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Honors Research Projects The Dr. Gary B. and Pamela S. Williams HonorsCollege

Spring 2016

Below-Grade Structurla Flexibility Study forSeismic-Resistant, Self-Centering, Concentrically-Braced FramesDerek A.J. HauffThe University Of Akron, dah64@zips.uakron.edu

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Recommended CitationHauff, Derek A.J., "Below-Grade Structurla Flexibility Study for Seismic-Resistant, Self-Centering, Concentrically-Braced Frames" (2016). Honors Research Projects. 28.http://ideaexchange.uakron.edu/honors_research_projects/28

BELOW-GRADE STRUCTURAL FLEXIBILITY STUDY FOR SEISMIC-RESISTANT,

SELF-CENTERING, CONCENTRICALLY BRACED FRAMES

Submitted By: Derek A.J. Hauff

Faculty Sponsor: Dr. David A. Roke

Faculty Readers: Dr. Anil Patnaik, Dr. GunJin Yun

Honors Faculty Advisor: Dr. Ala Abbas

Department Head: Dr. Wieslaw Binienda

Date: 4 May 2015

University of Akron College of Engineering: Department of Civil Engineering

University of Akron Honors College

i

Table of Contents

Table of Contents i

List of Figures ii

Acknowledgements iii

Abstract v

Introduction 1

Method 2

Design 5

Analysis 10

Results & Discussion 15

Conclusions 20

References 21

Appendix 22

ii

List of Figures

Figure 1: Location of Forces on Substructure 1 2

Figure 2: Location of Forces on Substructure 2 2

Figure 3: Load Case 1 (Provided by Dr. Roke) 3

Figure 4: Load Case 2 (Provided by Dr. Roke) 3

Figure 5: Load Case 3 (Provided by Dr. Roke) 4

Figure 6: Substructure Geometry 1 5

Figure 7: Substructure Geometry 2 5

Figure 8: Axial Force Demands for Substructure Geometry 1 based on 6-Story Load Case 1 6

Figure 9: Moment Demands for Substructure Geometry 1 based on 6-Story Load Case 1 6

Figure 10: Axial Force Demands for Substructure Geometry 2 based on 6-Story Load Case 1 7

Figure 11: Moment Demands for Substructure Geometry 2 based on 6-Story Load Case 1 7

Figure 12: Section Selection for 6-Story Substructure Geometry 1 8

Figure 13: Section Selection for 6-Story Substructure Geometry 2 9

Figure 14: Section Selection for 10-Story Substructure Geometry 1 9

Figure 15: Section Selection for 10-Story Substructure Geometry 2 9

Figure 16: Fixity nodes for the Static Dynamic models 10

Figure 17: Fixity nodes for Dynamic Static models 11

Figure 18: Schematic of Lateral Forces for the Static Analysis [2] 12

Figure 19: 6-Story Substructure 1 Roof Drift Percentage vs. Overturning Moment 13

Figure 20: 6-Story Substructure 1 Floor Drift Percentage vs. Overturning Moment 13

Figure 21: 10- Story Substructure 1 Roof Drift Percentage vs. Overturning Moment 13

Figure 22: 10- Story Substructure 1 Floor Drift Percentage vs. Overturning Moment 14

Figure 23: 6-Story Substructure Overturning Moment vs. Roof Drift Comparison 15

Figure 24: 6-Story Substructure PT Bar Force vs. Roof Drift Comparison 16

iii

Figure 25: 10-Story Substructure Overturning Moment vs. Roof Drift Comparison 17

Figure 26: 10-Story Substructure PT Bar Force vs. Roof Drift Comparison 17

Figure 27: 6-Story Dynamic output for Roof Drift from Earthquake la01 18

Figure 28: Typical output for Roof Drift for an Earthquake Simulation 18

Figure 29: Beam Section Information for Substructure 22

Figure 30: Substructure Nodes Position 22

Figure 31: Fixity for the Substructure 23

Figure 32: Fiber Elements being defined for the Substructure 23

Figure 33: Beam Elements being defined for Substructure 24

Figure 34: Loads of Substructure’s Beams, Columns, and Braces 24

Figure 35: Recorders that record and outputs the movement of the listed nodes of the Substructure 25

iv

Acknowledgements

I would like to thank Dr. David A. Roke for the opportunity to work on this project. His

assistance while conducting the research was greatly appreciated. All of our meetings help with

understanding the project and has better prepared me on what to expect at the graduate level.

