STATIC AND DYNAMIC ANALYSIS OF A MULTI- STORIED BUILDING

Transcription

1 STATIC AND DYNAMIC ANALYSIS OF A MULTI- STORIED BUILDING K RAMYA KRISHNA 1*, CH SURENDRA REDDY 2* 1. II.M.Tech, Dept of CIVIL ENGG, JOGAIAH INSTITUTE OF TECHNOLOGY & SCIENCES, PALAKOL, AP. 2. Asst.Prof, Dept of CIVIL ENGG, JOGAIAH INSTITUTE OF TECHNOLOGY & SCIENCES, PALAKOL, AP. ABSTRACT: Multi-storied buildings are supposed to be of engineered construction in the sense that they might have been analyzed and designed to meet the provisions of the relevant codes of practice and building bye-laws; the construction might have been supervised by trained persons. In such cases, even if earthquake forces have not been considered precisely, the structures would have adequate in-built strength and ductility to withstand some level of earthquake intensity. In this project a multi-storied building of three storey that is G+3 building is designed for the maximum lateral forces with the help of equivalent static analysis which is mentioned in IS: , part 1. The major steps involved in construction of a structure apart from analysis and design are site selection, survey of the site, orientation of the building. Selection of site plays a major role in any construction. The factors effecting site selection are topography, nature of soil, position of ground water table, facilities, neighborhood, vegetation, shape of the site. Surveying includes preliminary survey and quadratic survey. Levelling of the site is also done in surveying. Orientation of a building is the proper placement of the building and its component rooms with respect to the weathering elements. Three parameters which govern the orientation of the building are temperature, wind and humidity.. Moment Resisting Frames rely on the ability of the frame itself to act as a partially or fully rigid jointed frame while resisting the lateral loads. Due to their flexibility, moment resisting frames can be used for medium rise buildings having up to ten stories. Ordinary moment resisting frames doesn't meet special detailing requirements for ductile detailing.

2 single structural model can be used for a 1. SOFTWARE: wide variety of different types of analysis and design. SAP2000 can be used for all Structural Analysis Program of our analysis and design tasks. In SAP usually known as SAP is a very powerful and practical tool for structural design. SAP2000 Version follows in the 2000, Complex Models can be generated and meshed with powerful Templates built into the interface which is the major same tradition featuring a very advantage of this package. Bridge sophisticated, intuitive and versatile user Designers can use SAP2000 Bridge interface powered by an unmatched analysis engine and design tools for engineers. SAP2000 is a full-featured program that can be used for the simplest Templates for generating Bridge Models, Automated Bridge Live Load Analysis and Design, Bridge Base Isolation, Bridge Construction Sequence Analysis, Large problems and it can also be used for or Deformation Cable Supported Bridge most complex projects.sap has many features comprising of non-linear and pushover analysis, dynamic analysis, bridge modelling and design. Apart from this SAP2000 Version has many other features. Analysis and Pushover Analysis. From a simple small 2D static frame analysis to a large complex 3D nonlinear dynamic analysis, SAP2000 is the answer to all structural analysis and design needs. Advantages of SAP: From its 3D object based graphical modelling environment to the wide variety of analysis and design options. SAP2000 represents the most sophisticated and user friendly release all other computer programs. Creation and modification of the model, execution of the analysis, checking and optimization of the design and production of the output are all done under a single interface. A 1. It allows easier global integration. 2. It provides real time information. 3. It reduces the possibility of redundancy errors. 4. It provides a good knowledge like an expert about building and implementation of a system. Disadvantages:

3 1. To implement and use SAP can IS 875, part 2, 1987(imposed loads for be very expensive. buildings and structures) IS 875, part 3, 1987(wind loads for 2. CODE BOOKS Code books play a major role in the analysis and design of any structure. A building has to perform many functions satisfactorily. Amongst these functions are the utility of the building for the intended use and occupancy, structural safety, fire safety and compliance with buildings and structures) IS 875, part 4, 1987(design loads for buildings and structures) IS 875, part 5(special loads and combinations for buildings and structures) SP 16 (design aids for IS 456) SP24 (explanatory handbook for IS hygienic, sanitation, ventilation and 456) daylight standards. The design of the building is dependent upon the minimum requirements prescribed for each of the SP34 (handbook on reinforcement and detailing) IS 1893, part 1(A seismic Design Of above functions. The minimum Multi-storied Reinforced Concrete requirements pertaining to the structural safety of the buildings are being covered buildings) Proposed Draft Provisions and in different codes. Code books are referred to reduce the hazards to life and property caused by unsafe structures, but also eliminates the wastage caused by assuming unnecessarily heavy loadings Commentary on Indian seismic Code IS 1893, part 1, 2002 Review of Geotechnical Provisions in Indian Seismic Code IS 1893, part 1: 2002 without proper assessment. Explanatory Examples on Indian Seismic Code IS 1893, part 1 The code books referred for this project 3. DETAILS OF THE STRUCTURE are: IS 456:2000 (reinforced concrete for general building construction) Prior to the planning of a residential building, it is essential for the planner to consider the following: IS 875, part 1, 1987(dead loads for building and structures) 1. Size, shape and location of the plot

