Full structural analysis and design of commercial building project (part - 2)
Waffle slab of 35cm was the most economical type of slabs as an output of part-1, but due to serviceability aspects (deflections), waffle slab of 47cm is needed. Because of the large depth and reducing of clear height of floor, 35cm solid slab on beams will be analyzed and designed in this project.
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| Figure 1. 5-1:Section of the Commercial Center |
The building will be modeled using ETABS software.Moreover, a study of the structure’s lateral load resisting systems will be done to decide which system is to be used. Full design and detailing of structural elements will be achieved by the end of this project.
Introduction
General Description of the projectThe project is a commercial building with a total area of 15,000 m² distributed over fourteen floors and a height of 45m. The first five floors are located underground, which used as parking, such that each floor has a height of 2.5m. The next four floors are used as commercial floors with a different heights ranging from 3.1m to 3.6m. The remaining floors are used as offices with a height of 3.1m for each. The area of each floor is shown in the table 1.1.
Table 1. 1: Areas of floors
| Floor | Area (m2) |
|---|---|
| Basement 5,4,3,2 | 1236 (each floor) |
| Basement 1 | 1208 |
| Ground floor | 1019 |
| Mezzanine floor | 1036 |
| Floor 1 | 926 |
| Floors 2,3,4,5 | 959 (each floor) |
| Floor 6 | 910 |
| Floor 7 | 785 |
Figures 1.3 to 1.5 show architectural drawings of the Commercial Centre project as follows:
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| Figure 1. 3:Architectural Plan for Third Basement Floor |
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| Figure 1. 4:Architectural Plan for typical commercial Floor |
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| Figure 1. 5-2:Section of the Commercial Center |
It can be concluded from the soil report of the building site that:
1. Type of the project site soil is limestone with allowable bearing capacity 450 KN/m².
2. Elastic settlement (Si) was found to be 11 mm as acceptable value.
3. No groundwater encountered at the site.
4. For seismic design, the site of the project lies within zone 2A with an acceleration coefficient of 0.15g.
Project Outline
In this part of the project, all issues considered at the discussion of the project introduction in part-1 were taken into consideration. The first step is to analyze the chosen floor slabs using the equivalent frame method (EFM) by SAFE software instead of the tabulated coefficient method and hand calculation of EFM that used in the introduction.
Results obtained from the software for a 35cm solid slab on beams are almost similar to the hand calculations. However, smaller sections of beams are used.
Therefore, it was decided that two-way solid slab on beams is the floor system to be used for the design of the entire floors within the building.
The second step of this project is to choose and design the lateral load resisting system. First, the adequacy of shear walls to be checked using equivalent lateral force procedure (static analysis) and decide the lateral load resisting system that will be adequate to resist lateral load induced from earthquake.
The third step of the project considers the three dimensional modeling of the Commercial Center and applying both static and dynamic lateral load analysis using ETABS software.
The final step is preparation of detailed structural drawings of the designed structural elements of the building including beams, columns, slabs, shear walls, basement walls, footings and staircase.
1.3 Conclusions and Recommendations from part-1 of the project
It was recommended from part-1 to redesign the floors as a two-way waffle slab of 35cm thickness using Equivalent Frame Method and to use smaller sections for beams. Deflection check shows that 35cm is not sufficient for deflection control, and a thickness of 47cm is required. As a result, for serviceability requirements and maintaining a suitable clear height of the floor, two-way solid slab of 35cm on beams is going to be analyzed and designed.
1.4 Project Challenges
The main challenges in this project are:
1. Column Distributions
Architectural restriction on column distribution is an issue that can’t be ignored especially long spans which are needed for open spaces required for commercial use. Some unnecessary columns were eliminated and some were shifted for a small distance to maintain a grid of columns.
2. Long Spans
Most of the spans of the building are considered as long spans of around 10m length. This requires considering the most efficient and economical floor system that satisfies both strength and serviceability requirements.
3. Openings
Most of the openings within the floor plan are big openings which introduce a challenge in the analysis and design of the slabs.
4. Change in Building Layout
It is obvious from architectural plans and sections as shown above in figures (1.2-1.5) that the structure of the building changes where basement floors have larger area than floors above ground level.
Results obtained from the software for a 35cm solid slab on beams are almost similar to the hand calculations. However, smaller sections of beams are used.
Therefore, it was decided that two-way solid slab on beams is the floor system to be used for the design of the entire floors within the building.
