LIGHT STRUCTURE LABORATORY
LIGHT STRUCTURE LABORATORY
FULL REPORT
FULL REPORT
BFC21201
BFC21201
BFC BFC Course Code Course Code BFC21201BFC21201 Course NameCourse Name Makmal Hidraulik Dan Mekanik BahanMakmal Hidraulik Dan Mekanik Bahan
Date Date Group Group
Group Leader
Group Leader Norhafidzah Bt Abdul Rahman Norhafidzah Bt Abdul Rahman
Members of Group
Members of Group 1.Muhammad Amin Bin Rosli1.Muhammad Amin Bin Rosli 2.Mohd Ashraf Bin Mohd Azhan 2.Mohd Ashraf Bin Mohd Azhan 3.Muhammad Arif Bin Mohd Nazir 3.Muhammad Arif Bin Mohd Nazir 4.Mohamad Radzif Bin Mohd Raes 4.Mohamad Radzif Bin Mohd Raes
Lecturer/Instructor/Tutor
Lecturer/Instructor/Tutor Encik Ahmad Fahmy Bin KamarudinEncik Ahmad Fahmy Bin Kamarudin
Received Date Received Date Criteria Criteria 11 22 33 44 55 SCR SCR VTVT TSCR(X)TSCR(X) Attendance Attendance & Discipline & Discipline
Student in laboratory more than 1 Student in laboratory more than 1 hour late
hour late
Student in laboratory within 30 Student in laboratory within 30 minutes to 1 hour late minutes to 1 hour late
Student in laboratory within 10 to Student in laboratory within 10 to 30 minutes late
30 minutes late
Student in laboratory just Student in laboratory just before laboratory s before laboratory starttart
Student in laboratory 10 minutes earlier
Student in laboratory 10 minutes earlier 11 Aim
Aim&&
Purpose Purpose
Purpose is not identified Purpose is not identified Relevant variables are not Relevant variables are not described
described
Purpose is somewhat vague Purpose is somewhat vague Relevant variables are not Relevant variables are not described
described
Purpose is identified Purpose is identified Relevant variables are Relevant variables are described in somewhat unclear described in somewhat unclear
Purpose is identified Purpose is identified Relevant variables are Relevant variables are described described
Purpose is clearly identified Purpose is clearly identified RelevantRelevant variables are described
variables are described 11 Materials
Materials (optional) (optional)
There is not a list of the There is not a list of the necessary lab materials necessary lab materials
Most lab materials included
Most lab materials included All necessary lab materialsAll necessary lab materials included but not listed in any included but not listed in any
All necessary lab materials All necessary lab materials included and listed included and listed
All necessary lab
All necessary lab materials includedmaterials included and listed in an organized and listed in an organized
1 1
Procedure Procedure
Procedures are not listed
Procedures are not listed Procedures are listed but not inProcedures are listed but not in clear steps
clear steps
Procedures are listed in clear steps Procedures are listed in clear steps but not numbered and but not numbered and/or in/or in
complete sentences complete sentences
Procedures are listed in clear Procedures are listed in clear steps
steps
Each step is numbered and in Each step is numbered and in a complete sentence a complete sentence
Procedures are listed in clear Procedures are listed in clear steps
steps
Each step is numbered and in a Each step is numbered and in a complete sentence complete sentence
Diagrams are included to describe Diagrams are included to describe
1 1
Data Data
Data is not represented or is not Data is not represented or is not accurate
accurate
Data lacks precision Data lacks precision Greater than 20%; difference Greater than 20%; difference with accepted values with accepted values
Good representation of the Good representation of the data using tables and tor graphs data using tables and tor graphs Less than 15% difference with Less than 15% difference with accepted values
accepted values Precision is Precision is acceptableacceptable
Accurate representation of Accurate representation of the data using tables and/or the data using tables and/or graphs
graphs
Data is fairly precise Data is fairly precise Less than 10?% difference with Less than 10?% difference with accepted value
accepted value
Accurate representation of the a Accurate representation of the a usingusing tables and/or graphs
tables and/or graphs
Graphs and tables are labeled and data is Graphs and tables are labeled and data is precise with less than 5
precise with less than 5% difference% difference with accepted values
with accepted values
4 4
Analysis / Result
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Trends /patterns are logically analyzed for the most part Questions are answered in complete sentences Analysis is general
Trends / patterns are logically analyzed
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Tends / patterns are logically analyzed
Questions are answered thoroughly and in complete sentences
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Discussion
No discussion was included or shows little effort and reflection on the lab
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
Possible sources of error identified
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
Participation (during experiment
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
1
Interview
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
3
NAME OF LECTURER: SIGNATURE: DATE: TOTAL SCORE:
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.