4 2. Specific requirements of the occupants on a vertical plane which is represented by plane of the paper on which elevation 3. Fund resources available is drawn. Simply, elevation is the front 4. Locally available materials for view of the structure. construction. 5. Meteorological conditions of the area The units which are must for a residential building are the bedroom, kitchen, dining hall, w.c and bath and a stair if more than one storey is needed. In addition to these, other units like guest room, drawing room, store room, verandah etc. All the rooms in a structure are having a main function to provide proper ventilation for all the units. The orientation of the rooms, doors and windows are placed such that there is proper ventilation in the building. The rooms should be comfortable and spacious. The rooms should get adequate natural light and breeze. Especially in kitchen, much illumination provides safety, clarity, cheerfulness and prevents fatigue. Hence natural and artificial illumination is must for any building. Figure 1.1 Elevation of the structure 3.2 PLAN AND ELEVATION OF THE STRUCTURE: A plan is a graphical representation, to some scale, of the features on, near or below the surface of the earth is projected on a horizontal plane which is represented by plane of the paper on which plan is drawn. Simply, a plan is the top view of the structure. 3.1 ELEVATION: Elevation is a graphical representation, to some scale, of the features on, near or below the surface of the earth is projected

5 W N E S previously calculated shear (reaction at right end of the beam. No shear force acts through the beam just beyond the last vertical force or reaction. If the shear force diagram closes in this fashion, then it gives an important check on mathematical calculations. The bending moment diagram is Figure Plan of the structure 4. GRAVITY LOAD ANALYSIS: A shear force diagram can be constructed from the loading diagram of the beam. In order to draw this, first the reactions must be determined always. Then the vertical components of forces and reactions are successively summed from the left end of the beam to preserve the mathematical sign conventions adopted. The shear at a section is simply equal to the sum of all the vertical forces to the left of the section. obtained by proceeding continuously along the length of beam from the left hand end and summing up the areas of shear force diagrams giving due regard to sign. The process of obtaining the moment diagram from the shear force diagram by summation is exactly the same as that for drawing shear force diagram from load diagram. GRAVITY LOADS FROM SAP When the successive summation process is used, the shear force diagram should end up with the Figure Bending moment diagram for gravity loads from SAP.

6 explained in this chapter. The lateral load analysis is carried out in further chapters and compared with that of gravity load GRAVITY LOADS FROM SAP analysis. 5. EQUIVALENT STATIC ANALYSIS: Figure: Shear force diagram for gravity loads from SAP. The complete details of the residential building have been explained in this chapter. Location of beams and columns, grid line marking are clearly explained. Only gravity loads are taken into consideration and analysis is done manually and using a package SAP2000. Manual analysis comprises of load distribution of slabs on to beams and calculation of bending moment and shear force values by any approximate method. The steps for analysis by SAP are also The objective of seismic analysis is to access the force and deformation demands and capacities on the structural system and its individual components. ESA can be used to estimate the displacement demands for structures where a more sophisticated dynamic analysis will not be provide additional insight into behaviour. When loads are applied to a body, the body deforms and the effect of loads is transmitted throughout the body. The external loads induce internal forces and reactions to render the body into a state of equilibrium. For analysing such bodies static analysis is used. ESA determines the displacement, and forces in a structure or components caused by the loads that do not induce significant inertia and damping effects. ESA can be used to calculate the structural response of bodies spinning with constant velocities or travelling with