The second step of this project is to choose and design the lateral load resisting system. First, the adequacy of shear walls to be checked using equivalent lateral force procedure (static analysis) and decide the lateral load resisting system that will be adequate to resist lateral load induced from earthquake.
The third step of the project considers the three dimensional modeling of the Commercial Center and applying both static and dynamic lateral load analysis using ETABS software.
The final step is preparation of detailed structural drawings of the designed structural elements of the building including beams, columns, slabs, shear walls, basement walls, footings and staircase.
1.3 Conclusions and Recommendations from part-1 of the project
It was recommended from part-1 to redesign the floors as a two-way waffle slab of 35cm thickness using Equivalent Frame Method and to use smaller sections for beams. Deflection check shows that 35cm is not sufficient for deflection control, and a thickness of 47cm is required. As a result, for serviceability requirements and maintaining a suitable clear height of the floor, two-way solid slab of 35cm on beams is going to be analyzed and designed.
1.4 Project Challenges
The main challenges in this project are:
1. Column Distributions
Architectural restriction on column distribution is an issue that can’t be ignored especially long spans which are needed for open spaces required for commercial use. Some unnecessary columns were eliminated and some were shifted for a small distance to maintain a grid of columns.
2. Long Spans
Most of the spans of the building are considered as long spans of around 10m length. This requires considering the most efficient and economical floor system that satisfies both strength and serviceability requirements.
3. Openings
Most of the openings within the floor plan are big openings which introduce a challenge in the analysis and design of the slabs.
4. Change in Building Layout
It is obvious from architectural plans and sections as shown above in figures (1.2-1.5) that the structure of the building changes where basement floors have larger area than floors above ground level.
5. Distribution of Shear Walls
The most important challenge is that the building is divided by an expansion joint and so it becomes structurally two different buildings, and from architectural plans it is obvious that no shear walls in the east side of the building. Figure1.6 shows the location of expansion joint.
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| Figure 1. 6: Seismic joint location |
Analysis and Design Criteria
Codes used for analysis and design in the project :1. ACI 318-11 code: for analysis and design of reinforced concrete sections.
2. Jordanian code for loads and forces (2006).
3. UBC-97 for lateral load and seismic analysis.
Materials Strength
1. Concrete compressive strength (fc’) of 24 MPa is used for slabs, beams and ramp. 32 MPa for columns, retaining walls, shear walls and mat foundation.
2. Steel with yielding strength (fy) of 420 MPa is used for the reinforcement of all structural elements.
1. Concrete compressive strength (fc’) of 24 MPa is used for slabs, beams and ramp. 32 MPa for columns, retaining walls, shear walls and mat foundation.
2. Steel with yielding strength (fy) of 420 MPa is used for the reinforcement of all structural elements.
Minimum Concrete Cover
Minimum concrete cover for each structural element is illustrated as in table 2.1:
Minimum concrete cover for each structural element is illustrated as in table 2.1:
Table 2. 1: Minimum Concrete Cover
| Structural Element | Minimum Concrete Cover(cm) |
|---|---|
| Slabs | 2 |
| Beams | 4 |
| Columns | 4 |
| Mat foundation | 7.5 |
| Shear walls | 2 |
| Retaining walls | 5 |
| Ramps | 2 |
Loads
Loads on slabs due to live load or superimposed dead load are taken from Jordanian code for loads and forces in the following manner.
1. Live Loads
Live loads for each floor are selected according to its usage as shown in table 2.2.
Table 2. 2: Live loads according to Jordanian Code
| Usage | Live Load (KN/m²) |
|---|---|
| Parking | 4 |
| Storage | 5 |
| Offices | 4 |
| Commercial | 4 |
| Top roof | 3 |
Weight of interior partitions on slabs is taken as 1.35 KN/m².
2. Dead Loads
Dead load on the slab includes superimposed dead load from covering materials (sand, mortar, tiles, ...) over the slab in addition to the own weight of slab.
Unit weights of the materials used in slabs are summarized in table 2.3.
Table 2. 3: Materials unit weight
| Material | Material Unit weight (KN/m³) |
|---|---|
| Concrete | 25 |
| Tiles | 24 |
| Mortar | 22 |
| Plaster | 22 |
| Hollow Block | 9 |
| Fill | 20 |
Weight of exterior stone walls of 30 cm thickness is 20KN/m.
