Generally, the properties are sealed form structures that are supposed to cover the available spaces to make a safe destination to stay inside. Such need was usually fulfilled by the covering system and assisting system. For something of covering roof structure slab were made as the support for that covering is provided by the machine of beam and column. But for the reinforced concrete shell framework both of these systems are put together as one. So that the structure covers the large free areas between columns, providing more free spaces.
The framework whose thickness is very less set alongside the period and breadth of the structure are considered as the slim shell structures. For these types of structures the goal is to reduce its self weight by causing the composition as thin as is possible, permitted by the useful requirements. Which now will work as a membrane which is clear of the top bending stresses. Where optimum structural gain is obtained in more economic ways, with the use of less material.
Figure: Roof shell structure (Dekker, 2001)("Intro To THE OVERALL Shell Theory" 2001)
Nowadays, mostly found in commercial buildings, storage area facilities, residential complexes, well matched up for constructing intricate curves and so on.
1. 1 SHELLS IN ENGINEERING
As the shell set ups have more strength with respect to its do it yourself weight, it is gaining the popularity in the areas where there is a threat of earthquake and hurricane. There are plenty of places on earth where there's a threat of these natural disasters.
It is therefore essential to assess the shell structures to ensure the best and safe design method for future, to stay away from the potential accidents. The essential mechanics of the 3-D framework are different then your 2-D structure, therefore there is not any necessary that the model mixture method which produce the correct result for the 2-D composition should be valid for 3-D structure as well. The actual fact that the less research done up to now in the dynamics of shell composition is startling. In addition there were various limitations on the study done. On the basis of available research done up to now, it is difficult to conclude anything about the shell composition. Therefore there's a need for more research in the area to come quickly to one summary. (Shadi Ostavari Dailamani, 2008). This research paper examines the different model combination methods for shell structures and investigations their precision for shell structures.
1. 1. 1 ADVANTAGES OF SHELL STRUCTURES
High strength with respect to its personal weight. (Major requirements to evaluate efficiency )
Very High Stiffness
Large space covered
Lowers the building cost
Aesthetic value
1. 1. 2 DISADVANTAGES
Concrete being the porous materials can lead to the situation of seepage
Due to its geometry, it is not possible to include another floor above it. Essentially it's the roof covering structure.
1. 2 MAJOR SHELL TYPE STRUCTURES
Dome structure
Cylindrical Shell
Hyperbolic paraboloid Shell
Toroidal Shell
In real life practice cylindrical shells tend to be selected for covering considerable open spaces, as it requires less number of internal supports. We see the common examples of cylindrical shells used for covering the roofs near us, such as ability channels, garages, large supermarket, warehouses etc.
1. 3 Seeks OF YOUR PROJECT
The primary goal of the research is to create the result which ultimately shows the accuracy of different model mixture methods in shell composition using deeper knowledge and understanding about the dynamic response of shell buildings under earthquake launching.
1. 4 Targets FROM THE PROJECT
To understand the development of the shell ideas eventually.
To acquire the knowledge of powerful response and model combination for a shell composition.
To understand the mathematical and mechanical theory underpinning numerical modelling approaches for the response of buildings put through earthquake loading.
To verify the FEM programme by cross examining the rate of recurrence, displacement, stress etc.
To be able to develop and evaluate the 3-D civil engineering problems through available finite factor program (ABAQUS).
To interpret the response spectra of varied earthquakes.
To show the results and knowledge of the shell structure to the global community.
1. 5 PROJECT DELIVERABLES
Documentation of an books review and methodologies developed.
