A one-inch-diameter manganese bronze test specimen was subjected to an axial tensile load, and the following data were obtained. Gauge length 10 inches Final gauge length 12.25 inches Load at proportional limit 18,500# Elongation at proportional limit 0.016 inch Maximum load 55,000# Load at rupture

Question

A one-inch-diameter manganese bronze test specimen was subjected to an axial tensile load, and the following data were obtained.

Gauge length 10 inches

Final gauge length 12.25 inches

Load at proportional limit 18,500#

Elongation at proportional limit 0.016 inch

Maximum load 55,000#

Load at rupture 42,000#

Diameter at rupture 0.845 inch

Find the following:
a. Proportional limit.
b. Modulus of elasticity.
c. Ultimate strength.
d. Percentage elongation.
e. Percentage reduction in area.
f. Indicated rupture strength.
g. True rupture strength.

Accepted Answer

[latex]A_{orig.} =0.785 \space in.^{2} \space ; A_{rupture} =0.560 \space in.^{2}[/latex]

a. [latex]f_{prop.}=\frac{18,500\# }{0.785 \space in.^{2}} =23,567\space psi[/latex]

[latex]\varepsilon_{prop.}=\frac{0.016 \space in.^{2} }{10 \space in.}=0.0016 \space in./in.[/latex]

b. [latex]E=\frac{\Delta f}{\Delta \varepsilon} =\frac{f_{prop.}}{\varepsilon_{prop.}} [/latex]

[latex]E= \frac{ 23,567 \space \# /in.^{2}}{0.0016 \space in./in.} = 14,729,375 \space psi[/latex]

c. [latex]f_{ult}=\frac{max. load}{A_{orig.}} =\frac{55,000\# }{0.785 \space in.^{2}} =70,100 \space psi[/latex]

d. [latex]\% [/latex] elongation [latex]=\frac{2.25^{\prime \prime } }{10^{\prime \prime } } imes 100 \%=22.5\% [/latex]

e. [latex]\% [/latex] reduction of area [latex]=\frac{0.785 \space in.^{2} - 0.560 \space in.^{2}}{0.785 \space in.^{2}} imes 100 \%=28.7 \%[/latex]

f. [latex]f_{rupture}=\frac{load \space at \space rupture}{A_{original}} =53,503 \space psi[/latex] (indicated)

g. [latex]f_{rupture}=\frac{load \space at \space rupture}{A_{rupture}} =75,000 \space psi[/latex] (true)

Question 5.11: A one-inch-diameter manganese bronze test specimen was subje...

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