## Blog

# Performance of T-shape shear wall instead of rectangular shear wall at the periphery of Tall building

- May 29, 2020
- Posted by: Prof. Dr. Md. Jahangir Alam
- Category: Civil Engineering Structural Engineering

The paper depicts the comparison between using T-shape (flange) shear wall and regular rectangular wall in Tall building. In this paper, a special focus has been drawn regarding the total lateral displacement if a certain concrete volume is used for providing flange with a rectangular wall keeping the volume the same.The design of high rise buildings essentially involves to safely carry gravity and lateral load by an efficient system . Generally rectangular shear walls are used to control lateral displacement by using its stiffness characteristic. If T-shaped shear walls are placed at the periphery of the building and flange is aligned parallel to the direction of lateral load , the structure can be categorized as exterior structure and it gives more system efficiency than using only rectangular shear wall. Preliminary design and optimization steps are illustrated with example of conceptual tall buildings. These are also illustrated by STAAD Pro software to do approximate analysis of shear-wall frame where both the rectangular and T-shaped shear walls have been used. The results in terms of nodal lateral displacements for two building model were compared. The design criteria are strength, serviceability, stability and human comfort. The strength is satisfied by limit stresses, while serviceability is satisfied by drift limits in the range of H/500 to H/1000. Stability is satisfied by sufficient factor of safety against P-Delta effects through dynamic analysis. For human comfort acceleration of top floors has kept in 25 milli-g.

## Authors:

**Engr. Mostahid Azad**

Principal Design Engineer, Advanced Design Concept, Mirpur, Dhaka and Advisor of Structural Design Team, Geotech & Structures

And

**Professor Dr. Md. Jahangir Alam**

Department of Civil Engineering, BUET, Dhaka and Technical Adviser of Geotech & Structures

**Introduction**

High rise building or tower design pose some geotechnical and structural challenges. There are some issues which are additional to regular height building design. This article describes the issues related to high-rise building design. Shape of shear wall wall at periphery of the building has effect on the performance agaist lateral loads. T-shape and rectangular shear walls were examined and reported in this article. Structural Engineers and Geotechnical Engineers who are involved or interested in designing tall building will get a lot of useful information in this article.

## Design Criteria of Tall Building

The design of tall buildings essentially pertinent with conceptual design,approximate analysis ,preliminary design and optimization.It is done to carry gravity and lateral loads by the structure safely as well as efficiently. The predominating principles of tall building design are strength, serviceability, stability and comfort.

The strength is satisfied by limit stresses. It requires each member be sized to carry its design load without buckling, yielding or fracture. While serviceability issues are ensured by drift (lateral deflection) limits. Typical limits most widely used in design are H/400 to H/500 for wind load. On the other hand, an absolute inter story drift is limited about 10 mm (3/8”) considering damage to non-structural partitions, cladding and glazing of tall building.

Stability of tall building primarily depends on proper arrangement of vertical components, optimization of horizontal component and managing lateral loads by efficient lateral load resisting systems. The effectiveness of shear walls in resisting horizontal loading depends stongly on the rigidity of connected beams. Sufficient safety factor against buckling, secondary moment effect and torsional resistance play a vital role for the stability of any structure. The factor of safety is around 1.67 to 1.92. Non linear behavior must be investigated for any tall building.

The floor slabs of high rise building act as diaphragms and are often considered to be stiff in their plane and deformation in its plan is usually ignored. The slabs are connected to the stabilizing units, such as shear walls, columns. Floor slabs are often considered to horizontal load distributor through the building is due to the stiffness of the different stabilizing components.

Designers of wind sensitive buildings have long recognized that perception of building motion due to wind may be described by various physical quantities like maximum displacement, velocity and acceleration. But acceleration has, however, become the standard for the evalution of human comfort. Peak acceleration of 20-25 milli-g for commercial buildings and 15-20 milli-g for residential buildings have been successfully using for many tall building designs.

Damping strongly influences the motion of buildings. Damping levels used in building motion for wind load are generally taken as approximately 1% of critical damping for steel buildings, 1.50% for composite buildings and 2% for reinforced concrete buildings.

