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Abstract
Flying increase in world’s population and in economic development urged the civil engineers to design the multi-story structures. They should be well resistive towards earthquake especially in those regions where the earthquake had disastrous effects. These structures should have a sustainability level so that they could resist earthquakes. So more information is needed to be gathered in this regard, especially in seismic loadings, as it is one of the most doubtful form of loading that it might experience during the entire life. They are destroying our buildings and different structures and we are not doing anything as they are a lot of incidents in the history in which we had lost our people in a great number. Our buildings do not have the capacity and strength to resist against these. But now the knowledge and information about the earthquake protection is growing with the passage of time. Presently we are assessing and setting the rules that those structures which are as of now developed can endure the high force seismic tremor or not? For this purpose, we will use fragility curve to observe the buildings and then comprehend their results to similar R.C buildings.
We selected a specimen building and that building is a commercial building. This building follows the design procedures and specimen mentioned in Euro code.
After obtaining the fragility curve, we are capable of predicting the damage and behavior of those buildings in these regions. This information we accumulated through different investigations and work will be useful and valuable for various organizations, for example, Engineering firms, Insurance organizations and various experts for their future estimates. They are able to predict the amount of cost and supplies that would be required for repaying any kind of losses that might happen in future in the name of earthquakes. They can also take safety measures related to the fire fighting and many other happenings. It additionally assists with planning new buildings with better basic and better natural measures
At last the report briefly explains the two systems to absorb damping and make the structure safe against earthquake. One is base isolation. In base isolation system bottom of the building and floor is separated by a system and install heavy weight rubber, these rubber act as separator and absorbs all the earthquake forces and not transfer these forces into the building. The second system that report explains is mass tuned damper. They are heavy weight bodies install all the top of the building. They increase the weight of the structure as well. When earthquake comes, theses heavy weight tuned damper absorb all the earthquake forces and make the structure stronger against dynamics or earthquake forces.
Table of content
Contents
Seismic analysis of structure:
Static Lateral Force Procedure
Concerned Questions and Future research regarding seismic analysis and design of structure:
Draw fragility curve of the building against earthquake load
Design the structure against nonlinear analysis
Table of figure
Figure 2 3 D model of the building
Figure 4Lateral force procedure
Figure 6 Performance level of building
Introduction
An earthquake is the vibrating and shaking of the surface of the Earth which is caused due to the unexpected release of the energy from the Earth’s lithosphere that makes seismic waves. On the surface of Earth, earthquakes distinct themselves by vibrating, shaking or replacing the ground. Earthquakes can also activate landslides and volcanic activity. Its main cause is due to the burst of geological faults but it is also due to mine blast, volcanic activity and test of nuclear weapons.
The Earth’s crust is made of core, mantle and tectonic plates. These plates are always in motion due to convection current activated by molten lava which is present inside the Earth’s crust. This continuation in motion leads the latest to slide or move against each other. These interactions and floating separated of structural plates underneath the earth are seen by living creatures, people notwithstanding. When these plates move against each other they meet at a point which is known as fault line and that line is known as fracture in the Earth’s crust and as result Earthquake came as an outcome.
For the earthquake energy is released from a focal point and that is called epicenter. From this, seismic waves are generated and sent out in all directions. Seismic waves then go at varying speed depending upon the material from which they are passing.
The types of earthquakes depend upon the region where it occurs and also on the geological position of that region. But generally there are different types of earthquakes and among them tectonic, volcanic and explosion or collapse earthquakes are worth mentioning. Tectonic earthquakes occur when the rocks in the earth breaks because of powers that appeared because of development of structural plates. Volcanic earthquakes are less extensive. It took place before or after an eruption. The change in heat activates seismic waves resulting in earthquakes. Explosion earthquakes are caused by nuclear explosions. They are basically, man activated sort of quakes and speak to the greatest effect of advanced atomic war. Earthquakes damaged the buildings, infrastructure, landslides and rockslides and could become the cause of flood and many other destructions.
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Figure 1 Plan of the building |
· Two story high building
· 750 sq. m Plan area
· 8.5m height
· 6.5m Story height
· 2m foundation depth
· L = 65m
· B = 35m
· H = 7m
· Seismic zone 3
· Soil condition Hard soil site
· Beam size - 240mm x 540mm
· Column size - 450mm x 600
· Slab thickness – 150mm
· External thickness of wall – 250mm
· Internal thickness of wall – 160mm
· Concrete compressive strength – M25
· Steel yielding strength – 415 MPa
· Masonry strength – 2MPa
Figure 2 3 D model of the building
Literature review:
Basics of Dynamics
As for as linear dynamic analysis is concerned following properties of structure are very important these are stiffness, mass and damping. Stiffness is defined as the unit force required to displaced the structure. If the stiffness of the structure is more, the more earthquake forces the structure will carry. Similarly, the heavy weight structure carries more earthquake forces. For this reason, Engineers tries to make a structure lighter so they create less inertial forces in the building during ground motion. Damping is actually a system by which the structure releases energy. So these three parameters are very import while analyzing the structure for dynamics analysis.
For recording smaller magnitude of earthquake seismograph are used. While for strong motion earthquake accelero-graph are used. Magnitude of earthquake is defined as the energy releases by earth during plate tectonic effects. It is measured in Richter scale like 6.5 Richter scale. Another way of earthquake is intensity of earthquake Intensity is the way of measuring the effect of earthquake. It is indicated my Roman number.
Another important concept of dynamic analysis is of degree of freedom. DOF is defined as the number of coordinates required to defined the position of a vibrating body at any time. DOF is of Translational movement and Rotational movement in X, Y and Z directions.
Earthquake Effect
When earthquake comes, it creates inertial forces in the building. As earthquake is in three dimension. Vertical component of the earthquake is resisted by the weight of structure, while horizontal components is dangerous for the building. When earthquake forces induce in the building it creates unbalancing forces in the structure. To encounter these forces, according to DE Alembert principle F= ma. Additional force F is taken in the structure equal to the product of mass of building and acceleration of earthquake opposite to the direction of earthquake.
Elastic response Spectrum
Whenever horizontal load is applied in a structure it will create three type of deformation: Displacement, velocity and acceleration. These three parameter are called the response of the structure. Now take different building having different heights in a same zone means apply same ground motion. All the structure behaves different under the action of horizontal force. At each time structure displacement, velocity and acceleration changes. Take the maximum response at each time and plot the graph. This graph is called elastic response pf a structure. Now this graph helps you to find the maximum response of any structure or building located in that zone just by going to the time period of the building, graph will show the maximum response.
Figure 3 Response spectrum
Design of building
Load calculation
Density of concrete slab = 24KN/m3
Dead load on slab = 24 x thickness of slab
Dead load on slab = 24 x 150/1000 = 15KN/m3
Floor finish load = 1 KN/m^2
dead weight of external wall = 14 KN/m
dead weight of internal wall = 7.5 KN/m^2
Building model in ETABs
ETABs is an extended three dimensional analysis of building software. We model our building in this software by initially assuming the sizes of beams, column, slab, and foundation etc. After apply different iteration, where structure passes we select that member sizes as shown in above. Two types of loads are applied in the building: gravity loads and earthquake loads. Gravity loads include dead load, live load, super load and environmental load. For taking gravity load UBC 97 specification is used. Building is located in zone 3.
After the analysis of building in ETABs, export the file in SAFE software and design the few components of building here like slab and foundation.
Results generated from the software
Approximately the amount of reinforcement in beam = 0.0214
amount of reinforcement in column = 0.035
amount of reinforcement in slab = 0.011
amount of reinforcement in foundation = 0.018
Load combination
Following load combination is used in the design of building.
1.35 dead load + 1.5 variable load
Dead load + 1.5 wind load
1.35 dead load + 1.5 live load + 0.9LL
Dead load + Earthquake load
Dead load + Earthquake load + 0.3LL
Seismic base shear
Base shear is the maximum probable cumulative horizontal force at the base of the building. Base shear is very important parameter used to design a structure against dynamics force like earthquake forces.
At first design response spectrum is constructed as procedure is given below. Use Type 1 spectrum that is used for areas of high seismicity and soil type D.
Spectral parameters are (from EC8 Table 3.2)
The reference peak ground acceleration is = 3.2 m/s2.
The importance factor for the building is I = 1.0,
the design ground acceleration ag = γI agR = 3.4 m/s2. T
he resulting design spectrum is shown in Figure 3.17 for q = 1 and q = 4,
design spectral accelerations can also be obtained from the equations in Cl. 3.2.2.5 of EC8. The framing type has not yet been considered, so we will calculate base shear for three possible options:
Steel moment-resisting frame (MRF) • Concrete MRF • Dual system (concrete core with either concrete or steel frame)
The procedure follows E C 8 C l. 4. 3 .3. 2. 2
T = C H^ ¾
T = 0.085 x 8.5 ^ c/4
T = 0.57 Sec
The fundamental time period of the building is 0.57 sec. Put this value of time period in elastic response spectrum shown in below and find the maximum response of the structure.
Seismic analysis of structure:
After the design of structure, it is very compulsory to check assessment of building against earthquake loads. There are different methods used to ensures whether the structure is strong or not against earthquake force.
Ø Linear static analysis
Ø Incremental dynamics analysis
Ø Nonlinear static analysis
Ø Push over analysis
Ø Time history analysis
Ø Dynamics analysis
Ø Nonlinear dynamics analysis
Note: For our project we use push over analysis.
