EFFECT OF THE OPENINGS IN THE STRENGTH
AND STIFFNESS OF REINFORCED CONCRETESTRUCTURAL WALLS
Emilio Martín Ventura Díaz*

Supervisor: Dr. Hiroshi Fukuyama**

MEE06021
ABSTRACTThe purpose of this investigation is to study the openings effect (windows, doors, etc) in the lateralstrength and stiffness of RC structural walls. One solid wall and fifteen walls with different opening
shapes and opening positions were modeled in Displacement Method Analyzer software (DIANA).
The AIJ Guideline lateral strength equation, the ACI lateral strength equation and the strength
reduction factors due to openings proposed by AIJ Standard Calculation were used to predict thelateral strengths of the fifteen walls with openings and the solid wall. Regarding the stiffness of wallswith openings, it is calculated by means of two methods; one is a hand method procedure and theother one is using the stiffness reduction factor proposed in AIJ Standard Calculation. It was foundthat for those walls with same opening area but different opening positions, the seismic codes
equations predict the same lateral strength capacity for them; on the other hand, the DIANA
simulations show that such walls have different lateral strengths depending on the opening positioneven if the walls have the same opening area.
Keywords: Structural Walls, Openings, Lateral Strength, Lateral Stiffness

INTRODUCTION
A frequent problem in the seismic design of RC structural walls is how to consider the effect of
openings (such as doors, windows or holes for ducts of conditioner air, or electrical installation) in thestrength and lateral stiffness of the walls since it suggests that those structural characteristics will
undergo a reduction or high stress concentrations could occur around the openings. Furthermore, theconsideration of the openings effect in the walls seismic design is a big issue independently of the typeof material that is used to build the walls. In addition, the fact that El Salvador is a tropical country
with high temperatures and humidity, lead to houses or dwellings with large opening sizes forventilation, which clearly affects the structural behavior of the dwellings or buildings. This situation in
El Salvador shows the importance of taking into account the effect of the openings in the structural
capacity not only in RC structural walls but also in masonry structures.

REINFORCED CONCRETE (RC) STRUCTURAL WALLS WITH OPENINGS.
THEORETICAL BACKGROUND
The Architectural Institute of Japan (AIJ) has two Guidelines for Reinforced Concrete Structures, oneof them based on the Ultimate Strength Concept (AIJ Design Guidelines for Earthquake ResistantReinforced Concrete Buildings, 1990) and the other one based on the Allowable Stress Design (AIJStandard Calculation). On the Guidelines based on the Ultimate Strength concept a lateral strength*

Centroamericana Jose Simeon Cañas University-UCA-El Salvador.
Building Research Institute-BRI.

**1

equation taking into account the truss and arch mechanism is proposed to estimate the lateral strengthof RC walls without openings. A method to calculate the reduction in the strength and stiffness due toopenings is no specified in this guideline. On the other hand, the AIJ Standard Calculation proposes
reduction factors to take into account the effect of openings in both lateral strength and lateral stiffness,so it is common that the Japanese Designers or Researchers combine the two guidelines, and to apply
the strength reduction factors presented in the AIJ Standard Calculation to the lateral strength equation
proposed for walls without openings in the AIJ Guidelines based on the Ultimate Strength Concept.
The value of the strength reduction factor “r” shall be the lower value among three reductions factors
called “r1”, “r2” and “r3”. These reduction factors consider the opening dimensions but not the opening
positions. In the case of the elastic stiffness a reduction factor “r” is presented in the AIJ Standard
Calculation. On the other hand in the American Concrete Institute Code (ACI-318 Code) a lateralstrength equation taking into account the concrete and steel reinforcement contribution is proposed for
RC structural walls without openings. But when an opening is placed on RC walls, the ACI code does
not propose any reduction factors for both the strength and the stiffness of RC walls with openings.
Also regarding the stiffness for RC walls with openings Neuenhofer (2006) presents a hand method
procedure to calculate the lateral stiffness of cantilever walls with an opening.
MODELING RC STRUCTURAL WALLS WITH OPENINGS IN DIANAOne solid RC wall and fifteen RC walls with openings are modeled in DIANA. Beforehand, a solid
wall was designed according to the requirements and equations established for walls seismic design in
ACI Code. In ACI Code, the chapter 11, chapter 14 and chapter 21 contain the sections related tostructural wall design. Both the wall length and wall height are 3000mm (3m), therefore the wall
slender (hw/lw) ratio is 1. The wall thickness is 150mm (0.15m). The figure 1 shows the details
reinforcement for solid wall and edge members. The properties materials are a concrete compressive
strength of 20.6MPa and a steel yield stress of 275 MPa; both properties are used to model in DIANA.
Wall Reinforcement:
Transversal: 8 bars (φ=15.24mm) spaced at
450mm
Longitudinal: 7 bars (φ=15.24mm) spaced
at 450mm
Edge member reinforcement:
Transversal: Hoops (φ=15.24mm) spaced
at 100mm
Longitudinal: 10 bars (φ=15.24mm)

