Introduction
Preamble
Significant progress has been made in structural engineering; however, a straightforward answer to the question of what a building structure needs to withstand wind and earthquake forces for optimal serviceability at a reasonable cost remains elusive While there are some general guidelines and extensive computer-aided analyses available, these rigorous evaluations are supported by various software tools.
Analyzing building structures is crucial for understanding their actual behavior, particularly during the preliminary design phase where structural engineers rely on experience and thumb rules to determine the type of structural systems and approximate sizes of members For seismic-resistant structures, it is essential to integrate various elements that can resist inertia forces and effectively transfer them to the foundation Adequate diaphragm strength and stiffness are provided by suspended floors, but special attention must be given to the structural adequacy of diaphragms, especially when the spacing between vertical and horizontal members is increased The presence of cutouts can weaken the diaphragm and reduce its spanning capability, necessitating careful planning of structural member placement Ductility and hysteresis are critical interrelated factors that structural engineers must thoroughly understand Additionally, redundancy and collapse patterns significantly influence the design process, as the behavior of reinforced concrete structures can be complex However, innovative structural configurations can often mitigate negative impacts, leading to a more resilient design The following section will further explore these concepts in detail.
A Few Important Aspects of Structural Design
Reinforced concrete structures exhibit non-elastic behavior even under low stress levels, leading to cracking at higher stress levels While the stiffness of these elements significantly decreases and deformations increase, they will not collapse immediately if designed with sufficient ductility Understanding the behavior of reinforced concrete under dynamic loads, such as wind and seismic forces, can be challenging Therefore, it is crucial to incorporate ductile detailing in building designs to ensure they can withstand these forces effectively.
Ductile reinforced concrete allows for larger deformations without collapse, resulting in a high total energy level that promotes a reasonable and economical design while ensuring structural safety and minimizing damage Understanding both strength and serviceability is crucial, as ductility and hysteresis are interrelated concepts that structural engineers must grasp thoroughly Recognizing structural redundancy is essential for appreciating failure sequences and assessing overall ductility The following section will delve into these aspects, highlighting their design applications illustrated in Chapter 3 through specific design examples and detailing.
When the center of mass and center of stiffness of a building do not align at any floor level, the structure experiences torsion around its vertical axis Typically, in symmetrical buildings, both stiffness and mass are evenly distributed However, during the inelastic stage, if weaker structural members reach their limiting strength, their stiffness deteriorates compared to stronger members that remain intact This leads to a stiffness asymmetry issue, causing the centers of mass and stiffness to misalign Such discrepancies are common during the inelastic stage and warrant further investigation.
Understanding the inelastic behavior of Reinforced Concrete structures is crucial for ensuring safety and performance during earthquakes The hysteresis model plays a vital role in assessing strength and stiffness degradation, ductility, and energy dissipation Serviceability encompasses durability, stability, fire resistance, deflection, cracking, and vibration control Even a well-designed tall building may experience significant sway, potentially affecting occupant comfort, yet it may not collapse despite exceeding serviceability limits To maintain safety, building codes establish serviceability thresholds While economic considerations often dominate project priorities, advancements in design software simplify complex tasks, enabling structural optimization without compromising strength, serviceability, or stability for improved economic outcomes However, this topic requires more in-depth discussion.
Ductility in buildings refers to their ability to endure significant lateral deformations before collapse, measured by the ratio of maximum deformation to yield deformation The key aspect of ductility is the ability to sustain large inelastic deformations without a considerable loss of strength Effective building design incorporates favorable failure mechanisms, ensuring adequate lateral strength and stiffness Additionally, ductility plays a crucial role in dissipating earthquake energy through hysteretic behavior, making the ductile chain design concept in buildings, based on capacity design, highly favored in construction practices.
The "Strong Column-Weak Beam" concept is crucial in building design, as it ensures that beams, designed as ductile links, fail before the more critical columns during seismic events This approach enhances the overall ductility of structures, allowing them to endure significant deformations without collapsing Ductility is assessed through various interrelated concepts, including global, member, sectional, and material ductility Effective use of stirrups and lateral ties in beams and columns not only resists shear forces but also provides confinement to the core concrete, increasing its strength and strain capacity For optimal performance, materials like steel must meet minimum elongation standards specified in seismic design codes, such as IS 13920, which requires at least 14.5% elongation at fracture for earthquake-resistant construction Ultimately, a ductile building can sustain inelastic actions and allow for manageable, pre-determined damage while maintaining stability during seismic activity.
