Span Deflection Report Uthm
Short Description
Span Deflection Report...
Description
LIGHT STRUCTURE LABORATORY FULL REPORT BFC21201 BFC
Course Code
BFC21201
Course Name
Makmal Hidraulik Dan Mekanik Bahan
Date Group Group Leader
Norhafidzah Bt Abdul Rahman
Members of Group
1.Muhammad Amin Bin Rosli 2.Mohd Ashraf Bin Mohd Azhan 3.Muhammad Arif Bin Mohd Nazir 4.Mohamad Radzif Bin Mohd Raes
Lecturer/Instructor/Tutor Encik Ahmad Fahmy Bin Kamarudin Received Date Criteria
1
2
3
4
5
SCR
VT
Student in laboratory more than 1 hour late
Student in laboratory within 30 minutes to 1 hour late
Student in laboratory within 10 to 30 minutes late
Student in laboratory just before laboratory start start
Student in laboratory 10 minutes earlier
1
Purpose is not identified
Purpose is somewhat vague
Purpose is identified
Purpose is identified
Purpose is clearly identified Relevant variables are described
1
Purpose
Relevant variables are not described
Relevant variables are not described
Relevant variables are described in somewhat unclear
Relevant variables are described
Materials (optional)
There is not a list of the necessary lab materials
Most lab materials included
All necessary lab materials included but not listed in any
All necessary lab materials included and listed
All necessary lab materials included and listed in an organized
Procedures are not listed
Procedures are listed but not in clear steps
Procedures are listed in clear steps but not numbered and/or and/or in complete sentences
Procedures are listed in clear steps
Procedures are listed in clear
Attendance & Discipline Aim &
1
steps Each step is numbered and in a complete sentence
Procedure
1 Each step is numbered and in a complete sentence Diagrams are included to describe
Data is not represented or is not accurate Data
Data lacks precision Greater than 20%; difference with accepted values
Good representation of the data using tables and tor graphs Less than 15% difference with accepted values Precision is acceptable
Accurate representation of the data using tables and/or graphs Data is fairly precise Less than 10?% difference with accepted value
Accurate representation of the a using tables and/or graphs Graphs and tables are labeled and data is precise with less than 5% 5% difference with accepted values
4
TSCR(X)
Trends / patterns are not analyzed
Trends / patterns are not analyzed
Trends /patterns are logically analyzed for the most part
Trends / patterns are logically analyzed
Questions are not answered
Answers to questions are incomplete
Questions are answered in complete sentences
Questions are answered in complete sentences
Analysis is inconsistent
Analysis is general
Analysis is thoughtful
A statement of the results i s incomplete with little reflection on the lab
A statement of the r esults of the lab indicates whether results support the hypothesis
Accurate statement of the results of the lab indicates whether results support the hypothesis
Tends / patterns are logically analyzed
Analysis / Result
Questions are answered
4
Analysis is not r elevant thoroughly and in complete sentences No discussion was included or shows little effort and reflection on the lab Discussion
Accurate statement of the results of lab indicates whether results support hypothesis Possible sources of error and it was learned from the lab discussed
4
Possible sources of error identified Participation (during experiment
Interview
Student was hostile about participating
Participation was minimal
Did the job but did not appear to be very interested. Focus lost on several occasion
Used time pretty well. Stayed focused on the experiment most of the time
Showed interest, used time very well, guide other students and very focused on experiment
The student cannot answer questions about the experiment
The student can answer some questions about the experiment
The student can answer questions about the experiment and begins to make connections between the experiment and its applications
The student can explain the results of the experiment in detail and the ways in which they relate to the research focus
The student can explain the results of the experiment in detail and the ways in which they relate to the research focus. The student can also evaluate the significance of the experiment to the real situation
NAME OF LECTURER:
Comment by examiner
SIGNATURE:
DATE:
TOTAL SCORE:
Received
1
3
1.0
OBJECTIVE
To determine the relationship between span and deflection
2.0
INTRODUCTION
A beam must possess sufficient stiffness so that excessive deflections do not have an adverse effect on adjacent structural members. In many cases, maximum allowable deflections are specified by Codes of Practice in terms of the dimensions of the beam, particularly the span. The actual deflections of a beam must be limited to the elastic range of the beam, otherwise permanent distortion results. Thus in determining the deflections of beam under load, elastic theory is used.
3.0
THEORY
The double integration method is a powerful tool in solving deflection and slope of a beam at any point because we will be able to get the equation of the elastic curve.