The types of earthquakes depend upon the region where it occurs and also on the geological position of that region. But generally there are different types of earthquakes and among them tectonic, volcanic and explosion or collapse earthquakes are worth mentioning. Tectonic earthquakes occur when the rocks in the earth breaks because of powers that appeared because of progress of structural plates. Volcanic earthquakes are less wide-ranging. It took place before or after an eruption. The change in heat activates seismic waves resulting in earthquakes. Explosion earthquakes are caused by nuclear explosions.
When earthquake comes, it creates inertial forces in the building. As earthquake is in three dimension. Vertical component of the earthquake is resisted by the weight of structure, while horizontal gears is treacherous for the building. When earthquake forces induce in the building it creates unbalancing forces in the structure. To encounter these forces, according to DE Alembert principle F= ma. Additional force F is taken in the structure equal to the product of mass of building and acceleration of earthquake opposite to the direction of earthquake
Another technique to find the vulnerability of structure against earthquake is Push over analysis. As the name indicates, in this method structure is displaced in horizontal direction up to required displacement. Push over technique is a static analysis in which structure is displaced up to required limit of collapse. It is nonlinear analysis because the structure nominal strength is taken beyond the elastic range. Push over analysis is a step by step procedure, in which deformation increases until total structure collapse.
Incremental Dynamic Analysis:
Incremental Dynamic Analysis (IDA) is the method of figuring or estimating the thorough assessment of behavior of structures under the various seismic loads. It is the method which is very valuable for the earthquake engineering. It includes exposing an auxiliary model to (at least one) ground movement records, each scaled to numerous degrees of force, subsequently delivering (at least one) curves of reaction parameterized versus power level. To develop a reference which is common among all, we have to develop and analyses the basic and fundamental concepts so that it helps us to establish a common frame of reference. The properties of IDA curve are seen into both single degrees of freedom and mufti-degree of freedom of structures.
Incremental Dynamic Analysis (IDA) is capable of doing several nonlinear dynamic analysis of a structural model and each of it is labelled with different level of seismic intensity. The levels or range of scales are selected to push the structure through the complete range either from elastic to inelastic and in the end to the global dynamic instability and it is that point at which majority of the structures collapsed.
There are numerous steps which are required to be followed to perform Incremental Dynamic Analysis and their detail is discussed below
Ø Doing investigation of non - linear auxiliary structure showed to seismic excitation with in particular PGA and keep a record of the greatest float or drift of structure.
Ø Doing the same procedure by increasing the seismic excitation PGA incrementally.
Ø Keep on doing the same procedure until it reaches the state where it will collapse.
Ø Draw or plot the changing caused by the float or drift as function of PGA. The curve which is obtained as a result is the Incremental Dynamic Analysis curve.
Ø It is very useful because performing IDA helps us to go through the nature of the structure it was going to be shown during earthquake.
The main aim or goals of the IDA are:
1. To get a deep comprehension of the reaction versus the potential degree of ground movement records.
Push over analysis
Another technique to find the vulnerability of structure against earthquake is Push over analysis. As the name indicates, in this method structure is displaced in horizontal direction up to required displacement. Push over technique is a static analysis in which structure is displaced up to required limit of collapse. It is nonlinear analysis because the structure nominal strength is taken beyond the elastic range. Push over analysis is a step by step procedure, in which deformation increases until total structure collapse.
Push over analysis is used to find the seismic vulnerability of existing structures. It also helps us to find whether the structure requires retrofitting or not.
Figure 4Lateral force procedure
As the figure indicates a structure is displaced by lateral force by iteration. When the structure is displaced it creates roof displaced called as story drift or total drift. It also forms a base shear at the base of the building. A graph between total displacement (maximum displacement) at the roof and base shear is used to find the capacity curve of the building. This curve may help us to find the base shear corresponding to any value of displacement.
The intensity measure of the earthquake may be of displacement, velocity and acceleration. First derivative of the displacement gives you velocity and the derivative of the velocity called as acceleration. The collapse of the structure may of total collapse. Yield of the member depends upon the assumption taken before the analysis.
Plastic Hinge:
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Figure 5 Plastic Hinges |
Hinges are categorized into three types these are :
1. Flexural hinge
2. Shear hinge
3. Axial hinge
Beam is pure flexure member. Flexural hinges are formed at the ends of beams and columns. While the member that takes pure axial or compression stresses, axial hinges are developed at that members as shown in figure.
Limit states
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Figure 6 Performance level of building |
· Immediate occupancy level.
· Life safety level
· Collapse level
Immediate occupancy level:
When the structure is displaced, first limit occurs known as immediate occupancy level. This limit occurs beyond the elastic range, so all the deformation in this point is permanent.
Life safety level
This level is obtained just after the immediate occupancy level. In this level there is no drift seen
Collapse level:
This level is obtained after the life safety level. In this level there is permanent drift seen and residual strength remains. After this level structure collapse.
