Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4

311

ABSTRACT: This study is conducted to review the methods proposed by seismic codes in order to take account both of the concept of ductility and overstrength of structural elements. Otherwise, in order to assess how to take account of the overstrength in reinforced concrete structures, the factors that affect the overstrength and their possible sources are presented, and reinforced concrete building structures having moment resisting frames or mixed (frames + shear wall), are analyzed for their responses to lateral loading by applying the static non linear push-over analysis . These structures are assumed located in a region of high seismicity and are subject to lateral loads deducted from the European seismic code and are designed with the Algerian codes. The results of this study show the importance of the overstrength that has this type of structures in their ability to resist horizontal loads caused by earthquakes.

KEY WORDS: Reinforced concrete structure; Overstrenght; Base shear; Ductility; Pushover analysis; Code.

1. INTRODUCTION Past experience and observations of building behavior following severe earthquakes has shown that structural overstrength plays a very important role in protecting buildings from collapse [1, 2]. This is explained by the presence of such structures with significant reserve strength not accounted for in design. In the literature, several studies have been carried out in order to evaluate the effect of the overstrength on the seismic response of reinforced concrete (R/C) and steel moment-resisting framed buildings [1-7]. These studies have shown in their globality that the overstrength depends on different factors which the most important of them is member ductility factor. Recently, a study was conducted to investigate the overstrength factor of reinforced concrete frame irregular in elevation [7]. According to this study it is found that the geometry and ductility supply of the frames affect significantly the overstrength factor. The objective of this work tries to evaluate the overstrength factor of the R/C structures, having different geometric form in elevation and lateral force resisting structural system, through their seismic behavior by nonlinear static procedure or pushover analysis. Structural irregularities are commonly found in constructions and structures.

2. RELATION BETWEEN OVERSTRENGHT AND DESIGN STRENGHT

The overstrength, which is specified as member or structural capacity, is usually defined using overstrength factor, which may be defined as the ratio of maximum base shear in actuel behavior to first significant yield strength in structure. Figure 1 presents a typical relationship between base shear and top displacement of a structure [8-9]. The terms used in the figure are: Ve : elastic base shear, Vy : yield base shear, V1 : base shear at first plastic hinge and Vd : design base shear.

Figure 1. Definition of non-linear parameters.

3. ROLE OF OVERSTRENGHT IN SEISMIC CODES Many seismic codes permit a reduction in design loads, taking advantage of the fact that the structures possess significant reserve strength (overstrength) and capacity to dissipate energy (ductility) [4].

4. MAIN SOURCES OF OVERSTRENGTH The main sources of overstrength are reviewed in other researches [1-2]. These include: (1) the difference between the actual and the design material strength; (2) conservatism of the design procedure and ductility requirements; (3) load factors and multiple load cases; (4) accidental torsion consideration; (5) serviceability limit state provisions; (6) participation of nonstructural elements; (7) effect of structural elements not considered in predicting the lateral load capacity (e.g. actual slab width); (8) minimum reinforcement and member sizes that exceed the design requirements; (9) Redundancy of the structure and redistribution of forces

Accounting for ductility and overstrength in seismic design of reinforced concrete structures

Branci Taïeb_11, Bourada Sofiane_21

1Department of Civil Eng., Faculty of Engineering and Architectural, Hassiba Benbouali University of Chlef, Hai Es-Salam, BP. 151, Route de Senjas, 02000 Ech Chlef, Algeria

email: brancit@yahoo.fr, sofiane9500@yahoo.fr

V1

Ductility factor : μ = Ve/Vy

Overstrength factor :

Rs = Vy/V1 V1

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

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(stresses) between structural members; (10) strain hardening; (11) actual confinement effect; and (12) utilizing the elastic period to obtain the design forces.

5. DESCRIPTION OF THE MODEL STRUCTURES In this study three 6-storey moment resisting frame structures (regular and irregular in elevation) and one 6-storey frame-wall structure are assessed. The structures are designed and detailed in accordance with the Algerian seismic code (RPA 99/v.2003) [10] and Algerian code for concrete structures (CBA 93) [11]. The considered geometrical configurations are depicted in figure 2. The span length and the inter-storey height for all structures are equal to 5.0 m and 3.3 m, respectively. The member dimensions and reinforcements is provided in Table 1. The specified 28-day concrete compressive strength is 30 Mpa and the specified yield stress of the steel is 400 Mpa. The analysis of structures was carried out using SAP2000 software, which is a structural analysis program for static and dynamic analyses of structures [12]. The weights of the systems were assumed to consist of total dead load, Gk plus 20% of live load, Qk.

Figure 2. Geometry of the structures under investigation.