7 constant accelerations since the 1964, which was later revised in 1967, generated loads do not change with time. again in 1970 and again in Now it Steady loading and response conditions has only four seismic zones - II, III, IV are assumed in ESA. That is the loads and and V. The zone factors for different the structures response are assumed to zones. vary slowly with respect to time. Table: Zone factors Earthquakes are occasional forces on structures that may occur rarely during the lifetime of buildings. It is also likely that a structure may not be subjected to severe earthquake forces during its design lifetime. Even if earthquake forces have not been considered precisely, the structures would have adequate in-built strength and ductility to withstand some level of earthquake intensity. The main factors that should be taken into consideration in constructing a building with earthquake forces are as follows: Zone factor (Z): The varying geology at different locations in the country implies that the likelihood of damaging earthquakes taking place at different locations is different. Based on the levels of intensities sustained during damaging past earthquakes, the 1970 version of zone map subdivided India into five zones - I, II, III, IV and V. The Indian Standards provided the first seismic zone map in Zone II III IV V Zone factor(z) Soil type: Soils are of different types namely, soft, medium and hard soils. Recorded earthquake motions show that the response spectrum shape varies with the soil profile at the site. The variation in ground motion characteristics for different sites is accounted for by providing different shapes of response spectrum for each of the sites. Importance factor (I): Seismic design philosophy assumes that a structure may undergo some damage during severe shaking. However, critical and important facilities must respond better in a earthquake than an ordinary structure. Importance factor is used to obtain the design seismic force depending on the functional use of the structure, characterized by hazardous consequences of the risk resulting from

8 its failure. Here, the risk is associated The stiffness, k, of a body is a measure with hazardous consequences of the of the resistance offered by an elastic failure of the structure, its postearthquake functional need, historic defined as body to deformation. The stiffness is value and economic importance. k = P/δ Response reduction factor (R): The structure is allowed to be damaged in severe shaking. Hence, structure is designed for seismic force much less than what is expected under strong shaking if the structure were to remain linearly elastic. A building is expected to undergo damage in case of strong shaking and therefore should be detailed for ductility. Response reduction factor is the factor by which elastic responses of the structure, such as base shear and element forces, generated under the action of earthquake shaking as specified in IS1893:2002 are reduced to obtain the design values of the responses. 6. CALCULATION OF FRAME LOAD FOR EACH STOREY: For the calculation of frame loads, stiffness of each and every frame is required. In this project the stiffness values are directly taken from the software SAP which is used in the design of the structure. where P is the force applied on the body and δ is the displacement produced by the force along the same degree of freedom When a graph is plotted between load applied in X-direction and displacement in Y-direction, stiffness obtained is linear as shown in the graph below. Figure 2.3 Graph for stiffness calculation The figure 2.3 is taken from a journal with title "Seismic Strengthening of RC Frame buildings: The Formal Quantitative Approach" by C. V. R. Murty.

9 When a load of 1kN is applied on the top storey of the frame in lateral direction at one end, the frame tends to possess a displacement or deformation at the other end for the applied load as shown in the figure below. Then the load per displacement value gives the stiffness of that frame which is calculated below. The displacement of the frame 1 is shown in figure below. 7. DESCRIPTION: Torsion is the twisting of an object due to an applied torque. When the centre of mass and centre of stiffness of a structure doesn't coincide, it results in some eccentricity in one or both directions. This eccentricity further results in torsion forces. As per IS 1893:2002 Part1, the formula for calculating torsion is given by T = K xr i i xf xe i d i / R 2 i Where, T = torsion force; Ki = stiffness of each frame in both X and Y directions; For calculating the values of torsion for each frame, firstly centre of mass and centre of stiffness are to be calculated. Then eccentricities in both X and Y directions are calculated as done in ANALYSIS OF A FRAME: Building frames are most common structural form which is in practice. Usually the building frames are designed such that the beam column joints are rigid. Analysis of frames is carried out by considering planar frame in two perpendicular directions separately for both vertical and horizontal loads and finally superimposing moments approximately. In this case of building frames, the beam column joints are monolithic and can resist bending moment, shear force and axial force. The methods available for analysing vertical loads on frames are 1. Slope deflection method 2. Stiffness method Ri = radius of gyration from the centre of stiffness; Fi = load on each frame in both X and Y directions 3. Substitute frame method In this chapter, we are doing analysis only for lateral loads. A building frame may be subjected to wind and earthquake loads during its life time. Thus, the