A model is created
Verification the FEM program (ABAQUS)
Accuracy of model combination for shell structure is known
Presentation of research effects and suggestions
Preparation of a professional draft
CHAPTER 2
2. 0 Books SURVEY
2. 1 Short OUTLINE ON THE LINEAR SHELL THEORIES
Many ideas have been submit in earlier years. These ideas were based on the linear elasticity ideas. Generally it predicts the stresses and deformation for skinny shells put through the minutest deformation. Which means the Hooke's regulation can be employed to the shell composition. 2D examination of shell buildings leads to the wrong path, therefore to get the correct result 3-D evaluation should be done. Then the analysis is done using the theory of linear elasticity. Due to the intricacy of the research of this composition it is further deduced into the research of deformation of the center surface only, by the adoption of some hypothesis. i. e the composition can be considered as the 2D. (Dekker, 2001)
Love was the pioneer of the shell theory devised a shell theory which is also known as first- order approximation shell theory. This theory was based in the traditional linear elasticity. Several downsides were seen in the Loves theory which needs some corrections.
E. Resistor later develops the first order approximation theory which taken out some insufficiency in the Loves theory. The equilibrium equation, strain-displacement relationship and stress resultant formula were developed from by using the same Love-Kirchhoff hypothesis by neglecting the bigger order z/Ri, (Where Ri i= 1, 2) are the radii of curvature of the middle surface) which yeilds the tiny values.
Timoshenko's theory is slightly like the Love theory which adopts the Kirchhoff-Love hypothesis and dismissed the percentage of z/Ri near to the one.
Higher order approximation theory is separately developed by Lur'ye, Flugge, and Byrne. This theory combines the assumptions of Kirchhoff hypothesis and small deflection to give the general solution. Special concern is taken to omit the beliefs of z/Ri.
As this theory appears to be not elegant, many other theories were proposed then after. Stress conditions, geometry, selection of deformation and launching were the essential factors that impact different shell theories. Novozhilov, Vlasov, E. Reissner, Leissa and many more proposed the shell theory that was based on the essential basic principle of Love- Kirchhoff's assumptions. Gol'denveizer was the first man to formulate the conditions for compatibility of strain components and his contribution is considered as a treasured in the annals of shell ideas.
During the previous century, the membrane theory established by Beltrami and Lecornu was getting popularity. Sokolovskii modified the membrane theory and created the various characteristic properties. The usefulness of the Airy's stress function for resolving the membrane problem was found out by Pucher.
Shallow shells are the next exemplory case of specialized shell ideas developed by Donnel, Vlasov and Mustari. The thin shell which includes generally low surge compared to the course and used as roofing covering are known as the shallow shells. Due to their comfort and ease the governing formula of this idea were found to be amazingly easy in handling the issues. Additional assumptions were designed for simplification of strain-displacement relation, equilibrium and compatibility equations combined with the classical Kirchhoff-Love hypothesis to come up with a new formula.
According to the D'Alambert theory the dynamic formula of motion can be acquired by the amount of inertial power and body force and body point in time produced by the bottom acceleration of the mass. Initially the equation originated by Love and then various improvements were proposed in the course of time by different analysts like Kraus, Flugge and many others. (Dekker, 2001)
2. 2 THEORETICAL ANALYSIS
The basic theoretical evaluation is detailed by Anooshiravan Farshidianfar on his paper "free vibration evaluation of round cylindrical shells". (Anooshiravan Farshidianfar, 2012). A cylindrical shell was considered with the regular thickness(h), axial length(L), indicate radius(R), poission's ratio() density() and the Young's modulus of elasticity(E) as shown by the shape.
Figure: cylindrical shell with coordinate system (Anooshiravan Farshidianfar, 2012)
The formula of motion can be expressed by the following equations
In which Lij (i, j=1, 2, 3) is differential providers regarding x, and t. Various solutions are given by the many personal, but in this paper Love-Timoshenko method is used to compute the natural frequencies and corresponding mode designs.
Assumption of the synchronous movement is made as a way to resolve the formula 1
Where,
f(t) represents the scalar setting coordinate respective to mode shapes U(x, ), V(x, ) and W(x, ).