Ductility is a basic requirement. In a major earthquake, a building frame designed to code levels of lateral strength will be forced well beyond yield. The seismic resisting frame system must develop plastic hinges and subsequently undergo large inelastic lateral displacements in a ductile manner, in order to satisfy the dynamic energy demand and thus survive the earthquake attack. Ductile reinforced concrete design is therefore primarily concerned with actual strength (i.e. capacity) of members and joints in the real structure when built, and aims to ensure that hinging develops only at suitable locations while effectively preventing any form of premature, non-ductile failure. Thus, all reinforced concrete framed buildings designed to code loadings should be detailed for fully ductile earthquake performance.

The aim of the structural engineer is to develop a most efficient and optimum structural system to satisfy these criteria, and assess their structural weights in weight/ unit area. If the overall shape and structural subsystem of tall building are optimized, weight/unit area can be made more reasonable.

The assumptions can be categorized into the following main points:

- The analysis and the behavior of the tall building is linearly elastic;
- The frame sections of the core, the columns are constant along the height of the the tall building.

## Structural Loads and Responses of High Rise Building

The actual forces acting on tall building structure are seldom accurately known. But it is possible to make some reasonable assumptions. For simplicity, it is usually assumed that forces acting on building structures can be converted to static in nature. In fact, these loads are not always static, perhaps for tall buildings.Sometimes, they are dynamic or changing in nature or designers play with these static loads to get dynamic effect. Seismic loads, gusting of wind, movements of machinery and any other sources of rapid load variation will produce dynamic loads.

However, the effects of these more-or-less changing forces are expressed in terms of equivalent static load expressed by psf or kg/ sq.m uit. Sudden application of any static load can be a dynamic source of load. Live load in the form of lifting equipments, oscillatory machinery, cars in garage can be considered as dynamic source of load. Dynamic effect produced by impact forces act as additional to the gravity loads of the basic live load itself. Generally, these impact forces expressed by an “impact factor” is 20 to 30% of applied own load.

Wind load on tall building is absolutely dynamic. Lateral loads produced by earthquakes are also dynamic but are uaually expressed as a percentage of the overall mass or gravity loaf of a building.

Internal forces may also be produced in a tall building as a result of a temperature variation between various parts of the building. Relative shrinkage of the materials, or uneven settling of foundation produces internal forces.

### Dead Loads

Dead loads are caused by the weights of all the elements of the tall building, ceiling finishes,permanent partitioning walls, façade cladding,storage tanks, mechanical distribution systems,and so on. For steel buildings , the gross DL average will be on the order of 50 to 80psf while for ordinary reinforced concrete buildings , it will likely be between 100 and 150 psf. The estimated dead loads may be in error by 15 to 20% or little more.

### Live Loads

Live loads include allowance for the weights of people, furniture, movable partitions, books, mechanical equipment, and all other semipermanent or temporary loads. Due to the versatility of high rise building, it is difficult to predict the possible live load conditions to a structure. Through experience, survey analysis, and practice, however, recommended design load values for various occupancies have been developed.

The chance of full occupancy load simultaneously on every square foot of every floor supported by a column is very low. Again the occupancy loads on floors are never uniform. Building codes take this into account by allowing “ live load reduction factor”.

## Wind Load and variation of gust effect factor in Tall Building

The interaction between wind and a structure creates many different flow situations because of the winds complexity. Wind is composed of eddies that gives wind its gustiness and then turbulent character. The gustiness decreases with height but the wind speed over a longer time period increases. Due to that wind behavior is varies in time, i.e. dynamic, it will result in the magnitude of the static wind load on the tall building will vary.

The term along wind or simply wind is used to refer to drag forces while transverse wind is the term used to describe crosswind. Generally, in tall building design, the crosswind motion perpendicular to the direction of wind is often more critical than along –wind motion. At low wind speeds, since the shedding occurs at the same instant on either side of the building, there is no tendency for the building to vibrate in the transverse direction. Therefore the building experiences only along-wind oscillations parallel to wind direction.

