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 13E
Use the finite element method to determine the axial force P in each portion, AB and BC, of the uniaxial bar. What are the support reactions? Assume:
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Consider a rigid rod that is subjected to two external forces and is fixed to the wall at A. The following figure displays the rod's free body diagram. Answer the following questions using the provided FBD.
2.5 -1
1
3.5
The support reaction at A along x-axis (A) is
The support reaction at A along y-axis (Ay) is
The support reaction at A along z-axis (A.) is
The Moment reaction at support A about x-axis (Ma) is
-1
n
1 0
-2.5 2.5
-1 -3.5
5.5 -5.5 -0.5 0.5
A₂
Mx4
Z
M₂
My
KN
KN
KN
3m
KN.m
1m
1 KN
2m
2.5 KN
6. Three wires are used to support the 150-lb force. The wires AB and AC are made of steel, and wire
AD is made of copper. Assume that the three wires have constant cross-sectional area A = 0.0123 in?.
For steel wire, a = 8 x 10 in/ (in°F ) and E = 29000 ksi and for copper wire, a = 9.6 x 10 in/ (in°F ) and E
= 17000 ksi. Calculate the axial force exerted by the three wires if the temperature is raised by 80°F.
Answer: Pu= 10 Ib, Pu= 136 Ib
40 in.
60 in.
45°.
-45°
60 in.
V150 Ib
The steel box wrench (E=29,000ksi, v=0.32) is
loaded with a 40-lb horizontal force and a 25-lb
vertical force. Find the following for an element
located at point B on Section a-a:
24 in.
1. The non-vanishing resultant internal moments
on section a-a are which of the following?
4 in.
a. (160 i- 600 j+960 k)in · Ib
b. (-160 i+600 j+960 k ) in · lb
c. (-960 i+160 j+600 k)in - lb
d. (-960 i -160 ј-600 k)in-lb
a
e. none of the above
2. The normal and shear force components on
section a-a are:
a. V, = 65lb;V, = 40lb; N¸ = 25lb
b. V, = 0;V, =40lb; N, = 25lb
c. V, = 64;V, = 25lb; N, = 40lb
d. V, =0;V, =-40lb; N¸ = -25lb
e. none of the above
3. The non-vanishing stress components at point B are:
0̟ =1.60; t =-4.89ksi;
а.
0, =-4.89; 7 =3.60ksi;
0, = 2.50ksi; T,
d. o, = 4.91ksi; t =-4.89ksi;
b.
с.
=-4.89ksi;
е.
none of the above
4. The principal stresses at point B from most tensile to most compressive are:
O1,02,0; =4.16,–0.8,–5.76
b. o,,0,,0, =5.76,0,–4.16
а.
O1,02,0; =1.9,-2.45,-6.8
с.
d.…
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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