ISSN: (p); (e) AXIAL FORCE-MOMENT INTERACTION DIAGRAMS TO CALCULATE SHEAR WALL REINFORCEMENT

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1 AXIAL FORCE-MOMENT INTERACTION DIAGRAMS TO CALCULATE SHEAR WALL REINFORCEMENT Hamed Dabiri 1 *, Ahmad Kaviani 1, Ali Kheyroddin 1 1 Department of Civil Engineering, Semnan University, Semnan, Iran *(corresponding Author: Hamed Dabiri h.dabiri2010@gmail.com) ABSTRACT One of the most important resistant systems which are used in concrete structures is moment resisting frames. One of the defects of this type of resistant system is the great lateral drift, therefore concrete or steel shear walls are used to reduce lateral drift. Using resistance frame and shear wall together in a structure is known as dual system. Shear walls resist lateral forces due to earthquake or wind; therefore, calculation of shear walls dimension and reinforcement with few mistakes possible and in a correct way is very important. In this study, drawing axial forcemoment interaction diagrams to calculate shear wall reinforcement will be discussed. Uniform reinforcing approach based on ACI code was used to obtain equations which were independent of shear wall dimensions. Axial load-moment interaction diagrams are presented as results which can be used to calculate shear wall reinforcement. Mistake elimination and calculation speed increased are the most important benefits of these diagrams which are used to calculate shear wall reinforcement. KEYWORDS: Axial force-moment interaction diagram, longitudinal reinforcement, RC shear wall. INTRODUCTION Excising walls in a building are classified in two main groups: partition walls and structural walls. Partition walls are usually built in 10, 20 and 35 cm to separate building areas while structural walls are used to resist lateral and axial forces applied to structure and can be classified as three main groups [4]: a) Bearing walls: this type of walls, resist axial loads applied to the structure. b) Retaining walls: A retaining wall is a structure designed and constructed to resist the lateral pressure of soil when there is a desired change in ground elevation that exceeds the angle of repose of the soil [3]. c) Shear walls: this type of walls resist lateral forces applied to structure due to wind, earthquake, etc. They also may resist axial forces and are usually made of concrete, steel, wood and brick. Shear wall is a vertical RC 1 shell which is transversally and longitudinally reinforced so that the steel bars continue from the foundation to the top level of wall. RC shear wall perform as a cantilever beam which resist shear forces by bending deformation. Using shear wall in 30 to 40 stories buildings can be economical. In the buildings with more than 40 stories, shear wall width will be great to resist stresses of wind and earthquake loads how using it would not be economical. Shear walls can be classified as: cantilever shear wall, cantilever shear wall with boundary element and coupled shear walls [4]. As figure 1 show, shear wall reinforcement can be calculated in two main types: a) Boundary element Reinforcement b) uniform reinforcement Researches indicate that Boundary element reinforcement can have a better performance [4]. The novel goal of this study is to obtain axial force-moment interaction diagrams to calculate shear wall reinforcement according to ACI code. The main benefit of these diagrams is that they are free from shear wall dimensions (length, width and height) and depends on P u, M u, f y and f cc, which are axial load applied to the shear wall, moment applied to the shear wall, yielding strength of steel bars and 28 days strength of cylindrical specimen of concrete, respectively. 1 Reinforced Concrete Volume-3 (Special Issue 3) DAMA International. All rights reserved. 561

2 Figure1. types of shear wall reinforcement: a) boundary element reinforcing b)uniform reinforcing[4] MATERIALS AND METHODS The procedure of obtaining dimensions free formulas and drawing axial force-moment interaction diagrams is presented in this section.as mentioned before, ACI code is used to calculate and draw axial force-moment interaction diagram. ACI code equations for shear wall reinforcing calculation are as following [1, 2,3]: Where: f cc: 28 days specified compressive strength of concrete (kg/cm 2 ) l w: shear wall length(cm) h: shear wall width(cm) A s : reinforcement area(cm 2 ) f y : yielding strength of steel(kg/cm 2 ) ρ: ratio of reinforcement area to shear wall section area As above mentioned formula shows, equations (1) and (2) depend on shear wall dimensions and to make them dimensions independent we have: Volume-3 (Special Issue 3) DAMA International. All rights reserved. 562

3 By replacing and,in the equation number (2) we will have: As equations (8) and (9) show, and are independent dimensions. A simple shear wall with certain dimensions is used to draw axial force-moment interaction diagrams. The shear wall reinforcement ratio ( ) is chosen from 1 to 4 (by the step of 0.25) and and Are calculated for each As concrete and steel parameters are changed in diffrenet countries and different conditions, f y and f cc are considered as table 1. Table1. f y and f cc considered for diagrams Diagram number f cc (kg/cm 2 ) f y (kg/cm 2 ) Volume-3 (Special Issue 3) DAMA International. All rights reserved. 563

4 Figure2.Interaction diagram forf y =2400 و kg/cm 2 f cc =200 kg/cm2 Figure3.Interaction diagram forf y =2400 kg/cm 2 fو cc =250 kg/cm 2 Volume-3 (Special Issue 3) DAMA International. All rights reserved. 564

5 Figure4. Interaction diagram forf y =2400 و kg/cm 2 f cc =300 kg/cm 2 Figure5.Interaction diagram forf y =2400 kg/cm 2 fو cc =350 kg/cm 2 Volume-3 (Special Issue 3) DAMA International. All rights reserved. 565

6 Figure6.Interaction diagram forf y =3000 kg/cm 2 و f cc =200 kg/cm 2 Figure7.Interaction diagram forf y =3000 kg/cm 2 و f cc =250 kg/cm 2 Volume-3 (Special Issue 3) DAMA International. All rights reserved. 566

7 Figure8.Interaction diagram forf y =3000 kg/cm 2 و f cc =300 kg/cm 2 Figure9. Interaction diagram forf y =3000 kg/cm 2 و f cc =350 kg/cm 2 Volume-3 (Special Issue 3) DAMA International. All rights reserved. 567

8 Figure10.Interaction diagram forf y =4000 kg/cm 2 و f cc =200 kg/cm 2 Figure11.Interaction diagram forf y =4000 kg/cm 2 و f cc =250 kg/cm 2 Volume-3 (Special Issue 3) DAMA International. All rights reserved. 568

9 Figure12. Interaction diagram forf y =4000 و kg/cm 2 f cc =300 kg/cm 2 Figure13. Interaction diagram forf y =4000 kg/cm 2 fو cc =350 kg/cm 2 Volume-3 (Special Issue 3) DAMA International. All rights reserved. 569

10 RESULTS AND DISCUSSION As mentioned before, the main goal of this study is to obtain axial force-moment interaction diagrams which are dimensions free with the purpose of calculating RC shear wall reinforcement according to ACI To find the shear wall reinforcement ratio, and shall be calculated and also f y and f cc shall be clarified (for example to calculate reinforcement of a certain wall with f cc =350 kg/cm 2 and f y =4000 kg/cm 2, diagram in figure13 shall be used). After finding the in the related diagram, reinforcement area will be obtained by multiplying the in the shear wall section area: This study has been done to reduce probable mistakes in the calculation procedure and also increase the calculation speed. It should be mentioned that obtained diagrams can be redraw, using different codes for each country with special code. REFERENCES ACI Committee 318 (1983). Building Code Requirements for Reinforced Concrete (ACI ), American Concrete Institute, Detroit ACI Committee 318, Structural Building Code. (2002). Building Code Requirements for Structural Concrete (ACI ) and Commentary, (ACI 318R-2002). Ching F. D., Faia R. S. and Winkel P. (2006). Building Codes Illustrated: A Guide to Understanding the 2006 International Building Code. 2th Ed. New York, NY: Wiley. Kheyroddin A. (2009). Analysis and design of shear walls. Volume-3 (Special Issue 3) DAMA International. All rights reserved. 570