Figure 1: Simplified wind flow consisting along –wind and across-wind components.

Figure 2: Power spectral density of wind

Figure 3: Power spectral density of wind

Figure 4: Gust factor variability

Gustiness in wind introduces dynamic loading effect on the system.The dynamic action of a wind gust depends not only on how long it takes for the gust to reach its maximum intensity and decrease again,but on the period of the subject building itself. If the wind gust reaches its maximum value and vanishes in a time much shorter than the period of the building, its effects are dynamic.On the other hand ,the gusts can be considered as static loads if the wind load increases and vanishes in a time much longer than the period of the building. For example, a wind gust that develops to its strongest intensity and decreases to zero in 2s is a dynamic load for a tall building with a period of considerably larger than 2s, but the same 2s gust is a static load for a low-rise with a period of less than 2s.

ASCE7-05 defines a rigid building as “A building whose fundamental frequency of vibration is greater than or equal to 1 Hz”. For rigid structures, the engineer may use a single value of G=0.85, irrespective of exposure category. The commentary of ASCE-7 goes on to state ,”When buildings have a height exceeding four times the least horizontal dimension or when there is reason to believe that the natural frequency is less than 1Hz (natural period greater than 1 s, the natural frequency for it should be investigated”. The building may be considered rigid from the first definition given in ASCE 7-05 Commentary Section C6.2 . The second definition refers to the fundamental period *T* of the building. The formula given in Section 12.8.2.1 of the ASCE 7-05 is T=C_{t}*H^{3/4} where, T is the fundamental period of building, in seconds. C_{t} is the coefficient equal to 0.003 for concrete moment frame buildings. H is the height of the building , in feet.

The following easy and popular formula is used to calculate the fundamental period *T* of the building in wind tunnel analysis – T=H/150, where H is the height of the building, in feet.

Although the maximum lateral deflection is generally in a dirction parallel to wind (along wind direction) ,the maximum accelerarion leading to possible human perception of motion or evev discomfort may occur in a direction perpendicular to the wind (across-wind direction). Across-wind acceleration are likely to exceed along-wind accelerations if the building is slender about both the axes.

Natural wind is turbulent, especially near ground where friction between the air flow and the terrain causes turbulence. This turbulence varies in a complex, random way in both space and time, making it nearly impossible to accurately model the wind flow. Therefore the wind is described in statistical terms as a stochastic process. This means that the wind itself is seldom measured and instead statistical data is collected from measurements. This data often consist of a mean wind velocity averaged over a 10 minute time frame. To incorporate fluctuations in the wind, the wind velocity is described as the sum of this mean velocity and of fluctuations. Since the fluctuations are random variables they will tend to have zero mean value over a sufficient long period. As the mean wind velocity is usually described as a mean over a 10 minute period, the fluctuating parts are set to have zero mean value over the same period.

The numbers of frequency points are chosen so that the simulation becomes 10 minutes long. This is calculated by the following formula

where T is the time of the simulation in seconds, N is the number of frequency points and ∆t is the time step for the simulation given as

where fc is the cut of frequency in hertz. This gives the following equation to determine number of points for a 10 minute simulation with fc = 2 Hz:

The tributary area consists of half of the length between the two adjacent points to any given point, (Lseperation) and a chosen normalization measurement. The tributary area of the superstructure then becomes the width (B) multiplied with the separation of the adjacent points (Lseperation) in the FE-model.

A = B X Lseperation.

Figure 5: NAT HAZ Wind velocity Fluctuating Curve

Figure 6: STAAD input of NAT HAZ Wind velocity Fluctuating Curve

Figure 7: STAAD input of NAT HAZ Wind velocity Fluctuating Curve

## Aspect Ratio of High Rise Building

Aspect ratio is the ratio of height to the structural lateral system footprint width or depth. There is no code defined as what is a slender building and what is not. WSP a famous firm in designing tall slender buildings which also designed 432 Park Avenue in New York considered as one of the most slender building, defines that a slenderness ratio of above 1:7 is kind of considered as slender. Recently buildings with around slenderness ratio of 9 or above are considered as slender. Twin Towers were considered as slender buildings with a slenderness ratio of 1:8 or so, even Burj Khalifa is a slender building. 432 Park Avenue which is built in New York has a slenderness ratio of 1:25 and is considered as a pencil skyscraper. The name pencil came from the fact that it has a similar aspect ratio to that of a pencil. While Burj Khalifa has an aspect ratio of that of a ruler.