6. STATIC PUSHOVER ANALYSIS Static pushover analysis was performed to evaluate the ductility and overstrength of the structures under investigated. The four structures were subjected to an incremental static pushover analysis for the gravity and earthquake forces tributary to them. The gravity loads are held constant at their full value. The earthquake forces are assumed to be distributed along the height according to the provisions of EC8 [13]. The lateral forces were increased in suitable increments until a mechanism forms, or an interstorey

displacements goes past the design limit of 2% of the storey height. In the analysis it is assumed that the plastic hinges form only at the ends of the members. The moment-rotation relationship for a potential hinge is taken to be bilinear or elasto-plastic. The analysis includes an elastic and inelastic range. Inelastic range starts at the stage of first plastic hinge formation and ends when the mechanism is formed. The objective was to estimate the capacity curves, the overstrength factors and the ductility factors.

Table 1. Dimensions and the reinforcements of members.

Member Symbol

Dimensions (cm)

Longitudinal Reinforcement

C1 60x60 8-HD20 C2 45x45 8-HD16 C3 40x40 8-HD14 C4 50x50 12-HD20 C5 C6

45x45 40x40

12-HD16 12-HD14

B1 40x60 8-HD20 B2 40x50 8-HD20 B3 40x40 8-HD20

Wall 15x500 HD10

7. RESULTS OF PUSHOVER ANALYSIS The capacity curves (pushover curves), in terms of top displacement-base shear, are shown in figure 3. Each pushover curve is plotted until the displacement corresponding to the available capacity at near collapse limit state. In this study, analyses have been performed using SAP 2000 computer program. Maximum base shear in actual behavior, Vy, base shear relevant to formation of first plastic hinge, V1, overstrenght factor, Rs, ductility factor, µ, and behavior factor, R and q, for all structures under investigation are listed in Table 2. Displacement ductility is defined in terms of maximum structural drift and the displacement corresponding to the idealized yield strength. The behavior factors, R and q, are computed from table 4.3 in RPA and from table 5.1 in Eurocode 8 (for medium ductility class (DCM)), respectively. Code gives constant value of behavior factor, R, for all structures. The overstrength factor was found to be in the range of 1.29 to 2.33. Also, member ductility factors for the most critical beams and columns were plotted against calculated overstrength factors for all structures separately and are illustrated in figures 4 to 5. From this figure, it can be possible to obtain the overstrength factor directly using ductility factor.

Table 2. Summary of static pushover results.

Structures R (RPA)

q (EC8)

Vy (kN)

V1 (kN)

Rs=Vy/V1 μ

STR1 3.5 3.90 1800 1000 1.80 5.0 STR2 2.0 3.90 3500 1500 2.33 5.5 STR3 3.5 3.12 1350 1000 1.35 4.5 STR4 3.5 3.12 1100 850 1.29 4.0

STR3

C1

C2

C3

3 @ 5.0 m

C6

C5

C4

B3

B2

B1

STR2

3 @ 5.0 m

6 @

3.3

m

B3

B2

B1

C3

C2

C1

Wal

l

STR1

C3

C2

C1 C4

C5 B2

B3

B1

3 @ 5.0 m

C6

STR4

3 @ 5.0 m

C3

C2

C1

C6

C5

C4

B3

B2

B1

6 @

3.3

m

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Figure 3. Pushover curves of the structures under investigation : Base shear versus displacement.

8. DISCUSSION OF RESULTS Based on the results obtained above, the following conclusions were taken: 1- The overstrength factor, Rs, increases as the displacement ductility, μ, of the structures increases. 2- Structures with uniform profile in elevation (or regular) have more lateral load capacity compare to structures with non-uniform profile in elevation (or with setbacks). In other words, the structures with vertical geometric irregularity have lower demands than regular structures. 3- The behavior factor of the 6-storey regular structures calculated by EC8’s formula was much higher than the RPA value, while the opposite was observed for irregular structures. 4- For the same value of the ductility factor in all structures, the overstrength factor in the beams is higher than that in columns. In other words, the effect of beams ductility factors on overstrength factor is higher than columns ductility factors effect. 5- A comparison of overstrengths developed in the members show that overstrengths in resisting-moments frames are smaller than the corresponding ones in the frame-wall. In other words, the most rigid structures have the higher overstrength.

Figure 4. Overstrength-ductility relationship for structures under investigation.

Figure 5. Overstrength-ductility relationship for structures under investigation.

9. CONCLUSION In the present work the assessment of the performance of four reinforced concrete structures, with six stories and three bays, has been investigated through static non-linear (pushover) analyses. Two of these structures have irregularities in elevation. The results obtained from the pushover analyses leads to the following main conclusions: - The overstrength factor increases when the ductility of the frame increases. - The decrease in strength of the structure results in an decrease in overstrength. - The structures with vertical geometric irregularity have lower demands than regular structures.

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[2] A.S. Elnashai and A.M. Mwafy, Overstrength and force reduction factors of multistory reinforced concrete buildings.The structural design of tall buildings, 11(5).329-351, 2002.

[3] M.A. Rahgozar and J.L.Humar, Accounting for overstrength in seismic design of steel structures, Canadian Journal of Civil Engineering, pp.1-15, 1998.

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[4] R. M. Mahmoud and R. Akbari, Seismic behaviour factor, R, for steel X-braced and knee-braced RC buildings, Engineering Structures, Elsevier, 25 1505–1513, 2003.

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