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330812654-Lab-Report

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DEFLECTION OF CURVE BARS AND DAVITS
TITLE: DEFLECTION OF CURVE BARS AND DAVITS
1.0 OBJECTIVE
To investigate the relationships between load, horizontal deflection and vertical deflection
for a curved davit, an angled davit, a semicircle structure and quarter-circle structure.
2.0 INTRODUCTION
Figure 1 shows the Curved Bars and Davits experiment. It consists of a back
plate, a pair of dial indicators arranged at 90°, and one of four test structures. The two
indicators are on a magnetic base. We can move the base to any position on the back
plate. One of the indicators measures horizontal deflection, the other vertical deflection.
The four structures are a quarter circles, a semicircle, a curved davit and an angled davit.
Each structure has a boss fitted to the free end. This allows us to apply loads and measure
deflections in both the horizontal and vertical directions. Printed on the back plate of the
equipment is some useful information. Make a note of this - we will need it to analyze
our results after we have completed the experiment.
Figure 1
3.0 THEORY
1
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
We have seen that the elongation of a single truss member, when load is
applied, is usually quite insignificant. However, when the accumulative effect of
elongation in all members of a structure is taken into account, the displacements of
some parts of the structure are found to be appreciable. When a beam is subjected to
lateral loading, the deflection is usually much larger than for an axially loaded
member. We have an interest in beam deflection because the design of floor beams
is frequently controlled by the limit on deflection imposed by a code rather that by
the allowable stress. We must also understand beam deflection in order to solve
certain statically indeterminate problems that occur in beam design.
In engineering mechanics, deflection is a term that is use to describe the
degree to which a structural element is displaced under a load. The deflection of a
member under a load is directly related to the slope of the deflected shape of the
member under that load and can calculated by integrating the function that
mathematically describes the slope of the member under that load. Deflection can
be calculated by standard formula (will only give the deflection of common beam
configurations and load cases at discrete locations), or by methods such as “virtual
work”, “direct integration”, “Castigliano’s method”, “Macaulay’s method” or the
“Matrix stiffness method” amongst others. An example of the use of deflection in
this context is in building construction. Architects and Engineers select materials for
various applications. The beams used for frame work are selected on the basis of
deflection, amongst other factors. The elastic deflection f and angle of deflection φ
(in radians) in the example image, a (weightless) cantilever beam, can be calculated
(at the free end) using:
fB 
FL3
3EI
B 
FL2
2 EI
Where,
2
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
F = force acting on the tip of he beam
L = length of the beam (span)
E = modulus of elasticity
I = area moment of inertia
The deflection at any point along the span can be calculated using the
above-mentioned methods. From this formula it follows that the span L is the most
determination factor, if the span doubles, the deflection increases. Building codes
determine the maximum deflection, usually as a fraction of span e.g. 1/400 or
1/600. Either the strength limit state (allowable stress) or the serviceability limit
state (deflection considerations amongst others) may govern the minimum
dimensions of the member required. The deflection must be considered for the
purpose of the structure. When designing a steel frame to hold a glazed panel, one
allows only minimal deflection to prevent fracture of the glass. The deflective shape
of a beam can be represented by the moment diagram, integrated. Deflection occurs
when an object hits a plane surface. In physics deflection is the event where an
object collides and bounces against a plane surface. Deflection is also a tactic used
in battle that describes “leading the target” that is shooting ahead of a moving target
so that the target and projectile will collide. This tactic is only necessary when using
slow projectiles such as a crossbow bolt, or over long distances, such as in aerial
dogfight.
CAUTION: The most common mistake in computing deflection is caused
by using "w" as load per foot instead of load per inch. The derivation of the
deflection formulas uses the unit of inches for all the factors in the formula.
Uniformly distributed beam loads "w" are normally described as load per foot
which must be converted to the proper load per inch value before insertion into the
deflection formula. If "W" is used for the total distributed load instead of the load
per unit of length ("w") this conversion is not necessary.
3
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
4.0 EQUIPMENT
For student to investigate two common structures and two common davit structures
Curve bar and davit equipment
Curved davit deflections
4
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
5.0 PROCEDURE
1. Referring to Figure 1, set up the equipment to test the semicircle first. Ensure you
have mounted the semicircle with a plate each side of the end, and you have
damped in securely.
2. Measure and record the breadth and, depth of the section checking several places
on the structure and taking an average.
3. Clip the weight hanger onto the two lugs on the loading boss. Gently pull down
on the weight hanger and note the direction the loading boss on structure moves.
4. Set the indicator positions so they contact the horizontally and vertically and have
the maximum amount of travel in each direction.
5. Carefully zero the indicators
6. Apply a mass of 100g to the hanger; tap the test frame to reduce the effects of
friction then take readings of both indicators.
7. Repeat with masses up to 500g in 100g increments tapping the test frame each
time.
8. From the measurements of the section calculate the second moment of area ‘I’
Enter all of your results and values into Table 1.
9. Remove the semicircle and attaching it to the side of the frame rather than the
bottom member, replace it with the quarter circle.
10. Ensure there are clamp plates each side of the structure and the indicator positions
give the amount of travel needed for the maximum loading.
11. Repeat the experiment. Similarly repeat the experiment for the curved davit and
the angle davit.
12. Enter all results into Table 1. Calculate the ‘I’ value for each structure as the
manufacturing process may change the thickness and width of the material.
13. Plot graphs for each section, with load versus the horizontal and vertical
deflection. Calculate the gradient of each line in mm/N. Compare this to values
calculated form the standard formulae for each section or those calculated from
first principles
5
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
6.0 DATA
Breadth Breadth Breadth
1
2
3
(mm)
(mm)
(mm)
Semicircle
Deflection
Quarter
circle
Deflection
Curved
Davit
Deflection
Angle
Davit
Deflection
Depth Depth Depth
1
2
3
(mm) (mm) (mm)
Average
depth
(mm)
19.20
19.20
19.20
19.20
3.50
3.50
3.50
3.50
19.20
19.20
19.20
19.20
3.50
3.50
3.50
3.50
19.19
19.10
19.20
19.16
3.15
3.10
3.00
3.08
19.00
19.00
19.00
19.00
3.20
3.50
3.30
3.33
Mass(g) Load(N)
0
100
200
300
400
500
Average
breadth
(mm)
0
0.98
1.96
2.94
3.92
4.90
I value (m4)
Semicircle
Deflection (mm)
V
H
0
0.82
1.73
2.87
4.09
5.46
0
0.48
2.01
3.45
4.91
6.78
6.86x10-11
Quarter circle
Deflection (mm)
V
H
0
0.63
1.37
2.21
2.45
3.38
0
0.49
1.03
1.60
1.76
2.40
6.86x10-11
Curved Davit
Deflection (mm)
V
H
0
0.24
0.55
0.98
1.22
1.74
0
0.35
0.56
1.52
1.89
2.74
4.6652x10-11
Angle Davit
Deflection (mm)
V
H
0
0.13
0.47
0.74
0.91
1.19
0
0.23
0.91
1.46
1.79
2.38
5.8466x10-11
NOTE: All the data shown above, get from calculation.
6
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
7.0 CALCULATION
The following information as well as that printed on the back plate is:
type
radius
∆H
∆V
2PR3
π PR3
R=150mm
EI
2EI
R=150mm
PR3
π PR3
2EI
4EI
PRL (2R + L)
PR2 (4L+π R)
2EI
4EI
PL1L2(0.707L1+L2) + PL23
PL22 (3L1+L2)
Semicircle deflection
Quarter circle deflection
Curved davit deflections
R=75mm
L
L=150mm
Angel davit deflections
45o
L2
R=105mm
L1=150mm
L1
L2=105mm
2EI
6EI
6EI
For a rectangular section: I =bd 3 /12
Semicircle deflection
7
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
R = 150mm
E  69GNm 2
b = 19.20mm
d = 3.50mm
I 
bd 3
12
 19.20 x10 3  3.50 x10 3  3


