Equilibrium of Particles
For any object, or any part of any object, in static equilibrium, the following two vector
equations must be satisfied.
F 0
M O 0
(3.1)
(3.2)
Equation (3.2) states that the sum of the moments, about some point O, of all the forc
AP Calculus
Section 2.1: The Derivative and the Tangent Line
Problem
Goals for this Section:
Find the slope of the tangent line to a curve at a point.
Day 1
Use the limit definition to find the derivative of a
function.
Day 1
Understand the relationship b
4
5000
(increased d )
4000
Flexure: Behavior
and Nominal
Strength of Beam
Sections
4-1
Moment (kip-in.)
(increased As or fy)
(increased fc or b)
3000
(basic)
(As 0.5As )
2000
1000
0
0
0.0005
0.001
0.0015
0.002
0.0025
Curvature (1/in.)
INTRODUCTION
In this
Wide Flange Section Data
Designation
Area
A
Web
Depth Thickness
tw
d
Flange
Width
Thickness
bf
tf
Ix
Elastic Properties
Axis X-X
Axis Y-Y
Sx
rx
Iy
Sy
ry
2
in
9.00
8.75
8.50
8.25
8.12
8.00
in
0.570
0.510
0.400
0.360
0.310
0.285
in
8.280
8.220
8.110
8.070
8
Problem Set #3 Assigned: September 21, 2016
Due: September 28, 2016
CEE 421: Concrete Structures Review Problems
Partial Credit will be given when all work is shown.
1. A reinforced concrete beam has a width of 12 in and an effective depth (
5.10. EXAMPLES FOR THE FUNDAMENTALS OF ENGINEERING (FE) EXAM.
The reader is encouraged to check the NCEES for any late changes before taking the FE exam or
to simply download the latest copy of the FE Manual. The web page address is www.ncees.org.
Problem
MIT - 16.003/16.004
Spring, 2009
Unit M4.7
The Column and Buckling
Readings:
CDL 9.1 - 9.4
CDL 9.5, 9.6
16.003/004 - Unified Engineering
Department of Aeronautics and Astronautics
Massachusetts Institute of Technology
Paul A. Lagace 2009
MIT - 16.003/16.0
10. COMPRESSION AND BUCKLING
Whenever a structural member is designed, it is necessary that it satisfies specific
strength, deflection and stability requirements. Typically strength (or in some cases
fracture toughness) is used to determine failure, while
UIILIUIIIILUU A IVNIVNUJ wcolcuua OAI. I I rs"
UNIFIED SOIL CLASSIFICATION SYSTEM - ASTM D2488
COARSE
GRAINED
SOILS
CONTAINS
MORE THAN
50% FINES
FINE
GRAINED
SOILS
CONTAINS
MORE THAN
50% FINES
NOTES:
GRAVEL AND
GRAVELLY
SOILS
MORE THAN
50% OF
COARSE
FRA
BRIDGING COURSE FOR REGISTRATION OF RESIDENT ENGINEER
for graduates in BEng (Environmental Engrg) from NTU only
GEOTECHNICAL ENGINEERING (26 hrs)
CONTENT
Site investigations: subsurface exploration, drilling, sampling, field and laboratory testing, design
MIME 3330 Mechanics Laboratory
LAB 5: ROTATING BENDING FATIGUE
Introduction
In this experiment, the finite life fatigue behavior of a smooth cylindrical specimen as
shown in Figure 1 will be studied in rotating bending. The cyclic loading is applied to
th
Hydraulics
Prof. B.S. Murty
25.1 Computation of Gradually Varied Flow
Qualitative sketching of water surface profiles in channels having gradually varied flow
has been discussed elsewhere. However, quantitative information on the variation of the
flow dep
1999 Polaris Xlt Snowmobile Manual
If you are pursuing embodying the ebook 1999 polaris xlt snowmobile manual in pdf appearing, in that process
you approaching onto the right website. We interpret the unquestionable spaying of this ebook in txt, DjVu, ePu
Cement Concrete Roads Vs Bituminous Roads - A Cost Analysis
Cement Manufadurers Association
Background
Indias economic growth plan of over 6% per annum for the
next 20 years will, to a great extent, depend on an efficient
road infrastructure, not only N
M Tech. 1ST Sem. GTE: ANALYSIS & DESIGN OF SHALLOW
Foundation Engineering (M.Tech. 2nd -Semester)
FOUNDATIONS
Ch. 2
Bearing Capacity Of Soils
Bearing capacity : The load per unit area of the foundation at which the shear failure in soil occurs is
called t
9.
