laboratory report “Measurement of bending moment and shear forces for structural analysis” Azamat Omarov ID201102658... 1.Theory and background 1.1 Summary That performed laboratory session on bending moments and shear forces requires good understanding and sufficient knowledge of axial forces. Bending is defined as a behavior of any structural element that undergoes the external load, which is applied perpendicularly to longitudinal axis. That experiment helps us to find the maximum load...
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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...
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EXPERIMENT : CONTINUOUS BEAM 1.0 Learning outcome: 1.1 Determine the magnitude of the fixing moment in a continuous... beam by experiment and to compare this with the value predicted by theory. 2.0 Apparatus/Equipment: 2.1 Aluminium 2.2 Brounze 2.3 Weight 2.4 Dial gauge Weight Dial gauge Aluminium Brounze 3.0 Safety and health: 3.1 Make sure the...
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CONCLUSION After calculating and observing the values and action of shear force it is concluded that: The bending... moment is at maximum when the shear force is zero or changes sign. For every member the internal forces are described by shear force and bending moment. 7. SOURCES OF ERROR Following were the possible errors which produced a mark difference from the actualvalues: 1. Making the beam less stable. 2. Unstable positioning of loads i.e., not placing the loads on the exact middle...
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DEPARTMENT OF CIVIL ENGINEERING COLLEGE OF ENGINEERING CEMB 121 MECHANICS OF MATERIALS LABORATORY 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 ...
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for reactions, shear force and moment for: a. Simply supported beam b. Simply supported beam with one end overhanging c. Simply supported beam... with both ends overhanging. 2. To calculate shear force and moment using influence line 3. To determine maximum shear force and moment 4. Calculate Absolute Maximum Moment (MMM) 4.1 INTRODUCTIONS: Influence line is to: Analysis a structure due to moving load along the beam. Show the changes in reaction, shear stress, moment and displacement in certain point...
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Bending Moment EXPERIMENT 2B: SHEAR FORCE AND BENDING MOMENT 1. ABSTRACT... Performance-based design approach, demands a thorough understanding of axial forces. Bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. By this experiment we can verify the limit load for the beam of rectangular cross-section under pure bending. Moments at the specific points are calculated by the method of statics...
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Objective The objective of this experiment is to compare the theoretical internal moment with the measured... bending moment for a beam under various loads. Introduction and Background Theory Definition of a Beam Members that are slender and support loadings that are applied perpendicular to their longitudinal axis are called beams. Beams are important structural and mechanical elements in engineering. Beams are in general, long straight bars having a constant cross-sectional area, often classified...
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of a beam Bending Stress in a Beam Screenshot of the optionalnt Structures Software Shown with the Digital Force Display and fitted to a... Structures Test Frame (both supplied separately) • High-quality structures teaching module for students of mechanical, civil and structural engineering • Allows safe and practical experiments into bending stress in a beam • Realistic and verifiable experiment results • Optional TecQuipment’s Structures Software package for extra ‘virtual’ experiments that simulate...
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1.0 OBJECTIVE 1.1 To examine how bending moment varies with an increasing point load. 1.2 To examine how... bending moment varies at the cut position of the beam for various loading condition. 2.0 LEARNING OUTCOMES 2.1 To application the engineering knowledge in practical application 2.2 To enhance technical competency in structural engineering through laboratory application. 2.3 To communicate effectively in group. 2.4 To identify problem, solving and finding...
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MEM23061A Test Mechanical Engineering Materials Lab. BEAM BENDING The bending of beams is one of the most important types of... stress in engineering. Bending is more likely to be a critical stress than other types of stress - like tension, compression etc. In this laboratory, we will be determining the Modulus of Elasticity E (also called Young's Modulus) of the various materials and using Solid Edge to determine the Second Moment of Area for the different cross-sections. [pic] Equations ...
