D. R. Panchal, Lecturer, Applied Mechanics Department, Faculty of Technology and Engineering, The M. S. University of Baroda, Vadodara, & Dr. S. C. Patodi, Professor, Civil Engineering Dept., Parul Institute of Engineering & Technology, Limda, Vadodara.
Unlike static forces, amplitude, direction and location of dynamic forces, especially due to earthquake, vary significantly with time causing considerable inertia effects on building. Behavior of the building under dynamic forces depends upon the dynamic characteristic of the building which is controlled by both their mass and stiffness properties. In the present study, for evaluating the seismic performance of a typical B+G+9 multi-storey building, steel-concrete composite and R.C.C. options are considered. Two popular methods of seismic analysis i.e. Equivalent Static Method of Analysis and Linear Dynamic Response Spectrum Method of Analysis are used. For modeling, the composite and R.C.C. structures STAAD.Pro, V8i software is used and the results of the analysis are compared; composite structure is found to be more economical.
IntroductionSteel-concrete composite systems have become quite popular in recent times because of their advantages against conventional construction. Composite construction combines the better properties of both i.e. concrete and steel and results in speedy construction with a possibility of working on parallel front . In case of a composite structure, steel imparts ductility to the structure which has ability to absorb seismic energy imparted on the structure by the earthquakes and concrete prevents steel from corrosion and fire. The key feature of this system is composite action between a concrete slab and a steel beam which is achieved through the shear connection system which significantly increases the rigidity and the ultimate moment capacity of the composite beam compared with the properties of a bare-steel or reinforced concrete beam [2-4]. In this way much larger beam spans can be achieved.
Composite frames used for multi-storey buildings usually comprise of a bare-steel frame of H-section columns supporting I-section beams, laid out in a rectangular grid of primary (shortest span) and secondary members; supporting an overlaid composite floor deck. The composite deck system consists of cold-formed profiled steel sheets which act not only as the permanent formwork for an in situ cast concrete slab but also to some extent as tensile reinforcement.
Composite floors using profiled sheet decking as shown in Fig.1 have become quite popular for high- rise buildings. In composite floor, the structural behavior is similar to a reinforced concrete slab with the steel sheeting acting as the tension reinforcement. The main benefit of using composite floors with profiled steel decking is saving in steel weight up to 30 to 50% over non-composite construction. 
Figure 1: Composite Slab
Figure 2: Beam-Column Connection
The steel decking performs a number of roles, such as:
- It supports loads during construction and acts as a working platform.
- It develops adequate composite action with concrete to resist the imposed loading.
- It transfers in-plane loading by diaphragm action to vertical bracing or shear wall.
- It stabilizes the compression flange of the beams against lateral buckling.
- It reduces the volume of concrete in tension zone.
- It distributes shrinkage strains, thus preventing serious cracking of concrete.
A number of parameters for composite beam are compared in Table 1 with two different types of steel beams having I- and H- cross sections with no shear connection to the concrete slab. The load capacity is nearly the same but the difference in stiffness and construction height is noticeable.
In order to evaluate the seismic efficiency of a composite structure against an R.C.C. structure, a B+G+9 multi-storied building is analyzed in the present work using a professional software STAAD.Pro V8i, while following the guidelines of the IS: 800-2007  and AISC  codes. Results are compared to arrive at suitable recommendations.
Procedures for the Seismic Analysis
The linear static procedure is a method of estimating the response of the structure to earthquake induced forces by representing the effects of this response through the application of a series of static lateral forces applied to an elastic mathematical model of the structure and its stiffness. For this reason, this method is also known as Equivalent Static Method of Analysis (ESMA). The forces are applied to the structure in a pattern that represents the typical distribution of inertial forces in a regular structure responding in a linear manner to the ground shaking excitation, factored to account, in an approximate manner, for the probable inelastic behavior of the structure. It is assumed that the structure’s response is dominated by the fundamental mode and that the lateral drifts induced in the elastic structural model by these forces represent a reasonable estimate of the actual deformation of the building when responding inelastically.