12

 6.86 x10 11 m 4
V 
 
P N 




PR 3
2 EI
2 PR 3
EI
V
8
H
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
  0.98 150 x10 3 
2 69 x10 9  6.86 x10 11 
3
0.98
 1.0976 x10
3

 1.3975 x10
m
 1.96 150 x10 3 
2 69 x10 9  6.86 x10 11 
3
1.96
 2.1952 x10
3

  2.94  150 x10 3 
2 69 x10 9  6.86 x10 11 
 3.2928 x10
3

4.90
3

3


3

3

3

3

m


2 2.94 150 x10 3
69 x10 9 6.86 x10 11
3

m

m
  3.92  150 x10 3 
2 69 x10 9  6.86 x10 11 

 4.3904 x10 3 m
 5.5900 x10 3 m


2 3.92 150 x10 3
69 x10 9 6.86 x10 11
  4.90  150 x10 3 
2 69 x10 9  6.86 x10 11 

 5.4880 x10 3 m
 6.9876 x10 3 m
3

21.96 150 x10 3
69 x10 9 6.86 x10 11
 4.1925 x10
m
3
3.92
3
 2.7950 x10
m
3
2.94


2 0.98 150 x10 3
69 x10 9 6.86 x10 11


2 4.90 150 x10 3
69 x10 9 6.86 x10 11


Quarter circle
9
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
R=150mm
b=18.20mm
d = 3.20mm
E  69x10 9
I 
bd 3
12
 19.20 x10 3  3.50 x10 3  3