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determine both the theoretical and actual support reactions of a simple vertically loaded beam, showing that the loadings on the supports are directly... proportional to the distances of the loads from the supports; thus illustrating the principle of the moments of forces. 2. To determine the beam support reactions for a horizontal beam carrying vertical loads at positions across the span. APPARATUS Two support stands, beam of uniform round bar, load hangers, known loads, two spring balances with suitable...
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Sohar University Faculty of Engineering Strength of Materials Laboratory Manual MECH2308 Lab experiment # 3 Thick... cylinder Introduction: Thick -walled structures are widely used in .a viatiofi, chemistry, shipbuilding, vehicle nuclear and civil engineering and many other practical .and high-technology industries. The failure of the structures caused by elastoplastic buckling has attracted a .lot of attention of the researchers of mechanics and mechanical...
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ω = T = 2π …………………….(3) Making K the subject of the equation, T2 = ……………………..(b)... K = ……………………(4) METHOD OR PROCEDURE FOR THE FIRST EXPERIMENT (STATIC) * Hang the spring from the support end and place a weight hanger. * Measure the height from the bottom of the weight hanger to the top of the spring. * Suspend 1N weight on the hanger and measure the height. * ...
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EXPERIMENT 2 Title : Shear Force and Bending Moment Objective : To determine the shear force and... bending moment when concentrated load, symmetrical load and non symmetrical load are applied Introduction The shear force (F) in a beam at any section, X, is the force transverse to the beam tending cause it to shear across the section. The shear force at any section is taken as positive if the right-hand side tends to slide downwards relative to the left hand portion. The negative...
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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...
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Redesign. Throughout this experiment a number of random and procedural errors were apparent; these errors could have affected the results of... the experiment in a number of ways. One experimental error that occurred during the experiment was that some flies became stuck in the food source and died. The main cause of this was the fact that the fly vials were stood up (vertically) before the flies had fully recovered from the anaesthetic. This could be overcome in future experiments by ensuring that the vials...
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1. Objective: The objective of this experiment is to demonstrate the bending of a bean when loaded at the center of its length... and examine its deflection when positioned in two different ways, when the flat side of the beam is support and when the thin side is supported. In addition, try to find linear relationship between the load applied and the deflection of the beam and comparing the experimental deflection with the theoretical deflection. If the load is applied at the mid- length a=b=L/2...
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Lab report SHEAR FORCE & BENDING MOMENT Bachelor (Hons) of Civil Engineering Course: Structures l (ECS3213)... Lecturer: Ir Pan Submission date: 07-11-2013 Group 8: Members No. Name Student ID 1 Diallo Mamadou Aliou SCM-014804 2 Balmeiiz Abilkhaiyrova SCM-014742 3 Elmogdad Merghani Mohamed Elhag SCM-017223 4 Omar Mohamed Abdelgawwad SCM- 018031 5 Salah Mohammed Alesaei SCM-015473 6 Ali Abdulrahman Mohammed SCM-008879 7 Kasem Heiazi SCM-017913 Contents A. Introduction:...
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Experiment 1a: Cantilever Aim The aim of this experiment is to obtain and graph deflections and bending... stresses for a cantilever beam under a point load and observe the affect that changing the mass of the point load has on the deflection and bending stress graphs. Hypothesis As the loading on the bar increases, the magnitude of deflection and bending stresses will become greater. Procedure 1. Clamp the strain gauge instrumented steel beam to the rig. Place the dial gauge at 200mm and...
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ME 304 – Experimental Engineering Spring 2013 Lab Report Experiment # 3 Bending of Beams Section #... ThTh12 Group # 1 Ömer Ege Çalışkan Serhat Karakuz Noyan Uğur Renda Turgut Soydan 20.03.2013 Abstract In this experiment, a simply supported beam is used and the variations of deflection of a simply supported beam with load, beam thickness and material are investigated. It is found that the deflection of the beam changes linearly with the load and as the beam...