Linear Static Procedure
Linear Dynamic ProcedureThe main purpose of linear dynamic analysis is to evaluate the time variation of stresses and deformations in structures caused by arbitrary dynamic loads. The response spectrum provides the required information for design purposes and at the same time, simplifies the analysis by reducing the problem to a static problem of the estimated maximum responses. The response spectrum is defined, on a single degree of freedom system of varying frequency excited by a specific earthquake, as the maximum response of the system, ignoring the particular time of its occurrence [7, 8]. The Linear Dynamic Response Spectrum Analysis (LDRSA) is the standard procedure of modern seismic design codes. It aims to give directly the maximum effects of the earthquake in the various elements of the structure. It consists of computing the various modes of vibration of the structure and the magnitude of the maximum response in each mode with reference to a response spectrum. A rule is then used to combine the responses of the different modes. For this reason the method is also known as the superposition of modal responses method. The combination rule will generally be a square root of the sum of squares (SRSS) of the various modal responses. This combination rule is applied to all computed quantities, i.e. bending moments, shear forces, normal forces and displacements.
Non Linear Static ProcedureA simplified non linear analysis procedure, in which the forces and deformations induced by a monotonically increasing lateral loading are evaluated using a series of incremental elastic analyses of structural models that are sequentially degraded to represent the effects of structural nonlinearity.
Non Linear Dynamic ProcedureIn a non linear dynamic analysis procedure the response of a structure to a suite of ground motion histories is determined through numerical integration of the equations of motion for the structure. Structural stiffness is altered during the analysis to conform to nonlinear hysteretic models of the structural components.
Evaluation of the composite members at the ultimate limit state requires a procedure that takes into account of the actual redistribution capacity of the structure, which however, depends on complex phenomena of interaction between the concrete slab and steel profile . These aspects are vital for structures located in seismic zones. In reality, during earthquakes, buildings are generally subjected to large inertia forces which cause members of buildings to behave in a nonlinear manner, i.e. stress does not remain proportional to strain in addition to the nonlinearity associated with large deformations. Thus, the earthquake shaking of structure is a nonlinear dynamic problem and structural analysis should be able to incorporate the nonlinear behavior of members for evaluating the actual response of structure. Nonlinear analysis, however, requires a lot of input data related to material and section properties and loads, which are generally difficult to obtain accurately. Therefore, the national codes of most of the countries recommend nonlinear analysis only for highly irregular and important structures. The linear dynamic analysis is comparatively simpler. It adequately captures the dynamic behavior in elastic range and, therefore, it is a reasonably good indicator of the performance. The main purpose of the linear dynamic analysis is to evaluate the time variation of stresses and deformations in structures caused by the arbitrary dynamic loads.
Three Dimensional ModelingA structural model is a diagram which consists of a set of nodes and connections between the nodes. Analysis process of frames is conducted on a model based on many assumptions including those for the structural model, the geometric behavior of the structure and its members and the behavior of the sections and joints. Structures with irregular plans, vertical setbacks or soft stories will cause no additional problems if a realistic three dimensional computer model is created. This model should be developed at the early stages of design since it can be used for the static wind and vertical loads, as well as for the dynamic seismic loads.
Only structural elements with significant stiffness and ductility are modeled. Non-structural brittle components can be neglected . The beam-to-column connections play an important part in the overall stability of any frame so one has to model it properly by rigid (continuous construction), semi-rigid (semi-continuous construction) or pinned (simple construction) connection. For the purpose of elastic dynamic analysis, gross concrete sections, neglecting the stiffness of the steel, are normally used.
When bracing is provided, it is normally used to prevent, or at least to restrict, sway in multi-storey frames. Common bracing systems are trusses or shear walls as shown in Fig. 3. For a frame to be classified as a braced frame, it must possess a bracing system which is adequately stiff. The frame without the bracing system can be treated as fully supported laterally and as having to resist the action of the vertical loads only. Here reinforced concrete building is considered as unbraced frame and composite building is considered as braced frame. The bracing system resists all the horizontal loads applied to the frames it braces in addition to any vertical loads applied to the bracing system and the effects of the initial sway imperfections from the frames it braces.
