SPC208 Statics of Rigid and Elastic Bodies
Chapter 3 Rigid Bodies: Equivalent Systems of
Forces
Dr. Zakaria Elnaggar
Contents
1. Introduction
2. External and Internal Forces
3. Principle of Transmissibility: Equivalent Forces
4. Scaler, Vector and Mixed T
Chapter Four
Probability
In probability we have phenomena that produce different outcomes which are not
predictable and cant be controlled.
Random experiment: is a process that leads to one of several possible outcomes.
Sample Space: is the set of all pos
Chapter 1
Defining and collecting data
Statistics: is the science of collecting, organizing, presenting, analyzing, and
interpreting numerical data to make decisions based on such analysis.
Population versus sample:Population: is the group of all items of
Chapter 2
Organizing and graphing data
First Organizing and Graphing Qualitative Data(Categorical Variables)
Qualitative data could be organized through the summary table and the
contingency table, and graphed by both bar graph and pie chart.
ORGANIZING Q
Chapter (8)
Confidence Interval estimation
A point estimate is the statistic (or estimate), computed from sample
information, which is used to estimate the population parameter.
A confidence interval estimate is a range of values constructed from
sample d
Chapter 2
Organizing and graphing data
Visualizing Two Numerical variables
1-The scatter plot
Scatter plots are used for numerical data consisting of
paired observations taken from two numerical variables
One variable is measured on the vertical axis and
Example
A desk lamp produced by The Luminar Company was found to be
defective (D). There are three factories (A, B, C) where such desk lamps
are manufactured. Factory A produce 35% of the production in which
1.5% of its production is defective, factory B
Chapter three
Numerical Descriptive Measures
Measures of central tendency:1-Mean
Is called also the arithmetic mean and is obtained by dividing the sum of all
values by the number of these values.
Population mean ->
Sample mean ->
2-Median
Is the value in
Statics Truss Problem
2.1
Statics
We are going to start our discussion of Finite Element Analysis (FEA) with
something very familiar. We are going to look at a simple statically determinate truss.
Trusses are characterized by linear elements (beams) which
SPC208 Statics of Rigid and Elastic Bodies
Chapter 2 Statics of Particles
Dr. Zakaria Elnaggar
FORCE VECTORS, VECTOR OPERATIONS &
ADDITION COPLANAR FORCES
Todays Objective:
Students will be able to :
a) Resolve a 2-D vector into
components.
b) Add 2-D vec
SPC208 Statics of Rigid and Elastic Bodies
Course Schedule
Course Schedule
Week #
Topic
From - To
Practice and Assessment
1
Forces in a plane and Space
20/9 25/9
2
Equivalent systems of forces
27/9 2/10
3
Equivalent systems of forces
11/10 16/10
HW#01
4
E
SPC208 Statics of Rigid and Elastic Bodies
Lecture Notes Dr. Zakaria Elnaggar
Chapter 4: Equilibrium of Rigid Bodies
Equilibrium of Rigid Bodies
Conditions of Equilibrium:
For a rigid body to be in equilibrium:
The resultant of all forces acting on it is
SPC208 Statics of Rigid and Elastic Bodies
Lecture Notes Dr. Zakaria Elnaggar
Chapter 3: Rigid Bodies: Equivalent Systems of Forces
Introduction, Internal & External Forces
Rigid Bodies: Bodies in which the relative position of any two points does not cha
SPC208 Statics of Rigid and Elastic Bodies
Lecture Notes Dr. Zakaria Elnaggar
INCORPORATING A TRUSS DESIGN PROJECT INTO STATICS COURSE
INTRODUCTION
When teaching engineering mechanics, instructors are challenged to create realistic, hands on, intuitive de
SPC208 Statics of Rigid and Elastic Bodies
Lecture Notes Dr. Zakaria Elnaggar
Chapter 6: Analysis of Structures (Trusses)
Plan Truss
A framework composed of members joined at their ends to form a rigid structure is called a truss.
Bridges, roof supports,
Chapter 13
Simple Linear regression
Simple regression: a regression model is a mathematical equation that
describes the relation between two or more variables. A simple
regression model includes only two variables: one independent and one
dependent.
Linea
Measures of position :1-Quartiles and Interquartile range
Note that:
25th percentile -> 1st quartile Q1
50th percentile -> 2nd quartile Q2 which is the median
75th percentile -> 3rd quartile Q3
Location of 1st quartile
(
)
Location of 2nd quartile
(
)
Loc
Lecture 10: PCA, Model Selection
Nancy R. Zhang
Statistics 203, Stanford University
February 11, 2010
Nancy R. Zhang (Statistics 203)
Lecture 10
February 11, 2010
1 / 20
European Jobs Data
Percentage of jobs for 26
European countries in following
industri
Lecture 12: Ridge Regression, LARS, Logistic
Regression
Nancy R. Zhang
Statistics 203, Stanford University
February 18, 2010
Nancy R. Zhang (Statistics 203)
Lecture 12
February 18, 2010
1 / 30
Exploring the model space
1
Forward selection:
1
2
3
2
Start w
3-way tables: Alcohol Cigarette, and Marijuana Use
Survey asked 2276 students in their nal year of high school in a
nonurban area near Dayton, Ohio whether they ever used alcohol,
cigarettes, or marijuana.
Alcohol
Use
Yes
No
Cigarette
Use
Yes
No
Yes
No
Ma
Lecture 3: Inference and Diagnostics for Simple
Linear Regression
Nancy R. Zhang
Statistics 203, Stanford University
January 12, 2010
Nancy R. Zhang (Statistics 203)
Lecture 3
January 12, 2010
1 / 24
Review
Assumptions of the linear model
Yi = 0 Xi + 1 +
Lecture 14: Logistic and Poisson Regression
Nancy R. Zhang
Statistics 203, Stanford University
February 24, 2010
Nancy R. Zhang (Statistics 203)
Lecture 14
February 24, 2010
1 / 12
Count data
1
Men and women were asked whether they believed in the after l
A BRIEF INTRODUCTION TO R
STAT203
YuehWen Liao
Dept. of Statistics, Stanford Univ.
What is R
A software & a dialect of the S language
y
y
g p
A system for statistical analysis and graphics
Works in various OS.
F
Free (
(available at http:/www.r-project
STAT 203: Regression Models and ANOVA
Lecture 2: Simple Linear Regression
Nancy R. Zhang
Statistics 203, Stanford University
January 8, 2009
Nancy R. Zhang (Statistics 203)
Lecture 2
January 8, 2009
1 / 18
Last lecture.
Example: heights of husbands and wi
STAT 203: Regression Models and ANOVA
Lecture 1: Introduction and Review
Nancy R. Zhang
Statistics 203, Stanford University
January 7, 2009
Nancy R. Zhang (Statistics 203)
Lecture 1
January 7, 2009
1 / 17
Topics outline:
The goal of this course is to equi