In calculus, the radius of curvature of a curve
= ()
is given by = [1 + (
)
]
⁄
|
|
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
is very small, and squaringthis expression the value become practically negligible, hence
= 0
= 1
= 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
b d
−
=
= 2 =
2
−
=
=
4
4 +
−
= =
8
12 + +
When x = 0; dy = 0 ⸫ A = 0 When x = L/2; y = 0; ⸫0 =
+
=
−
When x = 0;
=
−
(mid span; c) X= L/2;
+
(at support)Where E can be obtained from backboard
=
4.0 APPARATUS
4.1 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
Young’s Modulus,
=
= 105 × 10
/
Second moment of area,
= 8.3
, = 3.3
=
=
(.)(.)
= 24.856
Mass of load, = 100 ×10
−
× 9.81
= 0.9810
Experiment 1: Span = 500 mmNo. Mass (N) Deflection (experimental) (mm) Theoretical Def.(
) (mm) % Difference1
0.9810
0.59
0.979
39.73
2
1.9620
1.15
1.958
41.27
3
2.9430
1.72
2.937
41.44
4
3.9240
2.26
3.915
42.27
5
4.9050
2.88
4.894
41.15
Experiment 2: Span = 400 mm
No. Mass (N) Deflection (experimental) (mm) Theoretical Def.(
) (mm) % Difference1
0.9810
0.34
0.501
32.14
2
1.9620
0.66
1.002
34.13
3
2.9430
0.96
1.504
36.17
4
3.9240
1.24
2.005
38.15
5
4.9050
1.55
2.506
38.15
Use any mass between
10
to500
Experiment 3: Span = 300 mm
No. Mass (N) Deflection (experimental) (mm) Theoretical Def.(
) (mm) % Difference1
0.9810
0.18
0.211
14.69
2
1.9620
0.40
0.423
5.44
3
2.9430
0.55
0.634
13.25
4
3.9240
0.67
0.846
20.80
5
4.9050
0.80
1.057
24.31
Specimen beam: Steel
Young’s Modulus,
= 207/
= 207 ×10
/
Second moment of area,
= 8.8
= 3.2
=
=
(.)(.)
= 24.03
Mass of load, = 100 ×10
−
× 9.81
= 0.9810
Experiment 1: Span = 500 mmNo. Mass (N) Deflection (experimental) (mm) Theoretical Def.(
) (mm) % Difference1
0.9810
0.29
0.514
43.58
2
1.9620
0.56
1.027
45.47
3
2.9430
0.81
1.541
47.44
4
3.9240
1.07
2.054
47.91
5
4.9050
1.33
2.568
48.21
Experiment 2: Span = 400 mm
No. Mass (N) Deflection (experimental) (mm) Theoretical Def.(
) (mm) % Difference1
0.9810
0.18
0.263
31.56
2
1.9620
0.31
0.526
41.06
3
2.9430
0.44
0.789
44.23
4
3.9240
0.57
1.052
45.82
5
4.9050
0.71
1.315
46.01
Use any mass between
10
to500
Experiment 3: Span = 300 mm
No. Mass (N) Deflection (experimental) (mm) Theoretical Def.(
) (mm) % Difference1
0.9810
0.08
0.111
27.93
2
1.9620
0.15
0.223
32.74
3
2.9430
0.20
0.333
39.94
4
3.9240
0.26
0.444
41.44
5
4.9050
0.33
0.555
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
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 EI PL 48 y 3 mak ) 03 . 24 )( 207000 ( 48 ) 500 )( 9430 . 2 ( 3 = – 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 EI PL 48 y 3 mak ) 856 . 24 )( 105000 ( 48 ) 500 )( 9430 . 2 ( 3 = – 2.937 When, P = 2.9430 N % Difference = {{-1.72 – (-2.937)}/-2.937}x100 = 41.44%
2. Calculate V makin experiment 2, no.2. a) Steel beam Given, Esteel= 207 x 109 Nm-2 Width, b = 8.8mm Thick, d = 3.2mm From Equation, 12 I 3 bd 12 ) 32 . 3 )( 8 . 8 ( 3 = 26.84 mm4
From Equation, EI
PL 16 v 2 mak ) 84 . 26 )( 207000 ( 16 ) 400 )( 9620 . 1 ( 3 = -1.413
b) Brass beam Given, E brass = 105 x 109 Nm-2 Width, b = 8.3mm Thick, d = 3.3mm From Equation, 12 I 3 bd 12 ) 3 . 3 )( 3 . 8 ( 3 = 24.856 mm4
From Equation, EI
PL 16 v 2 mak ) 856 . 24 )( 105000 ( 16 ) 400 )( 9620 . 1 ( 3 = -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.