10 building frames must be designed to at working loads, thus rendering the withstand lateral loads. Analysis of structure fit for its intended use, thus frames for lateral loads can be done using different methods mentioned below. limit state method includes consideration of a structure at both the working and the ultimate load levels with a view to satisfy 1. Moment Distribution Method the requirements of safety and 2. Cantilever Method serviceability. 3. Portal Frame Method The above mentioned methods are approximate methods. In this project we are using portal frame method to analyse the lateral loads of a frame. 8. LIMIT STATE METHOD: Working stress method gives satisfactory performance of the structure at working loads; it is unrealistic at ultimate state of collapse. Similarly, the ultimate load method provides realistic assessment of safety but doesn't guarantee the satisfactory serviceability requirements at service loads. An ideal method is the one which takes into account not only the ultimate strength of the structure but also the serviceability and durability requirements. The newly emerging limit state method of design is oriented towards the simultaneous satisfaction of all these requirements. In this method, a structure is designed against safety of collapse and checked for its serviceability 8.1 Types of limit state: Limit state is a state of impending failure beyond which a structure tends to perform its intended function satisfactorily, in terms of safety and serviceability. The acceptable limit for the safety and serviceability requirements before failure occurs is called a limit state. Two categories of limit state are considered in the design. i. Limit state of collapse ii. Limit state of serviceability 9. DESIGN OF STRUCTURE: The design of structure is done according to limit state method for compression members, beams, slabs and footings. 9.1 DESIGN OF SLAB A Reinforced Concrete Slab is the one of the most important component in a building. It is a structural element of modern buildings. Slabs are supported on Columns and Beams. RCC Slabs

11 whose thickness ranges from 10 to 50 centimetres are most often used for the construction of floors and ceilings. Thin concrete slabs are also used for exterior paving purpose. In many domestic and Singly reinforced beam A singly reinforced beam is a beam provided with longitudinal reinforcement in the tension zone only. industrial buildings a thick concrete slab, supported on foundations or directly on the sub soil, is used to construct the ground floor of a building. In high rises buildings and skyscrapers, thinner, precast concrete slabs are slung between the steel frames to form the floors and ceilings on each level. Doubly reinforced beam Beams reinforced with steel in compression and tension zones are called doubly reinforced beams. This type of beam will be found necessary when due to head room consideration or architectural consideration the depth of the beam is restricted. The beam with its 9.2 DESIGN OF EXTERIOR BEAM RCC beams are cast in cement limited depth, if reinforced on the tension side only, may not have enough moment concrete reinforced with steel bars. of resistance, to resist the bending Beams take up compressive and add rigidity to the structure. Beams generally moment. By increasing the quantity of steel in the tension zone, the moment of carry vertical gravitational forces but can resistance cannot be increased also be used to carry horizontal loads. indefinitely. Usually, the moment of The loads carried by a beam are resistance can be increased by not more transferred to columns, walls, or girders, which then transfer the force to adjacent than 25% over the balanced moment of resistance, by making the beam overreinforced structural compression members. on the tension side. Hence, in In Lightframe construction the joists rest on the beam. order to further increase the moment of resistance of a beam section of unlimited dimensions, a doubly reinforced beam is RCC beam construction is of two provided. types: Singly reinforced beam 9.2 FOOTING: Doubly reinforced beam

12 Foundation is the base of any structure. Without a firm foundation, the structure cannot stand. That is the reason why we have to be very cautious with the design 9.3 DESIGN OF STAIRCASE Stairs consist of steps arranged in a series for purpose of giving access to of foundations because our entire different floors of a building. Since a stair structure rests on the foundation. The strength of the foundation determines the life of the structure. Design of foundation depends on the type of soil, type of structure and its load. On that basis, the foundations are basically divided into is often the only means of communication between the various floors of a building, the location of the stair requires good and careful consideration. In a residential house, the staircase may be provided near the main entrance. In a public Shallow Foundations and Deep building, the stairs must be from the main Foundations. entrance itself and located centrally, to provide quick accessibility to the principal Reinforced Concrete Footings apartments. All staircases should be Footing comprises of the lower end of a adequately lighted and properly column, pillar or wall which is enlarged with projecting courses so as to distribute ventilated. load. Footings shall be designed to sustain the applied loads, moments and forces and the induced reactions and to ensure that any settlement which may occur shall be as uniform as possible and the safe bearing capacity of soil is not Various types of Staircases Straight stairs Dog-legged stairs Open newel stair Geometrical stair RCC design of a Dog-legged staircase exceeded. In sloped or stepped footings, the effective cross-section in compression In this type of staircase, the shall be limited by the area above the succeeding flights rise in opposite neutral plane, and the angle of slope or depth and location of steps should be such that the design requirements are satisfied at every section directions. The two flights in plan are not separated by a well. A landing is provided corresponding to the level at which the direction of the flight changes. Reinforcement Detailing:

