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BASEMENT MODELING AND THE BACKSTAY EFFECT

By

Sanya Levi

April 30, 2010

SEMM

Department of Civil and Environmental Engineering

University of California

Berkeley, CA

INTRO Modeling assumptions for at grade and below grade structural elements can have a significant impact on the analysis results and design of tall buildings. Perimeter basement walls, which form the foundation of a typical building, create a very stiff base structure. Ground and sub grade diaphragms couple the core with the perimeter foundation walls. This behavior distributes the overturning moments from the core to the much stiffer foundation walls. At the same time the shear demands on the core may increase significantly through a propped cantilever effect. The focus of this paper is to provide a discussion of this effect and its parameters and to provide an overview of current practice.

THE BACKSTAY EFFECT For simplicity this discussion will use a typical shearwall building although the concepts are the same or similar for other lateral force resisting systems. Also, although multiple below grade levels play a role in the backstay effect, this paper will generally use one basement for clarity. The site terrain will be assumed plane and the core will be assumed centrally located or more importantly not in the same plane as the foundation walls. In the most basic simplification a lateral system can be modeled as a cantilever beam fixed at the base with loads applied at the floor levels, the base may represent grade or the lowest basement level depending on the assumptions and choices of the designer. As loads accumulate floor by floor the shear and moment increase correspondingly, the shear at the base (Vbase) is equal to the total load input and the overturning moment (Mot) equal to the sum of the forces times their respective distances to the base (Figure 1).

2

Simple Cantilever Model

Shear Diagram

Moment Diagram

Figure 1: Simple Cantilever Model

The cantilever model is an accurate description of the building for behaviors above the ground floor such as shears, overturning moments and building drift. This model however does not consider the building configuration at the lower levels and can miss significant behaviors at the ground floor and below, which may result in forces that exceed structural capacity. A typical building has perimeter foundation walls below grade and these perimeter walls often have comparatively large inherent stiffness. The ground floor slab which engages these perimeter walls as well as the lateral system provides a link and effectively couples the two systems. Lateral forces are partially transferred out of the core to the much stiffer perimeter walls through the slab, in particular the walls that are parallel to the direction of loading. The degree of coupling is dependent upon a number of parameters such as the relative stiffness of the slab and foundation system compared to the lateral system, slab openings and drops, cracking and damage, and detailing of the slab to wall connections but in general there will be at least some degree of coupling between the two systems.

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Figure 2: Outrigger Effect

Figure 2 illustrates the effective outrigger that is created by the slab/foundation system, transferring lateral forces to perimeter foundation elements. It should be noted that the resisting forces of the walls perpendicular to the loading direction are not shown. The perpendicular walls, in particular the wall at the compression side of the loading may offer some resistance from soil pressure against the wall. The actual resistance provided will depend on the condition but is generally thought to contribute less than the parallel walls for most conditions. In some cases however this may be a significant source of stiffness and should be considered. In the simplified cantilever stick model the ground floor slab acting in conjunction with the perimeter foundation can be represented as an additional spring support; we will refer to this model as a propped cantilever. The stiffness of this spring should represent the effective combined stiffness of all contributing elements (slab, foundation walls, foundations, soil etc.). The effects of the ground floor on the building behavior are sometimes referred to as the „backstay effect‟. By examining the extremes of spring stiffness, zero and rigid, we can examine the magnitude of the backstay effect and the consequences of not properly capturing the actual behavior.

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At one extreme we consider a very soft outrigger system. The soft system could be the result of many factors coming from either the slab or the foundation system, or both. Some examples of where stiffness may be lost are large slab openings (for example a ramp opening), slab steps perpendicular to the load direction, detailing that does not allow shear transfer at the interfaces, a relatively thin slab, damage to the slab, a foundation system that is less stiff than the core foundation or some other factor. The slab may also be intentionally decoupled from the core with proper detailing. The very soft system will closely resemble the basic cantilever model where the base is the lowest basement level (not the ground). If we call Finput the total load input to the system, then the maximum shear in the core will be Vbase = Finput and Mot at the base will be the cantilever moments (refer to fig. 1). At the other extreme we consider an extremely rigid outrigger system. Here we use a pin support in the propped cantilever model as a limiting case. An extremely stiff system would be the result of all components individually being very stiff, this would be the result of a heavy/thick slab that is well detailed and has minimal slab drops and openings and a perimeter foundation which is stiff relative to the core foundation. The stiff system has significant impact on the below grade forces as can be seen in Figure 3. The most noticeable effect is the large reversal and magnification of shear forces in the core below grade. Assuming that the building is taller than the basement is deep, we will have Vbase > Finput and as the building height increases this shear magnification will increase correspondingly. From this it is clear that if a designer has neglected to model the true system stiffness or has opted to design the shear core for Vbase = Finput the below grade walls may have demands that are significantly over capacity. We also see that as the shear is shed the overturning moment is significantly reduced.

5

Pinned Ground Model

Shear Diagram

Moment Diagram

Figure 3: Rigid Propped Cantilever Model

The extremely soft system may be an accurate model for some cases, but a fully rigid and restrained ground is unrealistic for most situations. If we consider an intermediate model we replace the pin support with a spring of appropriate stiffness representing the total slab/foundation outrigger system (Figure 4). For this case the magnitude of shear and moment reduction is dependent on the relative stiffness between the outrigger system and the main lateral force resisting system. The change in shear may or may not lead to shear forces above Finput depending on the configuration.