I would like to thank Dr. Anil Patnaik and Dr. Gunjin Yun for being my readers. They

provided helpful insight on how to improve my paper that allowed me to submit an acceptable

honor’s project.

v

Abstract

Self-centering, concentrically braced frames (SC-CBFs) are seismic-resistant lateral-load

resisting systems for buildings that increase the lateral drift capacity in comparison to

conventional CBFs. Two different substructures were examined on a six-story and a ten-story

building to see which below grade structure was more efficient and how the flexibility from the

addition of a basement compares to previous research of SC-CBFs structures without basements.

The study was completed in phases: modeling of forces in SAP2000, sizing of structural

members, coding of structure into the modeling program Open System for Earthquake

Engineering Simulation (OpenSees), and comparison of the output data.

Substructure one proved to be the more efficient geometry choice for the basement

design. Substructure two had similar results as substructure one for the 6-story model, but

proved to add excessive flexibility when the geometry was examined on the 10-story model.

1

Introduction

Buildings being developed in seismic regions often have concentrically-braced frames

(CBFs) in their design. Unfortunately, typical CBFs have a limited lateral drift capacity due to

buckling of the steel braces. This means that structures with CBFs are susceptible to significant

damage during intense earthquakes. This results in the building sustaining damage that is either

non-repairable or costs a substantial amount of money to fix, and may cause residual

displacement of the structure.

To combat against the buckling in CBFs, self-centering, seismic resistant concentrically

braced frames (SC-CBFs) are being studied. SC-CBFs allow for the building to “uplift from the

foundation at specific levels of lateral loading” [1]. The structure will act as a normal

concentrically-braced frame depending on the magnitude of lateral loading. In order for the

building to realign itself to its original position, a post-tensioning (PT) bar is placed in the center

of the building. The PT bar acts as a spring pulling the structure back towards its foundation

while it is rocking during an earthquake. Once the building has been returned to its original

position, the PT bar may need to be restressed or replaced, since it is expected to yield. The SC-

CBFs incorporates the stiffness of CBFs while adding a flexibility factor in an attempt to

increase the ductility and reduce force demands in the building members. The expected outcome

is that the building survives the earthquake with minor structural damage while returning to its

initial position.

This paper will discuss two sub-structures that were design and analyzed in order to see

the effects of flexibility from having a basement level for the SC-CBF superstructure. Each sub-

structure design was modeled with both a 6-story and 10-story building to see how much each

building moved when subjected to seismic simulation. The buildings underwent static and

dynamic analysis in the Open System for Earthquake Engineering Simulation (OpenSees)

software to determine the roof drift, floor drift, and PT yield force.

2

Method

The study was completed in phases: Modeling of forces in SAP2000 (SAP) (forces

provided by Dr. Roke), sizing of structural members, coding of the structure into the modeling

program Open System for Earthquake Engineering Simulation (OpenSees), running both a static

model and dynamic model, and finally the analysis to determine the post-tensioning (PT) bar

yield point from the static model and the roof and floor drift from the dynamic model.

The two sub-structure geometries were already determined from previous research and

were provided by Dr. Roke. To accurately determine the size of the girders for the basement

substructures, they were first modeled in SAP2000. SAP2000 is a finite element analysis

program which allowed forces, provided by Dr. Roke, to be applied at various points on the

below-grade structure. Locations of the forces can be seen Figures (1) and (2).

Figure 1: Location of Forces on Substructure 1

Figure 2: Location of Forces on Substructure 2

3

Three load cases were considered when creating the SAP models, as shown in Figures

(3), (4), and (5). Case 1 was the loading at the PT bar yield force (PTy), case 2 was the

unloading at PTy, and case 3 was no applied lateral load. Case 1 showed the largest axial and

moment demands on the sub-structure members. Those forces were then imputed into a

Microsoft Excel spreadsheet, provided by Dr. Roke, to size the columns, top beam, bottom beam,

and braces by an iterative process.

Figure 3: Load Case 1 (Provided by Dr. Roke) Figure 4: Load Case 2 (Provided by Dr. Roke)

4

Figure 5: Load Case 3 (Provided by Dr. Roke)

The coding phase involves user recreation of the two different basements designs in the

pre-existing 6-story and 10-story SC-CBF superstructure models provided by Dr. Roke in the

OpenSees program. OpenSees is a finite element program that allows for the user to model

structures and run earthquake simulations. The program will produce user-defined output, such

as node displacements and member forces.

