High Rate-Dependent Interaction Diagrams for Reinforced Concrete Columns

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1 Amerian J. of Engineering and Applied Sienes 4 (1): 1-9, 2011 ISSN Siene Publiations High Rate-Dependent Interation Diagrams for Reinfored Conrete Columns 1 Taher Abu-Lebdeh, 1 Sameer Hamoush, 1 Wonhang Choi and 2 Moayyad Al Nasra 1 Department of Civil, Arhitetural and Environmental Engineering, North Carolina A and T State University, NC 27411, Greensboro, USA 2 Department of Engineering Tehnology, West Virginia University, Institute of Tehnology, Montgomery, WV 25136, USA Abstrat: Problem statement: There is a need to better understand the rate dependene behavior of reinfored onrete strutures in order to improve their response to impat and blast loads. Analysis and design of reinfored onrete strutures subjeted to seismi loadings has been reommended in many FEMA guidelines. However, reevaluation of design beomes extremely important in ases where large deformations are expeted suh as blast and impat resistant. Approah: This study presents a numerial model to evaluate reinfored onrete olumns submitted to high strain rates expeted for seismi, impat and blast loadings. The model utilizes dynami stress-strain response and onsiders the effet of strain rate on onrete strength; strain at peak stress; yield and ultimate strength of steel; and slope of the softening portion of the stress-strain urve. Results: Results are presented in the form of interation diagrams and ompared with the available analytial and experimental results. Comparison with available data shows that the proposed model an give onsistent predition of the dynami behavior of reinfored onrete olumns. Conlusion/Reommendations: The established interation diagrams may be used to design olumns to withstand high veloity impat loads. Also, knowledge gained an be used to improve dynami behavioral models and omputer-aided analysis and design of reinfored onrete olumns subjeted to severe blast loadings. Key words: High strain rate, interation diagrams, stress-strain urves, Dynami Inrease Fator (DIF), axial-flexural strength, reinfored onrete olumns, analytial model, veloity impat loads, analysis and design, dynami stress-strain, different strain rates INTRODUCTION Analysis and design of reinfored onrete strutures subjeted to seismi loadings has been reommended in many building odes. However, high veloity impat loads resulted from blast are different. These loads are applied over a signifiantly shorter period of time than seismi loads. Thus, material strain rate effets beome ritial and must be aounted for in prediting olumns performane for short duration loadings suh as impat and blast loadings. Many experimental researh results were reported in the area of ompressive and tensile strength of onrete at different strain rates (Abu-Lebdeh et al., 2010; Ravihandran et al., 2009; Kotsovos, 1983). A seletion of the ommonly published results is also reported by Saravanan et al., 2010; Bishoff and Perry, 1991; and Malvar and Crawford (1998) as presented in Fig. 1 and and Fig. 2. Analyzing these two figures, it may be notied that for both ompressive (Fig. 1) and tensile loading (Fig. 2), there exist two intervals with different strain rates. For onrete in ompression (Fig. 1) the first mode orresponds to a range of variations of strain rate ranging between έ = 10-6 se 1 and έ < 10 se 1 leading to 1.5 times inrease of the resistane in ompression. The seond mode for whih the strain rate ranges from έ > 10 se 1 to έ = 103 se 1 allows to multiply by four where the resistane of the onrete is onsidered to be of strutural origin. A model for strain rate dependene of onrete in tension and ompression is presented in the Committee Euro-International Conrete (1993) Model Code In this model, the hange in a moderate dynami inrease fator into the more dramati one is set to a strain rate of 30 se 1. Many experimental and analytial researh results were reported in the area of dynami stress-strain response of reinfored onrete members under monotonially inreasing loading (Sott et al., 1982; Grote et al., 2001; Ngo et al., 2007; Masti et al., 2008). Sott et al. (1982) onduted experimental and analytial investigations on the behavior of short reinfored onrete olumns subjeted to ompression at low strain rates, έ, that are ranging Corresponding Author: Taher Abu-Lebdeh, Department of Civil, Arhitetural and Environmental Engineering, North Carolina A&T State University, 1601 E. Market Street, NC 27411, Greensboro Tel: (336) ext. 664 Fax: (336)

