ISSN: 2319 - Sciencesciencejournal.in/data/documents/Life-Sci.-Special-Issue...Building Code Requirements for Reinforced Concrete (ACI 318-83), American Concrete Institute, Detroit

ISSN: 2319–4731 (p); 2319–5037 (e)

Volume-3 (Special Issue 3) 2014 www.sciencejournal.in © 2014 DAMA International. All rights reserved. 561

AXIAL FORCE-MOMENT INTERACTION DIAGRAMS TO CALCULATE SHEAR WALL

REINFORCEMENT

Hamed Dabiri1*, Ahmad Kaviani

1, Ali Kheyroddin

1

1Department of Civil Engineering, Semnan University, Semnan, Iran

*(corresponding Author: Hamed Dabiri +98-9124602510

[email protected])

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 force-

moment interaction diagrams to calculate shear wall reinforcement will be discussed. Uniform reinforcing approach

based on ACI 318-83 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 RC1 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 318-83 code. The main benefit of these diagrams is that they are free from shear wall dimensions

(length, width and height) and depends on Pu, Mu, fy and fcc, 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

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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 318-83 code is used to calculate and draw axial force-moment

interaction diagram. ACI 318-83 code equations for shear wall reinforcing calculation are as following [1, 2,3]:

Where:

fcc: 28 days specified compressive strength of concrete (kg/cm2)

lw: shear wall length(cm)

h: shear wall width(cm)

As: reinforcement area(cm2)

fy: yielding strength of steel(kg/cm2)

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:

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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, fy and fcc are considered as table 1.

Table1. fy and fcc considered for diagrams

Diagram number fcc (kg/cm2) fy (kg/cm

2)

1 200 2400

2 250 2400

3 300 2400

4 350 2400

5 200 3000

6 250 3000

7 300 3000

8 350 3000

9 200 4000

10 250 4000

11 300 4000

12 350 4000

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Figure2.Interaction diagram forfy=2400 kg/cm

2و fcc=200 kg/cm2

Figure3.Interaction diagram forfy=2400 kg/cm2fcc=250 kg/cmو

2

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Figure4. Interaction diagram forfy=2400 kg/cm2

و fcc=300 kg/cm2

Figure5.Interaction diagram forfy=2400 kg/cm2fcc=350 kg/cmو

2

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Figure6.Interaction diagram forfy=3000 kg/cm2

و fcc=200 kg/cm2


و fcc=250 kg/cm2

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و fcc=300 kg/cm2


و fcc=350 kg/cm2

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و fcc=200 kg/cm2


و fcc=250 kg/cm2

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و fcc=300 kg/cm2

Figure13. Interaction diagram forfy=4000 kg/cm

2fcc=350 kg/cmو

2

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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 318-83. To find the

shear wall reinforcement ratio, and shall be calculated and also fy and fcc shall be clarified (for example

to calculate reinforcement of a certain wall with fcc=350 kg/cm2 and fy=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 318-83), American Concrete

Institute, Detroit. 111.

ACI Committee 318, Structural Building Code. (2002). Building Code Requirements for Structural Concrete (ACI

318-2002) 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.

Documents

ISSN: 2319 - Sciencesciencejournal.in/data/documents/Life-Sci.-Special-Issue...Building Code Requirements for Reinforced Concrete (ACI 318-83), American Concrete Institute, Detroit