H.W.#6
y
a
x
q ( x)
The above simply supported plate at x = 0 and x = a and of infinite length in the y-direction is
subjected to the following loadings which vary in the x direction only:
q0
( a)
x
q
Chapter 6 Buckling of Plate Elements
1.
Differential Equation of Plate Buckling, a Linear Theory
Consider an isolated freebody of a plate element in the deformed configuration (necessary for
stability
AUBURN UNIVERSITY
Department of Civil Engineering
CIVL 7690 Analysis of Plate and Shell Systems
Final, Take Home, Due August 4, 2009
1.
A simply supported semi-infinite plate shown below is free at th
HW#10, Chajes, Problem 7-1
Using the energy method, investigate the behavior of the one-degree-of-freedom model of a
curved plate shown in Fig. P7-1. The model consists of four rigid bars pin connecte
AUBURN UNIVERSITY
Department of Civil Engineering
CIVL 7690 Analysis of Plate and Shell Systems
Final, Take Home, Due August 4, 2009
1.
A simply supported semi-infinite plate shown below is free at th
MECHANICS OF DIAGONAL
TENSION FIELD ACTION
TENSION
Chai H. Jay Yoo, Ph.D., P.E., F. ASCE
Professor Emeritus
Department of Civil Engineering
Auburn University
CIVL 7690
July 14, 2009
Yoo,
C.H., and Le
AUBURN UNIVERSITY
Department of Civil Engineering
CIVL 7690 Analysis of Plate and Shell Systems
Midterm Exam, Take Home, Due July 2, 2009
1.
Consider the plane stress problem shown in the sketch. Find
AUBURN UNIVERSITY
Department of Civil Engineering
CIVL 7690 Analysis of Plate and Shell Systems
Midterm Exam, Take Home, Due July 2, 2009
1.
Consider the plane stress problem shown in the sketch. Find
Plastic Analysis and Design of Beams
The current AISC specifications for structural steel buildings, both ASD and LRFD, allow the
plastic design of braced frame members (including beams) meeting the c
CIVL 7690 Analysis of Plate and Shell Systems/Yoo
Printed on September 24, 2011
AUBURN UNIVERSITY
Department of Civil Engineering
COPURSE:
CIVL 7690 Analysis of Plate and Shell Systems
CREDITS:
3 Seme
Uniqueness theorem
Let us consider now whether our equations can have more than one correct solution
corresponding to given surface and body forces.
The equations of equilibrium expressed in terms of
P Introduction to Calculus of Variations
The calculus of variations is a generalization of the minimum and maximum problem of
ordinary calculus. It seeks to determine a function, y = f ( x ) , that mi
Principle of Minimum Total Potential Energy
In a linear elastic body, the strain energy stored in the body due to deformation is
U=
1
T dV
2 V
(1)
and the loss of the potential energy of the applied
Yield Line of Reinforced Concrete Slabs
1. Problem description
Figure 1 shows a group of slabs subjected to uniformly distributed loading. The cracking
pattern of these slabs is examined and compared
HW#8
A rectangular plate of dimension a and b is clamped on all four edges. The plate is subjected to
a uniformly distributed load of q0 . Using the deflection equation of both ends clamped beam for
2
HW#7
1.
a
q0
x
x
a
z
qo a4
wmax = , = 0.0020932, at x = 0.55a, y = 0.5a
D
y
2.
a
4
a
4
a
2
a
4
x
a
4
x
q0
x
x
a
2
x
R
y
(a) Find the expression for R.
2
(b) If R = qo a , find . Take a minimum of 4 te
amn for a line load
x
b
p0
a
z, w
y
The previous computation for amn for a patch load of size c x d centered at and from the
origin of the coordinate system gives
amn =
16 p0
m
n
m c
n d
sin
sin
sin
s
Brachistochrone Challenge (Birth of Calculus of Variations)
Simon Stevinus (1548-1620) Dutch - father of statics
Galileo Galilei (1564-1642) Italian - father of dynamics
Isaac Newton (1642-1727)
Gottf
Chapter 1. Introduction and Mathematical Preliminaries
1.
Scope
Behavior of structures deals with
(a) Micro state of stresses, strains, and displacements at a point
(b) Macro global behavior, collapse
Chapter 2. Review of Elasticity
1.
Stress
h
Plane-Strain - The plane-strain distribution is based on the assumption that
= uz = 0
z
(2-1)
where z represents the lengthwise direction of an elastic elon
Chapter 3 Plates Subjected to In-plane Forces
1.
Derivation of Airys Stress Function, 2-D
From equations of equilibrium, we have (by crossing out the third row and column)
x xy
+
= 0
x
y
y yx
+
= 0
Chapter 4 Plates Subjected to Transverse Loads
1.
Equations of Plates
g
Assumptions
(1)
At the boundary, the plates are assumed to move freely in the plane of the plate; thus the
reactive forces at th
Chapter 5 Approximate Methods of Analysis of Plates
1.
Validity of Classical Plate Theory
As in the case of the classical beam theory, there are obvious discrepancies in the classical theory
of plates
Chapter 7 Behavior of Thin Shells
1.
Deformation of a Shell Element
Let ABCD shown in Fig. 7-1 represents an infinitesimal element of thin shell cut out by two pairs
of adjacent planes normal to the m
Development of Structural Mechanics
Structural Mechanics is a branch of structural engineering concerned with applying Newtonian
mechanics to the analysis of deformations, internal forces and stresses
AUBURN UNIVERSITY
Department of Civil Engineering
CIVL 7690 Analysis of Plate and Shell Systems
Final, Take Home, Due August 4, 2009
1.
A simply supported semi-infinite plate shown below is free at th
Galerkins Method
The requirement that the total potential energy of a column has a stationary value is
shown in the following equation:
( EIy
l
0
iv
+ Py ) ydx + ( EIy ) y l ( EIy ) y 0 = 0
0
l
(1)
Home Work #1
An equilateral triangle ABC is to be installed at a corner of a tunnel complex at a municipal
wastewater treatment plant to facilitate a passage of a utility vehicle. The equivalent unifo