Abstract

Analytical Comparison of Reinforced Concrete Columns

Designed According to ACI 318-63 & ACI 318-11

August, 2014

The columns of reinforced concrete structures designed according to ACI 318-63 tend to suffer

non-ductile shear-axial failure during earthquakes. A hybrid simulation to be completed in

September 2014 at the University of Illinois at Urbana Champaign’s (UIUC) Multi-axial Full-

scale Substructure Testing and Simulation (MUST-SIM) facility will be used to examine the

near-collapse performance of one of these existing reinforced concrete frame buildings. The

research described herein includes an analysis of local column elements used in the hybrid

simulation. Modeled and analyzed using FormWorks, VecTor2, and Response-2000, these

columns, designed according to ACI 318-63, and another similar set designed according to the

ACI 318-11 provisions for special moment frames were subjected to pushover and reverse cyclic

analyses. Results indicate that additional transverse reinforcement has an insignificant impact on

the capacity and ductility of reinforced concrete columns; however, because of the shortcomings

of the utilized software these results should first be validated before being regarded as

representative of real-world behaviors.

Author: Mitchell Knapp

REU Site & Home Institution: University of Illinois at Urbana-Champaign

Project PI: Mehrdad Sasani, Ph.D.

Mentors: Anahid Behrouzi, Weslee Walton

i

Table of Contents

Introduction ..................................................................................................................................... 1

Literature Review............................................................................................................................ 2

Theory ............................................................................................................................................. 3

Methods........................................................................................................................................... 4

Results ............................................................................................................................................. 8

Discussion ..................................................................................................................................... 11

Additional Contributions .............................................................................................................. 11

Conclusion .................................................................................................................................... 12

Future Work .................................................................................................................................. 13

Acknowledgements ....................................................................................................................... 13

References ..................................................................................................................................... 14

Appendix: VecTor2 Model Input Parameters ............................................................................... 15

1

Introduction

Reinforced concrete structures designed and constructed in the 1960s and early 1970s according

to provisions in ACI 318-63 pose a considerable seismic risk. The provisions in ACI 318-63

called for significantly less transverse reinforcement in structural columns than is required by

today’s standards given current considerations for ductility in seismic design; as a result, many

of these older columns have been shown to fail in shear during major earthquakes (Elwood &

Moehle, 2003). Nevertheless, local column failure does not necessarily lead to a progressive

structural failure or collapse. Whereas structural design is often done under the conservative

assumption that element failure immediately precedes total structural failure, this is not always

the case. Remaining structural elements may in fact have the capacity to accommodate the

redistribution of loads following a local element failure (Sasani & Sagiroglu, 2008; Giriunas et

al., 2010), and the columns themselves may even retain some residual axial capacity following

an initial shear failure (Elwood & Moehle, 2003). Additionally, the desired behavior of a

building may vary depending on its intended use, its occupancy, and its owner’s preference.

Performance-based seismic design (PBSD) takes these factors into consideration and provides a

more refined approach to seismic design than that outlined in ASCE7-10.

Given the brittle behavior of shear-axial failure in a reinforced concrete structure and the

potentially high occupancy of the buildings in question, a better understanding of the structural

failure mechanism and near-collapse behavior is highly desirable. Research being conducted by

Dr. Mehrdad Sasani, the project PI, and graduate student Justin Murray for the George E. Brown,

Jr., Network for Earthquake Engineering Simulation (NEES) utilizes a hybrid simulation to

examine this behavior. Their hybrid simulation involves a prototype structure analytically

modeled in OpenSees and three experimental column specimens subjected to pseudo-dynamic

loadings corresponding to those induced by the 1992 Landers earthquake. The simulation, to be

completed in September 2014 at the University of Illinois at Urbana-Champaign’s (UIUC)

Multi-axial Full-scale Substructure Testing and Simulation (MUST-SIM) facility, will provide

key insight into the behavior of the global structural system subject to seismic loading and the

performance of critical structural members which might require retrofit.

The research described herein is associated with the NEES Research Experience for

Undergraduates (REU) and involves an investigation of local column elements in this hybrid

simulation. Models correspond to the experimental specimens at the UIUC MUST-SIM facility,

and two sets were analyzed, one designed according to ACI 318-63 and another designed

according to ACI 318-11. Both sets of columns were subjected to pushover and reverse cyclic

tests run using the nonlinear finite element analysis software VecTor2. Results were compared

to those produced by cross-sectional analyses in Reponse-2000 and revealed differences in both

the capacity and ductility of the old and newly designed columns. Additional efforts were also

made to conduct a purely analytical hybrid simulation using the columns modeled in VecTor2

and a larger structural model made in Zeus-NL and SAP2000 by another REU student, Jacob

Gould.

