A rectangular specimen is subjected to a three-point bending test. The specimen is 10 centimeters long, 10 millimeters wide (b) and 10 millimeters tall (h). The specimen is placed on two supports that are 5 cm apart (L), and the actuator is applying a force in the exact middle of the two supports (L/2). Immediately before failure, the Instron records a force (F) of 50N, and a deformation ( ) of 2mm. We need to determine the maximum flexural strength (σ), and Young’s Modulus (E) of the specimen. To accomplish this task, we are going to use the two following equations: (Eq. 1.1 and 1.2)

Where M is the moment (or torque) applied at the middle of the specimen, y is the distance from the center of the specimen to the convex surface, and I is the “polar moment of inertia,” a term used to define how the geometry of the specimen influences its reaction to loads. First, we must calculate the reaction forces at the supports. We have two unknown values, and therefore must use two equations to solve the system. Based on static mechanics, we can use the following two equations: ∑ and ∑ (Eq. 1.4) (Eq. 1.3)

In our case, these equations are as follows: ∑ ∑ Or (Eq. 1.5) Using the (Eq. 1.4), we find: ∑ ( ( ) Solving for (

) (

( ) we find:
)

)

Substituting the value of 25N for

back into (Eq. 1.5), we find:

Therefore

Now that we have solved for the reaction forces at the supports, we can calculate the moment acting at the midpoint of the specimen by looking at half of the specimen and using the following equation: ∑ …in our case…

(Eq. 1.6)

Next we calculate y, the distance from the center of the specimen to the convex surface: (Eq. 1.7) …in our case…

Finally, we must calculate I , the polar moment of inertia, for our rectangular cross-section. The equation for a solid rectangular cross section is: (Eq. 1.8) If we plug in our values, we get:

Now that we have calculated specimen, by using (Eq....

...HITEC UNIVERSITY
ThreePointBending Test
By
Group#04
Members Name
Usman Rasheed (ME-131)
Sarnad Ali Shah (ME-108)
Farrukh Muhummad Aoun (ME-30)
Shahzaib bakht (ME-84)
Hafiz Abdul Hadi ()ME-32
A PROJECT SUBMITTED
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE COURSE OF
MECHANICS OF MATERIALS
IN MECHACNICAL ENGINEERING
B.Sc. Mechanical Engineering
HITEC UNIVERSITY
January, 2011
Projector Supervisor’s: Mr. Sheharyar Malik
Taxila, Pakistan
January, 2011
ABSTRACT
In this report different mathematical models for a ballistic missile are derived and simulated for the complete guided control system. In this research work V-2 rocket is taken as an example. Equations of motion are used in SIMULINK to perform simulations. An optimum trajectory is in accordance with launch angle and different burnout parameters. The missile would follow this ideal trajectory in the absence of any disturbance. But in real flight there are various errors and perturbations that make the vehicle not to follow the designated path. To have a successful flight it is required to remove the effect of these disturbances through a properly designed control and guidance system. 6DOF program is simulated which is then incorporated with the pitch orientation controller and a roll stabilization controller and results are simulated in accordance. Inertial navigation mechanization model is constructed in Simulink to propose an ideal...

...hand and arms wit soap and water before leaving the work area.
3.6 Never perform unauthorized work,preparation or experiments.
4.0 Theory:
1.Horizontal structural member used to support horizontal loads such as floors, roofs, and decks.
2. Consider a simply supported beam of length, L.
3. The The cross section is rectangular with width b and height h cross section is rectangular, with width, b, and height, h.
4. Beams have been used since dim antiquity to support loads over empty space, as roof beams supported by thick columns, or er of the approximate methods called "strength of materials methods.
5." These methods depend on the use of statics, superposition and simplifying assumptions that turn out to be very close to the truth.
6. They give approximate, not exact, results that are usually more than adequate for engineering work.
7. Calculus and a little differential equations are all the mathematics required for this approach, not the partial differential equations or tensor analysis that are typical tools in elasticity.
Types of beam loads
* Uniform
* Varied by length
* Single Single pointpoint
* Combination
5.0 Procedures
1. The apparatus as per diagram.Let L=800mm and initially x=100mm was set up.
2. The apparatus zero the dial gauge by turning the bezel was set up.
3. Apply 0.5N toW2 and 1.0N to W1.
4. The spring...