6

Spring Ground Model

Shear Diagram

Moment Diagram

Figure 4: Quantified stiffness at ground level

This model can be initially misleading in that the Vbase and Mot appear to be essentially disappearing. A more representative model, while still keeping with a simple stick frame, includes the foundation elements attached to the core via an outrigger which represents the slab (Figure 5). It should be noted that the outrigger elements are the foundation walls parallel to the load direction as these are considered the primary resisting force elements. This model comes closest to representing our total system and we can see that while M ot is reduced in the core these forces are redistributed to perimeter foundation elements, shear is also transferred to the foundation system.

7

Outrigger Model

Shear Diagram

Moment Diagram

Figure 5: Overturning moment redistribution

FORCE TRANSFER MECHANISMS The transfer of lateral forces through grade level diaphragms and into the foundation walls and footings is not wholly agreed upon. It depends on the particular configuration of slab drops and openings, the detailing of the slab and location of the shear walls relative to the perimeter. In general, force transfer through the ground floor slab is divided into two categories: strut-and-tie action and shear through the slab. One or both of these mechanisms may act to shed load from the core to the perimeter foundation walls. The diagrams below illustrate these mechanisms (Figure 6).

8

Idealized model showing transfer mechanisms

Shear V12 through slab

S22 Stress (Strut-and-Tie Stresses)

S11 Stress (Chord Forces)

Figure 6: Force mechanisms

MODELING From the above discussion it is clear that the backstay effect can have a significant impact on building demands and an attempt to capture this behavior should be made in the building lateral model. However, the level of detail and assumptions of behavior are not completely agreed upon. The two main sources of uncertainty are the properties of the slab and foundation walls and the soil-structure interaction. To accurately capture the effective stiffness of the ground floor (and below) slabs, semi-rigid diaphragms should be used. The majority of outrigger action is the result of in plane forces through the diaphragm to the parallel perimeter walls but there is also a small degree of flexural coupling provided by the slab. The slab element should reflect this behavior by using an element that transmits in plane forces only (membrane) or properly modifying the 9

out of plane stiffness to a relatively small value as the designer sees fit. Modifications to both the flexural and shear stiffness will be discussed later in this paper. Within the slab there are multiple areas where stiffness may be lost. Some factors such as geometry may be easily included in the model as in the case of slab drops or large slab openings. The more difficult question is what modification to stiffness should be assumed for the slab and walls. As in most concrete modeling, it is reasonable to assume that at a minimum some cracking will occur and more likely there will be significant cracking and inelastic behavior. Thus gross section properties are rarely appropriate. There are also other areas where stiffness may be lost such as slip at the interface of the slab to foundation wall or local crushing of concrete at the core interface. It may also be the case that the slab stiffness changes over time, as happens during cyclic loading. Modifications to the slab stiffness are an attempt to account for all sources of loss and arrive at an effective stiffness value. Since there is a large degree of uncertainty in estimating the actual effective stiffness of the system one option which is gaining traction is to bracket the stiffness within a reasonable range. Under even the smallest events it is safe to say that there is cracking, slip, and inelastic behavior which make a number less then unity likely for the stiffness. At the same time even a highly damaged slab or one that is not completely detailed to transfer the shear will offer some degree of stiffness, thus a number larger than zero on the low end is reasonable. A range for the bracketing will be recommended by Chapter 5 of ATC-72-1 PEER Tall Buildings Initiative Interim Guidelines on Modeling and Acceptance criteria (currently in 90% draft). The recommended upper bound of the flexural stiffness EI for the floor diaphragm and foundation walls is half of the gross section properties of the elements versus a lower bound of 0.2 times the gross section properties (or fully cracked, transformed section). The recommended shear stiffness for the floor diaphragms and perimeter foundation walls GAv has an upper bound of half the gross section properties, coupled with a lower bound of 0.05 to 0.2 times the gross section properties. The flexural and shear stiffness of other critical elements like the core wall, foundation mats, pile caps, etc is recommended at 0.3 times the gross section properties. (Maffei)

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Bracketing of the stiffness of the diaphragms provides a “belt and suspenders” approach by designing for a large spectrum of stiffness and thus demand possibilities. Some feel that the bracketing approach is overly conservative while others have complained that unless the approach is more standardized their designs do not appear competitive with others who are not using this methodology. The second major area of uncertainty in backstay modeling is the soil-structure interaction. In general the interaction of the structure with the subgrade is many times ignored in practice. Many engineers question whether accurate spring coefficients are possible and whether the added complexity is necessary. Due to the large degree of uncertainty of soil stiffness properties, a bracketing approach is sometimes recommended. In general this will be achieved by scaling the stiffness values provided by a geotechnical report. Some recommend using ½ and 2 times the expected values as boundaries. It should be noted that using rigid (or pin) supports at the base may provide an upper bound for the backstay effect and associated forces, it does not however provide accurate force distribution in general. In particular the force distribution to foundation elements and thus the associated forces in the walls will not be accurate as displacement compatibility is not satisfied. A simple diagram of a single wall comparing spring supports vs. pin supports illustrates this point in Figure 7, it can be seen that the soil springs provide a linear force distribution as expected while the pin supports produce a less logical distribution.

