Purpose or Aim :
To determine the relationship describing the effect of meter-stick projection (L) on the vertical depression (y) of the free end with constant load. Material & Apparatus:
One 1 kg mass
String
Clamp
Two Meter Sticks
Tape

Diagram:

Procedure:
First of all, gather all the materials that are required for the lab and setup accordingly for the lab. Place the ruler on the lab table so that 0 cm projects beyond the lab table. Measure the height from the free end of the ruler (bottom line of the ruler) to the floor and record the data in a table. Clamp a meter stick on the table horizontally such that 20 cm is projected beyond the table. Measure the height again from the free end of the ruler to the floor and record it. Attach a 1 kg load to the free end of the ruler and measure the height from the free end of the ruler to the floor and record the data. Repeat this same procedure for 30 cm, 40cm, 50cm, 60cm, 70cm, and 80cm. Remember to check the zero load height every time before putting on the load. Repeat the above procedure for second trial so that you can get more precise data for the experiment.

Analysis:
The relationship between vertical depression and the projection is not directly proportional as we can see from the table and the graph.
Therefore, y is NOT ∝ L.
The vertical depression increases at a faster rate than the projection and thus when graphed, a parabolic curve opening upwards is obtained.
In order to create a straight sloping line through the origin, the values of projection must be raised by a power and it has to be...

...Introduction to
Structural Analysis
Contents
Introduction .…………………………3
Type of beam …….…………4, 5, 6 & 7
References……………………………8
Introduction
A beam is a structural member which carried load. These loads are most often perpendicular to its longitudinal axis, but they can be varying types. A beam supporting any load develops internal stresses to resist applied loads. The types of beam is determined by the kind of support the beam has at its ends or anywhere along its length. This is because each type of support generates of specific kind and combination of reactions.
Types of beam
A. Cantilever beam
Used to create the floating or hovering effect. This is used to create of a bay window, balconies, and some bridges. The weight load is spread back to the main beams of the structure in the cantilever beams and allowing a portion of the structure to go beyond the supported perimeters of the structure foundation.
Building in downtown area Cincinnati. Overhang in building is supported on variable depth cantilevers. Loading on the cantilevers primarily tip loading due to outside columns.
(Cincinnati, Ohio)
Entrance to stadium taken during construction. Roofing supported on variable depth glue-laminated...

...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 mid-point of the beam.
3. Unlock the knife-edges of the load cells.
4. Place a dial gauge over the left-hand support A. Adjust the dial gauge to read zero. Move the same dial gauge to the top of support C, and then adjust the height of the knife-edge so that the dial gauge reads zero.
5. Remove the dial gauge.
6. Adjust the load cell indicators at the supports to read zero.
7. Apply loads as shown in Table 1 to the hangers.
8. Record the readings of the load cells in Table 1.
9. Use the calibration charts to obtain the support reactions at A & C, and enter the reactions in Table 1.
Summary of Data
The results of the test are shown below in Table 1. This table shows the reactions at the supports based on the applied load. Noted that both experimental and theoretical results are recorded/calculated. The differences and the percent error of experimental results...

...On the Large Deflections of a Class of Cantilever Beams
Moses Frank Oduori, Ph.D.,
Department of Mechanical and Manufacturing Engineering,
The University of Nairobi.
Abstract
An equation for the determination of large deflections of beams is derived from first principles. Laboratory tests were carried out in order to validate the theory. The theoretical and experimental results were found to be in good agreement.
Introduction
In much of the study and practice of mechanical and structural engineering, the equations used for the determination of beam deflections are derived with the assumption of small deflections. This is appropriate because, in most mechanical and structural engineering applications, small deflections are a functional requirement. However, there may arise cases in agricultural machinery engineering, for instance, where beam deflections can no longer be assumed to be small. Then, it becomes necessary to develop and use equations other than those commonly found in the mechanical and structural engineering literature. Such an equation is developed and evaluated in this presentation.
An example of an application that would involve large crop stem (beam) deflections, is to be found in the design and operation of the combine harvester reel, as illustrated in Fig. 1.
Model formulation
Assumptions
The assumptions made in formulating a model of the deflected crop stems are the...

...The Report of Deflections of Beams and Cantilevers
Summary:
There are four parts in this big experiment, including deflection of a cantilever, deflection of a simply supported beam, the shape of a deflected beam, and circular bending. In these four parts, a same set of laboratory instrument and apparatus is used, concluding a bracket, a moveable digital dial test indicator, U-section channel, moveable knife-edge, and three materialbeams: brass, aluminum, and steel. The experiment methods, and fixed point to the beam are the differences between these four small experiments. The aim of this experiment is to improve the ability to use the precision engineering components like moveable digital dial test indicator, also understand the formula: Deflection= WL＾3/3EI.
To explain this formula: W is load, its unit is N, L is distance from support to position of loading (m), E is Young’s modulus for cantilever material, and its unit is Nm＾-2, I is the second moment of area of the cantilever, its unit is m＾4. In addition, the experiment safety is very important.
Objective:
(1) Operation techniques. In this experiment, measuring data is very important, because of comparing the actual deflection to theoretical deflection. Every step of this experiment should be precise. To obtain the correct data, you must be sure that the all components are secure and fastenings are sufficiently tight. Also position the...