Reinforced Concrete structures experience various types of failures, including shear, bond slip, flexural over-reinforced, flexural under-reinforced, and torsional failures Among these, flexural under-reinforced failure is preferred as it allows the member to stretch in flexure on the tension side without compromising the compression concrete, thereby utilizing the ductility of the steel bars This behavior results in the formation of a plastic hinge over a small length of the member, enhancing the moment-curvature relationship and significantly increasing curvature ductility Although the moment-carrying capacity is primarily determined by the tensile strength of the steel rather than the concrete, the maximum strain capacity of confined concrete further enhances curvature ductility, positively impacting the global load-deformation response of structures The pushover responses of buildings with and without transverse confining reinforcement demonstrate substantial differences, with additional confining reinforcement significantly increasing global drift capacity It is crucial to avoid designing reinforced concrete columns to bear axial compression loads above the balanced condition to prevent brittle compression failure Imposed confinement below the balanced level greatly enhances curvature ductility, thereby safeguarding columns against brittle collapse during extreme seismic events Although ductility quantification is not yet standard practice, design for ductility typically involves prescriptive recommendations on reinforcement detailing, structural configurations, material specifications, and acceptable failure mode sequences Ultimately, the level of ductility in a building structure or structural element is assessed through pushover analysis.
To ensure economy and safety in building structures during earthquakes, it is crucial to allow for minor damages such as plasticity, fracture, or cracking while maintaining the strength needed to support vertical loads and prevent collapse Lateral ties are essential for confining concrete and preventing the buckling of longitudinal reinforcement, enabling columns to continue bearing vertical loads despite potential cracking or yielding of steel reinforcement However, this may significantly reduce the stiffness of the structural elements If a structure remains elastic, it experiences higher internal forces and total base shear, emphasizing the importance of incorporating ductility in materials to minimize these internal forces through controlled damage Building codes globally address these considerations, with the ductility factor influenced by the lateral structural system in place Additionally, understanding the failure mechanism of structural members is vital to ensure they fail in a ductile manner.
Structural redundancy is a concept that indirectly influences ductility and enhances a structure's ability to withstand earthquake shaking While increased redundancy is generally perceived as beneficial for reducing sensitivity to undesirable loads, it is essential to clarify its specific role during seismic events and differentiate it from overall structural capacity Notably, an increase in redundancy does not always guarantee a substantial improvement in seismic performance, highlighting the importance of examining how redundancy affects ductility in structural systems.
Architectural Requirements
The integration of architectural concepts and structural design is crucial for creating aesthetically pleasing and cost-effective buildings Effective collaboration from the project's inception ensures that architectural ideas are preserved while maintaining safety and budget considerations Key elements such as overall geometry, structural systems, and load paths significantly influence a building's performance, particularly under seismic conditions Buildings with convex geometries exhibit direct load paths, enhancing their seismic resilience, while concave geometries can lead to stress concentrations Architects play a vital role in determining a building's massing and must understand both good and poor structural stability Addressing configuration issues early on is essential to prevent conflicts between architects and structural engineers, especially when balancing innovative design with safety requirements.
To optimize the dynamic behavior of structures, it is essential to prioritize pure translation modes as the lower vibration modes while minimizing undesirable diagonal and torsional modes, often caused by asymmetrical plan shapes Complex building designs, particularly those with projections or re-entrant corners, experience diverse vibration modes, akin to a dog's tail wagging while the body remains still, which can lead to high stress concentrations at re-entrant corners and significant structural damage during earthquakes This issue is particularly pronounced in T and L-shaped buildings, where torsional modes are prevalent To mitigate these effects, constructing two separate rectangular buildings with a construction joint is advisable In contrast, regular buildings or those with minimal projections predominantly exhibit translational modes, and undesirable vibration modes can also be minimized in V, Y, or X-shaped buildings by maintaining small projections.
Buildings with a large plan aspect ratio and significant projections pose serious structural risks, especially in seismic zones When the projected length exceeds 15% of the overall building length, it is classified as a significant irregularity, increasing the likelihood of earthquake damage To mitigate these risks, IS 1893 recommends subdividing the structure into dynamically stable independent units While some irregularity may be acceptable for aesthetic purposes, it necessitates a rigorous design methodology to ensure safety and may lead to higher costs Interestingly, buildings with irregular configurations can perform surprisingly well compared to regular structures, although building codes typically advocate for stronger connections and members, which can further elevate costs Ultimately, it is advisable for codes to prohibit extremely irregular structures in high seismic areas to enhance safety.
The complexity of geometrical plans can increase significantly with the introduction of large floor openings or cutouts, which may be required by clients for various reasons such as enhancing natural light, improving ventilation, or fulfilling specific architectural design concepts When utilizing reinforced concrete slabs as rigid diaphragms, excessive cutouts can lead to numerous structural issues, while the behavior of slabs with minimal openings is influenced by the size and location of those cutouts, representing a form of irregularity Different building codes provide specific recommendations to address these structural behaviors, which may include horizontal irregularities such as torsional effects, re-entrant corners, diaphragm discontinuities, out-of-plan offsets, and non-parallel systems.
According to IS 1893, irregularities in buildings can be categorized into plan irregularities, such as torsional irregularities, and vertical irregularities, which include stiffness and mass irregularities A building is considered irregular from a torsional perspective if the ratio of maximum to minimum horizontal displacement exceeds 1.5 If this ratio falls between 1.5 and 2, it is essential to modify the building configuration to ensure that the fundamental torsional mode of oscillation is less than the first two translational modes in each principal plan direction Should the ratio exceed 2.0, a revision of the building configuration is necessary Additionally, the structure must be designed following the load combinations recommended by the code.