So basically there is no code defined clause for a slenderness of a building it is a judgement. Although most of the engineers would confirm that anything with aspect ratio of 1:7 to 1:8 or above is a slender building.

Slenderness could be > 10 if special features to improve wind comfort are included. BNBC-2006 state it is preferably equal or more than 5.

## Requirements for Time History Analysis for Wind Load

As per BNBC-2006, wind gust cause additional loading effects due to due to turbulence over the sustained wind speed. For slender buildings d structures, this additional loadings gets further amplified due to dynamic ind sucture interaction effects. A slender or wind-sensitive building shall be one having-

- a height exceeding five times the least horizontal dimension , i.e. building aspect ratio is greater than 5.0.
- a fundamental natural frequency less than 1.0 Hz. i.e. if f < 1.0 Hz.

But the commentary of ASCE 7 states “When buildings or other stuctures have a height exceeding four times the least horizontal dimension or when there is reason to believe that the natural frequency is less than 1 Hz (natural period greater than 1 s), the natural frequency for it should be investigated”.

## Natural Frequencies-

Natural frequency ( f_{o }) is the number of oscillations per second of a structure that may swing freely.

An oscillating structure has a tendency to develop greater amplitude of a swing at the natural frequency than at other frequency.

The natural frequency is primarily dependent on the building’s equivalent stiffness and mass.

f = 1/2π *√ (3EI / 0.23*m*L^3) L=Building Heght, m=Mass per unit ht of Building.

If EI (Stiffness ) increases , f (Frequency) increases. It indicates the building is becoming stiffer.

All structures have specific frequencies for when the structure begins to resonate, these frequencies are called the natural frequencies.

Table 1: Natural frequency for different cases.

Approximate equations of natural frequency developed for seismic design tend to give higher natural frequency .In the model frequency value input as 0.25 Hz.

## Frequency of vortex shedding

At low wind speeds, since the shedding ocuurs at the same instant on either side of the building, there is no tendency for the building to vibrate in the transverse direction. Therefore the building experiences only along-wind oscillations parallel to wind direction. However, at higher speeds, vortices are shed alternately, first from one side and then from the other side. When this occurs, there is an impulse in the along-wind direction as before, but in addition, there is an impulse in the transverse direction. However, the transverse impulse occurs alternately on opposite sides of the building with a frequency. This impulse due to transverse shedding gives rise to vibrations in the transverse direction. The phenomenon is called vortex shedding.

There is a simple formula to calculate the frequency of the transverse pulsating forces caused by vortex shedding: f=(V XS)/D

f= Frequency of vortex shedding in hertz.

V=Mean wind speed at the top of the builing in ft/sec.

S=Dimensionless parameters called the Strouhal number for thegiven shape=0.20

D=Diameter of the building in ft.

In our study, V=210 km/hr=210*0.92=193.2 ft/sec. D=140 ft., S=0.20

Frequency of vortex shedding, f=(V XS)/D=0.276 Hz.

Figure 8: Vortex shedding

## Structural system of Tower

Structural system of tall building can be divded into two broad catagories: interior structures and exterior structures. This classification is based on the distribution of the components of the primary lateral load-resisting system over the building. A system is categorized as an interior structure when the major part of the lateral load resisting system is located within the interior of the building. Likewise, if the major part of the lateral load-resisting system is located at the building parameter, a system is categorized as an exterior structure. It should be noted, however, that any interior structure is like to have some minor components of the lateral load-resisting system at the building perimeter, and any exterior structure may have some minor components within the interior of the building.