...Simply Supported Beam 08
4. Cantilever Beam 10
5. Simply Supported Beam with Uniformly distributed load 12
6. Beam with angular loads, one end hinged and at other end roller support 14
7. Beam with moment and overhung 16
8. Simply Supported Beam with Uniformally varying load 18
9. Bars of Constant Cross-section Area 20
10. Stepped Bar 22
11. Bars of Tapered Cross section Area 24
12. Trusses 26
13. Stress analysis of a rectangular plate with a circular hole 30
14. Corner angle bracket 32
15. Spanner under plane stress 34
16. Thermal Analysis 37
17. Modal Analysis of Cantilever beam for natural Frequency determination 41
18. Harmonic Analysis of Cantilever beam 42
19. Dynamic analysis of bar subjected to forcing function 44
20. Laminar Flow Analyses in a 2-D Duct 46CONTENTS
Sl No Title Page no
1. Getting Started with ANSYS 10 03
2. General Steps 07
3. Simply Supported Beam 08
4. Cantilever Beam 10
5. Simply Supported Beam with Uniformly distributed load 12
6. Beam with angular loads, one end hinged and at other end roller support 14
7. Beam with moment and overhung 16
8. Simply Supported Beam with Uniformally varying load 18
9. Bars of Constant Cross-section Area 20
10. Stepped Bar 22
11. Bars of Tapered Cross section Area 24
12. Trusses 26
13. Stress...

...Intro: This assignment consists of predictions to theories on measuring and comparing results on deflection on a beam.
Intro: This assignment consists of predictions to theories on measuring and comparing results on deflection on a beam.
Beam Defection Experiment
1) This graph and its table below showed the resultant forces which were achieved when the test on the relationship between deflection (Y) and the spacing achieved (L3) using a load of my choice which was 2.5kg (constant). The scientific instruments used in the lab for this experiment were a digital gauge to measure the final beam deflection and also a hanger to freelance the weight. Beam depth (d) of 0.0063 m. A prediction was made that this beam would indeed prove to be one with a high deflection point due to its depth. Gradient is identical to deflection.
This graph and its table below showed the resultant forces which were achieved when the test on the relationship between deflection (Y) and the spacing achieved (L3) using a load of my choice which was 2.5kg (constant). The scientific instruments used in the lab for this experiment were a digital gauge to measure the final beam deflection and also a hanger to freelance the weight. Beam depth (d) of 0.0063 m. A prediction was made that this beam would indeed prove to be one with a high deflection point due to its depth....

...Ruben Perez
Kanstantsin Varennikau
Adrien Francois
04/13/15
Deflection of Beams and Cantilevers
(Lab 3)
Objectives:
In the first experiment, our objective was to examine the deflection of a cantilever that had an
increasing point load. In the second experiment, our objective was to examine the deflection of
simple supported beam that had an increasing point load.
Experimental Setup:
During the experiment we will be using a Test Frame machine to calculate the deflection of a
cantilever. We used three different materials to see the varying deflections. We set the beams at
different lengths to see the relation between the deflection and the length.
Procedure for Experiment 1:
1. Use a vernier gauge to measure the width and depth of each kind of material (aluminum,
brass, and steel) and record the data in a table
2. Using the depth and and width find the second moment of inertia,
I
3. Set up the cantilevers to correct length of 200 mm
4. Slide and lock the Digital Dial Test Indicator to the 200 mm mark
5. Zero the indicator and apply the following masses to it and then record them
○ 100 g
○ 200 g
○ 300 g
○ 400 g
○ 500 g
6. Repeat and record the same steps for all the materials
Discussion Questions:
It’s a good idea to tap the frame each time we take a reading to make sure the indicator is
calibrated. ...

...Experiment to determine the Young’s modulus of an aluminium cantilever beam and the uncertainties in its measurement
1. Abstarct: The young’s modulus E, is a measure of the stiffness and is therefore one of the most important properties in engineering design. It is a materials ratio between stress and strain:
E=σε
Young’s modulus is a unique value for each material and indicates the strength of that material as well as how it will deform when a load is applied.
2. Introduction: The Young’s Modulus can only be derived experimentally, there are no theoretical methods by which the young’s Modulus of a material can be calculated therefore in this experiment our aims were:
* To calculate the Young’s modulus ,E of Aluminium from measurement of the end deflection of cantilever beam of aluminium loaded at its free end
* To assess the accuracy and precision of this method by comparing the calculated value of E to the known value Eal=72.6 GPa
* To measure the deflected shape of the aluminium beam for one loading condition (15N) and to compare this with the theoretical prediction of the beam bending theory for deflection of a cantilever
yx= PL32EIxL2-13xL3
3. Materials and Methods
The apparatus shown below was set up and the following equipments were used:
* Dial gauge was used to measure deflection of the beam
* Magnetic clamp stand (not to affect the bending of the...