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.
A rectangular piece of wood, 50 mm x 100 mm in cross-section is used as acompression block as shown in the figure. Determine the maximum axial load P whichcan be safely applied to the block if the compressive stress in the wood is limited to 20MPa.
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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