CE 463 Structural Analysis 2
Partial Answers to 2009 Final Exam
QUESTION 2:
(a) From the beak to ground one worm-bar element is enough.
Smaller elements inside the ground, especially near G, to capture high force gradient.
May increase in size as end E is
3
.
The Direct
Stiness Method:
Assembly and Solution
31
Chapter 3: THE DIRECT STIFFNESS METHOD: ASSEMBLY AND SOLUTION
32
3.1 INTRODUCTION
Chapter 2 explained the breakdown of a truss structure into components called members or elements.
Upon deriving the
4.3. The Plane Stress Problem
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35
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38
39
N is called the shape fcn matrix,
2 by 2n (n = # of nodes)
40
B has order 3 by 2n
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CE 463 Structural Analysis 2
Solution to Problem Assignment #01
Monday, January 14, 2010
Question 1:
Solution:
Question 2:
CE 463
Page 2
Assignement # 01
Solution:
Question 3:
Solution:
The principal stresses correspond to the eigenvalues of the stress te
4.4. The Linear Plane Stress Triangle
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4.4. The Linear Plane Stress Triangle
44
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4.4. The Linear Plane Stress Triangle
45
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4.4. The Linear Plane Stress Triangle
46
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4.4. The Linear Plane Stress Triangle
47
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4.4. The Linear Plane Stress Triangle
48
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Chapter Two
Deflections : Energy Approach
2.1 Introduction
Energy is stored in a body due to strain caused by applied loads. This energy
is called strain energy. Within elastic limits, strain energy is recoverable. Strain
energy can have the following fou
18
.
Shape Function
Magic
181
182
Chapter 18: SHAPE FUNCTION MAGIC
18.1 REQUIREMENTS
This Chapter explains, through a series of examples, how two-dimensional isoparametric shape
functions can be directly constructed by geometric considerations. The isopar
17
.
Isoparametric
Quadrilaterals
171
Chapter 17: ISOPARAMETRIC QUADRILATERALS
172
17.1 INTRODUCTION
In this Chapter the isoparametric representation of element geometry and shape functions discussed
in Chapter 16 is used for the construction of quadrilat
16
.
The Isoparametric
Representation
161
162
Chapter 16: THE ISOPARAMETRIC REPRESENTATION
16.1 INTRODUCTION
The technique used in Chapter 15 for the formulation of the linear triangle can be formally extended
to construct quadrilateral elements as well a
15
.
The Linear Plane
Stress Triangle
151
Section 15: THE LINEAR PLANE STRESS TRIANGLE
152
15.1 INTRODUCTION
This Chapter presents the element equations of a three-node triangle with assumed linear displacements for the plane stress problem formulated in
14
.
The Plane Stress
Problem
141
Chapter 14: THE PLANE STRESS PROBLEM
142
14.1 INTRODUCTION
We now pass to the variational formulation of two-dimensional continuum finite elements. The
problem of plane stress will serve as the vehicle for illustrating su
12
.
Variational
Formulation of
Bar Element
121
Chapter 12: VARIATIONAL FORMULATION OF BAR ELEMENT
122
12.1 A NEW BEGINNING
This Chapter begins Part II of the course. This Part focuses on the construction of structural finite
elements using a variational
13
.
Variational
Formulation of
Plane Beam Element
131
Chapter 13: VARIATIONAL FORMULATION OF PLANE BEAM ELEMENT
132
13.1 INTRODUCTION
The previous Chapter introduced the TPE-based variational formulation of finite elements, which
was illustrated for the
2
.
The Direct
Stiness Method:
Breakdown
21
Chapter 2: THE DIRECT STIFFNESS METHOD: BREAKDOWN
22
This Chapter begins the exposition of the Direct Stiffness Method (DSM) of structural analysis.
The DSM is by far the most common implementation of the Finite
CE 463 Structural Analysis 2
Solution to Problem Assignment #9
April 8, 2011
PROBLEM 1 Solution:
CE 463
Page 2
Assignement # 9 Solution
For the building shown in fig. 4.6, the mass and stiffness matrices are given by:
2
CE 463
Page 3
Assignement # 9 Solut
CE 463 Advanced Structural Analysis
Solution to Problem Assignment #7
Due: Wednesday, March 23, 2007
PROBLEM 1 Solution:
PROBLEM 2 Solution:
PROBLEM 4 Solution:
CE 463 Advanced Structural Analysis
Solution to Problem Assignment #1
Due: Monday, January 20, 2014
Question 1:
Solution:
Question 2:
CE 463
Page 2
Assignement # 1
Solution:
Question 3:
Solution:
The principal stresses correspond to the eigenvalues of the
CE 463 Structural Analysis 2
Solution to Problem Assignment #9
April 8, 2014
PROBLEM 1 Solution:
The general vibration of a three storey building is governed by the following system of ordinary
differential equations
M X(t ) C X(t ) K X(t ) F(t ) or
m 0