12

 6.86 x10
11
m




4
V 
 
PR 3
4 EI
PR 3
2 EI
V
10

MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
P N 
  0.98 150 x10 3 
4 69 x10 9  6.86 x10 11 
2 69 x10 9 6.86 x10 11
 0.5488 x10 3 m
 0.3494 x10 3 m
3
0.98
 1.96  150 x10 3 
4 69 x10 9  6.86 x10 11 

3
1.96
 1.0976 x10
3

 1.6464 x10

3

3
2 69 x10 9 6.86 x10 11
 2.1952 x10 3 m
 1.3975 x10 3 m
 3.92  150 x10 3  3

  4.90  150 x10 3 
4 69 x10 9  6.86 x10 11 
2 69 x10 9 6.86 x10 11
 2.7440 x10 3 m
 1.7470 x10 3 m
Curved Davit



m
  3.92  150 x10 3 
4 69 x10 9  6.86 x10 11 


m
 2.94  150 x10 3  3
 1.0481x10
m
3
4.90

2 69 x10 9 6.86 x10 11
3
3.92
1.96  150 x10 3  3
 0.6988 x10
m
  2.94  150 x10 3 
4 69 x10 9  6.86 x10 11 
3

2 69 x10 9 6.86 x10 11
3
2.94
 0.98 150 x10 3  3
 4.90  150 x10 3  3



Deflection
11
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
R = 75mm
L = 150mm
b=19.16mm
d = 3.08mm
E = 69 GNm-2
bd 3
12
I 


 19.16 x10 3 3.08 x10 3


12

 4.6652 x10
V 
m

3



4
PR 2
 4 L  R 
4 EI
 
P N 
11

PRL
 2R  L
2 EI

V
0.98
12
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
 0.98  75 x10 3  2
 4  69 x10 9  4.6652 x10 11 
 4150 x10     75 x10 
3
3
 0.2663 x10 3 m
1.96   75 x10 3  2
1.96
 4  69 x10 9  4.6652 x10 11 
 4150 x10     75 x10 
3
3
 0.5326 x10 3 m
 2.94  75 x10 3  2
2.94
 4  69 x10 9  4.6652 x10 11 
 4150 x10     75 x10 
3
3
 0.7989 x10 3 m
 3.92  75 x10 3  2
3.92
 4  69 x10 9  4.6652 x10 11 
 4150 x10     75 x10 
3
3
 1.0652 x10 3 m
 4.90  75 x10 3  2
4.90
 4  69 x10 9  4.6652 x10 11 
 4150 x10     75 x10 
3
3
 1.3314 x10 3 m
 0.98  75 x10 3 150 x10 3 
 2  69 x10 9  4.6652 x10 11 
 2 75 x10   150 x10 
3
3
 0.5137 x10 3 m
1.96   75 x10 3 150 x10 3 
 2  69 x10 9  4.6652 x10 11 
 2 75 x10   150 x10  
3
3
 1.0275 x10 3 m
 2.94  75 x10 3 150 x10 3 
 2  69 x10 9  4.6652 x10 11 
 2 75 x10   150 x10 
3
3
 1.5412 x10 3 m
 3.92  75 x10 3 150 x10 3 
 2  69 x10 9  4.6652 x10 11 
 2 75 x10   150 x10 
3
3
 2.0550 x10 3 m
 4.90  75 x10 3 150 x10 3 
 2  69 x10 9  4.6652 x10 11 
 2 75 x10   150 x10 
3
3
 2.5687 x10 3 m
Angle Davit Deflection
13
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
L1 = 150mm
L2 = 105mm
b = 19.00mm
d = 3.33mm
E = 69 GNm-2
bd 3
12
I 