Figure 7a: Force Distribution Using Soil Springs

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Figure 8b: Force Distribution Using Rigid Supports

For all bracketed assumptions (slabs, walls, soils etc.) the elements are not bracketed as separate parameter cases. Two bound cases are formed based on whether the parameter would cause an upper bound for the force in the diaphragm and shear in the core (equivalent to lower bound for the overturning moment under the core) and a second case of a lower bound of the force in the diaphragm (upper bound of the overturning moment in the core).

EXISTING GUIDELINES The research for this paper did not lead to many existing guidelines for modeling. The most instructive guide was ATC-7-1 PEER “Tall Buildings Initiative Interim Guidelines on Modeling and Acceptance Criteria”. The guidelines‟ 90% draft was completed in 2008 and the final draft is expected soon. ASCE-41 offers some guidelines. Especially helpful was found the text by Paulay and Priestly “Seismic Design of Reinforced Concrete and Masonry Buildings”. ACI offers guidelines related to design of the ground diaphragm depending on the force transfer method adopted (as described earlier). Shear transfer is described in Chapter 21 of the ACI. Strut and tie models are provided for in Appendix A of the ACI.

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CURRENT PRACTICE In the absence of accepted modeling guidelines and agreement on accepted practices it is of interest to survey what methods are currently employed in practice. A survey was conducted across design offices focusing on their usual practice in dealing with the described problem. The targeted design offices were from both high and low seismic areas as well as high and low wind areas. A copy of the survey that was submitted to them is included in Appendix A. Please note that the surveyed population sample of companies is not necessarily statistically representative of the whole industry and the survey responses are not necessarily representative of the whole company. Also, some bias should be noted in the results. Most of the engineers who filled out the survey are considered experts in their field hence the results here represent the opinion of the top portion of the engineering practice. Although some responses from young engineers were obtained, the large majority of results are from engineers very familiar with the backstay effect. Also, the survey did not consist of answers that were always easy to categorize in to a yes/no and the responses varied in length and complexity.

Fig. A

Fig. B

Fig. C

Fig. D

Description of figures: Fig. A -The structure is modeled to grade regardless of actual subgrade conditions. Fig. B -The structure is modeled to the foundation level, grade and below grade diaphragms are neglected. Fig. C -The structure is modeled to the foundation level, grade and below grade diaphragms are modeled, either with rigid or semi-rigid diaphragms. Foundation walls are included where relevant. Fig. D -Similar to Fig. C but the effects of soil/structure interaction are included through springs.

Figure 9: Modeling procedures

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The results from the survey are offered below: 1. Which figure most closely resembles your typical modeling procedure (Figures 7)? B

20%

C

30%

C or D

40% 10%

2a. Do your modeling procedures depend on seismic vs. wind controlled building?

30%

2b. Do your modeling procedures depend on height of building?

2c. Do your modeling procedures depend on number of below grade levels?

50%

50%

40%

Yes No

70%

D

Yes No

60%

2d. Do your modeling procedures depend on soil and foundation type?

Yes

Yes

50%

50%

No

No

From the pie charts above we see that although the majority of the responses employed models C and D to account for backstay effect, 30% use model B which completely ignores the backstay effect and any possible shear magnification in the core or increased diaphragm transfer forces. A third of these responses noted that when using model B they provide appropriate detailing to laterally separate the core from the foundation walls. The offices were asked what guidelines they use for their modeling and design. The common ones are enumerated here: FEMA 356 Prestandard and Commentary for the 14

Seismic Rehabilitation of Buildings, now superseded by ASCE 41, Seismic Rehabilitation of Buildings; FEMA 440, Improvement of Nonlinear Static Seismic Analysis Procedures; and FEMA 547, Techniques for the Seismic Rehabilitation of Existing Buildings. When employing models C or D, the response showed the following trends in procedures: 5a. Do your use rigid or semi rigid diaphragm to model yhe ground diaphragm

0% 0%

5b. Do you use full or reduced stiffness properties for your grade diaphragms and foundation walls? Reduced diaphragms/Reduced found walls

10% 10% 20%

Flexible

Full diaphragms/Reduced found walls

Semi-Rigid

100%

60%

Rigid

5c. How do you determine values for reduced stiffness ?

Reduced diaphragms/Full found walls

Full diaphragms/Full found walls

5d. Do you bracket the stiffness values?

10% Yes

40%

20%

Iterative

40%

Prescriptive

40%

Both

50%

No In special cases only

All of the participants use a semi-rigid diaphragm at the critical slabs as recommended. The majority of participants use reduced stiffness properties for the critical diaphragm but the full properties for the perimeter foundation elements. Only 20% of the responses use reduced stiffness properties for both the critical slab and the foundation perimeter walls as recommended by ATC-72-1. The majority of respondents use prescriptive values for the effective stiffness of these elements. Some prescribed values were offered in the Modeling section of this paper. These values were again obtained from Chapter 5 of ATC-72-1. The majority of respondents also do not generally bracket the prescriptive values of the stiffness. Responses seem to agree that lateral loads usually have significant effect on the grade level diaphragm and more negligible effect on the foundation walls. Half of the participants have