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Experiment 1 - Static Equilibrium - BEAM Objective 1. To study the vertical equilibrium of (a) a simply supported beam 2. To determine... the reactions of the beams by (a) the experimental set-up and (b) by using the principles of statics and method of consistent deformation Apparatus TecQuipment SM 104 Beam Apparatus Mk III Figure 1 Experimental Procedures 1. Set up the beam AC with a span of 675mm (as shown in Figure 1). 2. Place two hangers equidistant (100mm) from the...
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Moment of Inertia 1. Abstract The goal of this study is to understand the transfer of potential energy to kinetic energy of rotation and... kinetic energy of translation. The moment of inertia of the cross arm my group measured with the conservation of energy equation is: 0.01044 kg/m2 (with the mass of 15g), 0.01055 kg/m2 (with the mass of 30g), which is kind of similar to the standard magnitude of the moment of inertia of the cross arm: 0.0095 kg/m2 (Gotten by measuring the radius and the mass...
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Experiment #1: Introduction to Experimentation Submitted by: Neann Klara M. De Jesus... BS Psychology II Submitted to: Dr. Geraldine E. Tria ABSTRACT SUMMARY The first experiment done by the class was called “Introduction to Experimentation”. Its main objective is to give basic knowledge about some of the logic of experimentation. The class was divided into groups of 2. In each group there was an experimenter (E) and a subject (S). The...
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CONCLUSION Angiosperms (flowering plant) include in phylum Anthophyta.Angiosperms are plant that have flowers and fruit. Their part of... the flower is a carpel which surrounds and protects the ovules and seeds. The fruit surrounds the embryo and aids seed dispersal. The great majority of angiosperms are classified either as monocots or eudicots.Monocot embryos have a single seed leaf (cotyledon), and pollen grains with a single groove while eudicots (true dicots) have two cotyledons, and pollen...
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Conclusion In part A of this experiment, we transformed the bacteria into an antibiotic resistant form by inserting a plasmid... into it. We used heat shock in order to make the bacteria capable to uptake a plasmid in the presence of calcium ions that help disrupt the cell membrane (heat shock is the combination of altering hot and cold). When they are capable of accepting plasmids, the bacteria are incubated with plasmids that carry the resistance to a particular antibiotic, in this case ampicilin...
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Zuleika Rodriguez Professor Alan Schlechter/ Daniel Lerner (Nick Jensen) The Science of Happiness October 1, 2014 The Moment of... Change Faith, courage and willpower are some values that have shaped me into the character that I am today. Following upon the numerous and impacting conflicts I had throughout my life, I can recall my family reunion last summer. In a quote from Ralph Waldo Emerson, he states, “Be an opener of doors for such as come after thee, and do not try to make the universe...
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Experiment 2: IDENTIFICATION OF UNKNOWNS BY TLC AND MP IN COMBINATION Introduction: Thin layer chromatography (TLC) is one of... the most valuable techniques in organic chemistry. This is a best method of separating and identifying mixtures of two or more compounds. The separation is accomplished by the distribution of the mixture between two phases: one that is stationary and one that is moving or mobile. Chromatography works on the principle that different compounds will have different...
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Title: Mass Moment of Inertia Objective: To determine mass moment of inertia of a part using experimental method. Theory: If... a part has been designed and built, its mass moment of inertia can be determined approximately by a simple experiment. This requires that the part be swung about any axis (other than one that passes through its CG) parallel to that about which the moment is sought and its period of pendular oscillation measured. Figure 1 shows a part of connecting rod suspended on a knife-edge...
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Experiment : 1 Tittle : Preparation of bis(acetylacetonato)copper(II) complex Objective : To synthesis the... bis(acetylacetonato)copper(II) complex Introduction : A complex ion is usually form with high charge density metal ion as a central and formation of coordinate covalent bond (dative bond) with high electron molecules or ions. These molecules or ions are functioning as ligands (electrophile in organic compounds). They are easily attracted by electrophile (electron deficiency...
