7.2 Discussion of results
7.2.3 Time history analysis results
47 Chapter 7. 2D Modeling, Analyses, Results and Discussion
from time history analysis. Then, the maximum responses of all eight ground motions are added and then divided by eight. This gives the average response parameters from all eight ground motions of each model. Furthermore, to evaluate the response parameter errors from each simplified model compared toBenchmark model, the following equation are used
M odel error=
Response of M ass model i Response of T he becnchmark −1
∗100%
wherei=Mass model 1, 2, 3 and4.
This shows the percentage error for each model compared to theBenchmark model.
7.2. Discussion of results 48
0 1 2 3 4 5
-50.0 -40.0 -30.0 -20.0 -10.0 0.0 10.0 20.0
error in % Acceleration errors
Mass model 1 Mass model 2 Mass model 3 Mass model 4 Benchmark model
Figure 7.2.8: Acceleration errors for each model compared to theBenchmark model. x=0.0 implies theBenchmark model.
Discussion of shear forces
The X-axis in Fig. 7.2.9 represents the lower beams from Fig. 7.2.7 from beam 1 to beam 3.
The Y-axis represents positive and negative shear force errors for each mass model compared to theBenchmark model. Negative shear force errors implies less shear force compared to theBenchmark model and positive shear force implies more.
The entire discussion is based on Fig. 7.2.9 unless stated otherwise.
Mass model 1: The shear force errors ofMass model 1 shows that it is over 70% more shear force in the inner beam while there are very low otherwise compared to the Benchmark model. High shear forces in the inner beam comes from that the mass in this model are centered only in the middle of each floor.
Mass model 2: Mass model 2 shows that it is more shear forces in all beams compared to theBenchmark model. The biggest positive errors are 7% in the inner beam.
Mass model 3: Mass model 3 shows that it is less shear forces in all beams compared to the Benchmark model. However, the negative errors are less than 6% in all beams.
Mass model 4: Mass model 4 shows that it is slightly more shear forces in all beams compared to theBenchmark model. However, the negative errors are less than 2% in all beams Based on the shear force errors in Fig. 7.2.9, Mass model 1 is useless to simulate realistic shear force effects from vertical ground motion, Mass model 2, 3 and 4 shows accurate tendencies. However, onlyMass model 4 is very accurate compared to theBenchark model.
49 Chapter 7. 2D Modeling, Analyses, Results and Discussion
-20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
1 2 3
Error in %
Shear force errors
Mass model 1 Mass model 2 Mass model 3 Mass model 4 Benchmark model
Figure 7.2.9: Shear force errors for each model compared to theBenchmark model. y=0.0 implies theBenchmark model.
Discussion of axial forces
The X-axis in Fig. 7.2.10 and 7.2.11 represents the base columns showed in Fig. 7.2.7. The Y-axis represents positive and negative axial force errors for each mass model compared to theBenchmark model. Negative axial force errors implies less axial force compared to the Benchmark modeland positive force implies more. Fig. 7.2.10 and 7.2.11 shows compressive and tensile forces, respectively.
The entire discussion is based on Fig. 7.2.10 for compressive and Fig. 7.2.11 for tensile, unless stated otherwise.
Mass model 1: Both compressive and tensile forces inMass model 1 shows negative errors in column 2 and the errors are between 80 and 100% compared to the Benchmark model.
Similar for the inner column, although here there are positive errors of 60% and 50%.
Furthermore, the outer column shows 9% negative errors in compressive and 5% positive errors in tensile.
Mass model 2: Mass model 2 shows up to 17% positive compressive force errors compared to theBenchmark model while tensile force errors are low for all columns.
Mass model 3: Mass model 3 shows small errors in compressive, but significantly higher in tensile. In tensile, the error is at is maximum of 20% negative in the inner column compared to theBenchmark model. In compressive, the maximum error is 8% negative.
Mass model 4: Mass model 4 shows very small errors compared to the Benchmark model.
Errors from both tensile and compressive forces are less than 3%.
7.2. Discussion of results 50
The most accurate mass model compared to theBenchmar model is Mass model 4. Both tensile and compressive errors are here very low. Nevertheless, even ifMass model 3 shows some differences, this model needs considerably less computationally efforts thanMass model 4. Taken all analysis methods into account,Mass model 3 shows small errors and differences to theBenchmark model.
-80.0 -60.0 -40.0 -20.0 0.0 20.0 40.0 60.0 80.0
1 2 3
Error in %
Compressive force errors
Mass model 1 Mass model 2 Mass model 3 Mass model 4 Benchmark model
Figure 7.2.10: Compression force errors for each model compared to theBenchmark model.
y=0.0 implies theBenchmark model.
51 Chapter 7. 2D Modeling, Analyses, Results and Discussion
-120.0 -100.0 -80.0 -60.0 -40.0 -20.0 0.0 20.0 40.0 60.0 80.0
1 2 3
Error in %
Tensile force errors
Mass model 1 Mass model 2 Mass model 3 Mass model 4 Benchmark model
Figure 7.2.11: Tension force errors for each model compared to theBenchmark model. y=0.0 implies theBenchmark model.
Based on both eigenvalue analysis and time history analysis, Mass model 3 and 4 are simplified models which had overall small differences and small errors compared to the Benchmark model. However, terms to take into account is that the computational effort is twice as less inMass model 3 compared to4.
7.2. Discussion of results 52
Chapter 8
3D Modeling, Analyses, Results and Discussion
8.1 Introduction of the building
Similar to the building modelled in 2D, a fairly common building is modelled 3D. Fig. 8.1.1 shows 3D view of the building. The building is assumed to be reinforced concrete. A preliminary design to determine column, beam and slab sites were conducted. Properties of the building is to be found in Table 8.1.1 and Fig. 8.1.2 sizes the building’s overall dimensions at each elevation and plan view.
Figure 8.1.1: 3D view of the four story building. All structural members are modelled as elastic.
53
8.1. Introduction of the building 54
4000 mm 4000 mm 4000 mm 4000 mm 4000 mm
5000 mm
5000 mm
5000 mm
A1
A1
B1 B1
(a) Plan view.
3500 mm
3500 mm
3500 mm
3500 mm
4000 mm 4000 mm 4000 mm 4000 mm 4000 mm
(b) Section B-B.
3500 mm
3500 mm
3500 mm
3500 mm
5000 mm 5000 mm 5000 mm
(c) Section A-A.
Figure 8.1.2: Sections of the Building. (a) Plan view (b) Section A-A (c) Section B-B.
55 Chapter 8. 3D Modeling, Analyses, Results and Discussion
Both OpenSEES and ANSYS are used to model this building. To serve as theexactsolution, a highly refined element mesh over the slab is created in ANSYS where the consistent mass approach is used. Shear deformation effects are included in theexact model.
Several alternative models are developed in OpenSEES. First of all, the building is modeled using the common, rigid-diaphragm approach where the slab is assumed to possess in-plane stiffness. Later, slabs are physically modeled using shell elements. Two different mesh configurations are used to identify the optimum solution which can capture the vertical effects without compromising simplicity. Beam and columns are modeled using Bernoulli beams. All shear deformations are neglected.
Table 8.1.1: Structural Properties for the 3D building.
Properties Initials Values
Cross section beams and Girders Hb·Bb 600mm·400mm Cross section Columns Hc·Bc 500mm·500mm
Slab thickness ST 150mm
Young-module E 25000
Poisson’s ratio ν 0.18
Mass at each floor Mi 387tons
Total mass including Mtot 1548tons
8.1. Introduction of the building 56