varepsilon ext { and } \varepsilon_{y}=-275 \mu \varepsilon[/latex].
(a) Determine Poisson’s ratio for this specimen.
(b) If the measured strains were produced by an axial load of P = 19 kN, what is the modulus of elasticity for this specimen?

Accepted Answer

(a) Poisson’s ratio for this specimen is

[latex]v=-\frac{\varepsilon_{ ext {lat }}}{\varepsilon_{ ext {long }}}=-\frac{\varepsilon_{y}}{\varepsilon_{x}}=-\frac{-275 \mu \varepsilon}{900 \mu \varepsilon}=0.306[/latex]

(b) The bar cross-sectional area is

[latex]A=(30 mm )(6 mm )=180 mm ^{2}[/latex]

and so the normal stress for an axial load of P = 19 kN is

[latex]\sigma=\frac{(19 kN )(1,000 N / kN )}{180 mm ^{2}}=105.556 MPa[/latex]

The modulus of elasticity is thus

[latex]E=\frac{\sigma}{\varepsilon_{ ext {long }}}=\frac{105.556 MPa }{(900 \mu \varepsilon)\left(\frac{1 mm / mm }{1,000,000 \mu \varepsilon} ight)}=117,284.0 MPa =117.3 GPa[/latex]

Question 3.5 : A 6-mm-thick rectangular alloy bar is subjected to a tensile...

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