13 [ M ] [ Ü ] + [ C ] [U] +[ K ] [ U ] = - [ M ] [ Üg ] [ 1 ] (1) qi(t)+ 2ξi ωi qi +ωi 2 qi(t) = piüg (2) 18-8mmØbars@240mm c-c 12mmØbars@175mm c-c 24- Figure Reinforcement detailing of staircase 9. TIME HISTORY ANALYSIS The modal analysis procedure to determine the response of a structure to earthquake induced motion, identical at all support points of the structure is Time History Analysis (THA). Response of the structure can be calculated using numerical methods (Central Difference Method, Newmarks Method). Finding the response of the Multi Degree Of Freedom structure: The equation of motion is By using numerical methods calculate the response of the structure with any number of storeys. By multiplying the corresponding Eigen vectors we will get the final response of the structure. Generally, the first mode of vibration is one of the primary interests. The first mode usually has the largest contribution to the structure s motion. Actually infinite numbers of modes are existing within a building, but these are less during an earthquake. The significance of a mode is indicated by mass participation. This factor indicates the amount of the total structural mass that is activated by a single mode. If all modes of a structure are considered, the cumulative mass participation will be 100%. Structures

14 with 80% of the mass in the first mode these factors are taken into consideration will be dominated by the mode shape only. for the calculation of lateral loads. With the above mentioned factors, the design base shear is calculated. Later this base Time History Analysis is done in SAP to get the analysis values and shear is distributed to each floor and then to each frame of the structure. compare it with static analysis. Lateral loads, torsion forces also 10. CONCLUSIONS The complete details of the residential building have been explained in chapter 1. Location of beams and act on the structure if the structure is not symmetric. The structure clearly is not symmetric, that is the centre of mass and centre of stiffness doesn't coincide. Hence columns, grid line marking are clearly there is eccentricity in Y-direction. explained. Only gravity loads are taken into consideration and analysis is done manually and using a package SAP2000. Therefore torque is developed in the structure. Due to this torque torsion forces are developed. As the eccentricity Manual analysis comprises of load produced is minimum, the torsion forces distribution of slabs on to beams and calculation of bending moment and shear force values by any approximate method. The lateral load analysis is carried out and compared with that of gravity load analysis. are also minimum. When analysis is done for any building including torsion, the bending moment values were almost similar to that of bending moment values obtained only for lateral loads. Hence these torsion forces are negligible and the design of frame section is done only for In addition to gravity loads, lateral loads. lateral loads are calculated in this chapter as per the procedure in IS: ; Equivalent Static Analysis (ESA). Many factors, such as seismic weight of the The last chapter deals with dynamic analysis. Time History Analysis is a type of dynamic analysis where structure, zone factor, importance factor, ground motion is required without response reduction factor, have a great influence on the structure. Hence all applying any lateral loads. Time History Analysis has been done only in SAP2000

15 to check the analysis values with that IS 875, part 1, 1987(dead loads for obtained from static analysis and to check the response history that is acceleration, velocity, and displacement etc of every node in the structure. Response history for different ground motions (Uttarkasi, Chamoli, Bhuj) is done in this chapter. building and structures) IS 875, part 2, 1987(imposed loads for buildings and structures) IS 875, part 3, 1987(wind loads for buildings and structures) IS 875, part 4, 1987(design loads for buildings and structures) IS 875, part 5(special loads and 11. BIBILIOGRAPHY combinations for buildings and structures) SP 16 (design aids for IS 456) i) Illustrated Design of Reinforced SP24 (explanatory handbook for IS Concrete Buildings by Dr. S. R. Karve and Dr. V. L. Shah 456) SP34 (handbook on reinforcement and detailing) ii) Strength of Materials by S. IS 1893,part 1(Aseismic Design Of Ramamrutham. Multi-storied Reinforced Concrete iii) Design of Reinforced Concrete buildings) Structures by A. K. Jain iv) Structural Analysis by V. N. Vazirani, M. M. Ratwani and S. K. Duggal Proposed Draft Provisions And Commentary On Indian seismic Code IS 1893, part 1, 2002 Review Of Geotechnical Provisions In Indian Seismic Code IS 1893, part 1 : v) The code books referred for this 2002 project are: Explanatory Examples On Indian IS 456:2000 (reinforced concrete for Seismic Code IS 1893, part 1 general building construction)