The analysis phase involves taking the output data collected from the OpenSees program

and determining the PT bar yield strength and the roof and story drifts. This data is compared to

the output data from the OpenSees models of the six and ten story buildings without a basement

structure.

5

Design

The geometry of the two below-grade structure can be seen in Figures (6) and (7).

Figure 6: Substructure Geometry 1

Figure 7: Substructure Geometry 2

Both geometries were recreated in SAP2000 to analyze the static forces that they were designed

to resist. The very bottom of the columns for the basement were fixed, while the far top left and

right points were pinned connections, as shown in Figures (6) and (7).

SAP can show the magnitude of the axial and moment forces that the beams, columns, and

braces would experience for each load case, which are shown in Figures (8), (9), (10), and (11).

6

Figure 8: Axial Force Demands for Substructure Geometry 1 based on 6-Story Load Case 1

Figure 9: Moment Demands for Substructure Geometry 1 based on 6-Story Load Case 1

7

Figure 10: Axial Force Demands for Substructure Geometry 2 based on 6-Story Load Case 1

Figure 11: Moment Demands for Substructure Geometry 2 based on 6-Story Load Case 1

The SAP models of the two different geometries had their sections for the beams,

columns, and braces set to W14x132 as a starting point for selecting the member sizes. Using an

Excel spreadsheet provided by Dr. Roke, sections appropriate to handle the forces were

determined. The Excel file helped to determined that the selected girders were not oversized or

undersized. This was based off of the magnitude of the axial force and moment demands

collected from the SAP analysis using their current selected section. The process for the using

the Excel file follows these few simple steps:

1. Run the SAP model with the current section sizes for the beams, columns, and braces.

2. Take the largest axial and moment forces and input them into the excel file.

3. Review to see if the current section member gives an interaction number less than or

equal to 1 for beams, columns, and braces.

8

4. If the iteration number is larger than 1, the member is undersized; if the number is less

than 0.9, the section member may be oversized.

5. Select a new member that gets the interaction number closer to 1 and make the section

change in the SAP models.

6. Rerun the SAP model and then repeat steps 2 through 5 until the most efficient sections

have been chosen.

The Excel file used the load and resistance factor design (LRFD) method to determine the

interaction number close to one. The final section sizes are shown in Figures (12), (13), (14) and

(15).

The design of the basement structure had a few stipulations. Weight of the member was

a deciding factor, which meant that going from a W14 to W40 was acceptable (for beam

elements) as long as the weight per foot was smaller for the W40. The overall geometry could

not be changed; the only change acceptable would be the height of the bottom beam. It must be

between 12 to 20 inches above the very bottom of the column to accommodate the PT bar

anchorage.

Figure 12: Section Selection for 6-Story Substructure Geometry 1

9

Figure 13: Section Selection for 6-Story Substructure Geometry 2

Figure 14: Section Selection for 10-Story Substructure Geometry 1

Figure 15: Section Selection for 10-Story Substructure Geometry 2

10

Analysis

Models of the 6-story and 10-story SC-CBF superstructures were provided by Dr. Roke

to be used in the OpenSees program. These models contained the structural information of the

building above ground level. The addition of the substructure needed to be included into these

models before they could be run in OpenSees for analysis.

Taking the information gained using SAP2000, the models were updated with the new

below-grade structure. New section dimensions were included to be used for the basement

beams, columns, and braces. OpenSees works as a grid with x, y, and z coordinates. This means

that nodes were created at certain points along this grid. The locations of the nodes were where

the ends of the beams, columns, and braces would be for the frame of the substructure. The new

section dimensions were used to create new beam elements within the models that would connect

two nodes. Fiber elements were needed in order to closely model the stress and strain behavior

of the beams, particularly to capture yielding due to flexural loading.

New boundary conditions were needed once the basement was added to the model. For

the dynamic models, a large majority of the nodes were fixed in the z direction, which is

represented as a 1 in the code shown in Figure (16), while the x and y direction were allowed to

remain free. As shown in Figure (17), the static model required some nodal fixities to be

commented out in order for the model to run properly in OpenSees.

Figure 16: Fixity nodes for the Dynamic models

11

Figure 17: Fixity nodes for Static models

Additional fixed nodes in the original model lost some of their fixity or were completely

removed due to the addition of the substructure. The nodes that were removed were initially

there to act as the fixed ground level. Since the basement was added, those nodes were no longer

required because the building was now attached to the substructure.

The models were then tested multiple times to determine if there were any errors in the

code. The code did have a few mistakes that needed to be addressed in order for the model to

run correctly. Specific nodes (nodes 2, 4 and 1010) had to have their fixities commented out in

order for the static model to run properly, while during the dynamic analysis their fixities were

included.

