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acceleration parameters of a building are automatically determined by entering the site
class and risk category in SAP2000. Then, the load cases are defined to find the response
spectrum function. Automatically generated data is collected and tabulated in the
following table:
Period Acceleration
0 0.4
0.136 1
0.68 1
0.8 0.85
1 0.68
1.2 0.5667
1.4 0.4857
1.6 0.425
1.8 0.3778
2 0.34
2.5 0.272
3 0.2267
3.5 0.1943
4 0.17
4.5 0.1511
5 0.136
5.5 0.1236
6 0.1133
6.5 0.1046
7 0.0971
7.5 0.0907
8 0.085
8.5 0.08
9 0.0756
9.5 0.0716
10 0.068
Table 11. Parameters for RSA function
Data then are plotted:
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Figure 7. RSA Function Curve
Previous analysis demonstrates that the importance factor is equal to 1.25 and R is equal
to 8. Considering the unit defined in the beginning of the modeling, a 32.2 ft/s^2 gravity
acceleration is used. Hence, a scale factor can be expressed as g*Ie/R and has a value of
5.03. After the model analysis, the base shear from RSA is 1105.097 kips. By comparison,
the base shear from the equivalent static force method (from the previous section) is
1664.23 kips, which leads to a relative error of 30%.
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3. Modeling and Analysis
SAP2000 is used for modeling. Throughout the research purpose of this project, four
models are developed: Gravity load only model, gravity and wind load model, gravity and
earthquake model, and all load combinations model. This method is chosen to make the
specification of parameters required to assess each unique load combination easier. The
compressive strength of concrete columns and beams considered for design is 10,000 psi
since the structure is made of concrete. To keep the section sizes modest, compressive
strength concrete of 4 ksi is selected. The building is designed with the 100 ft long side
parallel to the x-axis and the 60 ft side parallel to the Y-axis. The slab is modeled as an
0.58 feet element with concrete compressive strength of 4000 psi. Each level has a live
load of 50 psf and 100 psf as required from the instructor.
Figure 8. Model Perspective 1
Figure 9. Model Perspective 2
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3.1 Gravity Load Only Analysis
Because there was no lateral load consideration, gravity only analysis was the first model
evaluated in this project. It was deemed to be the least controlling model.
The combinations included in this analysis are shown below:
1. 1.4D
2. 1.2D + 1.6L
The weight of structure and main structural members is shown as below:
1. Gravity only
concrete unit
weight
150 pcf
Beam # Dimension(ft) Volumn(ft^3) Weight(lbs)
Beam1 L1-15 0.6*1*20 12 1800
beam2 L1-3 0.6*1*20 12 1800
beam2 L4-8 0.6*1*20 12 1800
beam2 L9-15 0.6*1*20 12 1800
Sum Weight(lbs) 7200
Sum Weight(kips) 7.2 kips
Column # Dimension(ft) Weight(lbs)
Column 1-5 1.8*1.8*12 38.88 5832
Column 6-10 1.5*1.5*12 27 4050
Column 11-15 1*1*12 12 1800
Sum Weight(lbs) 11682
Sum Weight(kips) 11.682 kips
Floor
dead load 100
length 60
width 100
Wf = 600000 lbs
Wf = 600 kips
Table 12. Weight of main structural members for Gravity only case
Column # Beam 1 # Beam 2 #
24 18 20
Floor #
Column
Weight
Beam 1
Weight
Beam 2
Weight
Dead
Weight
Floor
Weight
in kips
1 139968 32400 36000 600000 808368 808.368
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2 139968 32400 36000 600000 808368 808.368
3 139968 32400 36000 600000 808368 808.368
4 139968 32400 36000 600000 808368 808.368
5 139968 32400 36000 600000 808368 808.368
6 97200 32400 36000 600000 765600 765.6
7 97200 32400 36000 600000 765600 765.6
8 97200 32400 36000 600000 765600 765.6
9 97200 32400 36000 600000 765600 765.6
10 97200 32400 36000 600000 765600 765.6
11 43200 32400 36000 600000 711600 711.6
12 43200 32400 36000 600000 711600 711.6
13 43200 32400 36000 600000 711600 711.6
14 43200 32400 36000 600000 711600 711.6
15 43200 32400 36000 600000 711600 711.6
11427840 lbs
11427.84 kips
Table 13. Weight of Structure for Gravity only case
3.2 Gravity and Wind Load Analysis
For gravity and wind load analysis in SAP2000, it is needed to define the wind load by
inputting key parameters in the software. The parameters needed are shown below:
Wind Direction Angle 0 (horizontal)
Windward Coefficient, Cp 0.8
Leeward Coefficient, Cp 0.5
Wind Speed [mph] 98
Exposure Type C
Topographical Factor, Kzt 1
Gust Factor 0.93
Directionality Factor, Kd 0.85
Table 14. Parameters needed for Gravity and Wind Load Analysis
Most of the coefficients are given in ASCE 7. Because the building is defined to be a
flexible structure, the gust factor is calculated based on the steps shown in the hand
calculations part. After setting up all the parameters, 12 scenarios of wind loads are given
by SAP. Each scenario represents different directions of the wind load, and all of them are
included in the design process to ensure the serviceability of the building.