Sufficient design of exterior frame for the purpose of resisting lateral loads allows the interior part of the building to only resist the gravity loads. Not only this concept is a clever solution for resisting lateral loads but also leaves the architect with the wonderful choices for the interior space of the buildings.

## Shear walls: Rectangular Vs T-shape

In the capacity design methodology, a flexural (ductile) shear wall is designed to promote inelasticity through formation of a plastic hinge at the base where the flexural demand is a maximum. This mechanism necessitates shear resistances corresponding to the development of the probable moment capacity of the wall system at its plastic hinge location. For rectangular-shaped shear walls, the evaluation of the moment capacity is a routine task; however, it is common in building construction to integrate L-, C-, T-, or H- shaped wall sections. For these section types the end flange walls participate in the moment capacity. Underestimating the effective flange width results in an underestimation of the probable moment capacity, which leads to design shear forces that are not necessarily conservative. A lower than required shear capacity would prevent the wall from developing a plastic hinge resulting in a shear-dominate failure mechanism with restricted ductility. Flange participation based on a percentage of the wall height. Introduction flanged sections are commonly considered in the design of lateral shear wall resisting systems, where part of the flange participates in the moment capacity of the section. However, in calculating the moment capacity, the effectiveness of the flange width requires attention to ensure a proper capacity design.

Previous design standards for concrete, ACI 318-89 recommended an effective flange overhang width of wh/10, where wh is the height of the wall above the section under consideration. This was based largely on results for T-beams, which is now considered to be a low value. Although a low effective width would underestimate flexural capacity, it is not necessarily conservative and could lead to inadequate shear reinforcement. Therefore, it was subsequently suggested that an effective flange overhang width of wh/4 be implemented for the tension flange (Wallace 1996). The new provisions of ACI 318-05 have incorporated this suggestion by stating that the effective width of overhanging flanges of structural walls shall not be assumed to extend farther from the face of the web than 25% of the total wall height above the section under consideration. Paulay and Priestley (1992) suggest an effective flange overhang of 50%wh and 15%wh for the tension and compression flange, respectively.

Structural walls constructed with flange overhangs exceeding the 25% effective flange width criteria specified by current standards. Barda (1976) tested eight low-rise flanged shear walls with height to length ratios ranging from 1:4 to 1:1 and flange overhang to height ratio from 0.133 to 0.533. An accurate assessment of the effective flange width can be significant and of practical importance in the design or analysis of shear walls. For slender walls, underestimating the effective flange width leads to an underestimated moment capacity resulting in a shear-dominant mechanism rather than flexural yielding. Further, it underestimates the compression demand for the compression flange.

Based on limited analyses the following observations are suggested:

1. Three-dimensional nonlinear continuum finite elements can successfully simulate the response of flanged walls.

2. The effectiveness of flanges in tension and compression increase with increasing flange width and no upper limit has been found.

3. The effectiveness of flanges in tension is larger than flanges in compression.

4. If the effective flange in tension as the actual overhang exceeds 25% of the wall height it is not desirable. If effective flanges in compression as the actual overhang width exceeds 50% of the wall height, it should be revised.

## Space efficiency & Structural plan density index of Tall building

### Space efficiency:

High-rise office buildings are more expensive to construct. Moreover, they furnishes with less usable space. The space efficiency, as well as, the shape and geometry of the high-rise building need to satisfy the value and cost of the development equation.

Building **efficiency** is most commonly expressed as a percentage **calculated** by dividing the usable **floor** area by the gross **floor** area.

Space efficiency=(Total floor area –Area of structural vertical component) /Total floor area.

=Net floor area / Gross floor area

In an easy sense, space efficiency is determined by the size of the floor slab, dimension of the structural elements and rationalized core, goes along with the financial benefit. Net area includes only usable floor not the lift core and common space.

Table 2: Space efficiency.

### Structural plan density index:

Structural plan density index=Total area of vertical structural elements /Gross floor area of the footprint of buildind at ground level.