When the center of mass of a building does not align with its center of stiffness, it leads to twisting around the center of stiffness, significantly impacting the outermost columns These column members experience substantial horizontal forces, resulting in increased stress and potential structural issues.
Out-of-plan offsets and deflections can significantly damage structures, potentially leading to collapse under vertical gravity loads, particularly in reinforced concrete buildings Post-earthquake surveys reveal that torsion effects are common, necessitating careful planning to minimize the distance between the center of stiffness and the center of mass Ground movement can also induce torsional motions, prompting various codes of practice to recommend a minimum design eccentricity to mitigate these effects To enhance torsional strength and stiffness, it is essential to maximize the horizontal offset between structural elements However, shear walls do not provide substantial resistance to torsional effects; instead, they tend to warp and bend around their weak axes, while the rotation of the floor diaphragm can also occur.
A Reinforced Concrete diaphragm acts as a rigid unit, providing significant stiffness and strength in its plane, enhancing resistance against torsion when walls are spaced appropriately The principles remain applicable even when shear walls are replaced with moment frames Buildings often face seismic damage due to re-entrant corners, which can vary in shape and result in different dynamic performances across wings During an earthquake, inertia forces generated at floor levels with substantial mass are distributed to columns, beams, and structural walls based on their stiffness and load-resisting capacities It is crucial for floor slabs to maintain minimal deformation to prevent excessive loading on structural members The maximum displacement of the diaphragm correlates with the aspect ratio, and IS 1893 advises limiting lateral in-plane displacement to 1.5 times the average displacement for buildings with an aspect ratio not exceeding 4 Proper distribution of inertia forces through columns and walls is essential for establishing direct load paths Inelastic actions can reduce the stiffness of structural elements, leading to increased stiffness eccentricity and adversely affecting building performance during seismic events Irregularities, such as large openings or cut-outs, exacerbate the uneven distribution of inertia forces, and IS 1893 recommends limiting openings to 50% of the diaphragm area to minimize in-plane flexibility Large lateral displacements can cause significant structural and non-structural damage, as well as second-order P-Δ effects that may lead to collapse Therefore, it is recommended that inter-storey drift under design earthquake forces be restricted to 0.4% of the storey height, ensuring that maximum damage is typically confined to the lower storeys of buildings.
When comparing two buildings of similar design, one constructed with conventional materials and the other using lightweight materials while maintaining the same total weight, the building with greater height experiences a reduced acceleration response This is due to the increased time period associated with taller structures, which leads to a decrease in total design inertia force However, this reduction in inertia force is not enough to offset the increased bending moments that arise from the additional height of the building.
Lateral Load- Resisting System
The subsystems or components of the tall building structural systems are essentially the following.
• energy dissipation systems and damping
These are broadly defined as follows:
• shear truss/ outrigger braced systems
• tube- in- tube systems with interior columns
• truss tubes without interior columns
The structural system must effectively support various load types, including gravity, lateral, temperature, blast, and impact loads Additionally, it is essential to maintain the tower's drift within specified limits, specifically H/500.
1.4.2 m oment - r eSiSting F rameS , b raced F rameS and S hear W allS
The most widely used vertical structural systems for resisting horizontal seismic forces include shear walls, moment-resisting frames, and braced frames These systems not only support gravitational loads but also provide essential horizontal stability Essentially functioning as vertical cantilevers anchored at the foundation, they are designed to effectively counteract horizontal forces from earthquakes and wind.
Building structures are three-dimensional frameworks composed of structural elements that work together to resist loads, with vertical elements and diaphragms serving as common resisting systems Moment-resisting frames are often chosen as seismic resisting systems, providing flexibility in architectural design These frames are utilized as lateral resisting systems, particularly when ductility and deformability are essential Special Moment-Resisting Frames (SMRF) require specific detailing to ensure ductile behavior and compliance with relevant codes and guidelines, making them crucial for effective seismic performance.
The Ordinary Moment-Resisting Frame (OMRF) is a structural design that lacks the special detailing necessary for ductile behavior, leading to potential vulnerabilities during seismic events While a highly ductile frame offers architectural flexibility and redundancy, poorly designed moment-resisting frames can experience catastrophic failures in earthquakes, often due to weak story formations and compromised beam-column joints Given that beam-column joints are critical stress concentration zones, they require meticulous attention in the design process to ensure structural integrity and resilience.
The design and detailing of Special Moment Frames must be executed with precision to withstand multiple cycles of inelastic stresses without significant strength loss These moment-resisting frames are recognized for their effective performance during severe earthquakes, as they create numerous dissipative zones where plastic hinges can form, allowing for substantial energy dissipation To enhance energy dissipation capacity and ensure overall structural integrity, it is crucial to adhere to code recommendations and expert guidance, which can lead to varying levels of strength and ductility in the frames.