The spatial dependence of the model condition between the longitudinal and circumferential course is carried out by the differing separation method. Hence the deformation in three dimensions (u, v, w) is obtained by
Where,
»m is the axial influx number
And n is the circumferential wave parameter.
is the circular regularity of the natural vibration
And A, B and C will be the constants
Substituting the equation (3) in the last formula (1) and handling it by using theory gives the homogenous matrix solution.
Where,
| Cij | (i, j=1, 2, 3) will be the function of »m, n and a consistency parameter.
According to Love-Timoshenko The coefficient matrix, | Cij | can be obtained by
For nontrival solution the determinant of the coefficient matrix in formula (4) must be zero.
det |Cij | = 0; i, j=1, 2, 3 (7)
On solving the equation the following two eigenvalue problems are obtained
For the known value of »m there can be found a number of proper worth for therefore the formula (7) vanishes.
Similarly, for the given value of one or multiple beliefs exist so the equation (7) vanishes.
The cubic equation in conditions of the non dimensional regularity parameter 2 is obtained by fixing the equation (7). The three positive root base obtained are the natural frequencies of the cylindrical shells classified as axial, tangential and radial. A minimal frequency usually associated with the radial motion.
2. 3 RESPONSE SPECTRUM
The basic setting superposition methodology, that is limited to linear elastic research, produces the complete time record response of member causes and displacements. Within the previous there are two major drawbacks by the use of the procedure. First, the strategy produces an oversized quantity of end result data that may require a big volume of process effort to carry out all doable style bank checks as a operate of your energy. Second, the research should be recurrent for numerous earthquake motions so as to assure that every one frequencies are thrilled, since a reply spectrum for just one earthquake during a such that course isn't a swish function.
The response spectrum method has computational benefits on predicting the displacement and member forces in virtually any structural research. The strategy entails the calculation of entirely the most values of the displacements and member forces in every method of response spectra that which is the common of many earthquake motion. A recently available development in neuro-scientific technology and computer has made easy and fast to investigate the tons of response spectra in less time than it used to adopt before.
The typical model response is distributed by the next equation
. . . . . . . . . . . . . . . . . . . . (8)
The involvement factors can be calculated as
where i represent to three orthogonal route x, y or z. To be able to obtain the approximate response variety one must pass the essential two hurdles. First, for the known ground motion the highest possible optimum displacements and pushes must be projected. Second, following the effect for the three orthogonal recommendations is fixed it is necessary to calculate optimum reaction due to the three components of earthquake movement performing concurrently. (Wilson, n. d. )
Typical types of response spectrahttp://eqtap. edm. bosai. go. jp/useful_outputs/article/fujino/images/figure_4. gif
Fig: 1 (a)
Fig: 1 (b)
Fig: 1 (a) Acceleration response range. (F. Yozo, 2003)
Fig :1(b) Displacement response range (Spyrakos, 2012)
2. 4 MODEL Mixture METHODS
As the maximum response of any framework cannot be considered this is the maximum of different modes, this problem gives surge to the model combo options for estimating the optimum response. Mix methods are the following:
Absolute - optimum worth are added together
Square base of the amount of the squares (SRSS)
Complete quadratic combo (CQC) - a method that is an improvement on SRSS for meticulously spaced modes
Complex complete quadratic mixture method (CCQC)
Impulsive mass contribution (IMP )
Convective mass contribution(CONV)
The absolute maxima of the model responses plus the rectangular base of the sum of the squares of the rest of the model replies (NRL)
The average of the total maxima of the model reactions plus the rectangular base of the amount of the squares of the model responses (CFE)
The most traditional approach that is used to compute an most effective value of displacement or make within a construction is by using the total of the entire of the modal response worth. This strategy represents that the highest possible modal principles, for all ways, occur concurrently.
(Alberto Lopez, 1996)
Other solution common solution to estimate the utmost model displacement and drive, is by using the Square Base of the Sum of the Squares, SRSS. The SRSS technique represents that all of optimum modal principles are statistically indie.
