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 1, Problem 38E
In the structure shown below, the temperature of element 2 is 50°C above the reference temperature. An external force of 20.000 N is applied in the x direction (horizontal direction) at node 2. Assume
a. Write down the stiffness matrices and thermal force
b. Write down the global matrix equations.
c. Solve the global equations to determine the displacement at node 2.
d. Determine the forces in each element. State whether it is tension or compression.
e. Show that force equilibrium is satisfied at node 2.
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A solid bar of length L = 4 m and diameter 200 mm is heated from 20 to 320 degrees celsius and restrained between two solid immovable walls.
Young's modulus of the material is 90 GPa and the coefficient of thermal expansion is 22 x 10-6/°C.
→Calculate the thermal strain, e, in micro-strain correct to two decimal places.
micro-strain.
Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places.
E:
σ:
MPa.
Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places:
F
MN.
L
A solid bar of length L = 2 m and diameter 50 mm is heated from 20 to 350 degrees celsius and restrained between two solid immovable walls.
L
Young's modulus of the material is 80 GPa and the coefficient of thermal expansion is 23 × 10 6/ºC.
Calculate the thermal strain, e, in micro-strain correct to two decimal places.
micro-strain.
Calculate the thermal stress, o, in megapascals (MPa) correct to two decimal places.
MPа.
Hence calculate the force exerted by the bar in meganewtons (MN) correct to two decimal places:
F:
MN.
tol
F = Fe
F= F + F
COs #
F F sin a.
# tan
Example (L):Find the two components of the force
(100 X) if: 0 = 30, 120 270° as shown in figure.
F = 100 N
F = 100 N
6%330
6 =120°
0 =270°
0 = 300
0 60
F = 100 N
ution:
Chapter 1 Solutions
Introduction To Finite Element Analysis And Design
Ch. 1 - Answer the following descriptive questions a....Ch. 1 - Calculate the displacement at node 2 and reaction...Ch. 1 - Repeat problem 2 by changing node numbers; that...Ch. 1 - Three rigid bodies, 2,3, and 4, are connected by...Ch. 1 - Three rigid bodies, 2,3, and 4, are connected by...Ch. 1 - Consider the spring-rigid body system described in...Ch. 1 - Four rigid bodies, 1, 2, 3, and 4, are connected...Ch. 1 - Determine the nodal displacements, element forces,...Ch. 1 - In the structure shown, rigid blocks are connected...Ch. 1 - The spring-mass system shown in the figure is in...
Ch. 1 - A structure is composed of two one-dimensional bar...Ch. 1 - Two rigid masses, 1 and 2, are connected by three...Ch. 1 - Use the finite element method to determine the...Ch. 1 - Consider a tapered bar of circular cross section....Ch. 1 - The stepped bar shown in the figure is subjected...Ch. 1 - Using the direct stiffness matrix method, find the...Ch. 1 - A stepped bar is clamped at one end and subjected...Ch. 1 - A stepped bar is clamped at both ends. A force of ...Ch. 1 - Repeat problem 18 for the stepped bar shown in the...Ch. 1 - The finite element equation for the uniaxial bar...Ch. 1 - The truss structure shown in the figure supports a...Ch. 1 - The properties of the two elements of a plane...Ch. 1 - For a two-dimensional truss structure as shown in...Ch. 1 - The 2D truss shown in the figure is assembled to...Ch. 1 - For a two-dimensional truss structure as shown in...Ch. 1 - The truss shown in the figure supports force Fat...Ch. 1 - Prob. 27ECh. 1 - In the finite element model of a plane truss in...Ch. 1 - Use the finite element method to solve the plane...Ch. 1 - The plane truss shown in the figure has two...Ch. 1 - Two bars are connected as shown in the figure....Ch. 1 - The truss structure shown in the figure supports...Ch. 1 - It is desired to use the finite element method to...Ch. 1 - Determine the member force and axial stress in...Ch. 1 - Determine the normal stress in each member of the...Ch. 1 - The space truss shown has four members. Determine...Ch. 1 - The uniaxial bar shown below can be modeled as a...Ch. 1 - In the structure shown below, the temperature of...Ch. 1 - Prob. 39ECh. 1 - The three-bar truss problem in figure 1.23 is...Ch. 1 - Use the finite element method to determine the...Ch. 1 - Repeat problem 41 for the new configuration with...Ch. 1 - Repeat problem 42 with an external force added to...Ch. 1 - The properties of the members of the truss in the...Ch. 1 - Repeat problem 44 for the truss on the right side...Ch. 1 - The truss shown in the figure supports the force ....Ch. 1 - The finite element method as used to solve the...Ch. 1 - Prob. 48E
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