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experienced that the shear reversals below grade sometimes present an “undesignable” wall and are forced to increase wall thickness. The majority of the participants did not typically have issues with overly large perimeter foundation elements. However, there were several responses from New York City where this may present more of a problem. It is often the case in NY that buildings are at the property line on all sides and thus pile foundations are typically eccentric (due to the offset distance required for the pile rig), the additional loads from lateral forces that are transferred to these eccentric elements have a larger design impact in these cases. While most of the participants would like to see further investigation of the issue of backstay effect and correct modeling procedures to account for it, 20% feel that bracketing the solutions for the various parameters is a sufficient approach and no further development is needed. What do you believe are the major impediments to more detailed modeling of the effect? Complexity

Lack of industry standards

Time/Manp ower/Fee Lack of Reliable soil spring stiffness

When asked to point out the major impediments to more comprehensive modeling, the participants pointed out pressures in the design fee as the greatest factor, creating time and manpower issues. These are followed by lack of industry standards which is believed to increase demand for time and manpower as it fails to streamline the design process and also does not provide a level playing field across design firms. Finally the complexity of the model and the lack of reliable geotechnical information on the soil structure interaction are pointed out to impede the process.

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Bibliography Maffei, J., Malley, J., Deierlein, G., Krawinkler, H., Pourzanjani, M., Wallace, J., Heintz, J.

ATC-72-1 90% Draft PEER Tall Buildings Initiative Interim Guidelines on Modeling and Acceptance Criteria. Maffei, J. R., & Schotanus, M. I. Computer modeling and effective stiffness of concrete wall buildings. San Francisco, California, USA: Rutherford & Chekene Consulting Engineers. Massone, L. M., Orakcal, K., & Wallace, J. W. Shear-Flexure Interaction for Structural

Walls. Nair, R. S. Belt Trusses and Basements as "Virtual" Outriggers for Tall Buildings. Nair, R. S. Modelling of Support Conditions at the Bases of Tall Buildings. Paulay, T., & Priestley, N. M. (1992). Seismic Design of Reinforced Concrete and Masonry Buildings. John Wiley & Sons, Inc. Sozen, M. A., Montetro, P., Moehle, J. P., & Tang, H. T. Effects of Cracking and Age on

Stiffness of Reinforced Concrete Walls Resisting In-Plane Shear.

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APPENDIX A

Survey Please return the filled out survey by email to Sanya Levi at [email protected]

Intro: Modeling assumptions for at grade and below grade structural elements can have a significant impact on the analysis results and design of tall buildings. Perimeter basement walls which form the foundation of a typical building create a very stiff base structure which is typically much larger in plan area than the building’s core. Ground and sub grade diaphragms, which typically engage these foundation walls, couple the core with the perimeter foundation walls. This behavior distributes the overturning moments from the core to the much stiffer foundation walls, at the same time the shear demands on the core will reverse direction and may increase significantly through a propped cantilever effect. The focus of this paper is to provide a survey of current practice in design offices for dealing with these effects. When answering the attached questions please provide what your/your office does rather than what you believe to be most ideal or correct. Any additional comments or information is welcome. Note that all responses will be kept confidential and names will not be associated with responses in the final paper. Figure: Illustrative shear diagrams of core with and without grade level diaphragm.

Figure: Illustrative overturning resisting forces with and without force transfer to foundation walls.

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Questions:

Fig. A

Fig. B

Fig. C

Fig. D

Description of figures: Fig. A - The structure is modeled to grade regardless of actual subgrade conditions. Fig. B - The structure is modeled to the foundation level, grade and below grade diaphragms are neglected. Fig. C - The structure is modeled to the foundation level, grade and below grade diaphragms are modeled, either with rigid or semi-rigid diaphragms. Foundation walls are included where relevant. Fig. D - Similar to Fig. C but the effects of soil/structure interaction are included through springs.

1. Which of the above figures most closely resembles your typical modeling procedure? 2. Do your modeling assumptions vary depending on: a. Seismic vs. Wind controlled building b. Height of building c. Number of below grade levels d. Soil and foundation type (deep vs. shallow) 3. What if any documents/guidelines do you follow for the modeling of at grade and below grade elements? 4. If you chose fig A or B: a. Do you provide seismic joints between the core and the slab or similar details to minimize force transfer? 5. If you chose Fig. C or D: a. Do you use rigid or semi rigid diaphragm for the ground slab? b. Do you use full or cracked/reduced section properties for: 19

6.

7. 8. 9.

i. Diaphragms ii. Basement wall c. How do you determine values for reduced stiffness – iterative based on demand/capacity or prescriptive? d. Do you bracket the above values of stiffness (for example run two models, each with a different diaphragm stiffness and envelope the results)? e. Do you account for slab openings and slab drops? f. How much impact do lateral loads typically have on your slab and wall design (at and below grade)? i.e. increased rebar, collectors, chords etc. g. As diaphragm and basement wall stiffness increase shear reversal forces grow, does this ever present an “undesignable” wall or force the below grade walls to grow in thickness? h. As diaphragm and basement wall stiffness increases overturning moment is shifted away from the core to the perimeter walls, does this ever create issues with perimeter foundation elements? If you chose Fig. D and use springs to represent soil stiffness: a. How do you determine spring stiffness? b. Do you use full or cracked/reduced section properties for: i. Diaphragms ii. Basement wall Do you consider the issue of modeling below grade levels to be one which requires further investigation/clarification or feel that it is sufficiently clear? What do you believe are the major impediments to a more detailed modeling procedure – lack of industry standards, computing time, model complexity, manpower, other. Please add any additional information or comments that you have:

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View more...
By

Sanya Levi

April 30, 2010

SEMM

Department of Civil and Environmental Engineering

University of California

Berkeley, CA

INTRO Modeling assumptions for at grade and below grade structural elements can have a significant impact on the analysis results and design of tall buildings. Perimeter basement walls, which form the foundation of a typical building, create a very stiff base structure. Ground and sub grade diaphragms couple the core with the perimeter foundation walls. This behavior distributes the overturning moments from the core to the much stiffer foundation walls. At the same time the shear demands on the core may increase significantly through a propped cantilever effect. The focus of this paper is to provide a discussion of this effect and its parameters and to provide an overview of current practice.

