Many reinforced concrete structures, such as bridges,

Transcription

1 Reliability analyses of interface shear transfer in AASHTO LRFD specifications model and an alternative model Mahmoodreza Soltani Many reinforced concrete structures, such as bridges, depend on the transfer of shear forces across concrete-to-concrete interfaces no or negligible moment is present. This phenomenon is explained by a theory called interface shear transfer (IST). One of the most common examples of IST occurs at the connection of precast concrete girders and cast-in-place concrete bridge decks (Fig. ). Composite action between the girder and deck, which is aided by the interface transfer of shear forces, results in bridge stiffness and strength. Previous research has shown that the interface-shear-transfer model of the AASHTO LRFD Bridge Design Specifications produces inconsistent levels of accuracy for different values of design variables. In this study, reliability analyses were performed on the AASHTO LRFD specifications model and an alternative model to evaluate and determine their resistance factors. The results of the reliability study showed that the alternative model performs better than the AASHTO LRFD specifications model. Soltani and Ross created a database from tests conducted between 99 and. This study showed that current code-based IST models produce inconsistent levels of accuracy for the ratio of experimental strength to nominal strength (bias factor) throughout the range of design variables. For example, bias factors in the IST model of the American Association of State Highway and Transportation Officials AASHTO LRFD Bridge Design Specifications were.9 and.8 (with and without resistance factor applied, respectively), and the model accuracy also varied significantly for different compressive strengths of concrete. Recognizing the limitations of the current AASHTO LRFD specifications based IST design model, Soltani et al. proposed a new IST design model developed through a multiple linear-regression analysis. Soltani et al. s revised IST model produced more accurate results and a bias factor of.9 with consistent levels of accuracy throughout the considered range of design variables. PCI Journal September October 8

2 Cast-in-place concrete deck A Horizontal shear at interface Shear interface Shear interface Cross section A-A Precast concrete girder A Figure. Graphic showing location of nterface shear transfer between precast concrete girder and cast-in-place concrete deck. The objective of the present study is threefold. First, the reliability level of the AASHTO LRFD specifications based model for predicting the nominal IST resistance is delineated based on the IST database created by Soltani and Ross. This is achieved by defining the mean and coefficient of variation of resistance and the load distribution models. Second, a resistance factor is determined for Soltani et al. s IST model to reach the AASHTO LRFD specifications reliability index target value of.. Third, this study illustrates the reliability indices in different intervals throughout the range of all IST design variables, including interface area of concrete A cv, interface shear reinforcement ρf y, compressive strength of concrete f c, roughness amplitude of interface R, and compressive force normal to the shear plane P c. These design variables are the main parameters that affect IST capacity, according to the sensitivity analysis performed by Soltani et al. Background Interface shear transfer Three mechanisms resist the shear forces passing through a concrete-to-concrete interface. These mechanisms are as follows: shear-friction, cohesion between concrete surfaces dowel action of reinforcement,8 Mast and Birkeland and Birkeland initially proposed the shear-friction mechanism to explain shear force transfer across cracks in reinforced concrete members. Figure illustrates the shear-friction mechanism using a sawtooth model. Shear force parallel to the interface causes a horizontal displacement h between two concrete surfaces. The horizontal displacement is accompanied by a vertical displacement v due to concrete interlock. The vertical displacement causes tension in the steel reinforcement crossing the interface; this tension results in a clamping force and friction along the interface. Cohesion is the bond between concrete interface surfaces. Dowel action is due to the direct shear resistance of the reinforcement crossing the interface. AASHTO LRFD specifications IST model Section.8. of the AASHTO LRFD specifications contains the provisions for the IST model, with the factored interface shear resistance V ri determined by Eq. (). φ V ni V ri = φv ni () = shear resistance factor (.9 for normalweight concrete and.8 for lightweight concrete) = nominal interface shear resistance In addition, the requirement in Eq. () must be fulfilled. V ri V ui () V ui = factored interface shear force due to the total load based on the applicable strength and extreme-event load combinations PCI Journal September October 8