2

Literature Review

Residual Axial Capacity in Reinforced Concrete Columns Following Initial Shear Failure

A common, conservative assumption in concrete design is to assume that a structural member

loses all load-bearing capacity upon failure. In reality, a member may retain residual load-

bearing capacity and serve to support some fraction of the intended design load following an

initial failure (Elwood & Moehle, 2003). Shake-table experiments conducted by Elwood and

Moehle in 2003 showed that the center column of a planar three-column reinforced concrete

frame retained its axial capacity while under low-level loadings following shear failure.

However, when subjected to larger axial demands, the column failed in shear under smaller

lateral displacements and subsequently experienced an axial failure. These results indicate that

some reinforced concrete columns, depending on the magnitude of loading, might still continue

to support a portion of their intended gravity loads following an initial shear failure.

Structural Behavior of Non-ductile Reinforced Concrete Structures

The ACI 318-11 code indicates that the shear capacity of a reinforced concrete column is directly

related to the degree of axial compressive force that is applied to it. Studies have also shown that

under increasing axial load, a reinforced concrete column loses ductility (Anam & Shoma, 2002).

Due to these two effects, reinforced concrete columns exhibit both a buildup of shear force under

high axial loads and incidences of non-ductile shear failure. As a result, when one column in a

structural system fails and gravity loads are redistributed to the remaining columns, increasing

axial loads in some locations may lead to more brittle behavior. Modern seismic design

provisions in the ACI code seek to address demands for greater ductility and shear capacity with

the addition of lateral reinforcement. It has been shown that closely spaced transverse

reinforcement in structural columns functions to meet both of these requirements with little to no

impact on the flexural capacity of the columns (Muin, 2011).

Progressive Structural Collapse

Removal or failure of structural elements dictates that loads, both lateral and gravity, be

redistributed throughout the remaining superstructure. If these redistributed loads are found to

exceed the capacities of the members they flow through, a progressive series of local element

failures could result in global structural failure. Nevertheless, several studies show that

structures possess a capacity to resist collapse despite failure of their individual members (Sasani

& Sagiroglu, 2008; Giriunas et al. 2010).

In 2008 Sasani and Sagiroglu observed that the Hotel San Diego, a non-ductile reinforced

concrete structure built in 1914, maintained its structural integrity following the explosive

removal of a corner and adjacent column. Furthermore, deflections of the structure following the

removal of the two columns were minimal. The maximum vertical displacement measured was

0.25 inches and occurred directly above the removed columns.

Giriunas et al., (2010) conducted similar studies with steel frame structures and concluded that

structural systems possess an inherent capacity to resist collapse following removal of several

elements. These case studies involved two steel frame structures constructed in the 1950s and

1960s and showed that the superstructures retained their integrity following the removal of four

3

supporting columns. It should be noted that with the removal of each subsequent column, time

to stabilization increased. This suggests that the effects of dynamic loading may influence the

mechanism by which progressive structural collapse occurs.

In the shake table analysis conducted by Elwood and Moehle (2003), the effect of dynamic

loading on progressive structural collapse was directly observed. Following axial failure of the

center column in a three column reinforced concrete frame, redistribution of vertical loads to the

two exterior columns was measurably greater than the sum of the actual gravity loads. For a

very brief period following axial failure, a dynamic amplification factor (“DAF, defined as the

change in the outside column axial loads from the start of the pulse divided by the change in the

center column axial loads from the start of the pulse”) of 1.5 was observed (Elwood & Moehle,

2003, p. 145). This indicates that dynamic effects may play a significant part in the progressive

collapse of a structure if even one of its columns experiences axial failure.

Theory

In lieu of physically modeling an entire structure for testing or assessing its behavior in one

general-purpose analytical model, a hybrid simulation can be used. Use of a hybrid simulation

involves segmenting elements of analysis to separate systems for increased efficiency or

accuracy. As it pertains to the research being conducted at the UIUC MUST-SIM facility, three

reinforced concrete columns are being experimentally tested and analyzed in conjunction with a

larger computer-generated structural model. These two systems are linked via University of

Illinois’ Simulation Coordinator (UI-SimCor), and for each time step during testing, information

regarding the redistribution of forces within the columns and the analytical structural model is

shared between the two. This sharing of data is iterative and occurs repeatedly until values in the

two systems converge, after which the next step is allowed to proceed. Small-scale testing

served as a useful tool for calibrating the various systems involved.