2 Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 Fig. 1: Strain rate effets on the onrete ompressive strength (Bishoff and Perry, 1991) Fig. 2: Strain rate effets on the onrete tensile strength (Malvar and Crawford, 1998) from se 1 (stati loading) to se 1 (seismi loading). Their results are shown in Fig. 3. Although the experimental results of Sot et al. show the strain rate effet on stiffness before the peak, their analytial model appears to ignore this effet. Urgessa, 2009 investigated omposite hardened walls subjeted to blast Loads and Zaidi et al., 2010 develop an empirial predition formula for penetration of hard 2 missile into Conrete Targets. Grote et al. (2001) onduted Split Hopkinson Pressure Bar (SHPB) experiments whih involve strain rates between 250 and 1700 se 1. They reported that the load-arrying apaity of the onrete inreases signifiantly with strain rate and hydrostati pressure. Ngo et al., 2007 studied stress-strain urves of onrete subjeted to high strain rates, έ, ranging from se 1 (quasi-

3 stati strain rate) to 264 se 1. They also show the experimental work of Gary and o-worker on the stressstrain urves of onrete at very high strain rates ranging from stati loading to 700 se 1. Nagaradjane et al., 2009; Nagaradjane, et al., 2009; and Soroushian and Obaseki, 1986 investigated the strain rate effets on the axial-flexural strength of reinfored onrete setions. Parviz reported an average of 25% inrease in axial-flexural apaity of retangular setions under strain rate of 0.5 se 1 over the orresponding apaity under quasi-stati strain rates. MATERIALS AND METHODS Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 This study deals with the response modeling of onrete under high rate dynami loadings. The model utilizes dynami stress-strain response and apable of apturing the important features of the onrete material submitted to high strain rates. It aounts for the Dynami Inrease Fator (DIF) of onrete, whih is the ratio of the dynami strength to the stati strength, ultimate strength of onrete and its orresponding dynami strain. The DIF of onrete an be as high as 4 in ompression and up to 6 in tension for strain rates in the range of se 1 (Sezen and Moehle, 2006). Based on experimental and analytial data reported by different researhers (Bishoff and Perry, 1991; CEB-FIP, 1993; Ngo et al., 2007; Saravanan et al., 2010; Abu-Lebdeh et al., 2010) the proposed strength inrease fator (k d or DIF) an be presented as indiated in Eq. 1 and 2 and shown in Fig. 4 and 5: Fig. 3: Stress-strain diagrams for reinfored onrete speimens submitted to failure at low strain rates (Sott et al.) a ε k d = for ε s ε 50 ε s 1 s (1) 036 ε k d =β for ε> 50 ε s Where: k d = Dynami inrease fator for onrete έ = Strain rate (1 se 1 ) έ s = se 1 (quasi-stati strain rate) α = β = 0.228(f ) (f ) 1 s (2) f = Conrete stati ompressive strength in MPa (145 psi) Dynami properties of reinforing steel: Both the yield and ultimate stresses of reinforing bars inrease with an inrease in strain rate, however, the ultimate stress inrease is less signifiant than that of yield stress. Malvar (1998) studied the effets of high strain rates on strength enhanement of steel reinforing bars. 3 Fig. 4: Dynami Inrease Fator of onrete (1 Mpa = 145 psi) The strength enhanement was desribed in terms of the Dynami Inrease Fator (DIF) whih an be evaluated for different steel grades and for yield stresses between 42 and 103 ksi (290 and 710 MPa). He onluded that the Dynami Inrease Fator depends on the grade of steel and that the DIF for both yield and ultimate stress is inversely related to the yield stress itself. In the present study, the experimental data reported by different researhers and summarized by Malvar (1998) is used to formulate the DIF for both yield and ultimate stress. It was notied that the date an be approximated by a straight line when log (DIF) versus log (έ) plot is used. The logarithm straight line equation is derived to formulate the proposed DIF as given in Eq. 3 and 4 for both yield and ultimate stress, respetively:

4 Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 k(1 10)() y y + γ ε (3) k(1 u + 10)() γ ε λ (4) 2 2ε ε f = k f for ε ε d d εd εd (5) Where: K y,k u = Dynami inrease fator for steel yield stress and ultimate stress respetively γ = and for grades 40 and 60 respetively λ = and for grades 40 and 60 respetively Stress-strain relationship of onrete under highstrain rates: The dynami stress-strain relationship an be established for a given strain-rate. To aurately predit the stress-strain behavior of onrete under high strain rate, the model should onsider the following fators: (1) onrete strength at a given strain rate, (2) strain at peak stress and (3) softening slope of the desending branh. Several onrete models have been proposed based on existing experimental evidene. Kent and Park (1971) have proposed the stress-strain urve in Fig. 6 for onrete onfined by retangular hoops. The asending part of the urve is represented by a seond-degree parabola and assumes that the maximum stress