(Alberto Lopez, 1996)
For 3d structures, in which a large range of frequencies are almost equivalent, SRSS assumption is not justified. Recently completed studies indicates the SRSS method is suitable for most of both dimensional constructions. Good facts and the dependability with this SRSS strategy containing the great effects on simple two dimensional framework, it has been used for active examination of the 3d structure, without substantiation. (E. L Wilson, 1981)
As the various studies were done then after it was proved that the SRSS method is good for analyzing both dimensional framework with well separated model frequencies. This drawback contributes to the new method of modal combination based on the random vibration theories, Complete Quadratic Combination, CQC, a way that was initially released in 1981.
(Alberto Lopez, 1996)
It was greatly accepted by designers and has made place in the many latest seismic evaluation computer programs too. It's observed which regarding nonclassical damped linear method, which includes complicated eigenvalues as well as eigenvectors, this seismal responses count on not merely the modal shift response but also the modal speed reaction.
A similar method is used to dectuct the CQC method. Since deduction associated with CQC algorithm regarding characteristically damped linear system, any closed-up method associated with response-spectrum complicated mode superposition calculation regarding highest seismal results at virtually pretty much almost every host to a linear elastic construction having elaborate modal features is really deduced, as well as a brand new modal displacement-velocity correlation coefficient are taking part form long-familiar modal displacement correlation throughout typical CQC formulation. The new criteria for computation of highest seismal results of constructions with nonclassical damping organic complete quadratic blend (CCQC) method is developed. (Xi-Yuan ZHOU1, 2004).
(Xi-Yuan ZHOU1, 2004)
Others appears to have be not importance, nonetheless they are calculated as
The average of the definite maxima of the model reactions plus the square base of the sum of the squares of the model reactions (CFE)
(Alberto Lopez, 1996)
And the definite maxima of the model replies plus the square root of the total of the squares of the rest of the model responses (NRL)
(Alberto Lopez, 1996)
Where,
Sj is the utmost of i | Si |
2. 5 RELEVANT WORK
A ALTERNATIVE TO The SRSS Method In Seismic Analyis
Various issues in using the traditional SRSS method on active evaluation was illustrated by E. L Wilson and his acquaintances in the year 1981. A symmetrical four storey building was used to demonstrate the result. Centre of mass of the model building was located 25 in. from the geometric focus on each floor of the building. Earthquake action was applied in one course and first 12 natural frequencies are obtained. Out of which some are tightly spaced, like 13. 869 and 13. 931 are first and second, 108. 32 and 108. 80 are eighth and ninth respectively. These tightly spaced frequencies show that the 3d building was created to resist earthquake equally.
A response range evaluation was conducted by the use of 12 frequencies, the building was subjected to one component of Taft, 1952. The effect demonstrates the SRSS method produces the values of foundation shear by significantly less than thirty percent approx, while the amount of the total beliefs overestimated all prices. Alternatively use of CQC method results were practical and enter into agreement with the precise time history solution. The CQC method also provides route of the model bottom shear which shows the elimination of SRSS method error. (E. L Wilson, 1981)
This paper exhibited that the CQC method is preferable to the SRSS method in model analysis. As it has a acoustics theoretical basis and accepted by many experts. Although it does not reveal any indications that CQC method is relevant to the shell structures as well.
On the exactness of response range examination in seismic design of concrete structure
Three prototype multi storey pre-cast building with varying connections (hinged, cross and moment in time resisting) was examined. The goal of the analysis was to show the value of higher methods with differing structural connection. Three prototype specifically model 1 (structure system with interconnection), model 2 (frame system with emulative interconnection only on the top floor) and model 3 (structure system with emulative connection) were put through pseudo-dynamic test at the Western Laboratory for Structural Assessment of the joint research center of the European Community (ELSA). For experimental research the east-west element of the improved Tolmezzo accelerogram was used for the inspection. The results expected by the model evaluation is found to be lower than the correct nonlinear analysis. The result showed the nature and worth of displacement is agreement while the storey forces didn't. Thus, the paper also demonstrates that it is wii idea to count on the conservative strategy of seismic design depending on modal evaluation with response range. It also clarifies that the difference in the results is due to the role of higher vibration settings. The force across the height is redistributed because of the aftereffect of opposing vibration. (Fabio Biondini, n. d. )
According to the paper the traditional method of structural evaluation for multi storey building is available to be unreliable. While there is not any evidence that it contains the same for shell structure.