3. Seismic Loads
Design base shear that depends on the weight of the building is to be fined and distributed over the height of the structure based on UBC97 procedure using ETABS software and to be validated manually. Seismic load analysis will be discussed.
Thickness of the Slab Systems
Slab thickness is selected according to deflection control requirements as indicated in the ACI-9.5.3.3. In Part-1 of the project the minimum thickness to control deflection of a two-way solid slab on beams is 27cm. Due to reduction in beams dimensions, thickness of slab determined based on long term deflection using SAFE software and it is 35cm. This thickness controlled by long spans. Framing System Vs. Beams - Columns System
Frame system is the system that consists of a combination of columns, beams and slabs that resist gravity and lateral loads.
There are two types of frames:
1. Rigid frames which could be pin or fixed ended. These frames are able to resist deformation and are able to resist moment, shear, axial and torsion effectively.
2. Braced frames are provided with bracing between beams and columns to increase ability of structure to resist lateral earthquake and wind loads.
Beams – columns system are structures that carry gravity loads including self-weight then transfer the load to the substructure.
In the introduction of the project a Beam –Column system was used. Whereas, here the building will be designed as a Frame system with shear walls to resist overall loading subjected to the building.
Foundation Type select
Dimensions of isolated footings are large due to heavy loads, in which sum of isolated footings areas and 5th basement area shown below:
Area of 5th Basement floor = 1236 m2
Area of isolated footings = 635 m2
Sum of isolated footings areas is larger than half of building area, and if walls footings areas added, sum of footings areas will be very large. As a result, mat foundation is more efficient in this case.
For detailed calculations see appendix (A).
Reinforcement
2.7.1. Minimum Reinforcement1. Beams and Slabs
Minimum steel area for beams and slabs for both positive and negative moments shall be determined based on ACI-10.5.
2. Columns Reinforcement Ratio
For columns as specified by ACI-21.6.3.1
0.01Ag ≤ ρ ≤ 0.06Ag
Where:
ρ: the percentage of
reinforcement
Ag: Gross area of concrete section.
In this project the reinforcement ratios of all columns are between 1% to 3% to achieve better ductile behavior.
1. Shear walls
Minimum longitudinal steel ratio to resist both axial and bending moment in the shear wall is 0.0025 as specified in ACI-21.9.2.1.
2. Retaining Walls:
Minimum reinforcement for retaining walls longitudinal direction is 0.0015 and in transverse direction is 0.002 as specified in ACI-14.3.2 and ACI-14.3.3 respectively.
2.7.2. Maximum Flexural Reinforcement
Maximum reinforcement ratio in flexural members equation is:
Ag: Gross area of concrete section.
In this project the reinforcement ratios of all columns are between 1% to 3% to achieve better ductile behavior.
1. Shear walls
Minimum longitudinal steel ratio to resist both axial and bending moment in the shear wall is 0.0025 as specified in ACI-21.9.2.1.
2. Retaining Walls:
Minimum reinforcement for retaining walls longitudinal direction is 0.0015 and in transverse direction is 0.002 as specified in ACI-14.3.2 and ACI-14.3.3 respectively.
2.7.2. Maximum Flexural Reinforcement
Maximum reinforcement ratio in flexural members equation is:
ρmax = 0.31875 β1 (fc’ / fy)
Where:
ρmax: Ratio of steel reinforcement
β1: Factor for the relation between depth of equivalent rectangular compressive stress and neutral axis depth, value of β1 determined based on ACI-R10.2.7.
fc’: specified compressive strength of concrete (MPa).
fy: specified yield strength of reinforcement (MPa).
β1: Factor for the relation between depth of equivalent rectangular compressive stress and neutral axis depth, value of β1 determined based on ACI-R10.2.7.
fc’: specified compressive strength of concrete (MPa).
fy: specified yield strength of reinforcement (MPa).
2.7.3. Shrinkage and Temperature Reinforcement
1. Two Way Solid Slab:
Shrinkage reinforcement is 0.0018 of gross sectional area based on ACI-7.12.2.1 and placed at the top of the slab between negative reinforcement in both directions.
2. Mat Foundation:
Shrinkage reinforcement is 0.0018 of gross sectional area based on ACI-7.12.2.1.
2.7.4 Skin Reinforcement
Skin reinforcement is provided for beams with depth greater than 400mm in order to increase rigidity and control cracking according to ACI-10.6.7. Spacing between bars is determined based on (ACI-10-4) equation.