It is of interest to obseverve that historically this ratio has been decreasing. Contemporary high –rises, because of their light weight construction, improved high –strength materials and innovative structural technique require a rather modest 2-4% of gross area of ground floor. The higher percentage is most often found in buildings using shear walls for resisting lateral loads. In our study 4.75% area of footprint has been required for moderate concrete strength. This percentage can be reduced for Model-2 as the lateral displacement is conservatively below than allowable limit.

## Description of Building Model

In the present study, an RCC 50-storeyed office building model and its loading conditions are taken from BNBC-2017. The general features of the building model , column, beam and shear walls sections used in the building are given in Table 3.

Table 3: General features of the model structure.

The building has been provided with RCC column and shear wall. The grades of reinforcing steel and concrete used in the building are assumed to be of Grade 500 and M50 respectively. The material properties used for concrete and steel are given in the Table 4.

Table 4: Material properties.

The dimensions of the shear wall of rectangular and Tee shaped are given Table 3 and the prismatic general section properties of L, T- sections given as input to STAAD Pro building model are given in Table 4. The plan of the building Model-1 & Model-2 are shown in Figures below.

Figure 9: plan of the model-1 structure

Figure 10: Plan of model-2 structure with T-shape shear wall

Figure 11: 3D view of the modeled structure

## Modeling of Loads in the Tall Building

### Gravity Loads-

The basic loads considered in this study are dead load, live load and wind loads.The values of Dead loads(DL) and Live loads (LL) are calculated in accordance with BNBC 2017. The summary of dead load and live load is given in Table 5. In load combinations involving imposed loads as per BNBC-2017 recommends.

Table 5: Code-prescribed Load value.

### Lateral Wind Force as per BNBC-2006

According to the proivisions of BNBC-2006, dynamic analysis for wind load is suggested for closed buildings with height to minimum lateral dimension ratio of more than 5 or fundamental frequency of the building less than 1 Hz . It is suggested to check for wind induced oscillations and a magnification factor called gust response factor needs to be included in the dynamic effects of the wind.Since the building considered for study has height to least lateral dimensions ratio is 4.29. The natural frequency of Model-1 and Model-2 calculated and shown Table-1.

It is seen that the natural frequency of the building is 0.25Hz less than 1Hz, the dynamic analysis of the building for wind loads need to be carried out. For considering dynamic effects in the present study, gust factor method given in BNBC-2017 is used. The designed wind pressure imposed in model by wind load generation. The parameters used for wind load generation have mentioned above. From the dynamic analysis, the base shear and base moment due to wind load for wind speed 210 km/hr in X direction mentioned page-13.

## Analysis of the Tall Building

Analysis of 50 storeyed RC building has been done considering the entire structure as a 3D moment resisting frame without brick infill panels using STAAD.Pro .Beam and columns are considered as beam elements.The slabs are considered as plate elements. There are 68164 nodes , 22600 Beams , 69950 plates in the STAAD Pro analysis model of the structure. The main objective Of modeling the whole structure as 3D model is to take into account the behavior of each and every component in space structure environment. The slab is modeled as an element to carry the live load as distributed pressure load. Plate elements are used for shear walls.

Figure 12: ASCE 7-10 input in STAAD

Figure 13: ASCE 7-10 input in STAAD

Figure 14: ASCE 7-10 input in STAAD

Figure 15: ASCE 7-10 input in STAAD

## Method of Analysis of High Rise Building

**P-delta-**

P-delta is second order effects. Second order effects can arise in every structure where elements are subject to axial load. When a model is loaded, it deflects. The deflection may give rise of an importance to consider this as additional moment may incur additional deflections which in turn again can incur additional moment, a third order, and so on until the loads can eventually exceed the capacity. Therefore in the design of members the total moment, summary of moments caused of the first order, and second order should be included or proportionately “decreased” capacity should be used. The magnitude of P-delta effect is related to the magnitude of axial load (label is often used therefore the name is P-delta) and stiffness and slenderness of members There are two different P-delta effects. The first one is P-δ, even called P – “small delta”, and the other is P-Δ, also called P-“big delta”. A P-δ effect is associated with local deformation relative to the element chord between end nodes. A P- Δ effect is associated with displacements relative to member ends. P-delta effect in a structure may be managed by increasing its strength or its lateral stiffness or by a combination of these.

