A circular aluminum tube of length L=500 mm is loaded in compression by forces P (see figure (a)). The outside and inside diameters are d₂ = 82 mm and d₁70 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 v=0.33. Assume that the material behaves linearly elastically. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) Strain gage d₂ 1d₁ L (a) @ (a) If the compressive stress in the tube is 51 MPa, what is the load P? (Enter the magnitude in N.) N (b) If the measured strain is 699 x 10-6, what is the shortening d of the tube? (Enter the magnitude in mm.) What is the percent change in its cross-sectional area? (Include the sign of the value in your answer.) % What is the volume change of the tube (in mm³)? (Include the sign of the value in your answers) mm² (c) If the tube has a constant outer diameter of d₂82 mm along its entire length & but now has increased inner diameter da with a normal stress of 64 MPa over the middle third (see figure (b)) while the rest of the tube remains at normal stress of 51 MPa, what is the diameter d₂ (in mm)? _P 4₂ d₂ d₁ L/3 @ + (b) f 1/3
A circular aluminum tube of length L=500 mm is loaded in compression by forces P (see figure (a)). The outside and inside diameters are d₂ = 82 mm and d₁70 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 v=0.33. Assume that the material behaves linearly elastically. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) Strain gage d₂ 1d₁ L (a) @ (a) If the compressive stress in the tube is 51 MPa, what is the load P? (Enter the magnitude in N.) N (b) If the measured strain is 699 x 10-6, what is the shortening d of the tube? (Enter the magnitude in mm.) What is the percent change in its cross-sectional area? (Include the sign of the value in your answer.) % What is the volume change of the tube (in mm³)? (Include the sign of the value in your answers) mm² (c) If the tube has a constant outer diameter of d₂82 mm along its entire length & but now has increased inner diameter da with a normal stress of 64 MPa over the middle third (see figure (b)) while the rest of the tube remains at normal stress of 51 MPa, what is the diameter d₂ (in mm)? _P 4₂ d₂ d₁ L/3 @ + (b) f 1/3
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Please answer parts A to C with legible and complete solutions.
Transcribed Image Text:A circular aluminum tube of length L = 500 mm is loaded in compression by forces P (see figure (a)). The outside and inside diameters are d₂ = 82 mm and d₁ = 70 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
v = 0.33. Assume that the material behaves linearly elastically. (Due to the nature of this problem, do not use rounded intermediate values in your calculations including answers submitted in WebAssign.)
Strain gage
P
d₂ 1d₁
L
(a)
(a) If the compressive stress in the tube is 51 MPa, what is the load P? (Enter the magnitude in N.)
N
(b) If the measured strain is ε = 699 x 10-6, what is the shortening d of the tube? (Enter the magnitude in mm.)
mm
What is the percent change in its cross-sectional area? (Include the sign of the value in your answer.)
%
What is the volume change of the tube (in mm³)? (Include the sign of the value in your answer.)
mm³
(c) If the tube has a constant outer diameter of d₂ = 82 mm along its entire length L but now has increased inner diameter d3 with a normal stress of 64 MPa over the middle third (see figure (b)) while the rest of the tube remains at normal stress of 51 MPa, what is the diameter d3 (in mm)?
îdz 1
d₂
1d₁
-L/3
+
-L/3-
(b)
+
-L/3
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