2.7.5 Development Length
1. Development length for tension bars is determined based on ACI-(12.2.2 -12.2.5) and shown in table 2.4.
2. Development length for compression bars is determined based on ACI-(12.3.1 -12.3.3) and shown in table 2.5.
Shrinkage reinforcement is 0.0018 of gross sectional area based on ACI-7.12.2.1 and placed at the top of the slab between negative reinforcement in both directions.
2. Mat Foundation:
Shrinkage reinforcement is 0.0018 of gross sectional area based on ACI-7.12.2.1.
2.7.4 Skin Reinforcement
Skin reinforcement is provided for beams with depth greater than 400mm in order to increase rigidity and control cracking according to ACI-10.6.7. Spacing between bars is determined based on (ACI-10-4) equation.
2.7.5 Development Length
1. Development length for tension bars is determined based on ACI-(12.2.2 -12.2.5) and shown in table 2.4.
2. Development length for compression bars is determined based on ACI-(12.3.1 -12.3.3) and shown in table 2.5.
Table 2. 4: Development length in tension
| Φ ≤ 18 mm | Φ ≥ 20 mm | |
|---|---|---|
| Mat foundation and columns | 36 Φ | 44 Φ |
| Other members | 40 Φ | 50 Φ |
Table 2. 5:Development length in compression
| Mat foundation and columns | 18 Φ |
|---|---|
| Other members | 20 Φ |
2.7.6 Lap Splice
1. Lap Splice for tension bars is determined based on ACI-(12.15.1 -12.15.3) and shown in table 2.6.
2. Lap splice for compression bars is determined based on ACI-(12.16.1 -12.16.2) and shown in table 2.6.
Table 2. 6: Lap splice in compression and tension
| Lap splice in tension | 1.3Ld tension |
|---|---|
| Lap splice in compression | 30 Φ |
1. Beams:
Shear reinforcement for beams of intermediate moment frames are done according to ACI- 21.3.4.
For drop beams 2 Φ 10 stirrups are applied while for hidden beams single Φ10 stirrup is used.
Spacing of hoops (S0) shall not exceed the smallest of the following:
- d/4 Eight * diameter of the smallest longitudinal bar enclosed
- 24 * diameter of the hoop bar
- 300 mm
Hoops must be provided for lengths not less than 2h measured from the
face of the supporting member in the direction of midspan.
Where:
d: is the effective depth of beam.
h: is column dimension in the direction of beam 2. Columns:
Shear reinforcement of columns (hoops) is provided according to ACI-21.3.5 as the requirements of intermediate moment frames.
Spacing of hoops (S0) shall not exceed the smallest of the following:
- Eight times of the smallest bar diameter 24 * bar diameter of hoop
- Half of the smallest cross sectional dimension of column
- 300 mm
The hoops with a spacing of S0 should be provided for a length (L0) not less than the following:
3. Joints:
For better behavior under lateral loads and since hinges formation at joints is not accepted, stirrups of columns are continuing through joints according to ACI-7.9.2.
4. Shear walls:
Minimum shear reinforcement ratio used for special shear walls is determined based on ACI-21.9.2.1 and equals 0.0025.
Two curtains of reinforcement used according to ACI-21.9.2.2.
2.8 Reinforcement Details
All reinforcement details done according to ACI315-99 (details and detailing of concrete reinforcement).
2.9 Computer Software
1. SAFE for design of slabs and mat foundation, and also for slabs long-term deflection check.
2. ETABS for structural modeling, analysis and design of beams, columns and shear walls.
3. PCAcolumn for axial and flexural longitudinal reinforcement in shear and basement walls check (Creates interaction diagrams).
4. SAP 2000 for basement walls analysis.
5. AutoCAD for structural drawings.
- 1/6 of the clear span of column
- Maximum Cross-sectional dimension of the column
- 450 mm
3. Joints:
For better behavior under lateral loads and since hinges formation at joints is not accepted, stirrups of columns are continuing through joints according to ACI-7.9.2.
4. Shear walls:
Minimum shear reinforcement ratio used for special shear walls is determined based on ACI-21.9.2.1 and equals 0.0025.
Two curtains of reinforcement used according to ACI-21.9.2.2.
2.8 Reinforcement Details
All reinforcement details done according to ACI315-99 (details and detailing of concrete reinforcement).