= () is given by )]⁄ [1 + ( = | |
In calculus, the radius of curvature of a curve
In the derivation of flexure formula, the radius of curvature of a beam is given as
= Deflection of beam is so small, such that the slope of the elastic curve this expression the value become practically negligible, hence
= 0 = 1
is very small, and squaring
= 1" Thus,
= 1 " " = = 1 If EI is constant, the equation may be written as:
" = Where, y
= deflection of the beam at any distance x
E
= modulus of elasticity of the beam
I
= moment of inertia about the neutral axis
M
= bending moment at a distance x from the end of the beam
EI
= flexural rigidity of the beam
− = = 2 = 2 − = = 4 4 + − = = 8 12 + + When x = 0; dy = 0 ⸫ A = 0 When x = L/2; y = 0; ⸫
0 = + = −
When x = 0;
= −
X= L/2;
+
(mid span; c)
(at support)
Where E can be obtained from backboard
=
d b
4.0
APPARATUS
Brass Strip Beam
Steel Strip Beam
Hanger and Masses
4.1
Digital Dial Test
PROCEDURE
1) The moveable knife-edge supports was positioned so that they were 400mm apart from each other. 2) The chosen beam was placed on the support. 3) The hanger and the digital dial test indicator was placed at the mid span. The digital reading were zero at first. 4) An incremental load was applied and the deflection for each increment was recorded in the table below. 5) The above steps are repeated using span of 300mm, 400mm and 500mm for both brass and steel beam.
5.0
RESULT
Specimen beam: Brass
= = 105 × 10/ Second moment of area, = 8.3 , = 3.3 Young’s Modulus,
= = (.)(.) = 24.856 Mass of load,
= 100 ×10− × 9.81 = 0.9810
Experiment 1: Span = 500 mm No.
1 2 3 4 5
Mass (N)
0.9810 1.9620 2.9430 3.9240 4.9050
Deflection
Theoretical Def.(
(experimental) (mm)
(mm)
0.59 1.15 1.72 2.26 2.88
0.979 1.958 2.937 3.915 4.894
Use any mass between
100 to 500
)
% Difference
39.73 41.27 41.44 42.27 41.15
Experiment 2: Span = 400 mm No.
1 2 3 4 5
Mass (N)
0.9810 1.9620 2.9430 3.9240 4.9050
Deflection
Theoretical Def.(
(experimental) (mm)
(mm)
0.34 0.66 0.96 1.24 1.55
0.501 1.002 1.504 2.005 2.506
Use any mass between
)
% Difference
32.14 34.13 36.17 38.15 38.15
10 to 500
Experiment 3: Span = 300 mm No.
1 2 3 4 5
Mass (N)
0.9810 1.9620 2.9430 3.9240 4.9050
Deflection
Theoretical Def.(
(experimental) (mm)
(mm)
0.18 0.40 0.55 0.67 0.80
0.211 0.423 0.634 0.846 1.057
Use any mass between
10 to 500
)
% Difference
14.69 5.44 13.25 20.80 24.31
Specimen beam: Steel
= 207/ = 207 ×10/ Second moment of area, = 8.8 = 3.2 = Young’s Modulus,
( ) . (.) =
= 24.03 Mass of load,
= 100 ×10− × 9.81 = 0.9810
Experiment 1: Span = 500 mm No.
1 2 3 4 5
Mass (N)
0.9810 1.9620 2.9430 3.9240 4.9050
Deflection
Theoretical Def.(
(experimental) (mm)
(mm)
0.29 0.56 0.81 1.07 1.33
0.514 1.027 1.541 2.054 2.568
Use any mass between
100 to 500
)
% Difference
43.58 45.47 47.44 47.91 48.21
Experiment 2: Span = 400 mm No.
1 2 3 4 5
Mass (N)
0.9810 1.9620 2.9430 3.9240 4.9050
Deflection
Theoretical Def.(
(experimental) (mm)
(mm)
0.18 0.31 0.44 0.57 0.71
0.263 0.526 0.789 1.052 1.315
Use any mass between
)
% Difference
31.56 41.06 44.23 45.82 46.01
10 to 500
Experiment 3: Span = 300 mm No.
1 2 3 4 5
Mass (N)
0.9810 1.9620 2.9430 3.9240 4.9050
Deflection
Theoretical Def.(
(experimental) (mm)
(mm)
0.08 0.15 0.20 0.26 0.33
0.111 0.223 0.333 0.444 0.555
Use any mass between
10 to 500
)
% Difference
27.93 32.74 39.94 41.44 40.54
5.1
Data analysis
The negative sign in deflection indicates that the deflection is below the unreformed neutral axis. Brass beam in experiment 1
= −
−.× = × × ×. ( )
= 0.979 % Difference = xpmtal−thotal thotal ×100 = −.−(−.) −. ×100 = 43.50% Steel beam in experiment 1
− = = −.× ×× × ( )
= 0.309 % Difference = xpmtal−thotal thotal ×100 = −.−(−.) −. ×100 = 81.23%
6.0
DISCUSSION
Comment on the different between the theoretical and experimental results. Referring to the results from the calculation, we can conclude that, the different between the theoretical and experimental results are different for all Experiment 1, 2, and 3 using steel beam and brass beam. Thus, the percentage (%) of the difference between the theoretical and experimental results are different also. From the experiment, we can notice that, the span with the shorter length will give us the smaller value of deflection when the load is place at the mid span for both theoretical and experimental results. While when the span with the longer length, the higher the deflection occurs to the span than the shorter span.
