Staircases Structural Analysis And Design Pdf
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Solved Example A cantilever slab mm thick is 1. We can however also design invisible supports for steps. The small notional horizontal load can generally be covered by wind What is the difference between Airport, Aerodrome and Airfield?
- Structural Analysis of Free-Standing Staircase
- Structural Analysis of Free-Standing Staircase
- Staircases Structural Analysis And Design
It follows the limit state design philosophy. Like the beam and slab elements, the staircase is design to check the ultimate limit and the serviceability limit states. Staircase is one such important component in a RCC structure. The riser The design of staircase, therefore, is the application of the designs of the different elements of the staircase.
Structural Analysis of Free-Standing Staircase
Reinforced concrete staircases are structurally designed as cantilevered, slab type or beam-slab type. Within this study an irregular cantilevered staircase is studied and its structural dynamic characteristics are explored. An eigen-value modal analysis is performed to determine the mode shapes, their corresponding modal participation factors and natural periods of vibration. The highest modes of interest are identified.
Following on that, a scaled record of a previous historical earthquake was applied within a direct integration time-history analysis in order to assess the performance of that irregular stair case under earthquake loading.
That load was applied within two perpendicular load cases representing the different possible directions of earthquake vibrations in which the effect of the structure irregularity was assessed per direction. The structure was found to have large drifts creating a need to change the structural system. The coastal city of Hurghada at the entrance of the southern Suez Gulf of the Red Sea was founded in the early 20 th century, and until a few years ago it was a small fishing village.
But since the s, it has been continually enlarged by Egyptian and foreign investors to become the leading coastal resort on the Red Sea. Throughout the most recent decade, the population in Hurghada city expanded quickly as a consequence of expanding of financial action identified with tourism.
Most of the structures there were not initially designed to resist earthquakes; thusly, generally little occasions later on can be source of socio-economic disasters. The Egyptian Red Sea city constitutes a major tourism destination, especially for diving, and the coral reefs Hilmi et al. Situated at The high rate of seismic movement there is mostly related to the modification in movement at the triple intersection between the African plate, the Arabian plate, and the Sinai micro plate.
This zone has been known as a range of significant moderate extent seismic action. It has different sources of earthquakes occur at the northern Red Sea and its two branches Gulf of Suez and Gulf of Aqaba Hamouda The irregular three-storey reinforced concrete staircase is supported on three columns and a bearing wall. Shell elements were meshed with maximum size of 0. The total number of frame elements was Shell and frame elements were connected using nodes.
The staircase was modeled to behave as cantilever staircase supported only on the beams and the wall by removing the connectivity between the shell elements at the intersections between adjacent slabs as shown in Fig.
This choice of maximum size of shell elements was meant to increase the accuracy of the analysis and to model the most realistic behavior. Moreover, the boundary conditions at each of the upper floor levels are set to restraint the motion in the horizontal plane to represent the lateral support that the museum slabs and beams provides to the staircase while the vertical motion was allowed at all the floors except for the foundation level which was considered to be a hinged support.
On the other hand, modes 2, 3, 4 and 5 have periods that range from 0. Hence, the fifth mode is considered to be the highest mode of interest when dynamically analyzing this structure. Also it could be noticed that none of the modes had a modal participation factor in any of the two horizontal axis that was exactly zero which is attributed to the irregularity of the structure that caused the center of rigidity to be deviated from the center of mass which excites a twisting component in most of the modes hence most of them have significant components in both x and y directions.
The first five modes have natural periods that are near to the dominant periods of earthquake excitations that are typically within the order of 0. That means that these first five modes are the ones expected to resonate with the earthquake load especially that these modes are the ones with the highest modal participation factors in the horizontal plane which is the main direction of action of earthquake loads. However, the effect of such uncaptured mode would be minor as the main component of earthquake vibrations is horizontal and the twelfth mode has a period of 0.
Hence, it is not expected to see a significant response due to vertical modes when dynamically analyzing such a structure under earthquake loads.
A non-linear dynamic analysis was performed taking into consideration p-delta and large deformations into account in order to investigate the dynamic behavior of this irregular staircase under specific earthquake loading conditions.
The earthquake record chosen to act as the seismic load was the El Centro earthquake that happened in California, USA with perceived intensity of X on the Mercalli intensity scale Wikimedia Foundation, Inc. The earthquake signal was scaled to match the peak ground acceleration of Hurghada that was found to be 0. The irregularity of the structure lead to the necessity of investigating two different seismic cases as it is difficult to determine which direction is the major direction and which is the minor direction.
The first seismic case was set so that the dominant acceleration loading direction is to be in the x direction while the other seismic load case was set so that the dominant acceleration loading direction is to be in the y direction. Modifiers for the moment for the moment of inertia were used as per Egyptian Code of Practice Housing and Building National Research Center to be 0.
These two coefficients were calculated based on a conservatively assumed damping of 0. Hence, the time step size was set to 0. Comparing the three curves of time versus displacement presented in each of Figs. Another common factor in these curves is that the trend of vibrations within the two horizontal axes were very similar due to the modes exciting these vibrations having components in both the x and y directions while the major direction of loading is the factor governing which of these two components will have a higher value.
On the other hand, comparing the response spectra presented in Figs. This could be seen from the comparing the areas beneath the resonant components of the vibrations at periods equal or near to the natural periods to the areas beneath the background and quasi-static components of vibrations at periods significantly larger than the natural periods.