...Introduction
A bending moment is simply defined as “the algebraic sum of the moments of all the forces which induces bending of an element” (1). The aim of this assignment is to work out the bending moment in a simply supported beam when different concentrated loads are applied to it. A simply supported beam is a structure, usually with a straight profile supported at the ends, often pinned on one side and simply supported or on a roller on the other. There will be three series of loads applied to this beam & the findings will be recorded. The results will then be compared with the theoretical bending moment & the reasons for any variation explained.
The main reason for the experiment to be conducted is to examine, not only the accuracy of the testing equipment, but also the accuracy of bending moment calculations and diagrams compared to a real-world assessment. It will hopefully prove that “the bending moment at a cut section is equal to the algebraic sum of the moments acting to the left or right of the section”. (2)
After this introduction, there will be a little background information about this experiment and its apparatus, followed by a breakdown of the experimental procedure. Then, there will be the displayed results before a comparison with the theoretical results that have been calculated. Finally, while the conclusions are made, I will attempt to explain the...

...INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, VOL. 15, 1771-1812 (1980)
A STUDY OF THREE-NODE TRIANGULAR
PLATE BENDING ELEMENTS
JEAN-LOUIS BAT02
Depamment de Ginie Micanique. Universiti de Technologicde Compiigne, Compi&ne, France
KLAUS-JORGEN BATHE AND LEE-WING HO
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachuscits, U.S.A.
SUMMARY
An assessment of flat triangular plate bendingelementswith displacementdegrees-of-freedomat the three
comer nodes only is presented, with the purpose of identifyingthe most effective for thin plate analysis.
Based on a review of currently available elements, specific attention is given to the theoretical and
numerical evaluation of three triangular 9 degrees-of-freedom elements; namely, a discrete Kirchhoff
element, a hybrid stress model (HSM) element and a selective reduced integration (SRI)
theory (DKT)
element. New and efficient formulationsof these elements are discussed in detail and the results of several
example analyses are given. It is concluded that the most efficient and reliable three-node plate bending
elements are the DKT and HSM elements.
1. INTRODUCTION
Since the earliest development of the finite element method, a considerable amount of research
has been devoted to the analysis of plate and shell structures. A great number of papers have
been published on...

...in certain point in structure when applied a unit load.
Determine the greatest position the greatest value of live load in beam.
4.2 DIFFERENCES BETWEEN INFLUENCE LINE DIAGRAM (ILD) AND BMD (BENDING MOMENT DIAGRAM)
INFLUENCE LINE DIAGRAM
(ILD)
BENDING MOMENT DIAGRAM (BMD)
a) Static and Moving Load
b) Diagrams show only one point on the beam.
c) Calculations based on the virtual load.
d) Straight line only
e) Calculations do not refer to reactions of beam.
f) Unit: m
a) Static load only.
b) Diagram shows the moment at all points on the beam.
c) Calculations based on real loads.
d) Straight lines and curves.
e) Calculations based on the SFD.
f) Unit : kNm
4.3 BASIC CONCEPT TO DRAW INFLUENCE LINE DIAGRAM (ILD)
1 unit
x
A B C
a b
RAY = [L-x]/L 1-x/L RCY=x/L
4.3.1 REACTION
ILD RAY L/L
b/L
[+]
0
ILD RCY
L/L
a/L
1 [+]
4.3.2 SHEAR FORCE OF BEAM
ILD Vc b/L
[+]
[-]
a/L
4.3.3 BENDING MOMENT OF BEAM
ILD Mc 0 0
[+]
ab/L
EXAMPLE 1: SIMPLY SUPPORTED BEAM
Draw Influence Line Diagram for reaction at A and B, Shear force and bending moment for the beam.
1 unit
x
A C B
7.5m 2.5m
RAY = [L-x]/L 10m RBY=x/L
=1-x/L
EXAMPLE 2: SIMPLY SUPPORTED BEAM WITH ONE...