In addition to this hybrid simulation, another purely analytical hybrid simulation involving the

VecTor2 columns models and both the ZEUS-NL and SAP2000 structural models was planned.

The VecTor2 column models served as stand-ins for the experimental specimens used in the

hybrid simulation being conducted at the UIUC MUST-SIM facility. Given the time constraints

of the NEESreu program, this additional hybrid simulation could not be completed, so

descriptions of the columns’ behavior when subjected to pushover and reverse cyclic analyses

are included in this paper. These behaviors were checked against simple cross-sectional analyses

conducted in Response-2000 in hopes of identifying any issues with the models.

4

Methods

Description of Columns

In total, four columns were modeled and analyzed using VecTor2. Two of these were designed

according to ACI 318-63 by Justin Murray, and they correspond to the 154 in. and 129 in. tall

physical specimens at the UIUC MUST-SIM facility. These physical specimens in turn

represent first and second floor edge columns in a 10-story, 2 by 6 bay building. The other two

columns, designed separately according to ACI 318-11 as if they were members of a special

moment frame in the same building, were included in the analysis to determine how much

additional capacity and ductility modern ACI provisions provide. The dimensions of these

columns were identical to the other two, but the reinforcement, specifically the sizing and

spacing of transverse reinforcement, differed (Figure 1). Longitudinal reinforcement was, for the

most part, identical; however, it was shifted inward slightly to maintain a 1.5 in. clear cover

about the larger transverse reinforcement (Figure 2). Normal weight concrete with a

compressive strength of 4000 psi was used in design of the columns, as was steel reinforcement

with a yield strength of 60 ksi.

Figure 1. Spacing of transverse reinforcement in columns. From left to right: Tall column designed according to ACI

318-63, tall column designed according to ACI 318-11, short column designed according to ACI 318-63, short column

designed according to ACI 318-11.

5

VecTor2 Models

Structural definitions and other model input parameters were entered via the VecTor2

preprocessor, FormWorks, which provides graphical user interface aids for determining the

location of user-defined nodes and the final configuration of the element mesh. Within

FormWorks, material properties were defined first.

While design values for the crushing strength of concrete and the yield strength of Gr. 60 steel

reinforcement were taken as 4 ksi and 60 ksi, respectively, examination of material specimens

used in the full-scale physical models at the UIUC MUST-SIM facility showed that 4.5 ksi and

72 ksi better described the actual strengths of the materials in the experimental columns. To

ensure that the behaviors of the analytical model and full-scale physical model were comparable,

these more accurate values were used as inputs for VecTor2. Additional inputs pertaining to the

geometric characteristics of the column cross-sections and the material properties of the concrete

and steel reinforcement are detailed in File A and File B in the Appendix. Furthermore, when

offered, the default values for some of the material properties were explicitly calculated using the

equations provided in the VecTor2 & FormWorks User’s Manual (Wong et al., 2013).

Transverse reinforcement, as indicated in Figure 3 by the interior blue regions, was not discretely

modeled in VecTor2; instead it was “smeared” across the concrete elements. In other words, the

properties of the transverse reinforcement were attributed to the concrete it confined by way of a

cross-sectional reinforcement ratio. For the columns designed according to ACI 318-63 a

reinforcement ratio of 0.13% was used; for the newly designed columns a ratio of 1.44% was

used. This difference in transverse reinforcement marks the only significant variation between

the old and newly designed columns. Given the uniform distribution of rectilinear hoops in the

columns designed according to both ACI 318-63 and ACI 318-11, only one region of smeared

reinforcement was used in each model.

Figure 2. Left, cross-section of columns designed according to ACI 318-63. Right, cross-section of columns designed

according to ACI 318-11.

6

Figure 4: Reverse cyclic loading protocol, cycles incremented by 12.7 mm (0.5 in).

Longitudinal reinforcement was modeled discretely as truss

elements. In Figure 3, the red lines correspond to locations

with three aligned #10 bars, and the green lines correspond to

two aligned #10 bars. When detailing these elements,

VecTor2 utilizes the total area of all reinforcement in a given

row as provided by the user rather than accounting

individually for the quantity and size of rebar.

