DEPARTMENT OF CIVIL ENGINEERING BACHELOR OF CIVIL ENGINEERING
BEC303 / CIVE3807 STRUCTURE, HYDRAULIC AND TRAFFIC LABORATORY GROUP REPORT - STRUCTURE REPORT TITLE THREE HINGED ARCH
GIVEN DATE SUBMISSION DATE LECTURER’S
Haslina Mohamed
NAME
NAME & MATRIC
1. Noor Affendi Bin Dikkir
152015122
2. Muhamed Hafiz Bin Ibrahim
151014220
3. Nabil Zaed Bin Shaiful Nizam
153015510
4. Muhamad Haziq Harahap B Mohd Azili
153015818
5. Hidayat Ahmad Faiz
151914674
Marks
Table of Contents 1.
2.
3.
Chapter 1 ...............................................................................................................2 1.1
Introduction ................................................................................................... 2
1.2
Theory ............................................................................................................3
1.3
Purpose of Work ............................................................................................ 5
1.4
Objective ........................................................................................................5
Chapter 2 ...............................................................................................................6 2.1
Apparatus ....................................................................................................... 6
2.2
Procedure ....................................................................................................... 7
Chapter 3 ...............................................................................................................9 3.1
4.
Chapter 4 ...............................................................................................................9 4.1
5.
6.
Data Analysis ................................................................................................. 9
Chapter 5 .............................................................................................................11 5.1
Discussion ..................................................................................................... 11
5.2
Conclusion .................................................................................................... 11
Chapter 6 .............................................................................................................12 6.1
7.
Data Collection and Recording .................................................................... 9
References .................................................................................................... 12
Chapter 7 .............................................................................................................12 7.1
Appendices ................................................................................................... 12
1
1. Chapter 1
1.1
Introduction In case of beams supporting uniformly distributed load, the maximum bending moment increases with the square of the span and hence they become uneconomical for long span structures. In such situations arches could be advantageously employed, as they would develop horizontal reactions, which in turn reduce the design bending moment. (Kharagpur, 2015)
For example, in the case of a simply supported beam shown in Fig. 1, the bending moment below the load is 3PL/16. Now consider a two hinged symmetrical arch of the same span and subjected to similar loading as that of simply supported beam. The vertic al reaction could be calculated by equations of statics. The horizontal r eaction is determined by the method of least work. (Kharagpur, 2015)
Now the bending moment below the load is 3PL/16 - Hy. It is clear that the bending moment below the load is reduced in the case of an arch as compared to a simply supported beam. It is observed in the last lesson that, the cable takes the shape of the loading and this shape is termed as funicular shape. If an arch were constructed in an inverted funicular shape then it would be subjected to only compression for those loadings for which its shape is inverted funicular. (Kharagpur, 2015)
2
a) Cable in Tension
b) Arch in
Compression
FIGURE 1: Cable and Arch Structure
Since in practice, the actual shape of the arch differs from the inverted funicular shape or the loading differs from the one for which the arch is an inverted funicular, arches are also subjected to bending moment in addition to compression. As arches are subjected to compression, it must be designed to resist buckling. (Kharagpur, 2015)
Until the beginning of the 20th century, since it is a pure compression form, the arch is useful because many building materials, including stone and unreinforced concrete can resist compression, but are weak when tensile stress is applied to them (Reid, 1984). Now, arches are mainly used in bridge construction and doorways. In earlier days arches were constructed using stones and bricks. In modern times they are being constructed of reinforced concrete and steel. (Kharagpur, 2015)
1.2
Theory There are mainly three types of arches that are commonly used in practice: three hinged arch, two-hinged arch and fixed-fixed arch. Three-hinged arch is statically determinate structure and its reactions / internal forces are evaluated by static equations of equilibrium. Twohinged arch and fixed-fixed arch are statically indeterminate structures. (Ambrose, 2012) 3
The indeterminate reactions are determined by the method of least work or by the flexibility matrix method. In this experiment three hinged arch is discussed.
a) Three-hinged arch
b) Two-hinged Arch
c) Fixed hinged Arch
FIGURE 2: Types of Arches
In this experiment, Three-hinged arch is used. The apparatus is set up with height of 200 mm, span of 1000 mm, distance of the load from pin support 125 mm(distance between hanger) x 4 = 500 mm, thickness of arch 8 mm, and width of arch 40 mm .
4
FIGURE 3: Typical Three Hinged Arch
To Find the theoretical values, use the formula H A = WkL/(2h), whereas W is load, h is height, and kL is the distance of the load from the pinned support.
1.3
Purpose of Work The purpose is to find the experimental horizontal thrust with increment of load and compare it with theoretical values of horizontal thrust. After that, a graph is plotted to compare them and to find the margin of error from theoretical and experimental values.