Reinforced concrete Special Moment Frames are designed to enhance the ductility of structures by ensuring a strong column-weak beam system, which is crucial for safety during significant earthquake ground shaking Building codes mandate that columns must be stronger than beams, and the strong column-weak beam concept is essential for achieving this safety To avoid non-ductile failures, a capacity design approach is employed, ensuring that the shear strength is sufficient to handle forces during seismic events Proper detailing of non-structural elements and reinforcement placement is critical, particularly avoiding lap splices near maximum bending moment sections Additionally, transverse reinforcements are necessary to confine joints and enhance ductility While Reinforced Concrete Braced Frames are less common, they provide an effective alternative to moment-resisting frames, utilizing diagonal bracing to transfer seismic forces efficiently Braced frames, especially X-braced systems, demonstrate superior performance in terms of base shear and reduced story displacement during earthquakes, offering greater stiffness and stability compared to unbraced frames.
Shear walls are essential structural components in reinforced concrete framed buildings, designed to withstand lateral forces from wind and earthquakes They enhance the strength and stiffness of structures, significantly minimizing lateral sway and potential damage While moment-resisting frames also handle lateral loads through flexure, they are generally more flexible and experience greater horizontal deflection In high-rise or slender buildings, shear walls are commonly used, although their energy dissipation capacity is often inferior to that of braced systems Experimental data indicates that braced and infill frames exhibit superior lateral strength and energy dissipation compared to bare frames A well-designed, ductile system offers flexibility in architectural design, but poorly constructed moment-resisting frames can fail catastrophically during earthquakes due to weak stories and compromised beam-column joints Although shear walls are typically rectangular, they can also take on other shapes like C, L, and I, but their effectiveness is limited to their length It is crucial that shear walls possess adequate strength to resist shear forces and bending moments, and care should be taken to avoid cutouts for windows and doors in highly stressed areas, especially near the base.
Collapse Pattern
Unintended stiffness additions, insufficient beam-column joint strength, and failures in tension and compression are critical factors contributing to structural collapse Additionally, issues such as wall-to-roof interconnection failures, local column failures, torsional effects, and the collapse of soft and weak stories play significant roles Understanding these elements is essential for preventing progressive collapse in buildings.
The following vertical irregularities repeatedly observed severe damages during earthquake shaking
• an abrupt change in the floor plan dimensions
• the columns on a particular floor level are more flexible and/ or weaker than those above
• discontinuous and offset structural walls
• a particular floor is significantly heavier than an adjacent floor
Shorter columns compared to adjacent columns can pose significant risks during earthquakes When a column is half the height of its neighboring columns, it exhibits much greater stiffness, as stiffness is inversely proportional to the cube of the column length (L³) Consequently, the shorter column can be up to eight times stiffer than the others, allowing it to withstand eight times the inertia force during seismic activity.
The "Short Column Effect" refers to the potential failure and instability of building frames when subjected to large inertia forces, particularly due to factors such as unreinforced masonry infill of insufficient height, deep spandrel beams, mezzanine slabs, stair beams or slabs, plinth beams, and unequal basement columns on sloping ground.
Good ductility in buildings is achieved when the collapse mechanism is of the desirable type, characterized by stable and full hysteretic loops in the load-deformation curve, which indicate effective energy dissipation through inelastic hinges at beam ends This behavior is typical in buildings that experience sway mechanisms, where beams yield before columns, resulting in ductile flexural damage at beam ends due to a strong column-weak beam design Conversely, buildings that fail through storey mechanisms concentrate damage in the columns at a specific level, leading to high ductility demands on the columns, especially in a weak column-strong beam configuration Ultimately, the hysteresis loop of a building structure is influenced by the type of collapse mechanism it undergoes.
Beam– column joints in moment- resisting frames need to be handled with care
Repairing damaged beam-column joints is challenging, as these joints must be designed to withstand seismic forces During earthquake shaking, beams connected to the joint experience bending moments that can either sag or hog This results in the top bars being pulled in one direction on one side and pushed in the same direction on the other, with a similar scenario for the bottom bars The bond between concrete and steel is crucial in the joint region, and bond slip can occur, leading to a loss of load-carrying capacity Additionally, the pull-push forces can cause distortion in the joints To enhance stability and resist shear forces, closely spaced closed-loop steel ties with 135° hooks are necessary around the column bars Although incorporating these closed-loop ties requires extra effort, seismic design codes advocate for their continuation through the joint region for improved structural integrity.
Strength discontinuity, characterized by a sudden reduction in lateral strength along a building's height, poses significant challenges, leading to increased inelastic demand at junctions To mitigate this issue, it is crucial to avoid poor seismic structural configurations whenever possible After designing the building for various load combinations, inelastic pushover analysis can provide valuable insights IS 1893 – Part I – 2016 offers several recommendations to address these concerns, emphasizing the importance of assessing the distribution of lateral strength and stiffness throughout the building to identify any irregularities.