Figure 1 Details of Wall Reinforcement
The lateral strength of solid wall was predicted using the seismic codes. According to ACI lateralstrength equations, the solid walls strength is 564 kN and using a strength reduction value of 0.6 thelateral strength is 339 kN. It is important to say that such strength reduction factor is not for openings,
the philosophy of the factor is due to the fact of safety reasons in the design. According to AIJ
Guideline equation the lateral strength value is 579 kN. Regarding to the model in DIANA of the
fifteen specimens with openings, the materials and geometric properties used in the modeled are thesame as those used for the solid wall. The table 1 shows the information of each specimen. The solid
wall was taken as base of the analysis in comparison with the walls with openings. The openings
reinforcement consists in to replace around the openings the same volume of reinforcement locatedwithin the openings area. Thus, the specimens with opening area ratio of 11.11%, 22.22%, 30% and
44% were reinforced with a steel volume around them of 1.2x10-3 m3, 2.2x10-3 m3, 3.02x10-3 m3 and4.0x10-3 m3 respectively.

2

Table 1 RC walls with openings modeled in DIANATo calculate the lateral strength of walls with
openings the strength reduction factors proposed
by AIJ Standard Calculation were applied to thesolid wall strength determined by ACI Code and
AIJ Guideline. To calculate the stiffness of walls
two methods were used, one consists in to apply
the stiffness reduction factor due to openings of
AIJ Standard Calculation to the elastic solid wall
stiffness; and the other one is the hand method
procedure mentioned in the previous section. By
using DIANA the capacity curves of all
specimens were obtained. The analytical results
together with the DIANA simulations arecompared and discussed in the next section.
DISCUSSION
For the walls with openings, it is notable that thelateral strength equations of AIJ Guideline and
ACI Code predict the same strength for wallswith same opening area ratio and those equations
do not take into account the effect of the variationof opening position in the wall. The same
situation happens when the stiffness is predictedby analytical methods (for instance the AIJ
Guideline stiffness reduction factor) and later compared with the stiffness in DIANA. The strength andstiffness reduction factors do not take into account the effect of the variation of opening position in thewalls. For instance, the specimens O11B, O11M and O11U (see chart 1 below) with same opening
ratio of 11.11% but different opening position have the same strength value predicted by AIJ
Guideline and ACI Code, 386 kN and 226 kN respectively. In comparison with DIANA results, thethree specimens reached different strengths; the AIJ Guideline overestimated the strengths of the three
specimens and ACI Code is conservative for O11B but not so conservative for O11M and O11U. For
the stiffness values, the hand method procedure overestimated the stiffness of the specimens andpredicted the same value for three of them. The stiffnesses obtained by using the AIJ stiffness
reduction factor overestimated the stiffnesses of O11M and O11U, but predicted very well the O11B
stiffness (see chart 2 below). Both strength and stiffness values decreased when the opening is closer
to the upper part of the wall.

Chart 1 Capacity Curves of specimens O11B, O11M, O11U andlateral strengths values predicted by seismic codes equations

3

Chart 2 Stiffness behavior O11B, O11M,
O11U and stiffness predicted for solid wall

The same situation is seen when the specimens O22B, O22M and O22U are analyzed and comparedwith DIANA results. The difference is that for these specimens the AIJ Guideline is conservative for
O22B and O22M but not for O22U, on the other hand ACI Code is conservative for three of them (seechart 3 below). For the stiffness, the hand method procedure overestimated the specimens stiffness, butnow, also the AIJ Guideline overestimated the stiffness values (see chart 4 below). Again, bothstrength and stiffness values decreased when the opening is closer to the upper part of the wall.

Chart 3 Capacity Curves of specimens O22B, O22M, O22U
and lateral strengths values predicted by seismic codes
equationsChart 4 Stiffness behavior of
O11B,O11M,O11U and stiffness predicted forsolid wall

It is notable that when the opening height is increasing, both stiffness and strength decrease, it isunderstood when the results for O11B, O22DB and O30DB are compared. The wall behavior trends tobe more flexible when the opening height is increasing (see charts 5 and 6).