3 In the AASHTO LRFD specifications, the nominal capacity is calculated based on the summation of cohesion at the interface and friction that results from interface reinforcement and clamping force. K = fraction of concrete strength available to resist interface shear According to the IST provisions of the AASHTO LRFD specifications (Eq..8..-), the nominal capacity can be found using Eq. (). V ni = ca cv + μ(a vf f y + P c ) () K = limiting interface shear resistance The specified compressive strength must be greater than. MPa (. ksi). Table gives the factors c, μ, K, and K (AASHTO LRFD specifications section.8..). Soltani et al. s revised IST model c μ A vf f y = cohesion factor = friction factor = area of interface shear reinforcement crossing the shear plane within the area A cv = yield stress of reinforcement Soltani et al. s IST model is determined through the summation of three terms: cohesion, friction from interface reinforcement, and friction from compression force normal to the interface. The predicted IST strength V pre is given by Eq. (). V pre = CA cv + M A vf f y + M P c () In addition, the requirements in Eq. () and () must be fulfilled. V ni K f c A cv () V ni K A cv () C M M = cohesion coefficient = friction coefficient for the shear-friction mechanism = friction coefficient for the normal force Interface reinforcement h σ stl σ comp Concrete layer τ V τ Concrete layer σ stl σ comp Figure. Interface shear transfer, sawtooth model. Source: Data from Santos and Júlio (). Note: h = horizontal displacement; v = vertical displacement; σ comp = compressive stress perpendicular to the interface; σ stl = tensile stress developed in steel reinforcement due to shear-friction; τ = shear stress developed at the interface. 8 PCI Journal September October 8

4 Table. Factors for use in metric (MPa) interface-shear-transfer model based on AASHTO LRFD specifications Condition c μ K K Cast-in-place concrete slab on clean concrete girder surfaces, free of laitance, surface roughened to an amplitude of mm.9.. (normalweight concrete) 8.9 (lightweight concrete) Normalweight concrete placed monolithically.... Lightweight concrete placed monolithically or nonmonolithically against a clean concrete surface, free of laitance, surface roughened to an amplitude of mm Normalweight concrete placed against a clean concrete surface, free of laitance, with surface intentionally roughened to an amplitude of mm Concrete placed against a clean concrete surface, free of laitance, but not intentionally roughened Concrete anchored to as-rolled structural steel by headed studs or by reinforcing bars all steel in contact with concrete is clean and free of paint Note: c = cohesion factor; K = fraction of concrete strength available to resist interface shear; K = limiting interface shear resistance; μ = friction factor. mm =.9 in. These coefficients are calculated in Eq. () to (9). k k k k k C = k R + k ʹ f c () M = k R fc + k R M = k + k f cʹ = cohesion factor applied to R =. MPa = cohesion factor applied to f c =. MPa = shear friction factor applied to R = MPa = shear friction factor applied to f c =. MPa (8) (9) = normal force friction factor applied to R =.8 MPa for normalweight concrete and. MPa for lightweight concrete k = normal force friction factor applied to f c =. MPa for normalweight concrete and MPa for lightweight concrete The units of V pre, A cv, A vf, f y, P c, R, and f c are kn, mm, mm, MPa, kn, mm, and MPa, respectively. The k to k factors were determined through the application of a multiple linear regression analysis conducted in the previous study. Previous reliability studies of the AASHTO LRFD specifications IST model Scott 9 performed push-off tests (the most conventional IST test method) to determine whether the current code equations accurately predict the horizontal shear strength at the connection of precast concrete girders and cast-in-place concrete decks for both normalweight and lightweight concrete members. A structural reliability analysis showed that the AASHTO LRFD specifications resistance factors provided a reliability index of.88 and. for normalweight concrete and lightweight concrete, respectively. The present study considered the minimum reinforcement requirement of the AASHTO LRFD specifications, unlike Scott s work, which considered the edition. Lang created a database with data from tests from previous research. A reliability analysis performed on the database showed that the reliability indices for normalweight concrete were.9 and. for rough and smooth interface roughness conditions, respectively. For lightweight concrete, the indices were. and. for rough and smooth interface roughness conditions, respectively. The present study differs from Lang s research in that it includes updated test data, focuses exclusively on uncracked reinforced specimens, and considers the minimum reinforcement requirements of the AASHTO LRFD specifications. Reliability analysis The most important objective in engineering design is to ensure structural safety, which relates to applied loads and structural resistance. Some of the uncertainties that result from the inherent variability in load and resistance mod- PCI Journal September October 8 9