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EXPERIMENT 1: REACTIONS OF ENOLATE IONS WITH CARBONYL GROUPS Aims In this experiment we used two techniques for the reactions... of enolate ions with carbonyl groups. One technique used was Doebner reaction and the other technique used was Claisen-Schmidt reaction. Therefore the aim of this experiment is to synthesize trans p-methoxycinnamic acid and to synthesize dibenzalacetone via an aldol condensation reaction between acetone and benzaldehyde. The products would be recrystallized using ethanol...
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Experiments in physics lab report Department of Electrical Engineering Isabela State University Ilagan Campus, Calamagui 2nd, City of... Ilagan, Isabela baccaljoemel@yahoo.com Submitted to: Engr. Rafael S. Ramos Physics12 Professor Submitted by: Joemel L. Baccal BSEE IIA Experiments in Physics Lab Report Joemel L. Baccal Department of Electrical Engineering Isabela State University - Ilagan Campus, Calamagui 2nd, City of Ilagan, Isabela baccaljoemel@yahoo.com Abstract In...
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Sadie D. Hood Lab 8: Moment of Inertia Partner: Florence Doval Due 16 November 2011 Aims: To use a centripetal force apparatus to calculate the... moment of inertia of rotating weights, using theories derived from ideas of energy transfer (Im = MR2 (g/2h)(t2-t02)) and point mass appoximation (m1r12 + m2r22). Set Up Procedure First we measured the weights of two masses and wingnuts that secure them. Then we placed one of the masses on the very end of a horizontal rod on the centripetal force apparatus...
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Poor or middle income group people 5. Businessmen 6. Creating Brands 7. Adds and promotions 8. Low price strategy 9. Varieties available... for different age groups 10. Various schemes for pre-paid and post paid customers Conclusion and Recommendation:...
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process of distillation. Distillation is the separation of volatile substances mixed with nonvolatile substances by boiling the mixture to alter the phase of... the volatile substance. The researchers used the simple distillation set up to conduct the experiment. 25 ml of The Bar Vodka was used and 7 ml of distillate was collected before a temperature of 95 degrees Celsius was reached. Collected distillate was then subjected to a flammability test to confirm ethanol content. The percent ethanol was computed...
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Theory of simple bending (assumptions) Material of beam is homogenous and isotropic => constant E in all direction Young’s modulus is... constant in compression and tension => to simplify analysis Transverse section which are plane before bending before bending remain plain after bending. => Eliminate effects of strains in other direction (next slide) Beam is initially straight and all longitudinal filaments bend in circular arcs => simplify calculations Radius of curvature is large compared...
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Experiment AM1.2—Centrifugal Force Student name JunJie Liu Student ID 1512042... Experiment Date 11 Feb 2015 Lab group Mech 7 Introduction In this lab report we show the basic methods of measuring centrifugal force using two counter balanced bell-cranks spin on a turntable (shows in figure 1) and able to calculate the centrifugal force with given conditions shows in figure 1. *Figure...
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Introduction 3 2. Theory 3 2.1 Bending Moment and Stresses 3 2.2 Deflection and Slopes 5 3. Equipment 6 4. Procedures 7... 4.1 Procedure 1 7 4.2 Procedure 2 8 4.3 Procedure 3 8 5. Results 8 5.1 Results from procedure 1 8 5.2 Results from procedure 2 10 5.3 Results from procedure 3 12 6. Discussion and Error Analysis 14 7. Conclusion 15 1. Introduction During this lab a beam was tested in order to find the relationships between load, bending moment, stress and strain, slope and...
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Experiment 22 Title: Reactions of aldehydes and ketones Aim: The purpose of this experiment is to compare some... reactions of ethanal and propanone. Introduction: We have chosen ethanal and propanone as relatively safe examples of aldehydes and ketones to illustrate their reactions in simple test-tube experiments. The reactions or properties to be investigated are as follows: A. Condensation (addition-elimination) B. Oxidation C. Triiodomethane (iodoform) reaction Requirements: ...