The dark gray regions in Figure 3 are rigid column caps that

have been assigned a high stiffness value. These were added

to prevent uncharacteristic local failures at the site of imposed

displacements atop the columns. At the base of the columns

are a series of pin connections used to simulate a fixed

connection and prevent translation and rotation.

For the pushover and reverse cyclic analyses, displacements

were imposed at approximately the midpoint of the column

caps, such that bending occurs about the column strong axis.

Compressive axial loads, corresponding to the estimated

gravity loads to be supported by the columns, were applied at

the tops of the columns. For the taller 1st story edge columns

a 370 kip load was applied; for the shorter 2nd

story edge

columns a 330 kip load was applied. In each case, the load

was divided equally between the nodes at the top of the

column. These vertical loads remained constant for the

duration of the tests; however, the imposed displacements

varied. (See Files C and D in Appendix)

Using the Job Definition menu in FormWorks, the loading protocol and analytical methods were

specified. For the pushover analyses, displacement at the top of the columns was increased from

0 mm to 100 mm in 1 mm increments. This range proved sufficient for capturing the behavior of

the column well beyond failure. A second set of analyses, whose loading protocol is presented in

Figure 4, involved a reverse cyclic displacement history. Analytical models for cracking and

stress-strain behaviors were set to their ‘Basic’ default selections. After defining the model and

the job and load cases, the VecTor2 analysis was executed.

-80

-60

-40

-20

0

20

40

60

80

0 200 400 600 800

Dis

pla

cem

en

t (m

m)

Loading Step

Figure 3: Left, column with uniform

distribution of transverse reinforcement

designed according to ACI 318-63. Right,

column with uniform distribution of

transverse reinforcement designed

according to ACI 318-11. Red lines

represent three aligned #10 bars, green

lines represent two aligned #10 bars.

7

Data Postprocessing

The Augustus postprocessor was utilized at the back end of the VecTor2 analyses. This tool

allows for the visualization of structural deformations, crack progression, and strain

development. Investigations can then be conducted at local element levels to better assess the

buildup of critical stresses and strains within the columns.

Failure, defined in this study as a 20% reduction in nominal capacity, was verified by exporting

force-displacement data to an Excel spreadsheet for further inspection. Additionally, to compare

the performance of the old and newly designed columns, a series of force-displacement graphs

were produced. These clearly indicated the difference in ductility between the two sets of

columns.

Comparison of VecTor2 & Response-2000 Analyses

To verify the overall behavior of the columns modeled in VecTor2, simple cross-sectional

analyses were conducted in Response-2000. Geometric and material properties were defined so

that they matched those used in the VecTor2 models. The size and spacing of transverse

reinforcement was explicitly detailed, as was the number of longitudinal bars. The single-legged

cross-tie, indicated in Figure 5, could not be modeled though. Given the columns’ mode of

failure, as discussed in the ‘Results’ section, it is not believed that this would have played a

critical role.

Loading in the Response-2000 model did not directly correspond to the VecTor2 loadings

because only forces, and not displacements, could be applied. As a result, a shear force was

applied at the top of the columns at 1 kN load increments. Axial compressive forces were

consistent with those applied to the tall and short columns in VecTor2. This loading protocol

was deemed to provide an adequate comparison to the pushover analyses conducted in VecTor2.

A similar loading protocol could not be devised to mimic that used in the VecTor2 reverse cyclic

analyses.

Figure 5: Left, Response-2000 cross-section of column designed according to ACI 318-63.

Right, Response-2000 cross-section of column designed according to ACI 318-11. Red line

indicates location of missing cross-tie.

8

Results

Shear cracking, as pictured in Figure 7, occurred for all columns subjected to the pushover

analyses. Figure 6 and Table 1 detail the results of the VecTor2 pushover analyses and also

clearly show the non-ductile mode of failure suffered by each of the columns. Similar peak

shear forces and peak lateral displacements were obtained for both the tall columns, designed

according to ACI 318-63 and ACI 318-11 respectively. However, in the case of the short

columns, the one designed according to ACI 318-11 exhibited a greater stiffness, displaying 44%

greater shear capacity, yet failing at a similar displacement level as the column designed

according to ACI 318-63.

Table 1: Results of VecTor2 pushover analyses

Column Peak Shear Force (kN) Peak Lateral Displacement (mm)

Tall (ACI 318-63) 188.6 37.46

Tall (ACI 318-11) 182.7 37.49

Short (ACI 318-63) 142.8 24.86

Short (ACI 318-11) 205.5 26.52

Figure 6: Pushover analyses, force-displacement results. Figure 7: Cracking at failure

of tall column designed

according to ACI 318-11.