 19.00 x10 3 3.33 x10 3

12


 5.8466 x10
V 
 
P N 
11
m


3



4
PL22
 3L1  L2 
6 EI
PL1 L2  0.707 L1  L2  PL32

2 EI
6 EI

V
0.98
14
MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
 0.98 0.15 0.105  0.707  0.15   0.105  
 2  69 x10 9  5.8466.x10 11 
 6  69 x10  5.8466 x10 
3x150 x10 3   105 x10 3 
 0.98 0.105 3
 0.2477 x10 3 m
 6  69 x10 9 5.8466 x10 11 
 0.98 105 x10 3  2
9
11
 0.4506 x10 3 m
1.96 0.15 0.105   0.707  0.15   0.105  
 2  69 x10 9  5.8466.x10 11 
 6   69 x10  5.8466 x10 
3x150 x10 3   105 x10 3 
1.96 0.105 3
 0.4955 x10 3 m
 6  69 x10 9  5.8466 x10 11 
1.96 105 x10 3  2
9
1.96
11
 0.9013 x10 3 m
 2.94 0.15 0.105  0.707  0.15   0.105  
 2  69 x10 9  5.8466.x10 11 
 6   69 x10 9  5.8466 x10 11 
3x150 x10 3   105 x10 3 
 2.94 0.105 3
 0.7432 x10 3 m
 6  69 x10 9  5.8466 x10 11 
 2.94  105 x10 3  2
2.94
 1.3519 x10 3 m
 3.92 0.15 0.105  0.707  0.15   0.105  
 2  69 x10 9  5.8466.x10 11 
 6  69 x10 9  5.8466 x10 11 
3x150 x10 3   105 x10 3 
 3.92 0.105 3
 0.9910 x10 3 m
 6  69 x10 9  5.8466 x10 11 
 3.92 105 x10 3  2
3.92
 4.90 105 x10 3  2
4.90
 6  69 x10
5.8466 x10 
3x150 x10   105 x10 
9
3
11
 1.8026 x10 3 m
 4.90 0.15 0.105  0.707  0.15   0.105  
 2 69 x10 9 5.8466.x10 11

3

 4.90 0.105 3

 6  69 x10 9 5.8466 x10 11 
3
 1.2387 x10 m
 2.2532 x10 3 m
Difference ratio
Difference ratio = theory value – experiment value x 100%
Theory value
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MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
Parts
P= 4.90N
V
Semicircle
deflection
Quarter
deflection
Curved Davit
deflection
Angle Davit
Deflection
5.4880  5.46
 100%
5.4880
 0.5%
2.7440  3.38
 100%
2.7440
 23.18%
1.3314  1.74
 100%
1.3314
 30.69%
1.2387  1.19
 100%
1.2387
 3.93%
H
6.9876  6.78
 100%
6.9876
 2.97%
1.7470  2.40
 100%
1.7470
 37.38%
2.5687  2.74
 100%
2.5687
 6.67%
2.2532  2.38
 100%
2.2532
 5.63%
9.0 OBSERVATION
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MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
From the experiments that have been done, we found that there was a deflection at
the horizontal and vertical axis. When the load had been applied to the structure; the
indicator gave a value for both of the axis.
The graph plotted is linear, when the more load applied to the structure using
hangers and mass, there are more deflection happened. From collected data, found that
there is a little bit different between theory and experiment. The most deflection was from
semicircle structure on the horizontal and the lowest deflections value came from quarter
circle structure.
Experiment value has a different from calculation value. The differences
percentage is 0.5% for the vertical axis and 2.97% for the horizontal axis for semicircle
deflection. For quarter circle deflection is 23.18% is for vertical axis and 37.38% for the
horizontal axis. Meanwhile for curved davit deflection for the vertical axis is 30.69% and
for horizontal axis is 6.67%. For the angle davit deflection, the result for differential
between calculation value and experiment value is 3.93% for vertical axis and 5.63% for
horizontal axis.
10. RECOMMENDATION
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MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
The valued from the experiment and calculation have a bit differences. This is because of
some error had happened when the experiment been done. This was happen because of
some rectification factor.
The factors are:
i)
ii)
iii)
It should be that the two digital deflection indicators is not really set at
90° to each other on the back-board
The experiment equipment place on the Jared table, and this influence
the reading of digital deflection indicators.
The experiment equipment not complete.
Solution:
i. It should have the gadget to make sure the indicator is set in 90°.
ii.
Do the experiment on the floor or on the stable place to avoid it from
jar.
iii.
There should be has a computer to transfer the data to get graph.
11. CONCLUSION
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MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
From the experiment, our objective which is to investigate the relationships
between load, horizontal deflection and vertical deflection for a curved davit, an angled
davit, a semicircle structure and quarter-circle structure are successful. There have the
differences of deflection between for a curved davit, an angled davit, a semicircle
structure and quarter-circle structure. The graph plotted is linear, when the more load
applied to the structure using hangers and mass, there are more deflection happened.
Even though there is a little bit difference between theoretical and experimental result.
This is because there are some errors occur as we mention in recommendation.
12.0 REFERENCES
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MAKMAL PEPEJAL
DEFLECTION OF CURVE BARS AND DAVITS
1. Mechanic of material, sixth Edition SI unit, R.C Hibbeler.
2. Engineering mechanic, third revised edition, Tata McGraw-hill
3. Engineering Mechanic, static and dynamic, third edition McGraw-Hill book
company, Singapore.
4. Engineering Mechanic( si unit), S.C Mathur, Fourth Edition, S.K. KATARIA &
SON.
5. www.tqstructure.com
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MAKMAL PEPEJAL