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For ASCE 7-16, the wind load combinations have a 1.0 factor for strength design and 0.6
factor for allowable stress. Based on Wind Hazard Map in section 26.5, for risk category
III, the buildings have a 1700-year MRI with Annual Exceedance Probability of 0.000588.
The commentary says the 1700-year MRI winds are “excessively conservative” for design
considerations. The serviceability load combination + 0.5 +௔ is not included to
avoid over design of the sections.
The combinations included in this analysis are shown below:
1. 1.4D
2. 1.2D + 1.6L
3. 1.2D + 1.0W +L
4. 0.9D + 1.0W
The weight of structure and main structural members is shown as below:
2. Gravity and
Wind Load
concrete unit
weight
150 pcf
Beam # Dimension(ft) Volumn(ft^3) Weight(lbs)
Beam1 L1-15 0.6*1*20 12 1800
beam2 L1-3 0.6*1*20 12 1800
beam2 L4-8 0.6*1*20 12 1800
beam2 L9-15 0.6*1*20 12 1800
Sum Weight(lbs) 7200
Sum Weight(kips) 7.2 kips
Column # Dimension(ft) Weight(lbs)
Column 1-5 1.8*1.8*12 38.88 5832
Column 6-10 1.5*1.5*12 27 4050
Column 11-15 1*1*12 12 1800
Sum Weight(lbs) 11682
Sum Weight(kips) 11.682 kips
Floor
dead load 100
length 60
width 100
Wf = 600000 lbs
Wf = 600 kips
Table 15. Weight of main structural members for Gravity and Wind Load case
Column # Beam 1 # Beam 2 #
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24 18 20
Floor #
Column
Weight
Beam 1
Weight
Beam 2
Weight
Dead
Weight
Floor
Weight
in kips
1 139968 32400 36000 600000 808368 808.368
2 139968 32400 36000 600000 808368 808.368
3 139968 32400 36000 600000 808368 808.368
4 139968 32400 36000 600000 808368 808.368
5 139968 32400 36000 600000 808368 808.368
6 97200 32400 36000 600000 765600 765.6
7 97200 32400 36000 600000 765600 765.6
8 97200 32400 36000 600000 765600 765.6
9 97200 32400 36000 600000 765600 765.6
10 97200 32400 36000 600000 765600 765.6
11 43200 32400 36000 600000 711600 711.6
12 43200 32400 36000 600000 711600 711.6
13 43200 32400 36000 600000 711600 711.6
14 43200 32400 36000 600000 711600 711.6
15 43200 32400 36000 600000 711600 711.6
11427840 lbs
11427.84 kips
Table 16. Weight of Structure for Gravity and Wind Load case
3.3 Gravity and Seismic Load Analysis
The combinations included in this analysis are shown below:
1. 1.2D + Ev + Eh +L
2. 0.9D - Ev + Eh
The weight of structure and main structural members is shown as below:
3. Gravity and
Seismic Load
concrete unit
weight
150 pcf
Beam # Dimension(ft) Volumn(ft^3) Weight(lbs)
Beam1 L1-15 1.5*1*20 30 4500
beam2 L1-3 2*1.5*20 60 9000
beam2 L4-8 2*1.5*20 60 9000
beam2 L9-15 2*1.5*20 60 9000
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Sum Weight(lbs) 31500
Sum Weight(kips) 31.5 kips
Column # Dimension(ft) Weight(lbs)
Column 1-5 2.5*2.5*12 75 11250
Column 6-10 2.5*2.5*12 75 11250
Column 11-15 2*2*12 48 7200
Sum Weight(lbs) 29700
Sum Weight(kips) 29.7 kips
Floor
dead load 100
length 60
width 100
Wf = 600000 lbs
Wf = 600 kips
Table 17. Weight of main structural members for Gravity and Seismic Load case
Column # Beam 1 # Beam 2 #
24 18 20
Floor #
Column
Weight
Beam 1
Weight
Beam 2
Weight
Dead
Weight
Floor
Weight
in kips
1 270000 81000 180000 600000 1131000 1131
2 270000 81000 180000 600000 1131000 1131
3 270000 81000 180000 600000 1131000 1131
4 270000 81000 180000 600000 1131000 1131
5 270000 81000 180000 600000 1131000 1131
6 270000 81000 180000 600000 1131000 1131
7 270000 81000 180000 600000 1131000 1131
8 270000 81000 180000 600000 1131000 1131