To prevent brittle failure, it is essential to use larger column sizes Additionally, the design, detailing, and construction of joints play a crucial role in effectively transferring forces and moments; improper execution can lead to inefficiencies.
The design and detailing of reinforced concrete beams, columns, and beam-column joints are crucial for structural integrity, as recommended by IS 13920 Shear walls, being stiffer than moment frames, effectively attract more earthquake forces, allowing moment frames to be lightly reinforced for cost efficiency However, the effectiveness of reinforced concrete structural walls must be utilized with specific objectives in mind, especially in open ground storey RC frame buildings, which are known for their poor performance To enhance safety, it is essential to avoid various types of irregularities, as outlined in IS 1893 (Part 1), 2016, which states that the strength of any storey should not be less than 80% of the storey above Additionally, when two parts of a building are constructed close together with a small gap for construction joints, careful calculation of the necessary separation is vital to prevent pounding during seismic events, particularly in closely spaced tall buildings where significant tip displacement increases the risk of such occurrences.
The soft storey problem occurs during earthquakes when a building's specific floor is significantly more flexible or weaker than the floor above, leading to severe damage to its columns This issue is exacerbated in buildings with open ground floors, particularly in highly seismic zones, increasing the risk of soft storey mechanisms The danger is heightened when open ground floors are combined with masonry infill frames To mitigate this risk, structural members must possess additional strength and ductility A building is classified as having a weak storey when its lateral strength is less than that of the floor above, particularly when the seismic weight of any floor exceeds 1.5 times that of the floor below, resulting in mass irregularity.
Dynamic Response Concept
The dynamic characteristics of buildings, including natural periods, mode shapes, and damping, play a crucial role in determining the structure's response to external forces Each natural frequency and its corresponding mode shape significantly influence the displacement experienced by the building Understanding these fundamental aspects is essential for effective structural analysis and design.
Natural periods of translational oscillation in buildings, denoted as T x, T y, and T z, correspond to horizontal movements along the X and Y axes and vertical movements along the Z axis, while T θ1 represents rotational oscillation around the Z axis Each building has multiple natural periods due to its nodes being able to translate and rotate in all three Cartesian directions, leading to 6N mode shapes for N nodes Irregular buildings, characterized by non-uniform mass and stiffness distribution, exhibit mixed mode shapes, with the overall response being the sum of these modes, often dominated by certain contributions To enhance stability, it's crucial to design buildings as regularly as possible and ensure that structural elements are appropriately located to minimize torsional and mixed oscillation modes Increasing torsional stiffness can prevent early torsional modes by adding in-plane stiffness in selected perimeter bays, ensuring no stiffness eccentricity The oscillation modes of buildings are influenced by their geometry, material properties, and the connections with the underlying soil, resulting in flexural or shear mode shapes, or a combination of both.
The natural period of a building refers to the duration required for one complete oscillation cycle, influenced by its mass and stiffness distribution Heavier and more flexible structures exhibit longer natural periods compared to lighter, stiffer buildings The natural frequency, measured in Hertz (Hz), is the inverse of the natural period Increasing column size enhances both stiffness and mass; however, if the increase in stiffness outpaces the increase in mass, the natural period decreases Accurate estimation of flexural stiffness for individual components is crucial for predicting a building's dynamic characteristics, especially under seismic loads Reinforced concrete presents challenges in determining optimal cross-sectional properties, particularly when significant cracking occurs during earthquakes While gross cross-sectional properties are typically used for linear analysis under gravity loads, they may not accurately reflect behavior in cracked conditions Effective properties, derived from extensive research on seismic loading, represent the reduced stiffness of damaged members and are expressed as a fraction of gross stiffness For example, the effective moment of inertia for columns is generally higher than for beams due to lower expected damage According to IS 1893, Part I, 2016, suggested ratios for effective moment of inertia are I b,eff = 0.3 I b,gross for beams and I c,eff = 0.70 I c,gross for columns, which are essential for calculating the fundamental natural periods of buildings.
Wind Load and Earthquake Load
Wind effects are particularly significant for tall buildings, as advances in architectural design and structural analysis have led to lighter high-rises that are more susceptible to sway The dynamic nature of wind load varies based on factors such as time period, building shape, and irregularities, with longer wind periods behaving more like static loads Shorter wind periods, however, require consideration as dynamic forces, producing vibrations in both along and across wind directions The severity of sway is influenced by wind velocity distribution, building mass, stiffness, and shape, with across-wind effects often being more critical than along-wind effects Accurate assessment of a building's response is essential, especially for flexible structures, as dominant mode shapes and resonance frequencies play a crucial role in predicting dynamic responses For small buildings, an "Equivalent static approach" may suffice, but flexible buildings face challenges due to lower resonance frequencies, which can lead to significant deflections and potential instability from aerodynamic interactions like galloping oscillations and vortex shedding Wind loads exert random forces across a wide frequency range, with the building's response primarily determined by wind energy near its natural frequencies The IS 875, part III, 2015 provides guidelines for wind assessment, emphasizing the importance of understanding wind-structure interactions, particularly the effects of turbulence and vortex shedding on building stability.