### Time History analysis

Elastic time history analysis for wind load were performed on the parametric study model. A time history will give the response of a structure over time during and after the application of a load . Time history method gives all possible forces which are generated, and there by displacement of structure, during entire duration of wind load force due to variation of wind speed at equal interval, typically 0.05 to 0.1 sec. In time history analyses the structural response is computed at a number of subsequent time instants. In other words, time histories of the structural response to a given input are obtained.

## Tall Building Roof displacement and peak inter-story drift due to lateral loads

According to BNBC-2017: for serviceability limit state against lateral deflection of buildings and structures due to wind effect, the followed combination is 1.0D+0.5L+0.7W. The total allowable lateral displacement is calculated as H/500 where H is the height of the building. Therefore, maximum allowable lateral displacement value for building height of 600 ft is 14.40 inch. The maximum value of displacement in serviceability limit condition obtained for wind loads from the finite element 3-D model of STAAD Pro is 11.63” for Model-1 and 8.658” for Model-2.

Table 6: Nodal lateral displacement for P-Delta analysis .

Table 7: Nodal lateral displacement for Dynamic analysis.

## Frequency, Period and Mass participation of tall building

**Model-01**

Figure 17: Acceleration-time history of Node 666839 in x direction

Figure 18: Acceleration-time history of Node 666839 in z-direction

Figure 19: Displacement-time history of Node 666839 in x direction

Figure 20: Displacement-time history of Node 666839 in z direction

**Model-02**:

Figure 21: Acceleration-time history of Node 666839 in x-direction (model 2 with T-shape shear wall)

Figure 22: Acceleration-time history of Node 666839 in z-direction (model 2 with T-shape shear wall)

Figure 23: displacement-time history of Node 666839 in x-direction (model 2 with T-shape shear wall)

Figure 24: Displacement-time history of Node 666839 in z-direction (model 2 with T-shape shear wall)

Table 8: Comparison between Model-1 and Model-2.

- In the 1
^{st}Mode Mass (Fundamental frequency which indicates lowest frequency) Participation =71.98 % for Model-1 and 72.66% for Model-2 in X-Direction (which is normally 60-80%.). So Fundamental natural frequency of this building is 0.141 Hz and 0.164 Hz respectively. - In the 2
^{nd}Mode (Second natural frequency) Mass Participation = 71.12 % for Model-1 and 71.92% for Model-2 in Z-Direction (which is normally 10-20%). - In the 3
^{rd}Mode (Third natural frequency) is for torsional mode. - More than 90% Mass participation is achieved by the 10th Mode where the frequency is 1.517 Hz for Model-1 and 1.666 Hz for Model-2. So, natural frequency of this building is 1.517 Hz and 1.666 Hz respectively.

Table 9: Coincidence of modal frequency and vortex shedding frequency of Model-1 and Model-2.

## Base shear for Dynamic analysis

### Base shear for Model-1.

### Base shear for Model-2.

It is seen that Model-1 subject to maximum base shear at 4.74 sec and for Model-2 the time is 4.15 sec.

## 1^{st} Mode Shape for Model-1 and Model-2 of the tall building

Figure 27: Shape of structure at 1^{st} mode (Model-1)

Figure 28: Shape of structure at 1^{st} mode (Model-2)

## Degree of Discomfort in High Rise Building

The dynamic effects should be considered both for serviceability and safety. When considering safety, the risk of resonance are of interest and when considering serviceability, the human response to motion are of interest. Movement in a tall building can have a wide range of human response, from anxiety to acute nausea. This can make a building undesirable and may produce difficulties renting floor area. Why it is of importance to not just consider stability issues but also consider motions. Movements in buildings are commonly generated from wind, earthquakes, machinery, nearby industrial plants and various types of transportation [34]. It would be expensive to construct a high-rise building that could withstand all movements. That is why there are various recommendations regarding accelerations in buildings depending on the occupancy.