THE BACKSTAY EFFECT For simplicity this discussion will use a typical shearwall building although the concepts are the same or similar for other lateral force resisting systems. Also, although multiple below grade levels play a role in the backstay effect, this paper will generally use one basement for clarity. The site terrain will be assumed plane and the core will be assumed centrally located or more importantly not in the same plane as the foundation walls. In the most basic simplification a lateral system can be modeled as a cantilever beam fixed at the base with loads applied at the floor levels, the base may represent grade or the lowest basement level depending on the assumptions and choices of the designer. As loads accumulate floor by floor the shear and moment increase correspondingly, the shear at the base (Vbase) is equal to the total load input and the overturning moment (Mot) equal to the sum of the forces times their respective distances to the base (Figure 1).

2

Simple Cantilever Model

Shear Diagram

Moment Diagram

Figure 1: Simple Cantilever Model

The cantilever model is an accurate description of the building for behaviors above the ground floor such as shears, overturning moments and building drift. This model however does not consider the building configuration at the lower levels and can miss significant behaviors at the ground floor and below, which may result in forces that exceed structural capacity. A typical building has perimeter foundation walls below grade and these perimeter walls often have comparatively large inherent stiffness. The ground floor slab which engages these perimeter walls as well as the lateral system provides a link and effectively couples the two systems. Lateral forces are partially transferred out of the core to the much stiffer perimeter walls through the slab, in particular the walls that are parallel to the direction of loading. The degree of coupling is dependent upon a number of parameters such as the relative stiffness of the slab and foundation system compared to the lateral system, slab openings and drops, cracking and damage, and detailing of the slab to wall connections but in general there will be at least some degree of coupling between the two systems.

3

Figure 2: Outrigger Effect

Figure 2 illustrates the effective outrigger that is created by the slab/foundation system, transferring lateral forces to perimeter foundation elements. It should be noted that the resisting forces of the walls perpendicular to the loading direction are not shown. The perpendicular walls, in particular the wall at the compression side of the loading may offer some resistance from soil pressure against the wall. The actual resistance provided will depend on the condition but is generally thought to contribute less than the parallel walls for most conditions. In some cases however this may be a significant source of stiffness and should be considered. In the simplified cantilever stick model the ground floor slab acting in conjunction with the perimeter foundation can be represented as an additional spring support; we will refer to this model as a propped cantilever. The stiffness of this spring should represent the effective combined stiffness of all contributing elements (slab, foundation walls, foundations, soil etc.). The effects of the ground floor on the building behavior are sometimes referred to as the „backstay effect‟. By examining the extremes of spring stiffness, zero and rigid, we can examine the magnitude of the backstay effect and the consequences of not properly capturing the actual behavior.

4

At one extreme we consider a very soft outrigger system. The soft system could be the result of many factors coming from either the slab or the foundation system, or both. Some examples of where stiffness may be lost are large slab openings (for example a ramp opening), slab steps perpendicular to the load direction, detailing that does not allow shear transfer at the interfaces, a relatively thin slab, damage to the slab, a foundation system that is less stiff than the core foundation or some other factor. The slab may also be intentionally decoupled from the core with proper detailing. The very soft system will closely resemble the basic cantilever model where the base is the lowest basement level (not the ground). If we call Finput the total load input to the system, then the maximum shear in the core will be Vbase = Finput and Mot at the base will be the cantilever moments (refer to fig. 1). At the other extreme we consider an extremely rigid outrigger system. Here we use a pin support in the propped cantilever model as a limiting case. An extremely stiff system would be the result of all components individually being very stiff, this would be the result of a heavy/thick slab that is well detailed and has minimal slab drops and openings and a perimeter foundation which is stiff relative to the core foundation. The stiff system has significant impact on the below grade forces as can be seen in Figure 3. The most noticeable effect is the large reversal and magnification of shear forces in the core below grade. Assuming that the building is taller than the basement is deep, we will have Vbase > Finput and as the building height increases this shear magnification will increase correspondingly. From this it is clear that if a designer has neglected to model the true system stiffness or has opted to design the shear core for Vbase = Finput the below grade walls may have demands that are significantly over capacity. We also see that as the shear is shed the overturning moment is significantly reduced.

5

Pinned Ground Model

Shear Diagram

Moment Diagram

Figure 3: Rigid Propped Cantilever Model

The extremely soft system may be an accurate model for some cases, but a fully rigid and restrained ground is unrealistic for most situations. If we consider an intermediate model we replace the pin support with a spring of appropriate stiffness representing the total slab/foundation outrigger system (Figure 4). For this case the magnitude of shear and moment reduction is dependent on the relative stiffness between the outrigger system and the main lateral force resisting system. The change in shear may or may not lead to shear forces above Finput depending on the configuration.