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EXPERIMENT 5 REDOX TITRATION: TITRATION USING SODIUM THIOSULPHATE Objectives 1. 2. To prepare a standard solution of potassium iodate for use... to determine the concentration of sodium thiosulphate solution accurately. To acquire the proper techniques of carrying out a titration. Introduction Redox titrations using sodium thiosulphate as a reducing agent is known as iodometric titration since it is used specifically to titrate iodine. The reaction involved is: I2 + 2Na2S2O3 I2 + 2S2O322NaI + Na2S4O6...
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AM1.4-Bending moments in a simply supported beam Name: Arif Firdaus Marzuki Student ID: 1504166 Due Date: 16 January... 2015 Introduction Bending moment is a rotational force that occurs when force is applied at any place away from at any point perpendicularly. A bending moment will occur when a moment is applied to a system so that the system will bend. According to Hibbeler, beams develop different internal shear force and bending moment from one point to another along the axis of the...
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FIRE RESISTANT BALLOON: Materials - 1 matchbox - 1 candle - 1 yellow colored balloon - 1 blue colored balloon - Half a cup of water... Procedure: 1. For this experiment, the independent variable is whether the balloon is filled with water or not. The dependent variable is what happens to the balloon when it is placed above the lit candle. This is determined by observing the balloon. The constants (control variables) are how much the balloon is inflated and the amount...
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Bending of a Channel Section Experiment Two: Stiffness Report from laboratory work performed on 12 May 2011 as a part... of the unit of study CIVL2201 Structural Mechanics Abstract This report has been written to describe an experiment performed on a channel section examining the stiffness of the beam through two differing types of deformation – curvature and deflection. The aim of the experiment was to determine the value of the flexural rigidity (EI) in two different ways; using the...
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Experiment 1 : Young Modulus Title :Bending of beam and coefficient of elasticity. Objective : To study the relationship... between load, span, width, height and deflection of a beam, places on two bearers and affected by a concentrated load at the centre. :To ascertain the coefficient of elasticity for aluminium, brass and steel. Results : Measurement of test specimen (a) For beam material – Steel | Length, L (mm) | Thickness, h (mm) | Width, b (mm) | 1st reading | 650...
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STANFORD PRISON EXPERIMENT One of the most interesting studies made in history was led by Philip Zimbardo, a psychologist and a former... classmate of Stanley Milgram (who was famous for his Milgram experiment). He sought to expand on Milgram’s experiment about impacts of situational variables on human behavior by simulating a prison environment, in which volunteering students were randomly assigned as prisoners or prison guards. Many controversies have been elicited from this experiment, and it was with...
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MM2MS3 Asymmetrical Bending Laboratory Report Date of Laboratory: Name of Student: Student ID: Summary Asymmetrical... bending is bending couples acting in a plane of symmetric. If loads do not act in plane of symmetry, this leads to deflection in a plane perpendicular to the loading plane as well as in the loading plane. This coupling does not occur if the loading is in principal plane. The experiment was conducted to investigate the deflections of the tip of a cantilever when loaded transversely...
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4…………………………………………………………………………………………………..7 o Question 5……………………………………………………………………………….…………………..8 •... Conclusion……………………………………………………………………………………………………………….. • Appendix……………………………………………………………………………………………………………….. OBJECTIVE The purpose of this assignment is to experimentally and analytically determine shear forces and bending moments when an external load is applied in various scenarios. In turn, we aim to investigate the relative accuracy of such...
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initial axes are called bending or flexural deflections. The amount of flexural deflection in a beam is related to the beams area... moment of inertia I, the single applied concentrated load P, length of the beam l, the modulus of elasticity E, and the position of the applied load on the beam. The amount of deflection due to a single concentrated load P, is given by δ=PL3kEI whereby k is a constant based on the position of the load, and on the end conditions of the beam. The bending stress at any location...
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CIVE 3202 A6E – Mechanics of Solids II (Winter 2013) Experiment 2: Bending of an aluminum I-beam... Introduction “Beams are long straight members that are subjected to loads perpendicular to their longitudinal axis and are classified according to the way they are supported”[1]. When a beam is subjected to an external load there are unseen internal forces within the beam that one must be aware of when implementing it into any design or structure....