Buildings experience oscillations during earthquakes, leading to inertia forces that vary at different levels The intensity and duration of these oscillations, along with the induced inertia forces, are influenced by both the building's dynamic characteristics and the earthquake's shaking dynamics When the ground shaking frequency aligns closely with a building's natural frequency, resonance can occur, resulting in significant displacement and potential collapse The ground motion consists of a range of frequencies that change randomly over time, and even brief exposure to frequencies near a building's natural frequency can cause severe damage The effective mass contributing to lateral oscillation during an earthquake is termed the seismic mass, which includes the total dead load and a percentage of the design live load, as specified by seismic design codes Heavier buildings have a larger natural period, and as a building's height increases, its mass grows while stiffness decreases, further extending the natural period The orientation of rectangular columns also affects lateral stiffness; typically, the longer side is placed in the weaker direction to optimize the column's section, which can inadvertently increase stiffness in that direction, leading to higher base seismic shear and necessitating larger column sizes and reinforcement Thus, careful consideration of column size and orientation is essential for achieving an optimal design solution.
Wind Analysis of Buildings
Preamble
Wind is primarily caused by Earth's rotation and variations in terrestrial radiation, with its speed influenced by ground roughness and height While the horizontal component of wind is usually dominant, the vertical component can also play a significant role Anemometers are commonly used to measure wind speed, which generally increases with height, peaking at the gradient height, influenced by terrain conditions Regardless of ground roughness, wind speeds above gradient heights tend to equalize Additionally, the magnitude of wind speed is affected by the averaging time; shorter averaging times result in higher mean wind speeds To fully develop the velocity profile for a specific terrain, wind must travel over a distance known as fetch length.
The gustiness of wind, represented by the fluctuating component, varies with the averaging time and is typically expressed in terms of turbulence intensity The response of flexible structures to wind turbulence is influenced by the time period of oscillation and damping Additionally, the presence of obstructions can modify wind characteristics and lead to interference effects with nearby structures Increased internal pressure from external openings can create suction or compressive forces on roofs and walls, making it essential to consider both external and internal wind pressures in design values The IS code defines basic wind speed based on a 3-second gust duration, as shorter gusts generally do not significantly impact pressure on buildings Buildings with high slenderness ratios are particularly susceptible to the effects of gusts, and codes specify reductions in wind pressures for tributary areas exceeding 100 m² Tornados, which have a more severe impact than cyclones, are narrowband phenomena of limited duration that remain difficult to assess accurately Overall, wind is inherently turbulent and causes random, time-dependent loads on structures, leading to dynamic oscillations primarily driven by its fluctuating component.
Short rigid buildings, defined by a natural time period of less than one second, are typically assessed using an equivalent static concept for design pressure, as recommended by various global codes of practice These guidelines must be adhered to during the construction phases, especially since strong winds and icing can occur simultaneously in different regions While wind pressure coefficients may vary across codes, they are primarily derived from wind tunnel studies, with the nature and magnitude of wind parameters influenced by factors such as building geometry and wind direction Pressure coefficients are usually based on a quasi-steady assumption, where the mean pressure at a point is compared to the dynamic pressure of the incident wind Additionally, wind turbulence is altered by vortex shedding as it approaches a building, with the angle of wind incidence significantly affecting edges and corners Recent updates to international codes have addressed various wind-related factors, considering rectangular buildings, those with different shapes, and both sharp and rounded corners in their assessments, while also taking into account force coefficients related to shape, aspect ratio, Reynolds number, and shielding.
Tall flexible buildings with a fundamental time period exceeding one second exhibit dynamic responses to wind, not only in the wind direction but also transversely This dynamic behavior arises from changes in incident and wake flow characteristics, leading to oscillations in the structure Additionally, these buildings respond to vortex shedding, particularly when the shedding frequency approaches their natural frequency The effects of interference, influenced by the distance and height of surrounding structures, necessitate wind tunnel studies for accurate assessment As vortex shedding occurs alternately from either side of the building, it generates dynamic forces in the cross-wind direction The frequency of vortex shedding is influenced by various factors, including the building's dimensions, shape, and wind speed, resulting in forces that induce both across-wind and torsional responses The Strouhal number, a non-dimensional parameter, is utilized in wind assessments to account for the periodic nature of vortex shedding, which is also dependent on the building's shape.
Different codes outline procedures for assessing crosswind effects on tall buildings, where higher modes of vibration are typically insignificant The magnitude of the across-wind force and the resulting pitching moment depend on factors such as turbulence levels, mean wind speed, and angle of attack Accurate computation of these forces requires both wind tunnel studies and computational fluid dynamics (CFD) analysis.