6

Spring Ground Model

Shear Diagram

Moment Diagram

Figure 4: Quantified stiffness at ground level

This model can be initially misleading in that the Vbase and Mot appear to be essentially disappearing. A more representative model, while still keeping with a simple stick frame, includes the foundation elements attached to the core via an outrigger which represents the slab (Figure 5). It should be noted that the outrigger elements are the foundation walls parallel to the load direction as these are considered the primary resisting force elements. This model comes closest to representing our total system and we can see that while M ot is reduced in the core these forces are redistributed to perimeter foundation elements, shear is also transferred to the foundation system.

7

Outrigger Model

Shear Diagram

Moment Diagram

Figure 5: Overturning moment redistribution

FORCE TRANSFER MECHANISMS The transfer of lateral forces through grade level diaphragms and into the foundation walls and footings is not wholly agreed upon. It depends on the particular configuration of slab drops and openings, the detailing of the slab and location of the shear walls relative to the perimeter. In general, force transfer through the ground floor slab is divided into two categories: strut-and-tie action and shear through the slab. One or both of these mechanisms may act to shed load from the core to the perimeter foundation walls. The diagrams below illustrate these mechanisms (Figure 6).

8

Idealized model showing transfer mechanisms

Shear V12 through slab

S22 Stress (Strut-and-Tie Stresses)

S11 Stress (Chord Forces)

Figure 6: Force mechanisms

MODELING From the above discussion it is clear that the backstay effect can have a significant impact on building demands and an attempt to capture this behavior should be made in the building lateral model. However, the level of detail and assumptions of behavior are not completely agreed upon. The two main sources of uncertainty are the properties of the slab and foundation walls and the soil-structure interaction. To accurately capture the effective stiffness of the ground floor (and below) slabs, semi-rigid diaphragms should be used. The majority of outrigger action is the result of in plane forces through the diaphragm to the parallel perimeter walls but there is also a small degree of flexural coupling provided by the slab. The slab element should reflect this behavior by using an element that transmits in plane forces only (membrane) or properly modifying the 9

out of plane stiffness to a relatively small value as the designer sees fit. Modifications to both the flexural and shear stiffness will be discussed later in this paper. Within the slab there are multiple areas where stiffness may be lost. Some factors such as geometry may be easily included in the model as in the case of slab drops or large slab openings. The more difficult question is what modification to stiffness should be assumed for the slab and walls. As in most concrete modeling, it is reasonable to assume that at a minimum some cracking will occur and more likely there will be significant cracking and inelastic behavior. Thus gross section properties are rarely appropriate. There are also other areas where stiffness may be lost such as slip at the interface of the slab to foundation wall or local crushing of concrete at the core interface. It may also be the case that the slab stiffness changes over time, as happens during cyclic loading. Modifications to the slab stiffness are an attempt to account for all sources of loss and arrive at an effective stiffness value. Since there is a large degree of uncertainty in estimating the actual effective stiffness of the system one option which is gaining traction is to bracket the stiffness within a reasonable range. Under even the smallest events it is safe to say that there is cracking, slip, and inelastic behavior which make a number less then unity likely for the stiffness. At the same time even a highly damaged slab or one that is not completely detailed to transfer the shear will offer some degree of stiffness, thus a number larger than zero on the low end is reasonable. A range for the bracketing will be recommended by Chapter 5 of ATC-72-1 PEER Tall Buildings Initiative Interim Guidelines on Modeling and Acceptance criteria (currently in 90% draft). The recommended upper bound of the flexural stiffness EI for the floor diaphragm and foundation walls is half of the gross section properties of the elements versus a lower bound of 0.2 times the gross section properties (or fully cracked, transformed section). The recommended shear stiffness for the floor diaphragms and perimeter foundation walls GAv has an upper bound of half the gross section properties, coupled with a lower bound of 0.05 to 0.2 times the gross section properties. The flexural and shear stiffness of other critical elements like the core wall, foundation mats, pile caps, etc is recommended at 0.3 times the gross section properties. (Maffei)

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Bracketing of the stiffness of the diaphragms provides a “belt and suspenders” approach by designing for a large spectrum of stiffness and thus demand possibilities. Some feel that the bracketing approach is overly conservative while others have complained that unless the approach is more standardized their designs do not appear competitive with others who are not using this methodology. The second major area of uncertainty in backstay modeling is the soil-structure interaction. In general the interaction of the structure with the subgrade is many times ignored in practice. Many engineers question whether accurate spring coefficients are possible and whether the added complexity is necessary. Due to the large degree of uncertainty of soil stiffness properties, a bracketing approach is sometimes recommended. In general this will be achieved by scaling the stiffness values provided by a geotechnical report. Some recommend using ½ and 2 times the expected values as boundaries. It should be noted that using rigid (or pin) supports at the base may provide an upper bound for the backstay effect and associated forces, it does not however provide accurate force distribution in general. In particular the force distribution to foundation elements and thus the associated forces in the walls will not be accurate as displacement compatibility is not satisfied. A simple diagram of a single wall comparing spring supports vs. pin supports illustrates this point in Figure 7, it can be seen that the soil springs provide a linear force distribution as expected while the pin supports produce a less logical distribution.