Numerical Analysis on reliability of mass spring model for cylindrical tanks under seismic Excitation
This newspaper compares the simplified Mass Spring and coil Model (MSM) suggested by Malhotra and his colleague, (Malhotra, 2000) way for determining the bottom shear, overturning minute and Maximum Sloshing Wave Elevation (MSWH) with the Results of Finite Factor Modelling (FEM) under the action of earthquake. The research was conducted on three the latest models of of cylindrical tank which has the many heights to the radius (H/R= 2. 6, 1. 0, 0. 3). Common cause of failure is pointed out to be the shell bucking towards the bottom. Three models were studied by the excitation of five available earthquakes whose peak floor acceleration amounts from 2. 9 to 8. 3 m/s2. The time history analysis was performed and the results were obtained by using Amount (summation of the utmost computed values), SRSS (Square Reason behind Amount of Squares), IMP (Impulsive mass contribution) and CONV ( Convective mass contribution). The period obtained through convective and impulsive and FEM shows an agreement although it also talks about that the reliability of the MSM in predicting natural period is straight proportional to sloshing method. SRSS method is found to be much better than SUM. However it is stated that the simplified MSM may provide the error up to 70% with esteem top FEM results. (M. A. Goudarzi, 2009)
This paper provides that the simplified MSM method cannot be respected as the results can vary greatly immensely which could mislead the composition design. Nevertheless the method of examining the roof structure shells may vary.
Dynamic Examination of Slender Steel Distillation Towers
Two metal distillation towers have been analyzed due to its high slenderness proportion and the chance of set up it in the seismic area. The effect was likened between five different model combination method to show the effect of choosing various methods. 1. Definite total of the model reactions (Ab muscles) 2. The rectangular root of the amount of the squares of the model response (SRSS) 3. The overall maxima of the model reactions plus the rectangular base of the sum of the squares of the rest of the model responses (NRL) 4. The common of the definite maxima of the model responses plus the square root of the total of the squares of the model responses (CFE) 5. The complete quadratic combo (CQC). The material property of the metal is A-516 metal, class 70, modulus of elasticity 187. 3 GPA, and Produce stress 254. 9 MPa. Ground impact is neglected, mass syndication and weight were symmetrical except the breeze load. Only the strain is compared with various model combination methods and it illustrated that ABS gives the higher bound response while the CFE and NFL guideline exhibits the similar mother nature and CQC and SRSS almost produce the same magnitude. As the structure was to be built on high seismic risk area CFE method was adopted and it suggests that the CQC can be utilized in case of economic profitability. In addition it also declares that the even a tiny deviation on damping may affect significant change in response. (Alberto Lopez, 1996)
They do not take the effect of soil as the soil could be the integral factor in designing in the place of high seismic risk, the newspaper didn't do any moment history nonlinear evaluation and low damping was considered. In my personal view the results may not succeed to utilize the results for rooftop shell structure.
The research newspaper has shown that the classical SRSS method is good for estimating the response of two dimensional framework, but fails to hold the reputation for 3d or multi storey set ups with strongly spaced regularity. That error is minimized through CQC method. Simplified MSM cannot be also trusted, but the interesting effect is shown by the paper written by Fabio Biondini and his fellow workers, that even the response spectrum might not always produce the right result. But do not require mentioned that the idea supports the same for roofing shells as well. So there's a huge need of research needed to know the real space and understanding in rooftop shells.
