REINFORCED CONCRETE SLABS DESIGN BASED UPON CONCRETE CODE OF IRAN (CCI) AND BRITISH STANDARD (BS) PROVISIONS

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1 CD REINFORCED CONCRETE SLABS DESIGN BASED UPON CONCRETE CODE OF IRAN (CCI) AND BRITISH STANDARD (BS) PROVISIONS O. Azadegan 1, M.A. Kazerooni 2 and M.J. Fadaee 3 1&2 Graduate Students 3 Associate Professor Civil Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran ABSTRACT One of the common methods for analyzing and designing two-way reinforced concrete slabs is the Moment Coefficients Method. In this paper, the Moment Coefficients Method for designing two-way slabs stated in the Concrete Code of Iran (CCI) is considered and compared with the same method stated in the British Standard (BS). For this purpose, the provisions recommended in the above mentioned codes are compared first, and then the differences are discussed. The effect of different provisions on determining the amount of the required steel for the slabs having different edge conditions is considered through a numerical study. In the end, the cases in which the use of a specific code gives conservative or economic results are concluded. Keywords: two-way slab, concrete code of Iran (CCI), British standard (BS), moment coefficient method, safety factors 1. INTRODUCTION Analysis of plates and shells to attain internal actions for designing structural elements is one of the fields that scientists and engineers have been working on for years. These attempts have led to some exact and approximate solutions. One of the approximate solutions which is used to analyse rectangular plates under uniform normal loads is the Moment Coefficients Method. This method is mostly used to analyze reinforced concrete slabs and helps one to find internal bending moments and shear forces by applying some coefficients. The amounts of these coefficients depends on slab supports conditions and the slab spans ratios. Moment Coefficients Method is a very restricted method but as it s rather simple to use, it has been mostly applied in analysis and design of concrete slabs. Each concrete design code has its own provisions for using Moment Coefficients Method. In this paper, the manner of using this method in CCI[1] and BS[2] codes is studied and compared to clarify which code leads to a more economical or conservative design.

2 326 / Reinforced Concrete Slabs Design Based Upon. 2. ANALISING SLABS BY MOMENT COEFFICIENTS METHOD The Moment Coefficients Method defines some coefficients to attain internal bending moments and shear forces. The amounts of these coefficients mainly depend on the ratio of the slab dimensions and the slab supports conditions. The larger the amount of the ratio of long span to short span the stiffer the short span becomes, and so it absorbs more energy. The moments would be calculated by the following relation: M 2 = C w l (1) in which, M is the maximum positive or negative internal moment of middle strip of the slab per unit length, C is the moment coefficient given by the code, w is uniformly distributed load and l is the span length. Based upon the code provisions, M is the maximum bending moment at the middle and is reduced linearly to one-third of this value at the sides as indicated in Figure 1. Figure 1.a is plotted based on CCI and Figure 1.b is plotted based on BS provisions. a b Figure 1. Schematic view of bending moment diagram 3. PARTIAL SAFETY FACTORS The partial safety factors which are used in both codes to attain ultimate loads are defined as follows: In CCI code: Ultimate dead load, D = 1.25 times service dead load, d Ultimate live load, L = 1.5 times service dead load, l In BS code: Ultimate dead load, D = 1.4 times service dead load, d Ultimate live load, L = 1.6 times service dead load, l Cited relations indicate that the ultimate loads in BS code are more conservative than the ultimate loads in CCI code.

3 3 rd International Conference on Concrete & Development / COMPARING THE MOMENT COEFFICIENTS To study the differences between the two codes, the differences of coefficients are studied first. In Figure 2 the ratio of CCI coefficients of negative moments to BS coefficients of negative moments are plotted versus the ratio of slab spans. The curves are related to the case of 4 continuous edges. Figure 2. Comparing coefficients of CCI and BS codes It can be seen that the value of coefficients for shorter span in CCI code is always more than in BS. But, for longer span CCI code decreases the coefficients values noticeably. For comparing effects of loads partial safety factors, dead load is assumed constant when the live load is varying (for dead load=5.75 kn/m 2 and live load varying from 1 to 7 kn/m 2 ) and the ratio of ultimate load in CCI on ultimate load in BS is plotted in Figure 3. Figure 3. Effect of live load on ultimate loads