9 270000 81000 180000 600000 1131000 1131
10 270000 81000 180000 600000 1131000 1131
11 172800 81000 180000 600000 1033800 1033.8
12 172800 81000 180000 600000 1033800 1033.8
13 172800 81000 180000 600000 1033800 1033.8
14 172800 81000 180000 600000 1033800 1033.8
15 172800 81000 180000 600000 1033800 1033.8
16479000 lbs
16479 kips
Table 18. Weight of Structure for Gravity and Seismic Load case
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3.4 All Load Combinations Analysis
In order to let the structure take all load combinations, the engineer decides to
maximize the dimension of the cross section of concrete beams and columns for all
level floors. And there are eight #9 rebars inside the beams and eight #11 rebars inside
the columns. The preliminary model cannot withstand the load combinations,
especially the seismic loads, which mainly causes the wobble on the first and second
floors. By comparing the total weight of this initial modeling with the previous three
cases, a weight around 24000 kips seems to be extremely unreasonable. Therefore,
decreasing the size of beams and columns on the upper level is the first measure.
However, this measure further makes the columns at mid and lower level unable to
withstand the wind and seismic load. Then, the team decides to reduce size one by
one, specifically the higher the number of layers, the smaller the size and distinguishes
the direction of the beams. There are more beams in the x direction, so the forces
applied are slightly greater than those in the longitudinal direction. So concrete beams
in the x direction have larger dimensions than those in the y direction. Table for beam
and column sizes are summarized and tabulated as follows:
4. All loads
combinations
concrete unit
weight
150 pcf
Beam # Dimension(ft) Volumn(ft^3) Weight(lbs)
Beam1 L1-15 1.5*2*20 60 9000
beam2 L1-3 1.8*2.5*20 90 13500
beam2 L4-8 1.8*2.5*20 90 13500
beam2 L9-15 1.5*2*20 60 9000
Sum Weight(lbs) 45000
Sum Weight(kips) 45 kips
Column # Dimension(ft) Weight(lbs)
Column 1-5 3*3*12 108 16200
Column 6-10 2.5*2.5*12 75 11250
Column 11-15 2*2*12 48 7200
Sum Weight(lbs) 34650
Sum Weight(kips) 34.65 kips
Table 19. Weight of main structural members for all load combinations
Column # Beam 1 # Beam 2 #
24 18 20
Floor #
Column
Weight
Beam 1
Weight
Beam 2
Weight
Dead
Weight
Floor
Weight
in kips
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1 388800 162000 270000 600000 1420800 1420.8
2 388800 162000 270000 600000 1420800 1420.8
3 388800 162000 270000 600000 1420800 1420.8
4 388800 162000 270000 600000 1420800 1420.8
5 388800 162000 270000 600000 1420800 1420.8
6 270000 162000 270000 600000 1302000 1302
7 270000 162000 270000 600000 1302000 1302
8 270000 162000 270000 600000 1302000 1302
9 270000 162000 180000 600000 1212000 1212
10 270000 162000 180000 600000 1212000 1212
11 172800 162000 180000 600000 1114800 1114.8
12 172800 162000 180000 600000 1114800 1114.8
13 172800 162000 180000 600000 1114800 1114.8
14 172800 162000 180000 600000 1114800 1114.8
15 172800 162000 180000 600000 1114800 1114.8
19008000 lbs
19008 kips
Table 20. Weight of Structure for all load combinations
After running analysis on this combination, the total weight of structure is 18621 kip and
the system is stable as shown below:
Figure 10. Model after analysis in SAP2000
The resulting information reveals that, for all load combinations, the design is governed
mostly by seismic loads and slightly affected by wind loads.