reahed by the onrete is the ylinder strength f. The parameter Z in the urve defines the slope of the desending portion. This slope is speified by the strain at stress of 0.5f. In region CD (Fig. 6), the equation f = 0.2f aounts for the ability of onrete to sustain some stresses at very large strains. Although, their model ombines many of the features of the previously proposed urves, it is not appliable for dynami loadings. On the basis of the Kent and Park (1971) model, Sott et al. (1982) developed a strain-rate dependent model for onfined onrete and inluded the effet of strain rates on the dynami properties of the stress-strain relationship. The Sott model was based on a relatively low strain rate data ranging from a quasi-stati rate of se 1. Based on alibration of Grote et al. (2001) experimental data whih involved high veloity impat tests using Hopkinson Bar apparatus, the authors revised Kent and Park and Sott models to inlude the effet of very high strain rates on the stress-strain relations. A new strainrate dependent model is proposed herein for onrete under impat and blast loadings. It onsiders the effet of strain rate on onrete strength; strain at peak stress; and slope of the softening portion of the stress-strain urve. The proposed model is desribed by Eq. 5-9 and is ompared with the available experimental and analytial results shown in Fig. 7 and 8: 4 f = k f Z ( ε ε )for ε>ε (6) d d d d The peak stress, f in Kent and Park model (Fig. 6) inreases to f to inlude the effet of high strain rate. The strain at peak stress is also inreased to ε d whih is strain-rate dependent, as shown in Eq. 7: d ε ε = 1.08e ε (7) Where: ε d = The dynami strain at peak stress ε = The stati strain = 1.75f / EC E = The modulus of elastiity of onrete Fig. 5: Dynami Inrease Fator for yield stress of reinforing steel Fig. 6: Kent and Park Model for onrete under stati loading

5 Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 Table 1: Parameters of the proposed model Parameter Kent model (Fig. 6) Proposed model Peak stress f k d f (Eq. 1 and2) Strain at peak stress ε d (Eq. 7) Maximum strain ε 20u ε max (Eq. 9) stress at maximum strain 0.2 f f d (Eq. 10) Softening slope Z Z d (Eq. 8) f = 0.15k f (10) d 2 d Fig. 7: Stress-strain urves of onrete at different strain rates Fig. 8: Stress-strain urves of onrete at high strain rates The equation for the linear desending portion of the stress-strain urve (Eq. 6) is given as a funtion of the dynami slope, Z d. This softening slope is determined based on the available experimental results (Grote et al., 2001; Ravihandran et al., 2009) and proposed as: Z ( ) d s d = f k f ( ) ε ε (8) +ε The proposed model assumes that the maximum strain, ε max is reahed when its orresponding stress level reahes f d (Similar to f = 0.2f in Kent and park model for unonfined onrete (Fig. 6)). The proposed maximum strain and its orresponding stress are also strain-rate dependent as shown in Eq. 9 and 10. Table 1 summarizes the parameters of the proposed model with their orresponding values in Kent and park model: kf f d d ε max = +ε d (9) Zd 5 Strain rate-dependent axial-flexural model: The main goal of this study is to investigate the strain rate effets on the behavior of reinfored onrete olumns subjeted to different strain rates ranging from quasistati loading to 700 se 1 (expeted for impat and blast loadings) to develop reinfored onrete onstitutive model apable of produing interation diagrams for dynami loadings. The proposed model is derived on the basis of the modeled dynami stressstrain relationships for onrete and steel and on the assumptions that the strain distribution is linear; the deformed setion remains plane; and perfet bond between the steel and onrete. The axial load and moment arrying apaities of the reinfored onrete setions are determined from the requirements of strain ompatibility and equilibrium of fores by varying the loation of the neutral axis. The urvature is the ompressive strain divided by the depth of the neutral axis. Effet of strain-rate on dutility: Dutility is a desirable feature of any strutural design as it safeguards a struture against unpredited overloading and/or load reversal. It is generally measured by the dutility fator whih is the ratio of the ultimate deformation to that at the first yielding of steel reinforement. It an be evaluated at the struture level (displaement dutility), member level (rotational dutility) and at the ross-setion level (urvature dutility). In the present study, dutility fator is defined as: DF φ u = (11) φ y Where: φ y = The urvature at the initial yielding of the steel φ u = The urvature orresponding to a moment equal to 80% of Mu This is beause the maximum usable deformation is the deformation at whih the resistane deays to 80% of resistane at ultimate.

