This is an exercise to illustrate the effects of mesh refinement on a 1-d rod. To estimate the self-weight elongation (8) of the tapered conical rod shown in the figure. The diameter varies linearly from Do at the bottom to aDo at the top, where 0.1 < E Young's Modulus y Unit weight aD, (Dameter at ep) elongation Do (Diameter at bottom) a<0.5. Solve for L= 5m, y unit weight of steel, E= young's modulus of steel, Do=3m and a=0.3. Solve the problem at least four times using an increasing number of rod elements (nels=2, 4, 6, 8). Make appropriate assumptions about how to deal with the changing cross-sectional area and self-weight loading along the length of the rod. A plot of the dimensionless tip deflection 6E/y? vs. mumber of elements (nels) used in the discretization to show convergence on the exact solu- tions of
This is an exercise to illustrate the effects of mesh refinement on a 1-d rod. To estimate the self-weight elongation (8) of the tapered conical rod shown in the figure. The diameter varies linearly from Do at the bottom to aDo at the top, where 0.1 < E Young's Modulus y Unit weight aD, (Dameter at ep) elongation Do (Diameter at bottom) a<0.5. Solve for L= 5m, y unit weight of steel, E= young's modulus of steel, Do=3m and a=0.3. Solve the problem at least four times using an increasing number of rod elements (nels=2, 4, 6, 8). Make appropriate assumptions about how to deal with the changing cross-sectional area and self-weight loading along the length of the rod. A plot of the dimensionless tip deflection 6E/y? vs. mumber of elements (nels) used in the discretization to show convergence on the exact solu- tions of
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:This is an exercise to illustrate the effects of mesh refinement
on a 1-d rod. To estimate the self-weight elongation (8) of the
tapered conical rod shown in the figure. The diameter varies
linearly from Do at the bottom to aDo at the top, where 0.1 <
E Young's Modulus
y Unit weight
(Diameter at top)
8 clongation
D
(Diameter at bottom)
a<0.5.
Solve for L= 5m, y= unit weight of steel, E= young's modulus
of steel, Do=3m and a=0.3. Solve the problem at least four
times using an increasing number of rod elements (nels=2, 4,
6, 8). Make appropriate assumptions about how to deal with
the changing cross-sectional area and self-weight loading
along the length of the rod.
A plot of the dimensionless tip deflection SE/yL? vs. number of elements
(nels) used in the discretization to show convergence on the exact solu-
tions of
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