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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Chapter 1, Problem 34E
Determine the member force and axial stress in each member of the truss shown in the figure using a commercial finite element analysis program. Assume that Young’s modulus is psi and all cross sections are circular with a diameter of 2 in. Compare the results with the exact solutions that are obtained from the free-body diagram.
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Problem 1
Calculate the displacements at nodes 1 and 2, the reactions at nodes 1 and 3, as well as the
axial strains and stresses in the three bars of the planar truss shown below. Use analytical (hand)
finite element formulation. Known are P₁ = 500 N, P₂= 1000 N. /= 0.05 m, the constant cross-
sectional area of all bars A = 0.0001 m², Young's modulus E= 2 x 10¹¹ N/m², and Poisson's ratio
v=0.3.
V
P₂
R
21
Problem 2
Remove the loads in Problem 1 and calculate the natural frequencies of the truss for a mass
density p= 7800 kg/m³ using analytical calculation.
Rod(1), rod (2) where 1, 2 rod numbers not the graded question
The bars of the truss, shown in the Figure, are made of
aluminium (yield strength-410 MPa), each with a cross-
sectional area of 30 mm². After applying the shown forces,
members EC and ED failed to support the applied loads. Do the
following:
5 m
MUN
3.5 m
BO
5 m
5 kN
9 kN
25%
DE
5 m
a)Calculate the normal stress in members EC and
ED and indicate whether these members are in tension or
compression.
b) As a potential solution, determine which member,
EC or ED, should be reinforced to prevent failure. Provide
a justification for your choice.
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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