Wind Load Provisions as per IS 875 (Part 3), 2015
The wind map as per IS 875 Part 3, 2015 have to be used to have wind speed in a particular place
Wind pressure on buildings as per IS 875-Part3, 2015
Consider, Basic wind speed (V b ) of the building site as per clause no 6.2, Fig.1 or Annexure –A of
IS 875 Part3, 2015 (It is based on 50 years return period and at height of 10m & terrain Category 2)
Topography factor (k 3 )† as per clause no
Importance factor cyclonic region (k 4 ) †† as per clause no
Note: ††k 4 is applicable only for coastal area.
Off shore wind factor as per Clause no 6.6 is 1.15, which has to be adopted over and above k 4 , if p z = 0.6 V z 2 as per clause no.7.2
Design wind pressure (p d ) p d = K d K a K c p z as per clause no 7.2
To calculate wind pressure on buildings, several factors must be considered The wind directionality factor, k d, is crucial and is defined in clause 7.2.1, with a typical value of 0.90 for design wind pressure; however, for circular structures or in cyclone-prone areas, it can be set to 1.0 The area averaging factor, k a, outlined in clause 7.2.2 and table 4 (amendment 1), addresses the correlation of pressure coefficients over varying areas, necessitating a multiplication factor for larger areas Additionally, the combination factor, k c, specified in clause 7.3.3.13, accounts for the differing pressures inside and outside clad building frames, requiring another multiplication factor to accurately calculate the combined wind loads.
* Factor k 1 is based on statistical concepts that take into account the degree of reliability and the return period, which is generally considered equal to the life of the structure.
** Basic wind speed calculated at 10 m height and terrain category 2 For other terrain categories and heights, a multiplication factor, k 2 , to be adopted.
The basic wind speed is determined for a flat site at sea level, but it does not account for the influence of local topography, such as hills, valleys, and cliffs, which can affect wind speed variations To accurately incorporate these topographical effects, the k3 factor must be applied.
In coastal regions extending up to 60 kilometers from the shore, the impact of severe cyclones results in wind speeds that surpass those observed in non-coastal areas To account for this increased wind intensity, it is essential to apply a k4 factor specifically for coastal areas.
According to clause 6.3.3.1 of IS 875 (Part 3), 2015, the topography factor k3 is set at 1.0 when the upwind slope is less than 3 degrees However, if the upwind slope exceeds 3 degrees, the value of k3 must be determined using the guidelines provided in annexure C of IS 875 (Part 3), 2015.
As per clause 7.2.1 of IS 875 (Part 3), 2015:
(but p d is not to be less than 0.7p z )
2.2.1 d iFFerent a pproacheS to W ind a nalySiS
Now, wind– structure interaction effects are considered to have a design load on structures.
IS 875 (Part 3), 2015, suggests three different concepts to arrive at the design loads These concepts are as follows:
As per clause 7.1, the wind load on a building may be calculated for individual struc- tural elements, such as the roof and walls.
As per clause 7.3.1 of IS 875 (Part 3), 2015:
Design wind force (F) = (Cpe– Cpi) A p d where
A = surface area of structural element or cladding unit p d = design wind pressure
According to clause 7.3 of IS 875 (Part 3), 2015, pressure coefficients are specified for specific surfaces or sections of a building To determine the wind load acting perpendicular to a surface, one must multiply the surface area or its relevant portion by the pressure coefficient (C p) and the design wind pressure at the corresponding height above ground level.
1 If the surface design pressure varies with height, the surface area of the struc- tural element may be subdivided, so that the specified pressures are taken over appropriate areas.
2 Positive wind pressure means that the pressure is acting toward the structure and negative means away from it.
The internal pressure coefficient depends upon the degree of permeability of the building, which depends primarily on the percentage of the external wall surface that consists of openings.
According to clause 7.3.2.1, for buildings with claddings that allow air flow through openings not exceeding 5 percent of the wall area and lacking large openings, it is essential to evaluate the potential for both positive and negative internal pressure Two design scenarios should be analyzed: one with an internal pressure coefficient of +0.2 and the other with a coefficient of -0.2.
Clause 7.3.2.2 deals with medium to large openings:
Buildings with medium and large openings can experience varying internal pressures based on wind direction For medium openings, which comprise 5 to 20 percent of the wall area, an internal pressure coefficient of +0.5 and -0.5 should be analyzed to determine which scenario causes greater member distress In contrast, buildings with large openings, exceeding 20 percent of the wall area, require evaluation with coefficients of +0.7 and -0.7, with the analysis yielding the highest member distress being the one to adopt.
So, internal pressure coefficient need to be adopted considering the percentage of opening of wall of the building.
Consider individual structural elements of the building like walls.
As per clause 7.3.1 of IS 875 (Part 3), 2015:
F = wind force acting at a particular point
C pi = internal pressure coefficient p d = design wind pressure
Numerical examples are available in Chapter 4.
The building is analyzed as a complete, enclosed structure, functioning as a vertical cantilever anchored at the foundation level The drag force coefficients (C f) must be determined in accordance with clause 7.4.
Clause 7.4 states: “The value of force coefficients (C f ) apply to a building or struc- ture as a whole, and when multiplied by the effective frontal area (A e ) of the building or structure and design wind pressure, (p d ) gives the total wind load (F) on that par- ticular building or structure.”