Table 10: Degree of Discomfort.

●Max. Acceleration = 25 mg. = 9.65 in/sec^2.

Table 11: Allowable Limit for Acceleration.

Table 12: Frequency of Vibration –Discomfort Relationship.

Figure 29: Evaluation curves for horizontal wind induced vibrations in a building caused by a one-year return wind. Line 1 represents office and line 2 represents residence. The axis represents the acceleration [m/s2] and the fundamental frequency of the building [Hz].

## Shear Lag Effect in Tall Building

The primary resistance to lateral loads comes from the web frames with windward columns in tension and the leewards columns in compression. The web frames are subjected to the usual in-plane bending and racking action associated with an independent rigid frames. The primary action is modified by the flexibility of the spandrel beams, which causes the axial stresses in the corner columns to increase and those in the interior columns to decrease. The principal interaction between the web and the flange frames occurs through the axial displacements of the corner columns. When the columns of the leeward side is under compression, it will tend to compress the adjacent column because the two columns are connected by a stiff spandrel beam.

Shear lag phenomenon existence is mainly because of rigidity levels of the spandrel beams. The primary action is modified by the flexibility of the spandrel beams, which causes the axial forces in the corner columns to increase and those in the interior columns to decrease. There are two types of shear lag: positive shear lag and negative shear lag. In positive shear lag the axial force is higher at the corner columns meanwhile, in negative shear lag case, axial force increases in the middle columns. Negative shear lag occurs in the upper levels of tall buildings.

Some researches focus on the structural system as an important factor in order to decrease the shear lag effect. It is seen that the effect of bracing the tubular frames as a solution to resist the shear lag phenomenon with other solutions. Structural section properties are assumed to be the same for the cases of comparison. Fig. 31 illustrates two models of analysis. The first model is a framed-tube structural system and the second one is braced-tube. The results of analysis for both models show braced-tube is showing an ideal distribution of axial force. It is clear that bracing reduces the axial force of edge columns.

Note that all the analyses made in this study are assumed to focus on the windward frame. Bracing the frame yields 27% of axial force reduction in the edge columns. Edge columns are responsible for the shear lag effect in the building which increases the lateral displacement of the structure.

In our case, Model-2 having flange shear wall at periphery is exterior categorized structure. It shows strong web frame against lateral loads. It’s in-plane bending and shear racking capacity is higher than model-1 having regular rectangular shear wall. The results of analysis for both models show model-2 is showing an ideal distribution of axial force shown in Table-12. Flanged shear walls reduce the axial force of edge columns.

Figure 30: Shear lag in framed tube

Figure 31: Shear lag in framed tube

Table 13: Column axial load (kip) under load combination D+0.5L+0.7W

## Conclusion

In drift controlled high-rise structures, flange shear walls at periphery of the building are more effective than purely rectangular shear walls. Generally the primary resistance to lateral loads comes from the web frames of any structure. Structure having flaged shear wall is exterior category structure and shows less lateral displacement.

It is observed that the time period Vs displacement graphs obtained were similar to that of Time Vs acceleration graph obtained from wind load data. Model -1 shows less acceleration compare to Model-2 due to lesser stiffness of the structure.

As the time period increases displacement of each floor also increases. As the height of structure increases time period increases. Time dependent displacement for Model-1 is more than Model-2.

There is a uniformity in column axial load distribution curve which indicates shear lag in Model-2.

Fundamental period of Model-1 is 0.139 Hz and Model-2 is 0.164 Hz. Which infer Model-2 is stiffer than Model-1.

In case of across-wind response, Model-2 shows better performance than Model-1.

In the case of coincidence of modal frequency of the building with the vortex shedding frequency, resonance may take place which causes significant problems for both survivability and serviceability designs of the building. In our study it is not coincident with each other.

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I honored from the core of my heart to the author of this amazing blog and willing to know more about this topic, Although my knowledge and experience are nearly zero about tall buildings but have a keen interest on it.