1.4
Objective 1. To determine the relationship between applied load and the horizontal thrust at the support of a three hinge parabolic arch. 2. To compare the value of theoretical and experimental value of horizontal thrust. 3. To draw and plot graph of horizontal thrust versus load for both experimental and theoretical value. 4. To find the percentage of error, % between experimental and theoretical horizontal thrust value.
5
2. Chapter 2
2.1
Apparatus 1.
Support Frame
2.
Three Hinge Arch assembly
3.
A simple support
4.
A roller support
FIGURE 4: Support Frame and Three Hinge Arch Assembly with a Roller and a Simple Support
5. Set of Weights
FIGURE 5: Set of Weights with 5 N each
6
2.2
Procedure 1. Digital indicator is connected to the load cell
2. The indicator is switched on. The indicator is switched on 10 minutes earlier before taking a reading for the purpose of the stability of the reading.
3. The load hanger is placed (where the load is) 500 mm from the distance of the load from the pinned support.
4. The initial reading on the indicator is noted. If the initial value is not zero, the tare button is pressed to make it zero.
7
5. The load is placed on the load hanger.
6. The indicator reading is then recorded. This represents the horizontal reaction of the pinned support.
7. The load on the load hanger is increased the horizontal reaction is recorded.
8. Step 7 is repeated for another four load increments.
9. The result is then tabulated.
10. The experiment is repeated for another set of readings.
8
3. Chapter 3
3.1
Data Collection and Recording Load (N)
Horizontal Thrust (N) Experimental
Theoretical
5
5.1
6.25
10
10.3
12.5
15
15.9
18.75
20
21.5
25
25
26.8
31.25
TABLE 1: Tabulated Result from Experiment and Theoretical Value
4. Chapter 4 4.1
Data Analysis Calculation of the Theoretical value of H orizontal Thrust By using the Formula of Horizontal Force,
HA = For Load 5 N , H A=
For Load 10 N, H A=
For Load 15 N, H A=
For Load 20 N, H A=
For Load 25 N, H A=
2ℎ
(5 )(125 4) (2 200)
(10 )(125 4) (2 200) (15 )(125 4) (2 200) (20 )(125 4) (2 200) (25 )(125 4) (2 200)
= 6.25 N
= 12.5 N
= 18.75 N
= 25.0 N
= 31.25 N
9
Then, a graph of Horizontal thrust of experimental versus theoretical value is produced.
HORIZONTAL THRUST OF EXPER IMENTAL V E R S U S T H E O R E T I C A L V A LU E 35 30 T 25 S U R H T 20 L A T N O15 Z I R O H10
Experimental Theoretical Linear (Experimental) Linear (Theoretical)
5 0 0
5
10
15
20
25
30
LOAD (N)
GRAPH 1: Horizontal thrust of experimental versus theoretical value
To calculate the percentage error, % =|
−ℎ ℎ
Experimental Value =
Theoretical value =
24−10
| x 100%
= 1.0769 (values obtain from graph slope)
22.5−9.5
25−12.5 20−10
Percentage error, % = |
= 1.25 (values obtain from graph slope)
1.0769−1.25 1.25
| x 100% = 13.848 % of error
10
5. Chapter 5 5.1
Discussion Based on the result, the experimental value is lower than the theoretical value. There are many causes of that, such as the d igital indicator cannot detect the remaining load that acted on that arch due to placement of the digital indicator is not correct enough. The type of arch material may also affect the distribution of load on its body.
5.2
Conclusion We can conclude that the relationship between horizontal thrust at the support and the applied load is directly proportional, the higher the load the higher the horizontal thrust at the support.
At hinge at the crown, the rotation of the connected structure is not prevented. Therefore, the moment is zero as it does not resists rotation. Whereas in fixed supports, the bending moment is nonzero as it resists rotation of the connected structure.
The probable source of error in this experiment is the human error; the person who take reading may read the value wrongly or another group member accidently touch the three hinge arch during reading the value. Furthermore, the digital indicator is not reset to zero may make the reading wrong to a minor scale. Moreover, the set of weights used may not identical in size even though the weight is the same could contribute some margin error.
11
6. Chapter 6 6.1
References
1) Kharagpur. (2015). Three Hinge Arch. Retrieved from Online Course NPTEL: http://nptel.ac.in/courses/105105109/pdf/m5l32.pdf
2) Reid, E. (1984). Understanding Buildings. A Multidisciplinary Approach, 12.
3) Ambrose, J. (2012). Hoboken. Building Structures, 32.
7. Chapter 7 7.1
Appendices
APPENDIX I: Support Frame And Three
APPENDIX II: Set of Weights
Hinge Arch
APPENDIX III: Digital Indicator 12