FRICTION LOSS ALONG A PIPE
Introduction
In hydraulic engineering practice, it is frequently necessary to estimate the head loss
incurred by a fluid as it flows along a pipeline. For example, it may be desired to
predict the rate of flow along a propose
CHAPTER 3 - MECHANICAL PROPERTIES
Mechanical properties are the characteristic responses of a material to applied stresses. Selection of mechanical
tests for a particular application is based primarily on experience that many lots of a particular grade of
Broad-Crested and Sharp-Crested Weirs
BY: MONICA PRYCEL, ERICK RITTER, AND CHRIS ROBERTS
Background
Weirs are overflow structures that alter the flow so that:
1. Volumetric flow rate can be calculated,
2. Flooding can be prevented, or
3. Make a body of wa
INSTRUCTIONS: Beam Deflection
CENE 253 Mechanics of Materials Laboratory
EQUIPMENT
Your test kit comes with the following equipment:
Work Panel
Weights, Masses, and Weight Hangers
Dial Gauge with Magnetic Base
Adjustable Supports
The Work Panel
The work p
Minimum Steel - Concrete Beam Design ACI 318-08
This example further explores the minimum steel requirements of ACI
Given:
fc = 6,000 psi
fy = 60 ksi
Required:
Determine if this section can carry a factored moment, Mu, of 40 kip*ft,
while satisfying all A
Designation: D 2487 06
Standard Practice for
Classification of Soils for Engineering Purposes (Unified
Soil Classification System)1
This standard is issued under the fixed designation D 2487; the number immediately following the designation indicates the
18-09-2014
CVL141
IIT DELHI
CIVIL ENGINEERING MATERIALS
Lecture 10
Cement: Properties and Tests
B. Bhattacharjee
CIVIL ENGINEERING DEPARTMENT
IIT DELHI
B. Bhattacharjee
DEPARTMENT OF CIVIL ENGINEERING, IIT DELHI
General Outline
Porosity of paste
Propertie
Example
The example problem we solved during the previous lesson, worked differently.
Determine the moment of the force about the origin, expressed in Cartesian coordinates,
and the magnitude of that moment.
First create the force vector. Remember that th
More Equilibrium of Rigid Bodies in Two Dimensions
Example
A simply supported beam with a uniform distributed force.
W0
A
B
a
b
O
Consider a FBD of the beam. Replace the distributed force with a statically equivalent
concentrated force
W0 b
a
b
2
b
2
AX
A
Free-Body Diagrams
Mr. Hibbeler states, in italics, near the top of page 201, A thorough understanding of
how to draw a free-body diagram is of primary importance for solving problems in
mechanics.
Mr. Hibbeler is correct. This entire class will be devote
Moments of Forces
Conduct a mental, two-dimensional experiment. Consider a thin circular disk, e.g., made
of plywood. Nail that disk to a wall through its center. Apply a series of forces to the disk, and
observe, for each force, the tendency of the disk
Equilibrium of Rigid Bodies in Three Dimensions
In three dimensions, there are two vector equations that must be satisfied.
F 0
(10.1)
M O 0
(10.2)
Equation (10.2) states that the sum of the moments, of all the applied forces and couples,
about some poin
More Equilibrium of Rigid Bodies in Two Dimensions
No new material will be introduced today. The problems worked in class during the last
lecture, and the problems you worked for homework, are representative of problems commonly
solved in statics courses.
Equilibrium of Rigid Bodies in Two Dimensions
In two dimensions there are three scalar equations of static equilibrium.
FX 0
(7.1)
The sum of all the horizontal forces applied to a rigid body, positive to the right, is equal
to zero.
FY 0
(7.2)
The sum
25-08-2014
CVL141
IIT DELHI
CIVIL ENGINEERING MATERIALS
Lecture 8
Cement: Structure & Hydration
B. Bhattacharjee
CIVIL ENGINEERING DEPARTMENT
IIT DELHI
DEPARTMENT OF CIVIL ENGINEERING, IIT DELHI
1
General Outline
Structure of cement compound.
U Structure
2142391 Engineering Mechanical Laboratory
DEFLECTION OF BEAM
Abstract
If a beam is supported at two points, and a load is applied anywhere on the
beam, the resulting deformation can be mathematically estimated. Due to improper
experimental setup, the actu