The original 6-story model did not run properly for the static analysis, which also meant

it would not run the dynamic analysis, and had to be recreated by chopping off the top four floors

of the 10-story model. Once it was determined that the code would execute, the static forces

were applied to the models. The building in the models experienced different loads on each floor

with increasing magnitude at each higher elevation, as illustrated schematically in Figure (18).

12

Figure 18: Schematic of Lateral Forces for the Static Analysis [2]

Static loading was used to determine the PT bar force after calibrating the slack initial stress in

the PT bar for the dynamic model. Roof drift and floor drift were also determined from the static

model, with the results show in Figures (19) and (20) for the 6-story model and Figures (21) and

(22) for the 10-story model.

13

Figure 19: 6-Story Substructure 1 Roof Drift Percentage vs. Overturning Moment

Figure 20: 6-Story Substructure 1 Floor Drift Percentage vs. Overturning Moment

Figure 21: 10- Story Substructure 1 Roof Drift Percentage vs. Overturning Moment

0.0

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6-Story Substructure 1 Roof Drift

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10-Story Substructure 1 Roof Drift

14

Figure 22: 10- Story Substructure 1 Floor Drift Percentage vs. Overturning Moment

For the dynamic simulations, twenty different earthquake scenarios on each model were

analyzed. The PT bar force was monitored along with the x-displacement of the building. Using

the x-displacement, roof drift and floor drift can be determined, which will show how much the

building moves and when it starts to uplift. This data is compared to existing data to evaluate the

difference between having a basement to the building and not having one.

0.0

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10-Story Substructure 1 Floor Drift

First Floor

Second Floor

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Fifth Floor

Sixth Floor

Seventh Floor

Eighth Floor

15

Results and Discussion

The static model showed that the 6-story models with the substructure showed very little

differences. Based on Figures 23 and 24, the two basements exhibit nearly identical overturning

moment-roof drift responses. Substructure 1 values are slightly to the left of substructure 2’s

values, indicating that its geometry is slightly stiffer. As expected, both models with below-

grade structures are more flexible than the 6-story model without a substructure.

Figure 23: 6-Story Substructure Overturning Moment vs. Roof Drift Comparison

0.0

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Roof Drift (%)

6-Story Substructure Overturning Moment Vs. Roof Drift Comparison

6-Story Substructure 1 Roof Drift

6-Story Substructure 2 Roof Drift

6-Story without Substructure

16

Figure 24: 6-Story Substructure PT Bar Force vs. Roof Drift Comparison

This was expected since the model without a basement was in theory secured to the

ground, making a very stiff (rigid) foundation. The addition of a basement meant a longer post-

tensioning bar in the building, which allowed for the building to sway to the side more before the

PT bars yielded. The basement design also contributed to the increase of flexibility; the basement

members are flexible and deflect upward under the PT bar force. The basement replaces the

rigid ground in the model without the substructure. These two factors increase the flexibility of

the buildings in the model.

The results for the 10-story models had the same outcome, as shown in Figures 25 and

26. The difference in the two substructures greatly increased with the additional floors. The roof

drifted further for substructure 2 and reached a drift percentage of about 5% before the PT bar

failed while substructure 1 drifted close to 3% before PT bar failure. This demonstrates that the

design for substructure 2 allows for a more flexible building, which is not necessarily ideal.

0

500

1000

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0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000

PT

Forc

e (

Kip

s)

Roof Drift (%)

6-Story Substructure PT Bar Force Vs. Roof Drift Comparison

6-Story Substructure 1

6-Story Substructure 2

6-Story without Substructure

17

Figure 25: 10-Story Substructure Overturning Moment vs. Roof Drift Comparison

Figure 26: 10-Story Substructure PT Bar Force vs. Roof Drift Comparison

Substructure 1’s geometry would be the preferred method in the design of taller

structures, as indicated by the results of the 10-story output. Substructure 2 could still be a

viable design if the particular beams were upsized which would require further analysis for the

10-story model. The cost of each substructure should also be taken in consideration. Since the

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10-Story Substructure Overturning Moment Vs. Roof Drift Comparison

10-Story Substructure 1 RoofDrift

10-Story Substructure 2 RoofDrift

0

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0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000

PT

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e (K

Ips)

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10-Story Substructure PT Bar Force Vs. Roof Drift Comparison

10-Story Substructure 1

10-Story Substructure 2

18

overall weight of substructure 2 is lighter than substructure 1, it would cost less when purchasing

the beams. This makes substructure 2 the preferred choice when examining the results for the 6-

story models. Since there was little difference in the stiffness of the two designs for the 6-story

models, then the factors that influence the choice would be the cost of material and the ability to

construct each design.