Figure 7a: Force Distribution Using Soil Springs

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Figure 8b: Force Distribution Using Rigid Supports

For all bracketed assumptions (slabs, walls, soils etc.) the elements are not bracketed as separate parameter cases. Two bound cases are formed based on whether the parameter would cause an upper bound for the force in the diaphragm and shear in the core (equivalent to lower bound for the overturning moment under the core) and a second case of a lower bound of the force in the diaphragm (upper bound of the overturning moment in the core).

EXISTING GUIDELINES The research for this paper did not lead to many existing guidelines for modeling. The most instructive guide was ATC-7-1 PEER “Tall Buildings Initiative Interim Guidelines on Modeling and Acceptance Criteria”. The guidelines‟ 90% draft was completed in 2008 and the final draft is expected soon. ASCE-41 offers some guidelines. Especially helpful was found the text by Paulay and Priestly “Seismic Design of Reinforced Concrete and Masonry Buildings”. ACI offers guidelines related to design of the ground diaphragm depending on the force transfer method adopted (as described earlier). Shear transfer is described in Chapter 21 of the ACI. Strut and tie models are provided for in Appendix A of the ACI.

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CURRENT PRACTICE In the absence of accepted modeling guidelines and agreement on accepted practices it is of interest to survey what methods are currently employed in practice. A survey was conducted across design offices focusing on their usual practice in dealing with the described problem. The targeted design offices were from both high and low seismic areas as well as high and low wind areas. A copy of the survey that was submitted to them is included in Appendix A. Please note that the surveyed population sample of companies is not necessarily statistically representative of the whole industry and the survey responses are not necessarily representative of the whole company. Also, some bias should be noted in the results. Most of the engineers who filled out the survey are considered experts in their field hence the results here represent the opinion of the top portion of the engineering practice. Although some responses from young engineers were obtained, the large majority of results are from engineers very familiar with the backstay effect. Also, the survey did not consist of answers that were always easy to categorize in to a yes/no and the responses varied in length and complexity.

Fig. A

Fig. B

Fig. C

Fig. D

Description of figures: Fig. A -The structure is modeled to grade regardless of actual subgrade conditions. Fig. B -The structure is modeled to the foundation level, grade and below grade diaphragms are neglected. Fig. C -The structure is modeled to the foundation level, grade and below grade diaphragms are modeled, either with rigid or semi-rigid diaphragms. Foundation walls are included where relevant. Fig. D -Similar to Fig. C but the effects of soil/structure interaction are included through springs.

Figure 9: Modeling procedures

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The results from the survey are offered below: 1. Which figure most closely resembles your typical modeling procedure (Figures 7)? B

20%

C

30%

C or D

40% 10%

2a. Do your modeling procedures depend on seismic vs. wind controlled building?

30%

2b. Do your modeling procedures depend on height of building?

2c. Do your modeling procedures depend on number of below grade levels?

50%

50%

40%

Yes No

70%

D

Yes No

60%

2d. Do your modeling procedures depend on soil and foundation type?

Yes

Yes

50%

50%

No

No

From the pie charts above we see that although the majority of the responses employed models C and D to account for backstay effect, 30% use model B which completely ignores the backstay effect and any possible shear magnification in the core or increased diaphragm transfer forces. A third of these responses noted that when using model B they provide appropriate detailing to laterally separate the core from the foundation walls. The offices were asked what guidelines they use for their modeling and design. The common ones are enumerated here: FEMA 356 Prestandard and Commentary for the 14

Seismic Rehabilitation of Buildings, now superseded by ASCE 41, Seismic Rehabilitation of Buildings; FEMA 440, Improvement of Nonlinear Static Seismic Analysis Procedures; and FEMA 547, Techniques for the Seismic Rehabilitation of Existing Buildings. When employing models C or D, the response showed the following trends in procedures: 5a. Do your use rigid or semi rigid diaphragm to model yhe ground diaphragm

0% 0%

5b. Do you use full or reduced stiffness properties for your grade diaphragms and foundation walls? Reduced diaphragms/Reduced found walls

10% 10% 20%

Flexible

Full diaphragms/Reduced found walls

Semi-Rigid

100%

60%

Rigid

5c. How do you determine values for reduced stiffness ?

Reduced diaphragms/Full found walls

Full diaphragms/Full found walls

5d. Do you bracket the stiffness values?

10% Yes

40%

20%

Iterative

40%

Prescriptive

40%

Both

50%

No In special cases only

All of the participants use a semi-rigid diaphragm at the critical slabs as recommended. The majority of participants use reduced stiffness properties for the critical diaphragm but the full properties for the perimeter foundation elements. Only 20% of the responses use reduced stiffness properties for both the critical slab and the foundation perimeter walls as recommended by ATC-72-1. The majority of respondents use prescriptive values for the effective stiffness of these elements. Some prescribed values were offered in the Modeling section of this paper. These values were again obtained from Chapter 5 of ATC-72-1. The majority of respondents also do not generally bracket the prescriptive values of the stiffness. Responses seem to agree that lateral loads usually have significant effect on the grade level diaphragm and more negligible effect on the foundation walls. Half of the participants have