5 els can be quantified through the application of reliability theory and eventually be taken into account in design codes. Reliability is a measure of the probability of a structural failure, which is defined within the context of a limit state (the boundary between desired and undesired performance). The load model Q and the resistance model R m are considered to be random variables in the structural reliability analysis. Per Nowak and Collins and Robert, the structural reliability or survival probability of structures p s is given by Eq. (). p s = P(R m Q > ) () This is the survival probability of the structural system if the resistance value is more than the load value. Considering Eq. (), the failure probability p f is determined by Eq. (). DC γ DW DW γ LL LL IM = dead load from the weight of structural components and nonstructural attachments = load factor of DW =. in the AASHTO LRFD specifications Strength I load combination = dead load from the weight of the wearing surface = load factor of LL =. in the AASHTO LRFD specifications Strength I load combination = live load from the forces from moving vehicles on the bridge = impact load from the forces produced by moving vehicles on the bridge p f = P(R m Q < ) () The reliability index β, which is related to the failure probability p f, is defined by Eq. (). β = φ (p f ) () From Eq. (), the nominal resistance V ni can be written as Eq. (). V ni = γ DCDC +γ DW DW +γ LL (LL + IM) φ The resistance model can be written as Eq. (). () R = V ni MFP () φ () = inverse standard normal distribution function If R m and Q are normally distributed, random, and independent variables, the reliability index can be determined by Eq. (). m Rm m Q σ Rm σ Q β = m R m m Q σ Rm +σ () Q = mean value of resistance model = mean value of load model = standard deviation of resistance model = standard deviation of load model Statistical details of the resistance model The AASHTO LRFD specifications consider the limit state factored load combination for horizontal shear resistance at the interface of a bridge deck and bridge girder to be a Strength I load combination. Thus, Eq. () in the AASH- TO LRFD specifications is defined as Eq. (). γ DC γ DC DC + γ DW DW + γ LL (LL + IM) = φv ni () = load factor of DC =. in the AASHTO LRFD specifications Strength I load combination M F P = material factor = fabrication factor = professional factor The material factor accounts for variation in material properties affecting the IST, including compressive strength of concrete, yield strength of reinforcement, and so forth. The fabrication factor reflects variation in member geometry, such as dimensions, moment of inertia, and reinforcement placement. The professional factor represents the accuracy of the IST model. The mean m Rm and coefficient of variation COV Rm values of the resistance model are given by Eq. () and (8), respectively. λ M λ F λ P = mean value of M = mean value of F = mean value of P m Rm = V ni λ M λ F λ P () COV Rm = COV M + COV F + COV P (8) PCI Journal September October 8