The areas beneath the resonant peaks were significantly larger than the remaining areas representing a higher contribution to the resonant component of vibration when compared to the background and quasi-static components. However, it could be noticed that the maximum lateral drift under any of the load cases and within any of the horizontal directions were all within the order of 0. Knowing that the floor height is 4. This relative displacement is quite high and is attributed to the large irregularity, the high twisting effect and the large resonance that occurs due to the earthquake signal.
Hence, it is highly recommended that the structural system should be changed in order to have lower periods and larger lateral stiffness. The natural periods for the twelve modes of vibrations studied ranged between 0. The first five modes of vibrations are the principle modes of vibration with the fifth mode being the highest mode of interest.
Due to the irregularity of the structure, most of the modes had twisting components. Displacements in the vertical direction were always less in magnitude than the displacements in the horizontal plane. Due to high twisting components in various modes, the horizontal deflections in directions perpendicular to the earthquake loads had the similar trends as the deflections parallel to the loads although with less amplitudes.
The resonant component of vibration is of higher contribution when compared to the background and quasi-static components confirming the high need of a dynamic analysis for that structure. The relative displacement is high due to the large irregularity, the high twisting effect and the large resonance that occurs due to the earthquake signal. It is highly recommended that the structural system should be changed in order to have lower periods and larger lateral stiffness. Skip to main content Skip to sections.
The present study attempts to estimate the dynamic response for a three-storey irregular staircase within the Hurghada National Museum project as shown in Figs.
The fact that the stair is irregular creates a challenge as it creates a necessity to analyze it dynamically when evaluating its performance under earthquake loads Tedesco et al. Open image in new window. The three dimensional finite element model of the staircase. Staircase plan.
These periods are extremely important in determining the time step size within the time-history analysis and expecting which modes will resonate due to the earthquake loads.
Modal analysis periods and modal participating mass ratios. In each seismic load case points of highest absolute displacement were studied. In the first load case two points with highest absolute displacement in x and y directions respectively were examined. The first point was found to be Joint with highest absolute displacement in x direction. Absolute displacement versus time was plotted as shown in Fig. From the response spectrum, several peaks could be noticed at periods ranging between 0.
Seismic load case 1 joint absolute displacement in meters vs time. Seismic load case 1 joint response spectrum x-direction. The second point in the first case was found to be Joint with highest absolute displacement in y direction. Absolute displacement vs time was plotted as in Fig. From the response spectrum the peak point significantly occurs at a period of 0. The trends of the vibrations in the x and y directions shown in Figs.
Seismic load case 1 joint response spectrum y-direction. In the second load case two points were also examined. Absolute displacement versus time was plotted as in Fig. Similar to what was experienced in the first load case, and from examining the response spectrum, several peaks could be noticed at periods ranging between 0. Seismic load case 2 joint absolute displacement in meters vs time.
Seismic load case 2 joint response spectrum x-direction. The second point in the second case was found to be Joint with highest absolute displacement in y direction. From the response spectrum the peak period is 0. Seismic load case 2 joint response spectrum y-direction.
The following conclusions could be drawn from the performed study: The natural periods for the twelve modes of vibrations studied ranged between 0. Bathe, K. Prentice Hall, Delhi Google Scholar. Bicanic, N. Computers and Sturctures Inc.
Farghaly, A. Steel Compos. Hamouda, A. Hazards 59 1 , — CrossRef Google Scholar. Hilmi, N. Topics Middle East.
Structural Analysis of Free-Standing Staircase
Reinforced concrete staircases are structurally designed as cantilevered, slab type or beam-slab type. Within this study an irregular cantilevered staircase is studied and its structural dynamic characteristics are explored. An eigen-value modal analysis is performed to determine the mode shapes, their corresponding modal participation factors and natural periods of vibration. The highest modes of interest are identified. Following on that, a scaled record of a previous historical earthquake was applied within a direct integration time-history analysis in order to assess the performance of that irregular stair case under earthquake loading. That load was applied within two perpendicular load cases representing the different possible directions of earthquake vibrations in which the effect of the structure irregularity was assessed per direction. The structure was found to have large drifts creating a need to change the structural system.
Emoticon Emoticon. Engineering Books. Very useful and rare books in all fields of Engineering. Preference :. Staircases is divided into five chapters: Specifications and basic data on staircases; Structural analysis of staircases — Classical methods; Structural analysis of staircases — Modern methods; Staircases and their analysis — A comparative study; Design analysis and structural detailing. Charts and graphs are included and numerous design examples are given of freestanding and other geometric staircases and of their elements and components.
In recent years both free-standing and geometric staircases have become quite popular. Many variations exist, such as spiral, helical, and elliptical staircases.
Staircases Structural Analysis And Design
In addition to that, you can create a movie of your staircase design in 3D in MOV format. Geometry of staircase Riser of each step Rise Erection Drawings 26 3. Steel Stair - Free download as Excel Spreadsheet. Staircase Reinforcement Calculation Definition: A staircase is defined as set of steps from one floor to another floor or combination of riser and tread to make easy transportation from one floor to another floor in a building.
In the analysis of a free-standing staircase with slab elements, approximate analytical methods are sometimes used because of the absence of specific code provisions due to their inherent limitations. These approaches, however, cannot predict the actual three-dimensional 3D behavior of the stair slab system. In addition, analytical methods cannot predict the stress resultant distribution in any section. These drawbacks highlight the need for the development of more rational but simple analysis methods for design purposes. Thus, in this study, an extensive numerical study on the behavior of free-standing staircases was performed using the finite element package SAP
design of staircase pdf
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