During the dynamic analysis, OpenSees would complete iterations for the 6 and 10 story

models; however, the output data was not correct. Figure 27 shows some output data obtained

from one of the earthquake analyses for the 6-Story model. Figure 28 shows a sample of what

the output should really look like.

Figure 27: 6-Story Dynamic output for Roof Drift from Earthquake la01

Figure 28: Typical output for Roof Drift for an Earthquake Simulation

-1.0

0.0

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of D

rift

(%

)

Time (s)

6-Story Substructure 1 Roof Drift

-1.0000

-0.8000

-0.6000

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0.0000

0.2000

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0 2 4 6 8 10

Ro

of

Dri

ft (

%)

Time (s)

19

There is an error somewhere in the code for the dynamic models that is producing these

undesirable results. More time is required to decipher the cause of this problem. Due to the

complexity of the models, simple changes that make little sense out of context must be made to

complete the analyses. For instance, it had been observed that a right bracket missing on one

load case allowed for the model to run. When that missing bracket was added, the model no

longer worked and OpenSees would display a message saying there is an extra right bracket.

There is also an increase in complexity with the calculations that OpenSees must

compute when running the dynamic model compared to a static model. Several factors

contribute to these harder calculations that increase the chances of the models producing

undesirable results or failing to converge on a solution. Many of the materials in the models have

nonlinear relationships between stress and strain. This means that unlike a linear model where

there is one answer, the nonlinear model can have multiple potential solutions. The nonlinear

model must follow a certain path in order to run properly and does iterations in order to get the

correct answer.

Another factor that affects the iteration process is the gap elements. These elements

create a stiffening effect on the model, which creates additional complication to the equilibrium

calculation at each time step. These elements are found in the gaps located by each floor

(horizontal gap elements) and where the substructure meets the superstructure (vertical gap

elements). This means there are both vertical and horizontal gaps whose friction components

affect the stress and strain values on two different axes. This further complicates the calculations.

Modifying the stiffnesses of these elements may allow OpenSees to successfully complete its

iterations to arrive at correct output data.

20

Conclusion

The results of the static analysis showed that substructure one was stiffer than

substructure two. This does not mean that substructure two is not a possible choice in the design

of basements for buildings. For structures with few floors, either basement geometry would

suffice since the roof drifts were extremely similar to each other, showing that both substructures

have relatively close stiffness. Structures with ten or more floors should consider substructure

one as the prefer choice since it is stiffer than substructure two as shown by the static analysis on

the 10-story models.

Since the output data for the dynamic analysis was poor, no conclusions can be made at

this time about the dynamic effects of adding a basement to the models. Based on the output

from the static analysis a few preliminary conclusions can be made. It has been determined that

the building in the models experience more flexibility with the addition of the basement. During

an earthquake we will potentially see that the building will experience a greater degree of roof

and floor drift. How the PT bar reacts due to the addition of the basement it currently unknown

and the static analysis provides zero insight its expected reaction during an earthquake. However,

the static responses suggest that larger drifts are necessary to cause the same increase in PT

force; therefore, the PT force response in the dynamic analyses may not be changed by the

substructure even though the drift response is increased.

21

References

[1] Hasan, M.R.; Roke, D.A.; and Huang, Q. (2013). “Higher Mode Effects on the Seismic

Response of Self-Centering Concentrically Braced Frames with Friction Based Energy

Dissipation,” 2013 ASCE Structures Congress, May 2013, Pittsburgh, PA.

[2] Roke, D.A.; Sause, R.; Ricles, J.M.; Gonner N. (2008). “Design Concepts For Damage-

Free Seismic-Resistant Self-Centering Steel Concentrically-Braced Frames,” The 14th

World Conference on Earthquake Engineering, October 2008, Beijing, China.

22

Appendix

Figure 29: Beam Section Information for Substructure

Figure 30: Substructure Nodes Position

23

Figure 31: Fixity for the Substructure

Figure 32: Fiber Elements being defined for the Substructure

24

Figure 33: Beam Elements being defined for Substructure

Figure 34: Loads of Substructure’s Beams, Columns, and Braces

25

Figure 35: Recorders that record and outputs the movement of the listed nodes of the Substructure