BASEMENT MODELING AND THE BACKSTAY EFFECT

By

Sanya Levi

April 30, 2010

SEMM

Department of Civil and Environmental Engineering

University of California

Berkeley, CA

2

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).

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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.

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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.

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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 Mot is

reduced in the core these forces are redistributed to perimeter foundation elements, shear is

also transferred to the foundation system.

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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).

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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

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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:

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

30%

10%

40%

20%

1. Which figure most closely resembles your typical modeling procedure

(Figures 7)?

B

C

C or D

D

30%

70%

2a. Do your modeling procedures

depend on seismic vs. wind controlled

building?

Yes

No

40%

60%

2b. Do your modeling procedures

depend on height of building?

Yes

No

50%50%

2c. Do your modeling procedures

depend on number of below grade

levels?

Yes

No

50%50%

2d. Do your modeling procedures

depend on soil and foundation type?

Yes

No

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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:

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

0%

100%

0%

5a. Do your use rigid or semi

rigid diaphragm to model yhe

ground diaphragm

Flexible

Semi-Rigid

Rigid

20%

60%

10%

10%

5b. Do you use full or reduced stiffness properties

for your grade diaphragms and foundation walls?

Reduced diaphragms/Reduced

found walls

Reduced diaphragms/Full found

walls

Full diaphragms/Reduced found

walls

Full diaphragms/Full found

walls

20%

40%

40%

5c. How do you determine values for

reduced stiffness ?

Iterative

Prescriptive

Both

40%

50%

10%

5d. Do you bracket the stiffness values?

Yes

No

In special cases

only

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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.

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.

Time/Manpower/Fee

Lack of Reliable soil

spring stiffness

Lack of industry

standards

Complexity

What do you believe are the major

impediments to more detailed modeling of the

effect?

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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 sylevi@berkeley.edu.

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:

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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?

6. 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

7. 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?

8. What do you believe are the major impediments to a more detailed modeling procedure – lack

of industry standards, computing time, model complexity, manpower, other.

9. Please add any additional information or comments that you have: