Strain gage P (a) dz - L3- U3- (b)
A circular aluminum tube of length
L = 600 mm is loaded in compression by forces P
(see figure). The outside and inside diameters are
d2 = 75 mm and d1 = 63 mm, respectively. A strain
gage is placed on the outside of the tube to measure
normal strains in the longitudinal direction. Assume
that E = 73 GPa and Poisson’s ratio is n = 0.33.
(a) If the compressive stress in the tube is 57 MPa,
what is the load P?
(b) If the measured strain is ε =781x10 -6 , what is
the shortening δ of the tube? What is the percent change in its cross-sectional area? What is the
volume change of the tube?
(c) If the tube has a constant outer diameter
of d2 = 75 mm along its entire length L but
now has increased inner diameter d3 with a normal
stress of 70 MPa over the middle third (see
figure, part b) while the rest of the tube remains at
normal stress of 57 MPa, what is the diameter d3?
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