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GCSE - Human Physiology and Health An experiment to investigate what affect sucrose solution has on potato tissue. Background Osmosis... is the movement of water molecules, across a partially permeable membrane from a region of high concentration of water to a low concentration of water molecules. A partially permeable membrane is a membrane with holes in it small enough for only water to go through it. Big molecules like glucose cannot fit through it. Osmosis allows plants to take in water...
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Experiment AM1.4--Bending moments in a simply supported beam Student name... JunJie Liu Student ID 1512042 Experiment Date 24 Nov 2014 Lab group Mech 7 Introduction In this lab report we show the basic methods of measuring bending moment at the “cut” assuming only simply supported beam with point loads (showed in figure 1) and illustrate the relationship among bending moment and distance between...
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HITEC UNIVERSITY 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 ...
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1 eng1201 tutorial 10 problem set (Set No. 6) 1. Calculate the area A, the location of the neutral axis, and the second moment of area... (cross section stiffness) IXX for each of the following shapes, and rank them in order of increasing stiffness. Scale the dimensions from the drawings, and work in mm. For a circle, π r4 I= . 4 X X X (b) (a) X (d) X X X X (c) X X X X X X (e) (f) (g) X X X X X X (h) (i) (j) 2 2. A rectangular beam with a cross...
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Introduction In my report I will discuss what I did as an experiment and what I hope for it to achieve. Firstly I carried out an... experiment to assay the effectiveness that a range of disinfectants have on the growth of ecoli and whether or not it can prevent it from growing. From the experiment i should be able to see that some disinfectants have a greater effect than others do. From this I shall then draw a conclusion and evaluation on what was the most effective, and could there have been...
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Conclusion The purpose of our experiment was to determine if reading off words in various colors helped improve memory. Our... hypothesis was that color helped memory and it was in fact proven by our experiments. According to data table 2, the average words remembered by the white control group was 6.4, while the other groups with the colors had averages of 6.8 and 8.2. Our hypothesis also proven in table 3, where the average words remembered by the control was 4.6 and the other two groups had averages...
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3 2.0 Experiment Design 4 2.1 Materials 4 2.2 Procedure 4 3.0 Results and Calculations 5 3.1 Tables 5 3.2... Graphs 7-9 3.3 Discussion 9 4.0 Conclusion and Recommendations 10 Abstract This experiment is conducted to measure the transverse bending deflection of the tie bar and at the same time comparing it to the theoretical values. The two theoretical formulae to get the central deflection in this experiment are simple theory...
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A Divided Class From the moment our country was created, one of the main liberties we asked for was the idea of equality, “that... all men will be created equal.” Although this has been a part of the American ideal since 1776, American’s have not fulfilled this liberty. Individuals do not admit it, but many are still prejudice against minorities, particularly African Americans. In the 1960’s, around the time when Martin Luther King Jr. was fighting for civil rights for people of color,...
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Experiments: Doctors, Experiments, and Results Melissa Anjeanette Edwards POLYTECH High School of Kent County, Woodside,... Delaware Abstract During World War II experiments were done on the prisoners of war in Nazi Germany. Doctors for these camps came in all shapes and sizes including former S.S. Troops, Women, and a variety of prisoner doctors. The experiments differed as much as the doctors themselves; however they stayed the same in one factor, medical curiosity become killing in atrocious...
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November 9, 2014 Madison Phillips Report Submitted: November 9, 2014 Title: Beers Law and Calorimetry Purpose: The purpose of this... experiment is to apply Beer’s Law by analyzing samples provided by Q laboratory to determine their absorbance and prepare a Beer’s law plot. Molarity of these samples was also calculated to determine concentration and percent error rate. Students also analyzed the concentration of blue dye #1 to determine the concentration of blue dye #1 in a commercial blue...
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Bending Beam Louisiana State University Joshua Board Table of Contents: Table of Figures:... ........................................................................................................................................... 4 Purpose.......................................................................................................................................................... 5 Introduction ...........................................................................................
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