4 328 / Reinforced Concrete Slabs Design Based Upon. As the variation of the cited ratio due to change of live load is negligible, the numerical study would be just done for a constant value of live load. The amount of long span to short span ratio would be changed to clarify its effect on designing results. 5. NUMERICAL STUDY A two-way slab having 150mm thickness is given in (Figure 4). The applied live load is supposed to be 2kN/m 2 and the dead load is taken as equal to 2kN/m 2 (the slab weight is not taken into account). This slab is designed having constant shorter span by the value of 4m when the longer span is 1.0, 1.1, 1.25, 1.42, 1.66 and 2.0 times the shorter span length, respectively. Figure 4. Slab view For a numerical study, both CCI and BS provisions are used and the analysis results are summarized in Table 1. Then the slab is designed upon both codes. Design results are given in Table 2 and compared in Table 3. This example would be solved by other supports condition. The values given in Table1 are the amounts of flexural moments calculated by using Table of CCI and Table 3.14 of BS which give moment coefficients values for analysis. Table 1 indicates that the CCI results, when the spans ratio gets close to 2.0, are almost identical to that of one-way slab. On the other hand, based upon BS provisions, the moment coefficients for shorter span do not change when the spans ratio varies. As the spans ratio gets closer to 2.0, BS presents a more economical design. Moreover, when the ratio gets closer to 1.0, BS would lead to a more conservative design. In the following tables, M - is the ultimate negative moment on slabs edges calculated by moment coefficients and given for both codes; M + is the ultimate positive moment at the middle of spans and given for both codes; and A s is the amount of flexural steel rebar area used in each case. The total A s given in Tables 3

5 3 rd International Conference on Concrete & Development / 329 and 6 would define the summation of whole rebar value which is used in slabs and is calculated by following relation: Total A s = (2A s (for M - on La) + A s (for M + on La) ) L A + (2A s (for M - on LB) + A s (for M + on LB) ) L B In which L A is the length of shorter span and L B is the length of longer one. Spans ratio Table 1: Analysis results Spans ratio Table 2: Rebar design results Table 3: Design comparison Spans ratio CCI/BS Total A s

6 330 / Reinforced Concrete Slabs Design Based Upon. To attain more reliable conclusions, the boundary conditions of the slab are changed. In the new conditions, only the longer spans are continuous. The analysis results are summarized in Table 4. The designing results and comparisons' ratios are given in Tables 5 and 6, respectively. The same as previous example, by using CCI provisions, obtained amounts show that the results would be close to the condition of one-way slab, when the spans ratio gets closer to 2.0. On the other hand, BS presents constant amount for shorter edge of span which means that shorter edge absorbs a greater amount of energy. As the spans ratio gets close to 2.0, BS presents a more economical design. However, when the ratio gets closer to 1.0, BS would lead to a more conservative design. Figure 5, indicates that the values of used steel amount ratio obey a uniform configure uration when spans ratio increases. Spans ratio to Y dir to Y dir to X dir Table 4: Analysis results to X dir to Y dir to Y dir to X dir to X dir Spans ratio Table 5: Rebar design results

7 3 rd International Conference on Concrete & Development / 331 Table 6: Design comparison Spans ratio CCI/BS (Total steel reinforcement) Figure 5: Variation of used steel amount ratio By the spans ratio of about 1.6, it seems that the ratio of CCI/BS total steel reinforcement would be more than one and indicated that BS provisions lead to a more economical design. 6. CONCLUSION In this paper, the Moment Coefficients Method for designing two-way slabs stated in the Concrete Code of Iran (CCI) is considered and compared with the same method stated in the British Standard (BS). As the numerical study shows, by changing the value of spans ratio in a two-way slab, the codes give a different result for the amount of steel flexural rebar. For the spans ratio about the codes lead to almost the same amount of steel rebar. For spans ratio more or less than the difference in steel amount increases as it is plotted in Figure 5. Obtained amounts show that by using CCI provisions, the results would be close to the results of one-way slab, when the spans ratio gets close to 2.0. On the other hand, BS presents constant amount for shorter edge of slab which means that

8 332 / Reinforced Concrete Slabs Design Based Upon. shorter edge absorbs a greater amount of energy. As the spans ratio gets close to 2.0, BS presents a more economical design. However, when the ratio gets closer to 1.0, BS would lead to a more conservative design. The maximum average variation occurs in span ratio of 1.0, for which CCI gives steel amount about 67 percent of the steel amount of BS. Therefore, it is very important to clarify the fundamental differences between two codes, to show which design is really safer or more economical. To define which code gives better provisions for slabs design the constructions and economical conditions must be considered. As CCI provisions give more economical results for spans ratio between 1.0 and 1.6, and more compatible with construction and economical conditions of Iran, would be more reliable to use. REFERENCES 1. British Concrete Standard, BS : 1997, ISBN Iranian Concrete Institude, concrete code of Iran (CCI), ISBN