6 Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 RESULTS Stress-Strain relationship of onrete under highstrain rates: Comparing the analytial and experimental data (Fig. 7 and 8), the proposed model an give onsistent predition of the dynami behavior of onrete materials. Figure 7 shows omparison between the proposed stress-strain relationship and Ngo et al. (2007) for strain rates ranging from stati loading to 264 se 1. The effet of very high strain rates (up to 700 se 1 ) is shown in Fig. 8 and ompared with the experimental results of Gary et al reported by Ngo et al. (2007). As shown in these figures, peak stress and its orresponding strain inrease with strain rates. Moreover, the elasti modulus inreases slightly. This moderate enhanement of the elasti modulus may be due to the derease in internal miroraking at a given stress level with an inreasing strain rate. Strain rate-dependent axial-flexural model: Results of the proposed model are presented in the form of interation diagrams for different strain rates. Figure 9 shows the proposed interation diagrams that were obtained for retangular onrete setions using the method desribed earlier. A omparison with the experimental and theoretial strain rate-dependent interation diagram is shown in Fig. 9a and b. It should be mentioned that the theoretial model proposed by Parviz and Obaseki follows the fiber modeling onept to ompute the axial and flexural resistane of a reinfored onrete setion at low strain rate (up to 0.5 se 1 ). In the present study, the approximate ranges of the expeted strain rates for different loading onditions were used to produe the interation diagrams shown in Fig. 10a, b. The quasi-stati rate is given as ε= se 1 and ompared with the ACI formulation, while ε of 0.05 and 0.5 se 1 were seleted for strain rates expeted under seismi loading, ε of 5, 50 and 100 se 1 for impat loadings and ε of 350, 500 and 700 se 1 for high veloity impat resulted from blast loadings. The ACI diagram shown in Fig.10 is based on quasi-stati tests in whih the rate of loading is of the order of se 1. Figure 10 indiates that inreasing the strain rate signifiantly inreases the axial-flexural apaity of the onrete setion. Influene of the longitudinal steel ratio: Figure 11 shows the influene of reinforement ratio at different strain rates for reinfored onrete setions with the same geometry and same steel positions, but with different reinforement ratios of 1, 3 and 5% respetively. 6 (a) (b) Fig. 9: Comparison of the proposed strain ratedependent interation diagram with the experimental and theoretial results Influene of the longitudinal steel position: Figure 12 ompares the interation diagrams of a olumn setion at four different strain rates /s, 0.5/s, 10/s and 250/s representing loading onditions from stati to blast loadings. Three different γ values of 0.6, 0.7 and 0.8 were used. γ is defined as the ratio of the enter to enter spaing of the extreme steel layers to the height of the setion. Effet of strain-rate on dutility: The proposed strainrate dependent model for onrete is used herein to investigate the effets of high strain-rate on the flexural apaity and dutility of reinfored onrete members (Fig. 13 and 14). The axial load and moment arrying apaities are determined from the fore equilibrium and the urvature is the ompressive strain divided by the depth of the neutral axis. Figure 14 shows the Dutility Fator (DF) with varying strain rates for three different steel positions. The dutility fator is alulated at axial load of 40% of the axial load arrying apaity.