For Experiment 1 that used 500mm span using steel beam, when the load of 0.981 N/100g was place at the mid span, test indicator give us the reading of deflection with -0.29. When the load is increased until the load reach 4.905 N/500g with difference 100g each reading respectively, the deflection recorded by test indicator are until the last one is -1.33 when the load placed at the mid span are 4.905 N/500g. The values of the deflection for both theoretical and experimental results increase proportionally to the load when the load of 100g, 200g, 300g, 400g and 500g are place on the mid span. For Experiment 2 that used 400mm span using steel beam, the first value of load are same with experiment 1 was place at the mid span, test indicator give us the reading of deflection with -0.18. When the load is increased with the same value in experiment 1, the test indicator also show the increasing reading and the v alue of deflection for this experiment is smaller than the experiment 1. Next, for Experiment 3 using 300mm span of steel beam, when the first load was place at the mid span, test indicator give us the reading of deflection with -0.08. When the load is increased with the same value with the load used in experiment 1 and 2, the values of the deflection for both results increase proportionally to the load as the load are increase. The value of deflection for this experiment is smaller than the experiment 1 and experiment 2 because the length of the span used, 300mm which is shorter than the span used for experiment 1 that is 500mm and experiment 2 that is 400mm. The values of the deflection for both theoretical and experimental results increase proportionally to the load when the load force to the span are increase.
To verify the experiment we done using steel beam, we done another experiment using the brass beam with the same length. From the result we obtain by using brass beam, it show the same as the steel beam experiment. When the value of load using increased, the higher the reading of the deflection. The value of deflection calculated using theoretical also will increase if the value of load is increase.
From the results we get from this experiment, though the different between the theoretical and experimental results are very big, but the deflection in the span increase when the load is increase. Besides that, the value of deflection also increase when the length of span u sed is longer. Thus, we conclude that, the deflection of span is proportional to the load we place on it and the len gth of the span we used.
EXTRA QUESTIONS
1.
Calculate the deflection when x = L/3 (experiment 1, no. 3). Check the result by placing
the digital dial at this position.
a) Calculation: Steel beam When x = L/3, this mean that x = 166.67 (500/3), the value for Deflection (Experimental) we get is – 0.81 and the Theoretical Deflection we get from the calculation is – 1.541. The percentage (%) of the difference between the theoretical and experimental results for this extra experiment is 47.44%.
When, P = 2.9430 N 3
y mak
PL
48 EI (2.9430)(500) 3
48(207000)(24.03)
= – 1.541
When, P = 2.9430 N % Difference = {{-0.81 – (-1.541)}/-1.541}x100 = 47.44%.
b) Calculation: Brass beam When x = L/3, this mean that x = 166.67 (500/3), the value for Deflection (Experimental) we get is – 1.72 and the Theoretical Deflection we get from the calculation is – 2.937. The percentage (%) of the difference between the theoretical and experimental results for this extra experiment is 41.44%.
When, P = 2.9430 N 3
y mak
PL
48 EI (2.9430)(500)3
48(105000)(24.856)
= – 2.937
When, P = 2.9430 N % Difference = {{-1.72 – (-2.937)}/-2.937}x100 = 41.44%
2.
Calculate V mak in experiment 2, no.2.
a) Steel beam Given, Esteel= 207 x 109 Nm-2
Width, b = 8.8mm Thick, d = 3.2mm
I
bd
From Equation,
12
(8.8)(3.32)
3
3
12
= 26.84 mm4
2
From Equation,
v mak
PL
16 EI
(1.9620)(400) 3
16(207000)(26.84)
= -1.413
b) Brass beam Given, E brass = 105 x 109 Nm-2
Width, b = 8.3mm Thick, d = 3.3mm
I
bd
From Equation,
3
12
(8.3)(3.3) 3
12 = 24.856 mm4
2
From Equation,
v mak
PL
16 EI
(1.9620)(400)
3
16(105000)(24.856)
= -3.007
7.0
CONCLUSION
From this experiment, our group managed to determine the relationship between the deflection happened and the span. To determine the deflections happened when the beams under load, elasticity theory is used. From the results we get from this experiment, we knows that, the span with shorter length will give us the smaller value of deflection when the load is place at the mid span for both theoretical and experimental results. While for the span with the longer length, the deflection is higher than the shorter length of the span even though the load used is same for both of the span. Even the different in percentage between the theoretical and experimental results are very big, but the deflection in the span also increase when the load is increase. Thus, we conclude that, the deflection of span is proportional to the length of the span and the load we place on the span.
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