Introduction To Finite Element Analysis And Design
2nd Edition
ISBN: 9781119078722
Author: Kim, Nam H., Sankar, Bhavani V., KUMAR, Ashok V., Author.
Publisher: John Wiley & Sons,
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Textbook Question
Chapter 2, Problem 25E
Consider the tapered bar in problem 21. Use the Rayleigh-Ritz method to solve the same problem. Assume the displacement in the form of
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A 50-mm diameter cylinder is made of a brass for which the stress-strain diagram is as shown. The angle of twist is 5° in a length L =
845 mm. The three points on the nonlinear stress-strain diagram used are (0, 0), (0.0015, 55 MPa), and (0.003, 80 MPa). By fitting the
polynomial T = A + By+ Cy2 through these points, the following approximate relation has been obtained.
T= 46.7 x 10y-6.67 × 10122
Determine the magnitude T of torque applied to the shaft using this relation and the two equations given below.
P4
Y =
Ty = 2π] ρ?τὰρ
7 (MPa)
100
80
60
40
20
0
0,001 0.002 0.003 Y
d = 50 mm
"K
The magnitude T of torque applied to the shaft is
KN-m.
A²
A 50-mm diameter cylinder is made of a brass for which the stress-strain diagram is as shown. The angle of twist is 5° in a length L =
725 mm. The three points on the nonlinear stress-strain diagram used are (0, 0), (0.0015, 55 MPa), and (0.003, 80 MPa). By fitting the
polynomial T = A + By + Cy² through these points, the following approximate relation has been obtained.
T= 46.7 × 10%y-6.67 × 1012/2
Determine the magnitude Tof torque applied to the shaft using this relation and the two equations given below.
Y
Ty
-
ρφ
T (MPa)
2π ζ ρ?τὰρ
100
80
60
40
20
0
0.001 0.002 0.003 Y
d = 50 mm
L
The magnitude T of torque applied to the shaft is
kN.m.
Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th
axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme
at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 =
19kN.
a
W1
L/2
W2
Multiple Choice Answers
Multiple Choice Answer: Axial force at point A (kN, tension positive):
a. 3.31
b. 31.97
c. 37.33
d. 31
Multiple Choice Answer: Displacement at point B (mm, positive to right):
a. 0.0061
b. 0.0395
c. 0.0193
d. 0.0261
Axial force at point A (kN, tension positive):
Displacement at point B (mm, positive to right):
L/2
P1
P2
(type in your multiple choice answer, e.g. a, b, c or d)
(type in your multiple choice answer, e.g. a, b, c or d)
Chapter 2 Solutions
Introduction To Finite Element Analysis And Design
Ch. 2 - Answer the following descriptive questions.
a....Ch. 2 - Use the Galerkin method to solve the following...Ch. 2 - Solve the differential equation in problem 2 using...Ch. 2 - Prob. 4ECh. 2 - Using the Galerkin method, solve the following...Ch. 2 - A one-dimensional heat conduction problem can be...Ch. 2 - Solve the one-dimensional heat conduction problem...Ch. 2 - Prob. 8ECh. 2 - Solve the differential equation in problem 8 for...Ch. 2 - Prob. 10E
Ch. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Using the Galerkin method, calculate the...Ch. 2 - The boundary-value problem for a clamped-clamped...Ch. 2 - The boundary-value problem for a cantilevered beam...Ch. 2 - Prob. 16ECh. 2 - Consider a finite element with three nodes, as...Ch. 2 - A vertical rod of elastic material is fixed at...Ch. 2 - A bar in the figure is under the uniformly...Ch. 2 - Prob. 20ECh. 2 - A tapered bar with circular cross section is fixed...Ch. 2 - The stepped bar shown in the figure is subjected...Ch. 2 - A bar shown in the figure is modeled using three...Ch. 2 - Consider the tapered bar in problem 17. Use the...Ch. 2 - Consider the tapered bar in problem 21. Use the...Ch. 2 - Consider the uniform bar in the figure. Axial load...Ch. 2 - Determine shape functions of a bar element shown...Ch. 2 - Consider a finite element with three nodes, as...
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- Solvearrow_forwardThe dimensions are of the graph are d1 = 7 cm , L1 = 6 m , d2 = 4.2 cm , and L2 = 5 m with applied loads F1 = 130 kN and F2 = 60 kN . The modulus of elasticity is E = 80 GPa . Use the following steps to find the deflection at point D. Point B is halfway between points A and C. What is the reaction force at A? Let a positive reaction force be to the right.arrow_forwardb(x) is a (nonzero) constant along the entire length of the bar. A, E -- constant L b- constant » b(x) d a. Solve for R(x) as a piecewise function of x b. Solve for o(x) c. Solve for ɛ(x) d. Solve for u(x) e. Plot R(x) and u(x) (by hand is fine) on two separate plots arranged vertically so that the x-axes line up. Label values on the graph.arrow_forward
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