Three Point Bending 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 navigation model for the rocket system. The controller analysis is performed at various points in the trajectory and the measurements are made in frequency domain. A comprehensive roll control model is designed along with pitch controller using Simulink and various frequency domain plot; bode plots & root locus for analysis.

Aim
To calculate the modulus of elasticity in bending Ef, flexural stress σf, flexural strain εf and the flexural stress-strain response of the material by performing three point bending flexural test Theory...

...Example 1: Rectangular ThreePointBending
A rectangular specimen is subjected to a three-pointbendingtest. 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...

...Distribution Protocol (LDP) in order to build a complete datagram of the network, that along with the Label Forwarding Information base (LFIB) which is a type of routing table that MPLS routers use provide faster lookup and addressing. Once the packet is received by the LSR the label is examine and compare to its LFIB table to determine the best path to the next router or hop these paths are referred to as Label Switched Paths (LSP). During this process different things might happen to the label depending on its contents, sometimes a new label is added or if the packet contained more than one label (label stack) a label might be removed from the stack or in some cases labels get swap. This process continues until the exit LER is reach at this point the LER removes the MPLS label or label stack and the payload is then handed out to a device or different type of IP network outside of the MPLS domain. In addition, MPLS provides Traffic Engineering (TE) which gives network administrators the ability to configure static LSP, this act as predefined static routes that connect LERs and LSRs; these static LSPs are created for a variety of purposes such as prioritization of traffic, maximizing bandwidth utilization or to prevent network congestions and bottlenecks. LSP routes are most popularly used to create Virtual Private Networks (VPN).
The main thing to keep in mind about MPLS is that it’s a networking technique and not a service. Being that MPLS is a...

... The urge to understand the way materials behave when an external force is applied to them has lead to the discovery of some important properties such as elasticity, stiffness, strength and ductility.
Elastic deformation:
The concept of elastic deformation refers to the ability of a material to return to its original shape after the force applied to it is removed. However, at a certain point the material will not be able to resist the force applied to it and the material will plastically deform (i.e. will break and not recover its original shape). This point is called the yield point and the stress applied at this point is called the yield stress. The rate of deformation differs from one material to another depending on several factors. The nature of a material is a major factor that determines how elastic it is regardless its geometry and shape. For example, if the same load was applied to two beams of different materials (aluminium and glass) that have the same shape, cross section and separated from the support by equal distance, the glass beam will reach its yield point and hence break first. Therefore, Young’s modulus was incorporated from Hooke’s law to refer to a measure of resistance of a material to elastic deformation when a stress is applied to it and in the previous example, the glass has a smaller young’s modulus, therefore it breaks first (Dobson, 2001). Other factors include the...

...MEMORIAL UNIVERSITY OF NEWFOUNDLAND
FACULTY OF ENGINEERING AND APPLIED SCIENCE
Engineering: 4312
Mechanics of Solids I
Lab Test #4 – Torsion Test
OBJECTIVES:
To carry out a torsion test to destruction in order to determine for a 1020 carbon steel rod specimen: 1. The modulus of rigidity, 2. The shear stress at the limit of proportionality, 3. The general characteristics of the torque, angle of twist relationship.
REFERENCES:
1. Hibbeler, R. C. "Mechanics of Materials", Prentice-Hall, 7th Edition. 2. Instruction Bulletin of Tecquipment Ltd.
MATERIAL:
Mild Steel rod 6 mm diameter over 3" length (overall length including hexagon ends = 5⅝").
EQUIPMENT:
1. Torsion testing Machine and Torsiometer of Tecquipment Ltd. 2. Steel rule and micrometer.
THEORY:
From the general torsion theory for circular specimen:
T Gθ = J l
where, T = Applied Torque; J = Polar Second Moment of Area; G = Modulus of Rigidity; θ = Angle of Twist (over length l); l = Gauge Length. (Nm) (mm2) (N / mm2) (radians) (mm)
PROCEDURE:
1. Measure the overall length and test diameter of the specimen. 2. Draw a line down the length of the test section of the specimen with a pencil; this serves as a visual aid to the degree of twist being put on the specimen during loading. 3. Mount the specimen firmly in the torsion testing machine as indicated in the operating instructions – see later. (If the Torsiometer...

...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...

...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...

...Abstract
A tensile test was conducted on an Instron tensile machine using a 3/16 inch copper rod. Using data acquired stress and strain was calculated and plotted on Excel to analyze stress strain curve. Modulus of elasticity, 0.2% yield stress, ultimate tensile stress and % elongation were also calculated.
Introduction
A tension test is probably the most fundamental type of mechanical test you can perform on material. Tensiletests are simple, relatively inexpensive, and fully standardized. By pulling on something, you will very quickly determine how the material will react to forces being applied in tension. As the material is being pulled, you will find its strength along with how much it will elongate. During tensile testing the tensile load is measured by a load cell while extension of the specimen is measured over the gauge length. Data is provided by a computer program, which is used to determine stress and strain, therefore allowing a stress-strain curve to be plotted.
Experimental Procedure
A 3/16“ diameter specimen (Cu rod) was loaded onto an Instron tensile testing machine. The appropriate extensometer was attached for the given specimen and gage length. Calibration of the extensometer and load cell was done prior to tensile testing. Data is recorded until specimen reaches ultimate tensile strength and snaps; recorded data is processed into Excel to create a Stress-Strain curve....

...Point load test
Aim: To determine the strength characteristics of a rock using the point load test and visual judgement.
Materials
Loading device
Loading frame
Pump
Ram
Platens
Rock
Caliper
Method (Standard, 2007)
1. Measure the dimensions of the rock which includes the diameter and length
2. Find the length to diameter ratio to determine which test will be used. If the ratio is greater than 1 use diametrical test. But if the ratio is between 0.6 and 1 use axial test
3. The axial test was carried out for this rock which is then placed in the loading device upright and closed the platens so they are aligned to the centre
4. Increase the load until failure and record the distance between the platens
5. Record the failure load and mode for the rock
Results
Discussion
Strength characteristic of a rock is an integral part in engineering and geotechnical practice as it can be the base of structure or the structure itself hence the pointtest was utilised to determine this crucial parameter. The rock is initially a round cylindrical shape that is intact. During the testing it split in a roughly 2:3 ratio vertically at the load of 21.373kN with the platen distance of 29mm.
From the experimental data and calculations of the rock, the UCS has value is of more than 250MPa and the Is of...