2.9 Computer Software
1. SAFE for design of slabs and mat foundation, and also for slabs long-term deflection check.
2. ETABS for structural modeling, analysis and design of beams, columns and shear walls.
3. PCAcolumn for axial and flexural longitudinal reinforcement in shear and basement walls check (Creates interaction diagrams).
4. SAP 2000 for basement walls analysis.
5. AutoCAD for structural drawings.
Methods of Analysis
In the introduction of this project in part-1, different types of methods used for analysis including tabulated coefficients and equivalent frame method for two-way slab systems.Here, 3-D analysis done using software and checked manually by hand and 2-D analysis. 3-D analysis depends on a method called Finite Element Method (FEM).
FEM is an analysis approach in which numerical discretization of the structure into small elements defined by nodes.
Nazzal stated that because the exact deformation characteristics of structures are not always known, finite element analysis can then be used to assume a deformed shape known as the shape function. The finite element concept states that if the displacements at the ends of any element are given, the displacements between the end points can be interpolated using some shape functions. (Nazzal S. Armouti, PH. D, P.E.,2006).
For example, if the displacement of the beam end, i, as shown in Figure 3.1 is given as vi, the displacement, V(x), of any point inside the beam between ends i and j may be interpolated if the deflected shape is known or approximated by the function, ᴪ (x), such that V = ᴪ (x) Vi.
Nazzal stated that because the exact deformation characteristics of structures are not always known, finite element analysis can then be used to assume a deformed shape known as the shape function. The finite element concept states that if the displacements at the ends of any element are given, the displacements between the end points can be interpolated using some shape functions. (Nazzal S. Armouti, PH. D, P.E.,2006).
For example, if the displacement of the beam end, i, as shown in Figure 3.1 is given as vi, the displacement, V(x), of any point inside the beam between ends i and j may be interpolated if the deflected shape is known or approximated by the function, ᴪ (x), such that V = ᴪ (x) Vi.
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| Figure 3. 1: Beam Deformation (Nazzal S. Armouti, PH. D, P.E.,2006) |
Because the shape function plays an important role in finite element analysis, the accuracy of the solution will be as good as the accuracy of the shape function in representing the exact deformed shape. (Nazzal S. Armouti, PH. D, P.E.,2006).
Chapter 4: Seismic Analysis and Lateral Load Resisting System
4.1 Distribution of Shear Walls
As mentioned in challenges in the first chapter, the building is divided into two separated structures by a seismic joint and the east part of the structure does not include any shear walls. To solve this problem shear walls added in both directions x and y such that architectural plans does not affected. Added shear walls can be seen in figure 4.1.
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| Figure 4. 1: Added shear walls in the east part of structure |
4.2 Sway and Non-Sway (Stability):
P-∆ effect (second order effect) which results from lateral loads is considered by calculation of stability index (Q). Stability index which can be calculated based on ACI-(10-10) equation must be less than 0.05 so columns can be designed as non-sway columns. Here, Maximum Q equals to 0.04 which is less than the limit and so columns designed as non-sway columns.
ΣPu the total vertical loading in each level of the building - "According to ACI10-10"
Vus the total horizontal shear in each level of the building - "According to ACI10-10"
Δo : is relative lateral deflection between the upper slab level and bottom slab level of the story due to horizontal shear of the story. - "According to ACI10-10"
lc: c/c between the joints of the member in which is under compression in the frame - "According to ACI10-10"
4.3 Seismicity of The Location
According to the soil report and seismic hazard map shown in figure 4.3, the site area of the structure lies within seismic zone 2A with seismic zone factor of 0.15.
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Figure 4. 3: Seismic Hazard Map of the
West Bank
(ESSEC, USAID-MERC (M18-057) |
4.4 Equivalent Static Lateral Force Procedure
Base Shear Calculation:
Base shear calculations carried out using equivalent static lateral force analysis with reference to UBC 1630.2 as follows:
But should satisfy the limits:
V: Base Shear
T: Fundamental period of structure - seconds
I: Seismic importance factor -UBC97 (Table 16-K)
R: coefficient represent over strength and global ductility capacity of lateral load resisting system -UBC97 (Table 16-N)
Cv: velocity seismic coefficient -UBC97 (Table 16-Q)
Ca: acceleration seismic coefficient -UBC97 (Table 16-R)
Z: Seismic zone factor –UBC97 (Table 16-I)
Nv: Near source factor -UBC97 (Table 16-T)
W: seismic load includes total dead load and 25% of live load
Constants values according to the structure properties as follows:
I =1 R = 5.5 (Building frame system as initial assumption)
For soil profile SB
Cv = 0.15
Ca =0.15
The period of the building is Calculated to equal (T= 0.623 sec) using the equation:
Where:
Ct: 0.0488
hn: free height of the building (m) above ground level and equals 30m.