2. 6 Destruction OF STRUCTURES DUE TO EARTHQUAKE
The main factor that governs the look of the building is its do it yourself weight and the live weight that it's expected to hold. Usually the small vibration and the Rayleigh movements in the vertical route created by the small tremors are tolerated by the most buildings. Those buildings that are situated on the lateral area of the epicenter are inclined to more problems as it induces the back and forth motion. Structural failing may be of various types, Some basic method of failures are (Khan, 2007)
Foundation settlement
It might occur due to the difference in base settlement. As the excess moments/ tensions will be developed, it will cause the serious cracking of wall space, sagging of the floor and stress to the structural framework.
Shear Activity of structural columns
Shear Motion of the Column anticipated to Freezing Joint
Collapse of Block-Masonry Cladding
Alligator Cracking of the Brick-Masonry
Buckling of main Support of Columns
Fig b: Shear activity of column scheduled to frigid joint
Fig b: Breaks scheduled to non-uniform
foundation settlement
Fig a, Fig b, . Different settings of inability (Khan, 2007)
Fig c: Chilean Earthquake Harm, Credit: U. S. Geological Review, Picture: Walter Mooney
Causes of Failures in developing countries
Conceptual
Soft-storey
Short column effect
Irregularity of plan stiffness
Detailing
Poor is detailing
Lack of ties
Inadequate ductility
Construction
Poor construction
Poor material quality
Others (A. W. Charleson, 2001)
CHAPTER 3
3. 0 METHODOLOGY
The methodology is dependant on quantitative research, which include an immense experiment of the shell buildings, statistical and correlation research of model mixture. In the beginning of the project the information is gathered about the shell framework and screening process of information is carried out so that only the mandatory information remains. Then following the books review is completed to get the knowledge of the shell composition and the finite component program (ABAQUS). The shell composition is modelled in the ABAQUS and the framework is subjected to several available earthquake data for energetic analysis. The various model mixture method is then applied to find the response of the composition and weighed against the accurate response to find the appropriate modal mixture for shell buildings. In the event the results obtained is unsatisfactory then your model is updated and reanalysis is completed. The conclusion is attracted from the results obtained and finally the survey is drafted. The brief summary of the methodology is shown in the block diagram below.
Information Collection
Different earthquake input
Preparation of Report
yes
no
Litrature Review
Conclusion and Conversation.
Result:
Happy?
Different model combination
Modelling Shell Composition in FEM
Fig: Methodologies developed
3. 1 WORK PLAN
The task schedule of the job is shown in the Gant graph below. The proposed task runs for per year. The precise work description carried out during each activity is identified below
PLEMINARY PHASE
Task 1: The induction program is were able to add the researcher, supervisor and the university or college to familiarize with the other person. The program and hardware is installed and discovered. Information is collected for the research.
Task 2: literature review is carried out by the by using collecting information
Deliverables: Paperwork of the literature review is done and the methodology is developed.
CALCULATION PHASE
Task 3: A preliminary calculation of the shell structure is completed and the model is created
Task 4: A same model is created in ABAQUS and the effect is confirmed with the known results.
Deliverables: Finite Aspect Program is verified and the restriction of the program is well known.
Task 5: The true style of the task is tested subjected to several earthquake data and the results are collected. Additionally the response of the composition is calculated through the various modal method
Deliverables: A audio model is created.
ANALYSIS PHASE
Task 6: careful evaluation of the result is carried out during this phase. Comparison is made with the exact data.
Task 7: If the results obtained will not show any arrangement with the exact result, then there might be a difficulty in modeling the framework. Therefore, the model is kept up to date again and re evaluation is done.
Task 8: Summary is made with the help of obtaining results and an appropriate method is advised for the study of active response of shell framework.
Deliverables: Correctness of the modal blend is known for the shell structure.
Task 9: Last document will be presented like the methodologies, execution and results of case studies.
Deliverables: display about the research findings and the future suggestions in looking into a shell framework.
