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. Gradient is identical to deflection. The slope K1

The graph below labelled (1/d3 ) and its graph are used to show the relationship between the deflection (y) and the Depth (d) of 0.007900 m, on the spacing used will remain a constant to enable a versatile range of results to be obtained. We use the same instruments from the previous test. The only variables we shall change are the Depth (d) but the Weight (w). We shall be recording the Deflection (y) alongside the reciprocal of depth (1/d3). This test showed indeed that the trend did not remain versatile and indeed a trend was discovered with reasonable data entry. The...

...BACKGROUND OF STUDY
The deflections of a beam are an engineering concern as they can create an unstable structure if they are large. People don’t want to work in a building in which the floor beams deflect an excessive amount, even though it may be in no danger of failing. Consequently, limits are often placed upon the allowable deflections of a beam, as well as upon the stresses.
When loads are applied to abeam their originally straight axes become curved. Displacements from the 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 of a beam section is determined by the flexure formula, σ=MyI whereby M is the moment at the section, y is the distance from the neutral axis to the point of interest and I is the moment of inertia.
2.0 OBJECTIVES
2.1 EXPERIMENT 1
To investigate, for a simply...

...Summary
The primary goal of the experiment was to determine the structural stiffness of two cantilevered beams composed of steel and aluminum while maintaining both beams at a constant thickness and cross sectional area. The experiment also investigated material properties and dimensions and their relationship to structural stiffness. The experiment was divided into two separate parts. The results for the first part of the experiment were obtained by clamping the beam at one end while applying different masses at a specified length across the beam and then measuring deflection. The measuring device was set a specified distance from the clamped end. The following procedure was employed for both the steel and aluminum beam. The second part of the experiment required placing a single known mass at various lengths across the supported beam and then measuring the resulting deflection. This method was only completed for the steel beam. The deflections from both parts of the experiment were then averaged independently to ascertain final conclusions. The first part of the experiment resulted in a much greater deflection for the aluminum beam, with its greatest deflection spanning to an average of 2.8 mm....

...Laboratory Three: Parallam BeamDeflection
Lab Group - 1st Mondays, Late: Jesse Bertrand, Ryan Carmichael, Anne Krikorian, Noah Marks, Ann Murray Report by Ryan Carmichael and Anne Krikorian
E6 Laboratory Report – Submitted 12 May 2008 Department of Engineering, Swarthmore College
Abstract:
In this laboratory, we determined six different values for the Elastic Flexural Modulus of a 4-by10 (100” x 3.50” x 9.46”) Parallam wood-composite testbeam. To accomplish this, we loaded the beam at 1/3 span with 1200 psi in five load increments in both the upright (9.46 inch side vertical) and flat (9.46 inch side horizontal) orientations. We then used three different leastsquare methods (utilizing Matlab and Kaleidagraph) on the data for each orientation to fit the data, resulting in the following:
E: Upright Orientation Units Method One Method Two Method Three
E: Flat Orientation 10 ksi 103 ksi
3
0.981 ± 0.100 1.253 ± 0.198 1.065 ± 0.247
1.880 ± 0.046 2.080 ± 0.083 1.881 ± 0.106
1
Purpose:
The purpose of this lab is to determine the flexural elastic modulus of a Parallam woodcomposite beam by examining its behavior when simply supported and under flexural stress, and to analyze deflection data using different least-squares methods to fit theoretical deflection curves.
Theory:
In theory, a beam’s deflection can be mapped by the governing...

...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 material beams: 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...

...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 material beams: 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 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...

...Objectives:
Calculate deflection in statically determinate beams and frames
Various Methods
• • • • Double Integration Method Moment-Area Method Elastic Load Method Conjugate Beam Method
Slope at A negative
Slope at B positive
Deflection at point B
Tangential deviation between points A and B
Change in slope
Change in slope and tangential deviation between points A and B
Moment-Area MethodBeam and moment curve
M/EI curve between points A and B
Moment Area Theorems
•The change in slope between any two points on a smooth continuous elastic curve is equal to the area under the M/EI curve between these points •The tangential deviation at a point B on a smooth continuous elastic curve from the tangent line drawn to the elastic curve at the second point A is equal to the moment about B of the area under the M/EI curve between these two points.
Moment-Area Method
Horizontal, therefore the vertical distance between tangent line and elastic curve are displacements
Cantilever, point of tangency at fixed support
Moment-Area Method
Symmetric members with symmetric loading, point of tangency at intersection of axis of symmetry and elastic curve
Moment-Area Method
Point of tangency at left end of member AB
t BA L tan θ A = θ A in radians tan θ A =
θA=
t BA L
Caution 2.The theorem is applicable for continuous elastic curve 3.Presence of hinge...

...BeamDeflection
By Touhid Ahamed
Introduction
• In this chapter rigidity of the beam will be considered
• Design of beam (specially steel beam) base on strength
consideration and deflection evaluation
Introduction
Different Techniques for determining beamdeflection
• Double integration method
• Area moment method
• Conjugate-beam method
• Superposition method
• Virtual work method
Double Integration Method
The edge view of the neutral surface of a deflected beam is
called the elastic curve
1 M ( x)
EI
ρ
Double Integration Method
• From elementary calculus, simplified
for beam parameters,
d2y
2
2
1
d
y
dx
2
2 3 2
dx
dy
1
dx
• Substituting and integrating,
1
d2y
EI EI 2 M x
dx
x
dy
EI EI
M x dx C1
dx
0
x
x
EI y dx M x dx C1x C2
0
0
Double Integration Method
Boundary conditions for statically determinate beam
x
x
0
0
EI y dx M x dx C1 x C2
Solved Problem
SOLUTION:
• Develop an expression for
M(x) and derive differential
equation for elastic curve.
W 14 68
I 723 in 4
P 50 kips L 15 ft
E 29 106 psi
a 4 ft
For portion AB of the overhanging
beam, (a) derive the equation for
the elastic curve, (b) determine
the maximum deflection,
(c) evaluate ymax.
• Integrate...