Period equals 0.62 seconds.
Base shear is found to be 4818 KN for west part of structure and 2214 KN for the east, then base shear distributed on the floors as follows:
Period equals 0.62 seconds.
Base shear is found to be 4818 KN for west part of structure and 2214 KN for the east, then base shear distributed on the floors as follows:
Where:
wx: weight at a particular level.
wx: weight at a particular level.
hx: height of a particular level above the shear base.
Fx: force at level x.
Vx: shear at level x which equals the sum of all forces above level x.
Ft: that portion of the base shear, considered concentrated at the top of the structure in addition to Fn. (Ft need not exceed 0.25V and may be considered as zero where T is 0.7 second or less).
Base shear calculation and vertical distribution on the floors done manually and by ETABS software, while horizontal distribution done by ETABS. Vertical distribution of base shear on stories for both parts of the building is shown in table 4.1 and 4.2 respectively.
Ft: that portion of the base shear, considered concentrated at the top of the structure in addition to Fn. (Ft need not exceed 0.25V and may be considered as zero where T is 0.7 second or less).
Base shear calculation and vertical distribution on the floors done manually and by ETABS software, while horizontal distribution done by ETABS. Vertical distribution of base shear on stories for both parts of the building is shown in table 4.1 and 4.2 respectively.
Table 4. 1: Vertical distribution of base shear on stories for the west part of the building
| Level | Fx (KN) | Vx (KN) |
|---|---|---|
| 7th floor | 985 | 985 |
| 6th floor | 906 | 1891 |
| 5th floor | 775 | 2666 |
| 4th floor | 661 | 3327 |
| 3rd floor | 554 | 3881 |
| 2nd floor | 422 | 4303 |
| 1st floor | 287 | 4590 |
| Mezzanine floor | 160 | 4751 |
| Ground floor | 67 | 4818 |
Table 4. 2: Vertical distribution of base shear on stories for the east part of the building
| Level | Fx (KN) | Vx (KN) |
|---|---|---|
| 7th floor | 392 | 392 |
| 6th floor | 386 | 778 |
| 5th floor | 375 | 1153 |
| 4th floor | 1472 | 1472 |
| 3rd floor | 268 | 1470 |
| 2nd floor | 202 | 1942 |
| 1st floor | 2073 | 2073 |
| Mezzanine floor | 96 | 2169 |
| Ground floor | 45 | 2214 |
4.5 Regularities and Irregularities
To decide whether the building has a torsional irregularity or not the following limit in the equations below should be calculated:
δmax and δavg determined from ETABS.
If (δmax / δavg) ≥ 1.2 the building is torsionally irregular and so the accidental eccentricity should be magnified by a magnification factor (δmax / 1.2*δavg) ≤ 3.0
Where:
δmax: the average displacement at level x.
δavg: the maximum displacement at level x.
Static analysis results shows that the east side of the building is torsionally irregular and so eccentricity is magnified. Due to irregularity and since UBC97 allows using static analysis for irregular structures in zone 2 with occupancy categories 4 and 5 which is the case here; dynamic analysis will be performed for more accurate results. Response Spectrum Analysis will be used as a dynamic procedure recommended by UBC97.
4.5 Dynamic Lateral Force Procedure (Response Spectrum)
Response spectrum Analysis carried out by ETABS. Modeling and scaling of response spectrum results will be discussed in the next chapter.
4.6 Lateral Load Resisting System
In this project one of the following lateral load resisting system will be used:
Building frame system: In this system the lateral load resistance due to seismic load is by carried on braced frames and shear walls according to UBC 1629.6.3
Dual system: According to UBC 1629.6.5, moment resisting frames will carry at least 25% from the design base shear and shear walls carry the remaining.
4.7 Drift Limitations and Seismic Joint
Stories elastic drifts values taken from ETABS and limitations checked manually as follows:
Inelastic Drift Δm = 0.7 R Δs UBC97 (30-17)
Where:
Δm: The maximum inelastic response displacement.
Δs: The design level response displacements (elastic displacement).