Static Lateral Force Procedure
Static lateral force method is used to find the maximum shear at the base of structure. In this method at first according to the weight of whole structure and basis of other different parameters like type of structure, importance factor of building, over strength factor base shear is calculated. Then the maximum base shear is divided into the whole story height according to the stiffness and height of that floor.
The design base shear (V) can be calculated
V = (Cν I/RT) W
Cν= coefficient of seismic based on velocity
I= Seismic importance factor based on building type like hospital etc.
R= Over strength factor depending upon the type of structure takes load like Intermediate moment resisting frame, Special moment resisting frame etc.
W= the total seismic dead load defined 100% of dead load and 25% of live load
V = (Cv x I / R T) W
W = 25KN/m2 x area of slab
Dead load W = 25 x 750 = 18750 KN
25% of Live Load W= 25 / 100 x 18750 = 7500 KN
Total weight of a structure = 18750 KN + 7500 KN = 26250 KN
Cv bases on velocity coefficient = 0.4 from table
Ca bases on velocity acceleration= 0.28 from table
Importance factor = 1
Fundamental time period of a building = 0.57 sec
R = 5.5 Intermediate moment resisting frame
V = (0.4 x 1 / 5.5 x 0.57) x W
V = 0.4 x 1 / 5.5 x 0.57 x 26250 = 3350 KN
Max design base shear = (2.5 Ca x I) R x W
Max design base shear = (2.5 x 0.28 x I) 5.5 x 26250 KN
Max design base shear = 3340 KN
Minimum, design base shear = 0.11 ca x I x W = 0.11 x 0.28 x 1 = 308K
So the design base shear = 3340 KN
Now distributing the value of base shear in each story depending on the stiffness, mass and height of building
F x = (V- Ft) wx hx / Sum wi hi
F1 in first story = 1150 KN
F2 in second story = 2190 KN
Concerned Questions and Future research regarding seismic analysis and design of structure:
Draw fragility curve of the building against earthquake load
Fragility curve represents the probability of a collapse along the movement of ground motion. The intensity measure of the earthquake may be of displacement, velocity and acceleration. First derivative of the displacement gives you velocity and the derivative of the velocity called as acceleration. The collapse of the structure may of total collapse. Yield of the member depends upon the assumption taken before the analysis. Fragility curves helps us to find
· Seismic Risk Assessment: It tell us whether the structure is vulnerable against earthquake or not
· Help to develop future local codes: When your analysis the structure in a specific zone you identify the plastic hinge or location from where the structure fails, so you may make a code that helps you for future design in the given earthquake zone.
· Probability aftershock may also be investigated
· Insurance companies need this data: Any insurance company wants to know the life of structure so they are interested to find the useful life and condition in the given zone whether these structure collapse or not during earthquake.
· Retrofitting: retrofitting is the process of strengthen the structure. Fragility curve helps us to find whether the structure need further strength or new construction.
Design the structure against nonlinear analysis
Usually a structure is designed on the basis on linear analysis. It means the strength is taken below the elastic range. So modern research needs to find the structure up to the collapse means take the full strength of the structure.
Mass tuned damper
Mass tanned damper is the technique to absorb the shock of the building. It is trick equestrian in structures to reduce the bounty of mechanical vibrations. Their presentation can check discomfort, damage, or structural failure. They are habitually used in power transmission, automobiles, and building etc. to absorb dynamics forces.
Base Isolation
Base isolation is another technique to absorb earthquake forces. In this system the structure will took separated from the bottom of the structure. In context of seismic design of structures, base isolation can be replaced with seismic isolation i.e., the structure above the ground, which is most affected during earthquake is separated from the effects of earthquake forces by introducing a mechanism that will help the structure to hover. In other words, if structure/building is moving from its base, the movement of ground will have no effect on the structure due to separation.
References
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Fajfar, P., & Krawinkler, H. (1992). Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings: Workshop on Nonlinear Seismic Analysis of Reinforced Concrete Buildings, Bled, Slovenia, Yugoslavia, 13-16 July 1992: CRC Press.
Sedlacek, G., & Stangenberg, H. J. J. o. c. s. r. (2000). Design philosophy of Eurocode—background information. 54(1), 173-190.
R.C Hibbler. (2012). Structure analysis, Upper saddle river, New jersey: Pearson Practice Hall.
Aslam Kassimali. (2010). Structure analysis, Stamford, USA: Cengage learning
Kenneth M. Leet., & Chia-Ming Uaing., & Joel T. Lanning., & Anne M. Gilbert., (2018). Fundamental of structure analysis, New York, NY: McGraw–Hill education.
Moment distribution method for beams. (2013). Structural analysis. Retrieved from
Rainer, J., Pernica, G., & Allen, D. E. J. C. J. o. C. E. (1988). Dynamic loading and response of building. 15(1), 66-71.
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