9

The set of results presented in Figure 8 and Table 2 is from the Response-2000 analyses but

corresponds to the VecTor2 pushover analyses. As indicated, only a small difference in peak

capacity and relative displacement distinguishes the columns designed according to ACI 318-63

and ACI 318-11. Similar to the VecTor2 results, the loss of capacity of the columns analyzed in

Response-2000 is marked by a brittle mode of failure. Table 3 presents a comparison of results

from the Response-2000 cross-sectional analyses and VecTor2 finite element analyses.

Figure 8: Response-2000 pushover analyses, force-displacement results.

Table 2: Results of Response-2000 pushover analyses.

Column Peak Force (kN) Peak Lateral Displacement (mm)

Tall (ACI 318-63) 227.4 49.98

Tall (ACI 318-11) 223.5 48.76

Short (ACI 318-63) 271.6 36.11

Short (ACI 318-11) 266.8 34.79

Table 3: Comparison of Response-2000 with VecTor2 pushover analyses results

% Difference in Peak Force

Relative to VecTor2 Results

% Difference in Peak Lateral Displacement

Relative to VecTor2 Results

20.6 33.4

22.3 30.1

90.2 45.2

29.8 31.2

0

50

100

150

200

250

300

0 10 20 30 40 50 60

Forc

e (

kN)

Displacement (mm)

Force-Displacement

Tall, New

Tall, Old

Short, New

Short, Old

10

Results from the reverse cyclic analyses, presented in Figure 9 and Figure 10, reveal little

difference between the sets of columns designed according to ACI 318-63 and ACI 318-11. The

short columns, as expected, were stiffer than the taller columns, but no distinguishable benefit of

the additional confinement called for in ACI 318-11 can be observed. Of note however, is the

post-failure behavior of the short columns; in the region of shear failure, plastic hinges formed,

and the column continued to displace briefly before losing all capacity. Table 4 details the peak

force-displacement values presented in Figures 9 and 10 and reveals a minor loss in the ultimate

shear capacity and ductility of the columns designed according to ACI 318-11 relative to those

designed according to ACI 318-63.

Figure 9: Reverse cyclic hysteresis depicting force-displacement data for tall columns.

Figure 10: Reverse cyclic hysteresis depicting force-displacement data for short columns.

-250

-200

-150

-100

-50

0

50

100

150

200

250

-80 -60 -40 -20 0 20 40 60 80 Forc

e (

kN)

Displacement (mm)

Tall Columns: Reverse Cyclic Hysteresis

New

Old

-250

-200

-150

-100

-50

0

50

100

150

200

250

-80 -60 -40 -20 0 20 40 60 80

Forc

e (

kN)

Displacement (mm)

Short Columns: Reverse Cyclic Hysteresis

New

Old

Force (

kN

)

Displacement (mm)

Tall Column: Reverse Cyclic Hysteresis

-30.0

-60.0

-90.0

-120.0

-150.0

-180.0-180.0

-150.0

-120.0

-90.0

-60.0

-30.0

0.0

30.0

60.0

90.0

120.0

150.0

180.0

-10.0-20.0-30.0-40.0-50.0-60.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0

Force (

kN

)

Displacement (mm)

Tall Column: Reverse Cyclic Hysteresis

-30.0

-60.0

-90.0

-120.0

-150.0

-180.0-180.0

-150.0

-120.0

-90.0

-60.0

-30.0

0.0

30.0

60.0

90.0

120.0

150.0

-7.0-14.0-21.0-28.0-35.0-42.0 0.0 7.0 14.0 21.0 28.0 35.0 42.0

Force (

kN

)

Displacement (mm)

Short Column: Reverse Cyclic Hysteresis

-30.0

-60.0

-90.0

-120.0

-150.0

-180.0-180.0

-150.0

-120.0

-90.0

-60.0

-30.0

0.0

30.0

60.0

90.0

120.0

150.0

180.0

-10.0-20.0-30.0-40.0-50.0-60.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0

Force (

kN

)

Displacement (mm)

Short Column: Reverse Cyclic Hysteresis

-30.0

-60.0

-90.0

-120.0

-150.0

-180.0-180.0

-150.0

-120.0

-90.0

-60.0

-30.0

0.0

30.0

60.0

90.0

120.0

150.0

180.0

-10.0-20.0-30.0-40.0-50.0-60.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0