7 Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 (a) Fig. 12: Influene of reinforement position on the strain rate effet (b) Fig. 13: M-Φ Curves of a ross-setion of a olumn at different strain rates. Fig. 10: Comparison of the proposed and the ACI interation diagrams (reinforement ratio, ρ s =1%) (a) Low strain rate; (b) High strain rate Fig. 14: Effet of strain rate and onfinement on the dutility of onrete olumns Fig. 11: Influene of reinforement ratio on the strain rate effet 7 DISCUSSION Strain-rate dependent onrete model: Examining Eq. 1-2 and Fig. 4, we an distinguish two different intervals with different strain rate dependenies: the

8 Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 first interval orresponds to a range of variations of strain rate ranging between the quasi-stati έ = se 1 and έ < 50 se 1 leading to DIF of 1.35 and 1.17 for onrete strengths of 4350 psi (30 MPa) and 10,150 psi (70 MPa) respetively. The inrease in strength for this interval is moderate inrease. Researhers agree on the explanation for suh strength inrease pertinent to a material visosity (Rossi, 1991), that is visous effets with free water in the miropores. The seond interval for whih the strain rate έ > 50 se 1 up to έ = 10 3 se 1 allows to multiply by four the strength of the onrete. The inrease in strength for this interval is sharp inrease. Explanations for this behavior an mainly be asribed to inertia effets and lateral onfinement. When onrete ylinder is subjeted to stati ompressive loading, it exhibits lateral expansion due to the effet of Poisson s ratio; also, the behavior will be affeted by the propagation of miroraks. However, when subjeted to rapid axial loading, the time available for initiation and propagation of miroraks will be redued. Moreover, the material will not be able to expand in the radial diretion at an instant due to inertial restraint. This lateral onfinement will initially leave the speimen in a similar stress state as that of uniaxial strain with orresponding lateral stresses. Thus, result in a substantial inrease in ompressive strength. Influene of the longitudinal steel ratio: It an be onluded from Fig. 11 that for strain rates ranging from quasi-stati to έ=75/s, the perent inrease in axial-flexural apaities is not influened by the longitudinal steel ratio. For the three ratios shown in Fig. 11, inreasing the strain rate from /s (stati loading) to έ = 75/s (breaking point) results in an average inrease of 60% in axial-flexural apaity. However, for strain rates higher than 75/s, the lower the steel ratio the higher the perent inrease in axialflexural apaity. At high strain rate (έ=500/s, for instane) ompared to those apaities under stati loading, it an be observed from Fig. 11 that the inrease in axial-flexural strength may reah 195%, 170% and 150% for reinforement ratios of 1%, 3% and 5% respetively. Influene of the longitudinal steel position: From Fig. 12, it an be observed that: for eah strain rate, the average inrease in axial-flexural apaity at e/h of 0.45 is 35, 50 and 95% for γ values of 0.6, 0.7 and 0.8 respetively. This inrease in apaity with γ may be due to the resulting inrease in onfinement. Effet of strain-rate on dutility: As shown in Fig. 13 the flexural apaities of a reinfored onrete olumn 8 were signifiantly inreased due to the inrease in yield strength of steel and ompressive strength of onrete at high strain rate. Moreover, beause the dynami strain orresponding to ompressive strength inreases with strain rate, onsequently, urvature and bending moment arrying apaity will inrease. For the three steel positions (Fig. 14), the Dutility Fator (DF) inreases with strain rate up to 75 se 1. This is beause of the fat that as the strain rate inreases, the ompressive strength and the orresponding strain inrease, hene both the flexural apaity and the urvature inrease. Moreover, the ultimate strain of the onrete setion inreases, onsequently, the tensile reinforement steels undergo strain hardening range resulting in inrease in the bending moment arrying apaity and the dutility. However, for strain rates higher than 75 se 1, the rate of inrease of the urvature at first yielding of reinforement is larger than that at the maximum urvature, resulting in derease in the dutility fators. CONCLUSION Based on this study, the following onlusions may be drawn: Comparison with available test results shows that the proposed model an give onsistent predition of the dynami