F = wind force acting in a specified direction on the frontal area
C f = force coefficient on the building (as per clause 7.4.2)
A e = effective frontal area of the building
The force coefficients for different rectangular- shaped buildings are given in figures 4(a) and 4(b) of IS 875 (Part 3), 2015, depending on the plan ratio (a/ b) and the height/ breadth (h/ b)ratio.
The design wind force acting on a structure can be calculated using values obtained from Table 25, which depend on various ratios such as the plan ratio (a/b), height/breadth ratio (h/b), wind speed/width ratio, and surface roughness For accurate calculations, it is essential to refer to the higher values presented in Table 25 and Figure 4 of IS 875 (Part 3), 2015.
As per clause 9.1 of IS 875 (Part 3), 2015, the dynamic effects of the wind have to be considered, and the wind- induced oscillation effect has to be examined, if
(i) h/ b > 5 where h = height of the building b = width of the building and/ or ii) Natural frequency of the building in first mode < 1 Hz (cycles/ second)
(again, as per clause 9.2.1, note 4)
The vortex shedding effect needs to be considered if l/ b < 2 where l = length of the building b = width of the building
Calculation of the wind force proceeds as follows.
F z = design peak along- wind load on the building structure at any height z
C f,z = drag force coefficient of the building structure corresponding to the area A z p d = design hourly mean wind pressure corresponding to V zd and obtained as 0.6 V zd 2 (N/ m 2 )
V zd = design hourly mean wind speed at height z, in m/ s
A z = effective frontal area of the building structure at any height z, in m 2
G = gust factor: 1 + r √[g v 2 B s (1 + ỉ) 2 + H s g r 2 SE/ ò] where r = roughness factor, which is twice the longitudinal turbulence intensity, I h,i g v = peak factor for upwind velocity fluctuation (3.0 for category 1 and 2 terrains, 4.0 for category 3 and 4 terrains)
The background factor (B s) quantifies the slowly varying component of fluctuating wind loads due to low-frequency wind speed variations It is calculated using the formula B s = 1 / [1 + √(0.26(h – s)² + 0.46 b sh² / L h)], where b sh represents the average breadth of the building or structure between the specified heights s and h This factor is essential for understanding wind load impacts on structures.
L h = measure of effective turbulence length scale at the height, h, in m (= 85 [h/ 10] 0.25 for terrain category 1 to 3, = 70 [h/ 10] 0.25 for terrain category 4) ỉ = factor to account for the second- order turbulence intensity: = g v I h,i √B s / 2 where
I h,i = turbulence intensity at height h in terrain category 1
H s = height factor for resonance response: = 1+ (s/ h) 2 where s = size reduction factor, given by = 1/ [1 + (3.5f a h)/ V hd ][1 + (4f a b oh )/ V hd ] where b oh = average breadth of the building/ structure between 0 and h
E = spectrum of turbulence in the approaching wind stream: = ᴨ N/ (1 + 70.8 N 2 ) 5/ 6 where
N = effective reduced frequency = f a L h / V hd where f a = first mode natural frequency of the building/ structure in along- wind direc- tion, in Hz
V hd = design hourly mean wind speed at height, h in m/ s ò = damping coefficient of the building/ structure (for Reinforced Concrete struc- tures, it is 0.020) g r = Peak factor for resonant response = √2ln(3600f a )
As per clause 6.4: k 21 = hourly mean wind speed factor for terrain category 1: = 0.1423[ln(z/ z 0i )] (z 0i ) 0.0706 where z = height or distance above the ground z 0i = aerodynamic roughness height for i th terrain
The design hourly mean wind speed
As per clause 10.3 of IS 875 (Part 3), 2015, the across- wind load on the building will be a distributed one
The distribution of loads is as follows.
F z,c = across- wind load per unit height at height z
The equation M c = 0.5 g h p h b h 2 (1.06 – 0.06k) √(ᴨC fz / ò) describes the dynamic response of a structure to wind forces, where g r represents the peak factor, calculated as 2 √(2 ln(3600 f c )) In this formula, p h denotes the hourly mean wind pressure at a specific height h in Pascals, b indicates the breadth of the structure perpendicular to the wind in meters, and h signifies the height of the structure in meters The mode shape power exponent k is utilized to represent the fundamental mode shape, expressed as – ᴪ (z) = (z/ h) k, while f c refers to the first mode natural frequency of the building in the across-wind direction, measured in Hertz.
The cross- wind force spectrum coefficient (C fs ) can be calculated from Figure 11 in
According to IS 875 (Part 3), 2015, the calculation of C fs for rectangular buildings involves considering a turbulence intensity of 0.2 at the 2/3 h curve For slender-framed structures that are moment-resisting, the mode shape power exponent (k) is set at 0.5, while the damping coefficient (ò) for reinforced concrete structures is established at 0.02.
A numerical example has been done in Chapter 4.