11

Table 4: Results of reverse cyclic analyses

Column Peak Force (kN) Peak Lateral Displacement (mm)

Tall (ACI 318-63) 186.1 37.56

Tall (ACI 318-11) 180.7 37.16

Short (ACI 318-63) 205.8 24.95

Short (ACI 318-11) 201.4 24.94

Discussion

The results of the Response-2000 analyses varied considerably with those from the VecTor2

analyses. Nevertheless, the behavior of columns relative to one another (with the exception of

the short column designed according to ACI 318-63) proved to be similar for the two analytical

programs. For example, the two tall columns analyzed with VecTor2 shared similar peak shear

force capacities and reached similar peak displacements; the same columns also shared similar

shear force capacities and displacements when analyzed using Response-2000. This lends some

credence to the observation that the additional transverse reinforcement called for in ACI 318-11

has little impact on the performance of the modeled columns.

The results obtained in this investigation defy the reasoning behind several ACI 318-11

provisions which call for additional transverse reinforcement to improve ductility; therefore, the

validity of these analyses remains uncertain. Furthermore, FormWorks and VecTor2 were both

limited in their capabilities. For example, truly rigid connections could not be applied to the base

of the columns in VecTor2. As mentioned previously, a series of pin connections was utilized

instead to simulate fixed effects. Additionally, a uniform vertical deflection along the tops of the

columns could not be imposed. Compromises were also made with the Response-2000 analyses.

As indicated in Figure 6, all cross-ties could not be included in the models. There were also

concerns with the accuracy of the selected support conditions. It is difficult to assess how each

of these compromises might have affected the results, and it is also worth mentioning that errors

could have remained in the structural model despite extensive efforts to investigate and eliminate

them.

Additional Contributions

In addition to the analyses performed, calibration and installation of sensors on the full-scale

physical specimens at the UIUC MUST-SIM facility were carried out. The majority of this work

involved 30 in. linear potentiometers, otherwise referred to as control sensors (Figure 11).

Calibration of these sensors took place prior to installation and involved the verification of a

linear relationship between the measured potentiometer displacements and output voltages.

Installation involved the drilling of holes in the concrete caps and the construction and placement

of brackets to hold the sensors.

12

Figure 11: Short column, 30” control sensors circled.

Verification of proper channel routing for these and other sensors, like the linear variable

differential transformers (LVDTs) and Krypton camera LEDs, was also conducted.

Troubleshooting for sensors that did not work was then completed, and those that were

confirmed to be defective were replaced.

To view the data produced by these sensors a series of widgets was produced. These widgets

served as easy-access applications that displayed real-time data for small collections of some of

the sensors.

Conclusion

Despite several adjustments to the structural models themselves and to the chosen analytical

methods, the results produced by both VecTor2 and Response-2000 consistently showed

negligible differences in both the capacity and ductility of columns designed according to ACI

318-63 and ACI 318-11. Furthermore, the columns consistently failed at similar levels of lateral

displacement during the pushover and reverse cyclic analyses, despite the degree of confinement

and iterative analyses for each of the aforementioned adjustments. As such, the ability of

VecTor2 and Response-2000 to accurately model the effects of confinement is uncertain. If they

are truly adequate, then results indicate that larger, more closely spaced transverse reinforcement

has almost no impact on the shear capacity and ductility of reinforced concrete columns. This

would defy the logic upon which several provisions in ACI 318-11 is based; furthermore, a large

body of experimental research currently suggests that additional shear reinforcement (in either

area or reduced spacing) leads to more ductile performance of columns. In conclusion, further

investigation should be conducted to either validate these results or to refine the models and

analytical methods.

13

Future Work

The column models and VecTor2 analyses methods should be validated before any firm

conclusions are drawn from this report. Once corroborated or corrected, the models will then be

utilized in a hybrid simulation. This hybrid simulation will involve a larger structural model

constructed by Jacob Gould in Zeus-NL and SAP2000. It will be configured using UI-SimCor

and will serve to increase understanding of the progressive nature of collapse in pre-existing

reinforced concrete structures subject to seismic events.

Acknowledgements

Funding for this research was provided by the National Science Foundation (NSF) via NEES

research grant CMMI-1135005, NEES REU grant EEC-1263155, and NEES Operations award

CMMI-0927178. Personal thanks goes to Anahid Behrouzi, Weslee Walton, and Justin Murray

for their technical assistance and guidance in the lab. Jacob Gould, my fellow NEESreu

participant, also deserves recognition for his collaboration.