behavior of onrete materials. However, for more aurate estimation of the P-M interation diagrams, more strain rate-dependent experimental tests are needed A Dynami Inrease Fator (DIF) of 1.35 was determined for onrete at strain rates of έ = 50 s 1. In the seond interval, a fator of four is used for έ = 10 3 s 1 Both the yield and ultimate stresses of reinforing bars inrease with an inrease in strain rate. The ultimate strength inrease is less signifiant than that of yield strength Inreasing the strain rate signifiantly inreases the axial-flexural apaity of the onrete setion due to the signifiant inrease in strength of onrete and steel reinforing bars. Inreasing the strain rate from /s to έ = 75 se 1 results in an average inrease of 60% in axial-flexural apaity. For strain rates higher than 75 se 1, the inrease in axial-flexural strength may reah 195% The strain rate effet is influened by the position of the longitudinal steel. Plaement of steel loser to extreme ompressive and tensile layer, inrease the strain rate effets. For a typial onrete

9 Am. J. Engg. & Applied Si., 4 (1): 1-9, 2011 setion, an average inrease in axial-flexural apaity of 35, 50 and 95% were determined for γ values of 0.6, 0.7 and 0.8 respetively The proposed model assumes perfet bond between the steel and onrete, hene, it does not onsider the strain rate effets on the rebar/onrete interfae behavior. To better understand this behavior and its effet on the interation diagrams, more high strain rate-dependent experimental tests are needed ACKNOWLEDGMENT The researhers would like to graiously thank the Defense Threat Redution Ageny (DTRA) for funding of this researh. REFERENCES Abu-Lebdeh, T., S. Hamoush and B. Zornig, Rate effet on pullout behavior of steel fibers embedded in very-high strength onrete. Am. J. Eng. Applied Si., 3: DOI: /ajeassp Bishoff, P.H. and S.H. Perry, Compressive behavior of onrete at high strain rates. Mater. Strut., 24: DOI: /BF Committee Euro-International Conrete, CEB- FIP model ode 1990: design ode. 1st Edn., Thomas Telford, Switzerland, ISBN: pp: 437. Grote, D.L., S.W. Park and M. Zhou, Dynami behavior of onrete at high strain rates and pressures: Experimental haraterization. Inter. J. Impat Eng., 25: DOI: /S X(01) Kent, D.C. and R. Park, Flexural members with onfined onrete. J. Strut. Div. ASCE., 97: Kotsovos, M.D., Effet of testing tehniques on the post-ultimate behavior of onrete in ompression. Mater. Strut., 16: DOI: /BF Malvar, L.J. and J.E. Crawford, Dynami inrease fators for onrete. Proeeding of the 28th Department of Defense Explosives Safety Seminar (DDESB), Aug , ANSI Std, Orlando, pp: &AD=ADA Malvar, L.J., Review of stati and dynami properties of steel reinforing bars. ACI Mate. J., 95: Masti, K., A.A.B. Maghsoudi and R. Rahgozar, Nonlinear models and experimental investigation of lifetime history of HSC flexural beams. Am. J. Applied Si., 5: DOI: /ajassp Nagaradjane, V., P.N. Raghunath and K. Suguna, Reliability of axially loaded fibre-reinforedpolymer onfined reinfored onrete irular olumns. Am. J. Eng. Applied Si., 2: DOI: /ajeas Ngo, T., P. Mendis, A. Gupta and J. Ramsay, Blast loading and blast effets on strutures-an overview. EJSE Int. J. Load. Strut., Speial Issue: l/ pdf Ravihandran, A., K. Suguna and P.N. Ragunath, Strength modeling of high-strength onrete with hybrid fibre reinforement. Am. J. Applied Si., 6: DOI: /ajassp Rossi, P., A physial phenomenon whih an explain the mehanial behavior of onrete under high strain rates. Mater. Strut., 24: DOI: /BF Saravanan, J., K. Suguna and P.N. Raghunath, Confined high strength onrete olumns: An experimental study. Am. J. Eng. Applied Si., 3: DOI: /ajeassp Sott, B.D., R. Park and M.J.N. Priestley, Stressstrain behavior of onrete onfined by overlapping hoops at low and high strain rates. Strut. J. ACI., 79: etails.asp?home=jp&id=10875 Sezen, H. and J.P. Moehle, Seismi tests of onrete olumns with light transverse reinforement. ACI Strut. J., 103: atdetails.asp?id=18236 Soroushian, P. and K. Obaseki, Strain ratedependent interation diagrams for reinfored onrete setions. ACI J., 83: etails.asp?home=jp&id=1751 Urgessa, G.S., Finite element analysis of omposite hardened walls subjeted to blast loads. Am. J. Eng. Applied Si., 2: DOI: /ajeassp Zaidi, A.M.A., Q.B.A.I. Latif, I.A. Rahman and M.Y. Ismail, Development of empirial predition formula for penetration of ogive nose hard missile into onrete targets. Am. J. Applied Si., 7: DOI: /ajassp