...of Defense for Special Operations and Combating Terrorism in the USA states that “Enabled by 21st-century technology, extremists have optimized the use of Internet chat rooms, Web sites and e-mail chains to spread their virulent messages and reach a global audience of potential recruits”.[1] But it is not only terrorists who are utilizing the Internet at a detriment to society. Various reports have linked a sharp rise in paedophilia with the growth of the Internet[2] as it is an easy and often anonymous way to share such material with the world. The ability for anyone to publish anything online could clearly do considerable harm to society, which would have otherwise been much less prevalent and easier to control and regulate.
Counter Point
The Internet gives millions of people access to information they would not otherwise have had, which is a huge benefit. People who read the news, offline or online, are not inherently dupable, they like all people do not simply accept messages they are, to varying degrees, critical of what they read and not simply passive. When people spend a lot of time reading online content they can differentiate between bloggers who are untrustworthy or extremely biases from bloggers who carefully refer to legitimate sources. The problem of bad information in news-making is not unique to the Internet; there are lots of trashy magazines and poorly researched news content in traditional print channels of communication as well. We...

...beam. A beam is a structural member (horizontal) that is design to support the applied load (vertical). It resists the applied loading by a combination of internal transverse shear force and bending moment. An accurate analysis required in order to make sure the beam is construct without any excessive loads which affect its strength.
A bending moment exists in a structural element when a moment is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres (N·m). The concept of bending moment is very important in engineering (particularly in civil and mechanical engineering) and physics.
A shear stress, denoted [pic](Greek: tau), is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section. Normal stress, on the other hand, arises from the force vector component perpendicular or antiparallel to the material cross section on which it acts.
Objective : To show that at any section of a beam subjected to transverse loads;
i. The shearing force is defined as the algebraic sum of the transverse components of the forces to one side of the section.
ii. The bending moment is defined as the algebraic sum of the moments of the forces to one side of the section.
The applications of the...

...LABORATORY EXPERIMENT NO. 3
BENDING OF BEAMS - (a) Bending Moment I
(b) Bending Moment II
SECTION 1
GROUP NUMBER 3
GROUP MEMBERS
1. YEOW SU LEE ( CE085335 )
2. JOUDI J. MOOSOM ( CE085338 )
3. NINI EZLIN ROSLI ( CE086340 )
4. MOHD AFIQ AFIFE BIN ABAS ( CE085310 )
5. ROHAM HADIYOUN ZADEH ( CE085851 )
DATE OF LABORATORY SESSION 6 DECEMBER 2010
DATE OF REPORT SUBMISSION 13 DECEMBER 2010
LAB INSTRUCTOR MISS SITI ALIYYAH MASJUKI
LAB REPORT MARKING |
CRITERIA | Scale |
| Poor | | Acceptable | | Excellent |
A. Appearance, formatting and grammar/spelling | 1 | 2 | 3 | 4 | 5 |
B. Introduction and objective | 1 | 2 | 3 | 4 | 5 |
C. Procedure | 1 | 2 | 3 | 4 | 5 |
D. Results: data, figures, graphs, table, etc. | 1 | 2 | 3 | 4 | 5 |
E. Discussion | 1 | 2 | 3 | 4 | 5 |
F. Conclusions | 1 | 2 | 3 | 4 | 5 |
TABLE OF CONTENT
Section | Page |
Summary | |
Objective | |
Apparatus | |
Procedure | |
Results | |
Discussion | |
Conclusions | |
SUMMARY
When applied loads act along a beam, an internal bending moment which varies from point to point along the axis of the beam is developed. A bending moment is an internal force that is induced in a restrained structural element when external forces are applied. Failure by bending will occur when loading...

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