14

References

ACI Committee 318 (1963). Building Code Requirements for Reinforced Concrete (ACI 318-63).

American Concrete Institute, Farmington Hills, MI.

ACI Committee 318 (2011). Building Code Requirements for Structural Concrete (ACI 318-11)

and Commentary. American Concrete Institute, Farmington Hills, MI.

Anam, I. & Shoma, Z. (2002). “Nonlinear Properties of Reinforced Concrete

Structures.” 2nd

Canadian Conference on Nonlinear Solid Mechanics, Vancouver, Canada,

2, 657-66. <http://www.uap-bd.edu/ce/tech_bulletinn&journal/TechBull/Nonlinear.htm>

(June 9, 2014).

American Society of Civil Engineers (ASCE). (2010). Minimum Design Loads for Buildings and

Other Structures ASCE/SEI 7-10. American Society of Civil Engineers, Reston, VA.

Elwood, K. & Moehle, J. (2003). “Shake Table Tests and Analytical Studies on the Gravity Load

Collapse of Reinforced Concrete Frames.” Pacific Earthquake Engineering Research

Center (PEER Report 2003/01), University of California, Berkeley, Berkeley, CA.

<http://peer.berkeley.edu/publications/peer_reports/reports_2003/0301.pdf> (June 9,

2014).

Giriunas, K., Sezen, H., & Song, B. (2010). “Experimental and Analytical Assessment on

Progressive Collapse Potential of Two Actual Steel Frame Buildings.” 2010 Structures

Congress, Orlando, FL, 1171-1182.

Muin, S. (2011). “A parametric study of RC moment resisting frames at joint level by

investigating Moment-Curvature relations.” International Journal of Civil and Structural

Engineering, 2(1), 23-32.

Sasani, M., & Sagiroglu, S. (2008). “Progressive Collapse Resistance of Hotel San Diego.”

Journal of Structural Engineering, 478-488.

Wong, P. S., Vecchio, F. J., & Trommels, H. (2013). VecTor2 & FormWorks User’s Manual,

2nd

Ed. University of Toronto, Department of Civil Engineering, Toronto, Canada.

15

Appendix: VecTor2 Model Input Parameters

Note: VecTor2 performs analyses using metric units, so the data in the following files are all

provided in metric units.

File A: VecTor2 Input Material Properties, ACI 318-63 Models

* * * * * * * * * * * * * * * * * * *

* V e c T o r 2 *

* S T R U C T U R E D A T A *

* * * * * * * * * * * * * * * * * * *

STRUCTURAL PARAMETERS

*********************

Structure Title (30 char. max.) : Enter Structure Title

Structure File Name ( 8 char. max.) : Struct

No. of R.C. Material Types : 3

No. of Steel Material Types : 2

No. of Bond Material Types : 0

No. of Rectangular Elements : 448

No. of Quadrilateral Elements : 0

No. of Triangular Elements : 0

No. of Truss Bar Elements : 159

No. of Linkage Elements : 0

No. of Contact Elements : 0

No. of Joints : 513

No. of Restraints : 18

MATERIAL SPECIFICATIONS

***********************

(A) REINFORCED CONCRETE

-----------------------

<NOTE:> TO BE USED IN RECTANGULAR AND TRIANGULAR ELEMENTS ONLY

CONCRETE

--------

MAT REF Ns T f'c [ f't Ec e0 Mu Cc Agg Dens Kc ] [Sx

Sy]

TYP TYP # mm MPa MPa MPa me /C mm kg/m3 mm2/s mm

mm

1 1 0 406.400 31.026 1.838 30635.540 2.033 0.150 0.000 10.000

2400.000 1.200 1000.000 1000.000

2 1 1 406.400 31.026 1.838 30635.540 2.033 0.150 0.000 10.000

2400.000 1.200 1000.000 1000.000

3 1 0 406.400 9999999.000 9999999.000 9999999.000 9999999.000 0.150

0.000 10.000 2400.000 1.200 1000.000 1000.000

/

REINFORCEMENT COMPONENTS

------------------------

MAT REF DIR As Db Fy Fu Es esh eu Cs Dep b/t

TYP TYP deg % mm MPa MPa MPa me me /C me

2 1 361.000 0.129 9.525 496.400 675.700 200000.000 10.000 180.000

0.000 0.000 12.6

/

16

(B) STEEL

---------

<NOTE:> TO BE USED FOR TRUSS ELEMENTS ONLY

MAT REF AREA Db Fy Fu Es esh eu Cs Dep b/t

TYP TYP mm2 mm MPa MPa MPa me me /C me

1 1 1638.706 32.260 496.423 675.686 200000.000 10.000 180.000

0.000 0.000 12.600

2 1 2458.060 32.260 496.423 675.686 200000.000 10.000 180.000

0.000 0.000 12.600

/

File B: VecTor2 Input Material Properties, ACI 318-11 Models

*Highlighted selection denotes only difference with File A.