R: coefficient represent over strength and global ductility capacity of lateral load resisting system -UBC97 (Table 16-N)
Story drift limitations:
R: coefficient represent over strength and global ductility capacity of lateral load resisting system -UBC97 (Table 16-N)
Story drift limitations:
As mentioned in UBC 1630.10.2
For structures with a period less than 0.7 seconds, the maximum story inelastic drift is limited to:
For structures with a period greater than 0.7 seconds:
Where:
Δa = 0.025 Δh
For structures with a period less than 0.7 seconds, the maximum story inelastic drift is limited to:
Δa = 0.02 Δh
For structures with a period greater than 0.7 seconds:
Where:
Δa: The maximum inelastic story drift.
h: story height.
Here, the period is less than 0.7 as mentioned in section 4.4, and hence the first equation used. Table 4.1 shows max elastic and inelastic drifts in both separated structures.
Seismic Joint:
h: story height.
Here, the period is less than 0.7 as mentioned in section 4.4, and hence the first equation used. Table 4.1 shows max elastic and inelastic drifts in both separated structures.
Table 4. 3: Max elastic and inelastic drifts in both separated structures.
| Direction | Elastic drift (mm) | Inelastic drift (mm) | Inelastic limit (mm) | |
|---|---|---|---|---|
| West building | x | 0.594 | 2.2869 | 85 |
| y | 1.453 | 5.59405 | 85 | |
| East building | x | 0.601 | 2.31385 | 85 |
| y | 0.958 | 3.6883 | 85 |
Seismic Joint:
In order to avoid this pounding effect in the structures, UBC requires that building be set back enough distance to prevent pounding.
Clear distance calculated by a combining the total displacement of the two buildings by Square Root of Sum of Squares (SRSS) method as follows:
Clear distance calculated by a combining the total displacement of the two buildings by Square Root of Sum of Squares (SRSS) method as follows:
ΔMT: Clear distance between two buildings.
ΔM1 and ΔM2: The inelastic displacements of the two adjacent buildings.
Table 4.2 shows elastic and inelastic maximum displacements and clear distance required.
Table 4.2 shows elastic and inelastic maximum displacements and clear distance required.
Table 4. 4: Clear distance required for building separation.
| Direction | Elastic last story displacement (mm) | Inelastic last story displacement (mm) | |
|---|---|---|---|
| East building | x | 14.17 | 54.57 |
| West building | x | 15.91 | 61.24 |
| 82.02 |
As shown in table 4.2, 82 mm is required for building separation.
References
➧ Wang, Chu, and Charles G. Salmon. Reinforced Concrete Design. 7th ed. Hoboken, NJ: John Wiley & Sons, 2007. Print.
➧ Uniform Building Code. 1997 ed. Whittier, CA: International Conference of Building Officials, 1997.
➧ PIQUE, J. & BURGOS, M. Effective Rigidity of Reinforced Concrete Elements In Seismic Analysis And Design. 14th World Conference on Earthquake Engineering October, 2008. (12-17).
➧ Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary. Farmington Hills, MI: American Concrete Institute, 2011. Print.
➧ Qudaimat, Musa. Seismic Design of Concrete Structures, 1st ed. Babel Printing Press. 2012. Print
➧ Nazzal S. Armouti, and International Code Council., Earthquake Engineering: Theory and Implementation. 2nd ed. Country Club Hills, IL: International Code Council, 2008.
➧ Das, Braja M. Principles of Foundation Engineering, SI. 7th Ed.; SI ed. Stamford, CT: Cengage Learning, 2011. Print.
➧ Uniform Building Code. 1997 ed. Whittier, CA: International Conference of Building Officials, 1997.
➧ PIQUE, J. & BURGOS, M. Effective Rigidity of Reinforced Concrete Elements In Seismic Analysis And Design. 14th World Conference on Earthquake Engineering October, 2008. (12-17).
➧ Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary. Farmington Hills, MI: American Concrete Institute, 2011. Print.
➧ Qudaimat, Musa. Seismic Design of Concrete Structures, 1st ed. Babel Printing Press. 2012. Print
➧ Nazzal S. Armouti, and International Code Council., Earthquake Engineering: Theory and Implementation. 2nd ed. Country Club Hills, IL: International Code Council, 2008.
➧ Das, Braja M. Principles of Foundation Engineering, SI. 7th Ed.; SI ed. Stamford, CT: Cengage Learning, 2011. Print.
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