It should be noted that in a frame with a truss type or frame type bracing system, some members participate in the bracing system in addition to being a part of the frame structure. For frames without a bracing system, and also for frames with a bracing system but which is not sufficiently stiff to allow classification of the frame as braced, the structure is classified as unbraced. In all the cases of the unbraced frames, a single structural system, consisting of the frame and of the bracing when present, shall be analysed for both the vertical and horizontal loads acting together as well as for the effects of imperfections. The existence of a bracing system in a structure does not guarantee that the frame structure is to be classified as braced. Only when the bracing system reduces the horizontal displacements by at least 80% can the frame be classified as braced.
The following guidelines are considered here for the modeling of the structure:
- The members and joints are modeled for global analysis in a way that appropriately reflects their expected behavior under the relevant loading.
- The basic geometry of a frame is represented by the centerlines of the members.
- Members are represented as the linear structural elements located at their centerlines, disregarding the overlapping of the actual widths of the members.
- Alternatively, account is taken of the actual width of all or some of the members at the joints between the members.
Design ExampleA "B+G+9 Storied Commercial Building"  depicted in Fig. 4 is considered here with the following parameters:
- Place of construction : Vadodara
- Built-up area : 720 sq. m.
- Storey height : 4.0 m
- Soil Type : Class II – Medium Soil
- Grade of concrete : For composite decks, concrete beams and concrete columns - M 25
For concrete columns – M 30 & M 35
- Grade of reinforcement : Fe 415
- Grade of steel : Fy 250
D.L. at any typical floor level
- Moving Partitions = 1.5 kN/m2
- Floor Finishes = 1.2 kN/m2
- Metal Deck = 0.15 kN/m2
- Duct & Plastering = 0.80 kN/m2
D.L. at roof level
- Metal Deck = 0.15 kN/m2
- False Ceiling, Ducts etc. = 1.00kN/m2
- Screened concrete 50 mm thk. = 1.20 kN/m2
- Live Load = 4.00 kN/m2 at floor level
- Deck slab definition : One way floor load, rib width: 0.18 m, rib height: 0.05 m
- Analysis Methods : ESMA and LDRSA
Results obtained for the composite and R.C.C. buildings by the Equivalent Static Method of Analysis (ESMA) for nodal displacements, support reactions and beam end-actions are compared in Tables 2 to 6 whereas the results obtained by Linear Dynamic Response Spectrum Analysis (LDRSA) are reported in Tables 7 to 11. For LDRSA, twelve mode shapes and twentyfive load cases are considered as per the guidelines of IS: 1893 code .
The main purpose of the linear dynamic analysis is to evaluate the time variation of stresses and deformations in structure caused by the arbitrary dynamic loads. Structure can vibrate in different mode shapes, as shown for an eleven-storey composite building in Fig. 5. There can be as many mode shapes possible as number of dynamic degrees of freedom in the building. The first three mode shapes of the eleven storeys R.C.C. building are depicted in Fig. 6.
- The basic assumption in equivalent static method of analysis is that only the first mode of vibration of building governs the dynamic behavior and therefore the effects of higher modes are not considered in the analysis. Thus, ESMA cannot adequately capture the true behavior of multi-storey building; the design forces for the members may be grossly underestimated. On the other hand, several uncertainties and approximations are involved in dynamic analysis in describing the true dynamic loads, estimating the actual material and sectional properties etc. and therefore, dynamic analysis must be used with great caution. However, compared to equivalent static method of analysis, it is certainly a better indicator of the structural performance.
- From Tables 2 and 7, it is clear that the nodal displacements in a composite structure, by both the methods of seismic analysis, compared to an R.C.C. structure in all the three global directions are less which is due to the higher stiffness of members in a composite structure compared to an RCC structure.
- As the dead weight of a composite structure is less compared to an R.C.C. structure, it is subjected to less amount of forces induced due to the earthquake. A comparison of Figs. 5 and 6 clearly indicates that the displacement of composite structural system is less compared to an R.C.C. structural system so the time period required by the composite structure for one cycle is also less and the frequency of structure is higher.
- From Tables 3 and 4, it is evident that the downward reaction (FY) and bending in other two directions for composite structural system is less. Thus, one can use smaller size foundation in case of a composite construction compared to an R.C.C. construction.
- In case of a composite structural system, because of the lesser magnitude of the beam end forces and moments compared to an RCC system (Tables 5, 6, 10 and 11), one can use lighter sections in a composite structure. Thus, it reduces the self-weight and cost of the structural components.
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