REINFORCEMENT COMPONENTS ------------------------

MAT REF DIR As Db Fy Fu Es esh eu Cs Dep b/t

TYP TYP deg % mm MPa MPa MPa me me /C me

2 1 361.000 1.438 15.875 496.400 675.500 200000.000 10.000 180.000

0.000 0.000 3.150

File C: VecTor2 Input Job File, Pushover Analyses

VER 3.5

* * * * * * * * * * * *

* V E C T O R *

* J O B D A T A *

* * * * * * * * * * * *

Job Title (30 char. max.) : Enter Job Title

Job File Name ( 8 char. max.) : VecTor

Date (30 char. max.) : Enter Date

STRUCTURE DATA

--------------

Structure Type : 2

File Name ( 8 char. max.) : Struct

LOADING DATA

------------

No. of Load Stages : 101

Starting Load Stage No. : 1

Load Series ID ( 5 char. max.) : ID

Load File Name Factors

Case (8 char. max.) Initial Final LS-Inc Type Reps C-Inc

1 Case1 0.0000 100.0000 1.0000 1 1 0.0000

2 Case2 180.0000 180.0000 0.0000 1 1 0.0000

3 NULL 0.0000 0.0000 0.0000 1 1 0.0000

4 NULL 0.0000 0.0000 0.0000 1 1 0.0000

5 NULL 0.0000 0.0000 0.0000 1 1 0.0000

17

ANALYSIS PARAMETERS

-------------------

Analysis Mode (1-2) : 1

Seed File Name (8 char. max.) : NULL

Convergence Limit (>1.0) : 1.000010

Averaging Factor (<1.0) : 0.600

Maximum No. of Iterations : 60

Convergence Criteria (1-5) : 2

Results Files (1-4) : 2

Output Format (1-3) : 1

MATERIAL BEHAVIOUR MODELS

-------------------------

Concrete Compression Base Curve (0-3) : 1

Concrete Compression Post-Peak (0-3) : 1

Concrete Compression Softening (0-8) : 1

Concrete Tension Stiffening (0-6) : 1

Concrete Tension Softening (0-3) : 1

FRC Post-Crack Tension (0-9) : 0

Concrete Confined Strength (0-2) : 1

Concrete Dilation (0-1) : 1

Concrete Cracking Criterion (0-4) : 1

Concrete Crack Stress Calculation (0-2) : 1

Concrete Crack Width Check (0-2) : 1

Concrete Bond or Adhesion (0-3) : 1

Creep and Relaxation (0-1) : 1

Concrete Hysteresis (0-2) : 2

Reinforcement Hysteresis (0-2) : 1

Reinforcement Dowel Action (0-1) : 1

Reinforcement Buckling (0-1) : 1

Element Strain Histories (0-1) : 1

Element Slip Distortions (0-4) : 1

Strain Rate Effects (0-1) : 0

Structural Damping (0-1) : 0

Geometric Nonlinearity (0-1) : 1

Crack Allocation Process (0-1) : 1

<<< JOB FILE NOTES>>>

File D: VecTor2 Input Job File, Reverse Cyclic Analyses

*Highlighted selection denotes only difference with File C.

LOADING DATA

------------

No. of Load Stages : 901

Starting Load Stage No. : 1

Load Series ID ( 5 char. max.) : ID

Load File Name Factors

Case (8 char. max.) Initial Final LS-Inc Type Reps C-Inc

1 Case1 0.0000 12.7000 2.5400 3 3 12.7000

2 Case2 180.0000 180.0000 0.0000 1 1 0.0000

3 NULL 0.0000 0.0000 0.0000 1 1 0.0000

4 NULL 0.0000 0.0000 0.0000 1 1 0.0000

5 NULL 0.0000 0.0000 0.0000 1 1 0.0000