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experienced that the shear reversals below grade sometimes present an “undesignable” wall and are forced to increase wall thickness. The majority of the participants did not typically have issues with overly large perimeter foundation elements. However, there were several responses from New York City where this may present more of a problem. It is often the case in NY that buildings are at the property line on all sides and thus pile foundations are typically eccentric (due to the offset distance required for the pile rig), the additional loads from lateral forces that are transferred to these eccentric elements have a larger design impact in these cases. While most of the participants would like to see further investigation of the issue of backstay effect and correct modeling procedures to account for it, 20% feel that bracketing the solutions for the various parameters is a sufficient approach and no further development is needed. What do you believe are the major impediments to more detailed modeling of the effect? Complexity

Lack of industry standards

Time/Manp ower/Fee Lack of Reliable soil spring stiffness

When asked to point out the major impediments to more comprehensive modeling, the participants pointed out pressures in the design fee as the greatest factor, creating time and manpower issues. These are followed by lack of industry standards which is believed to increase demand for time and manpower as it fails to streamline the design process and also does not provide a level playing field across design firms. Finally the complexity of the model and the lack of reliable geotechnical information on the soil structure interaction are pointed out to impede the process.

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Bibliography Maffei, J., Malley, J., Deierlein, G., Krawinkler, H., Pourzanjani, M., Wallace, J., Heintz, J.

ATC-72-1 90% Draft PEER Tall Buildings Initiative Interim Guidelines on Modeling and Acceptance Criteria. Maffei, J. R., & Schotanus, M. I. Computer modeling and effective stiffness of concrete wall buildings. San Francisco, California, USA: Rutherford & Chekene Consulting Engineers. Massone, L. M., Orakcal, K., & Wallace, J. W. Shear-Flexure Interaction for Structural

Walls. Nair, R. S. Belt Trusses and Basements as "Virtual" Outriggers for Tall Buildings. Nair, R. S. Modelling of Support Conditions at the Bases of Tall Buildings. Paulay, T., & Priestley, N. M. (1992). Seismic Design of Reinforced Concrete and Masonry Buildings. John Wiley & Sons, Inc. Sozen, M. A., Montetro, P., Moehle, J. P., & Tang, H. T. Effects of Cracking and Age on

Stiffness of Reinforced Concrete Walls Resisting In-Plane Shear.

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APPENDIX A

Survey Please return the filled out survey by email to Sanya Levi at [email protected]

Intro: Modeling assumptions for at grade and below grade structural elements can have a significant impact on the analysis results and design of tall buildings. Perimeter basement walls which form the foundation of a typical building create a very stiff base structure which is typically much larger in plan area than the building’s core. Ground and sub grade diaphragms, which typically engage these foundation walls, couple the core with the perimeter foundation walls. This behavior distributes the overturning moments from the core to the much stiffer foundation walls, at the same time the shear demands on the core will reverse direction and may increase significantly through a propped cantilever effect. The focus of this paper is to provide a survey of current practice in design offices for dealing with these effects. When answering the attached questions please provide what your/your office does rather than what you believe to be most ideal or correct. Any additional comments or information is welcome. Note that all responses will be kept confidential and names will not be associated with responses in the final paper. Figure: Illustrative shear diagrams of core with and without grade level diaphragm.

Figure: Illustrative overturning resisting forces with and without force transfer to foundation walls.

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Questions:

Fig. A

Fig. B

Fig. C

Fig. D

Description of figures: Fig. A - The structure is modeled to grade regardless of actual subgrade conditions. Fig. B - The structure is modeled to the foundation level, grade and below grade diaphragms are neglected. Fig. C - The structure is modeled to the foundation level, grade and below grade diaphragms are modeled, either with rigid or semi-rigid diaphragms. Foundation walls are included where relevant. Fig. D - Similar to Fig. C but the effects of soil/structure interaction are included through springs.

1. Which of the above figures most closely resembles your typical modeling procedure? 2. Do your modeling assumptions vary depending on: a. Seismic vs. Wind controlled building b. Height of building c. Number of below grade levels d. Soil and foundation type (deep vs. shallow) 3. What if any documents/guidelines do you follow for the modeling of at grade and below grade elements? 4. If you chose fig A or B: a. Do you provide seismic joints between the core and the slab or similar details to minimize force transfer? 5. If you chose Fig. C or D: a. Do you use rigid or semi rigid diaphragm for the ground slab? b. Do you use full or cracked/reduced section properties for: 19

6.

7. 8. 9.

i. Diaphragms ii. Basement wall c. How do you determine values for reduced stiffness – iterative based on demand/capacity or prescriptive? d. Do you bracket the above values of stiffness (for example run two models, each with a different diaphragm stiffness and envelope the results)? e. Do you account for slab openings and slab drops? f. How much impact do lateral loads typically have on your slab and wall design (at and below grade)? i.e. increased rebar, collectors, chords etc. g. As diaphragm and basement wall stiffness increase shear reversal forces grow, does this ever present an “undesignable” wall or force the below grade walls to grow in thickness? h. As diaphragm and basement wall stiffness increases overturning moment is shifted away from the core to the perimeter walls, does this ever create issues with perimeter foundation elements? If you chose Fig. D and use springs to represent soil stiffness: a. How do you determine spring stiffness? b. Do you use full or cracked/reduced section properties for: i. Diaphragms ii. Basement wall Do you consider the issue of modeling below grade levels to be one which requires further investigation/clarification or feel that it is sufficiently clear? What do you believe are the major impediments to a more detailed modeling procedure – lack of industry standards, computing time, model complexity, manpower, other. Please add any additional information or comments that you have:

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