Chart 5 Capacity Curves of specimens O11B, O22DB and
O30DBChart 6 Stiffness behavior of O11B, O22DB
and O30DB

Another important issue, it is that mainly the seismic codes consider the openings on walls centeredand the analysis of not centered openings is not presented in codes. It was observed according to thestress distribution and cracking pattern obtained by DIANA that the behavior of specimens without
centered openings depend on the load condition (forward loading or backward loading). The principal
compressive stress distributions and cracking patterns of the specimens are presented in the fullversion of this investigation. For instance, the specimens O22NCD and O22NCD2 reached almost thesame lateral strength (see charts 7 and 8 on the next page), but O22NCD (forward loading) was more
flexible than O22NCD2 (backward loading), it is understood when the principal compressive stress
distribution is studied. Also the specimen O30NCD (forward loading) was more flexible than
O30NCD2 (backward loading), but in this case O30NCD2 reached a higher value of lateral strengththan O30NCD (see charts 9 and 10). On the other hand, the specimens O11NCW and O11NCW2
showed similar behaviors (see charts 11 and 12), not so big difference in the strengths, similar initialstiffness and rigid behavior.

4Chart 7 Capacity Curves of specimens O22DB, O22NCD,
O22NCD2 and lateral strengths values predicted by seismic
codes equations for themChart 8 Stiffness behavior of O22DB, O22NCD
and O22NCD2Chart 9 Capacity Curves of specimens O30DB, O30NCD,O30NCD2 and lateral strengths values predicted by seismic
codes equations for themChart 10 Stiffness behavior of O30DB,
O30NCD and O30NCD2Chart 11 Capacity Curves of specimens O11B, O11NCD,
O11NCD2 and lateral strengths values predicted by seismic
codes equations for themChart 12 Stiffness behavior of O11B, O11NCD
and O11NCD2CONCLUSIONS
It is notable that only the Japanese Seismic Codes consider strength and stiffness reduction factors
when an opening is placed on RC structural walls. The others seismic codes are not so clear about this
topic especially in the stiffness calculation. During the investigation it was verified a strength andstiffness reduction when an opening is placed on RC walls. About DIANA, it is valid to say the5software can simulate experimental testing successfully; therefore the results obtained in DIANA canbe used as whether DIANA simulation is a real testing. Of course a real testing never can be
represented one hundred percent accurate by software.
The seismic codes do not take into account the opening positions in the calculation on thestrength; it was notable when walls with equal opening area ratio but different opening position
reached distinct strengths in DIANA and the seismic codes equations predicted same strength values
for them. It was found that for both strength and stiffness, the more critical position is when the
opening is closer to the upper part of the wall since the lowest values of strength and stiffness wereobtained in that case. The walls with openings showed a more flexible behavior in comparison with thesolid wall, and such flexibility was increased when the opening area ratio was increased.
In some cases walls with opening area ratio greater than 0.2 reached more strength than thestrength predicted by the codes equations, and some walls with opening area ratio less than 0.20
reached less strength than the strength predicted by the seismic codes equations. In most the specimens
the lateral stiffness was overestimated by using both the hand method procedure and the AIJ stiffness
reduction factor. Furthermore, it was seen that for walls with not centered openings and opening area
ratio greater than 0.2, the walls behavior depends on loading direction (forward loading and backward
loading). It was not the case for walls with not centered openings and opening area ratio less than 0.2
because the walls behavior was similar for both cases loading direction, forward and backward. Finallyaccording to cracking patterns and principal compressive stress distributions of the specimens
presented in the full version of this investigation, the walls damage was concentrated around the edges
and corners of the openings or in the piers located next to the openings.

ACKNOWLEDGMENT
I want to thank Dr. Taiki Saito my advisor. Special thanks to Haruhiko Suwada from BRI, he taught
me how to use DIANA software and supported me with helpful advises during my study.

REFERENCE
American Concrete Institute, 2005, Building Code Requirements for Structural Concrete andCommentary, ACI 318-05 and ACI 318R-05.
Architectural Institute of Japan, 1991, AIJ Standard Calculation for Structural Calculation of
Reinforced Concrete Structures, Revised Edition.
Architectural Institute of Japan, 1990, Design Guidelines for Earthquake Resistant Reinforced
Concrete Buildings Based on Ultimate Strength Concept.
Daniel, J.I., Shiu, K. N. and Corley, W. G., 1986, Journal of Structural Engineering, ASCE, 16601676.
DIANA version 8.1, 2002, TNO Building and Construction Research, Delft, The Netherlands.
Emin, M., and Altin, S., 2006, ACI Structural Journal, 701-709.
Girijavallabhan, Ch. V., 1969, Journal of Structural Engineering, ASCE, 2093-2103.
Johansson, M., 2000, Journal of Structural Engineering, ASCE, 190-199.
Kato, D., Kabeyasawa, T., Otani, S., and Aoyama, H., 1995, ACI Structural Journal, 495-500.
Neuenhofer, A., 2006, Journal of Structural Engineering, ASCE, 1846-1851.
Paulay, T., Priestley, M. J. N., 1992, 1st ed. John Wiley & Sons, Inc.
Penelis, G. G., Kappos, A. J., 1997, 1st ed. Taylor & Francis, Oxon, UK.
Yamada, M., Kawamura, H. and Katagihara, K., 1974, ACI SP-42, American Concrete Institute, 55978.

6