6 Table. Statistical parameters of resistance model Statistical parameters Bias factor λ Coefficient of variation Material factor M.. Fabrication factor F.. Professional factor P (Soltani et al. 8) Professional factor P (AASHTO LRFD specifications) COV M = coefficient of variation of M Normalweight concrete.8. Lightweight concrete..9 Normalweight concrete.. Lightweight concrete.. Results and discussion COV F = coefficient of variation of F Normality of the IST professional factors COV P = coefficient of variation of P For the professional factor, Eq. () (AASHTO LRFD specifications) and Eq. () (Soltani et al.) were used to predict the IST nominal resistance in two categories: normalweight concrete and lightweight concrete. Table summarizes the statistical parameters of resistance used in this study, based on previous research. Statistical details of the load model The load model Q is given by Eq. (9). Q = DC + DW + (LL + IM) (9) The mean m Q and coefficient of variation COV Q values of the load model are given by Eq. () and (), respectively. m Q = DCλ DC + DWλ DW + (LL + IM)λ LL+IM () The professional factor, bias factor, and coefficient of variation were calculated from the ratio of experimental IST strength to nominal IST strength predicted by the AASHTO LRFD specifications (Eq. []) and Soltani et al. s IST model (Eq. []) using the IST database created by Soltani and Ross. The statistical parameters were computed for normalweight and lightweight concrete (Table ). To use Eq. (), the normality of the resistance and load models needs to be checked. The load model has a normal distribution because all of the parameters used in the equation have normal distributions. However, in the resistance model, the professional factor needs to be checked. To check the normality of distributions of P, the standard normal variable Z value was calculated using Eq. (). Z value = V exp Vn Avg V exp Vn i SD V () exp Vn λ DC λ DW λ LL+IM = bias factor of DC = bias factor of DW = bias factor of LL + IM V exp = measured experimental IST strength (for the sample number of i) V n = predicted nominal IST strength (for the sample number of i) Table. Statistical parameters of load model COV Q = COV DC +COV DW +COV LL+IM () Statistical parameters Bias factor λ Coefficient of variation DC.. COV DC COV DW = coefficient of variation of DC = coefficient of variation of DW COV LL+IM = coefficient of variation of LL + IM Table gives the bias factors and coefficients of variation of the load model. DW.. LL + IM.8.8 Note: DC = dead load from the weight of structural components and nonstructural attachments; DW = dead load from the weight of the wearing surface; IM = impact load from the forces produced by moving vehicles on the bridge; LL = live load from the forces produced by moving vehicles on the bridge. PCI Journal September October 8

7 Normalweight concrete Lightweight concrete Linear (normalweight concrete) Linear (lightweight concrete) Bias factor R² =.8 R² =.9 Bias factor R²=.98 R² = Z value - - Z value AASHTO LRFD specifications Soltani et al. (8) Figure. Normal variable distributions of interface-shear-transfer models. Note: R = roughness amplitude of interface; Z value = standard normal variable. Avg V exp Vn = mean value of the strength ratios ( LL + IM ) LR = DC + DW + ( LL + IM ) () SD V exp Vn = standard deviation of the strength ratios If the professional factor is normally distributed, the data in the graph will be in an approximately straight line. Figure illustrates the test data in both categories, normalweight concrete and lightweight concrete, for each IST model. Considering the linear regression of the bias factors and Z value, the minimum value of the statistical parameter R is.8, and the maximum professional factor P value is.9 8. These values indicate that the professional factor P is normally distributed in both categories. Reliability analysis The data in each model were separated into two categories: normalweight concrete and lightweight concrete. In the AASHTO LRFD specifications database, there were 9 tests with normalweight concrete and tests with lightweight concrete. In Soltani et al.s model database, there were tests with normalweight concrete and 98 tests with lightweight concrete. To investigate the reliability indices for different load values, the reliability indices were calculated using Eq. () and () for a dead load ratio DR and live load ratio LR, respectively. DR = DW DC + DW + LL + IM ( ) () The resistance factor φ, used in Eq. () to calculate the reliability index from Soltani et al. s model, was adjusted to.9. With this value, Soltani et al. s model calculated the reliability index to be approximately., which is the target reliability index of most structural design codes, such as the AASHTO LRFD specifications. This target value of. means that the probability of failure is approximately equal to.%. Figure compares the reliability index with the dead load ratios DR from the wearing surface and the live load ratios LR. In the AASHTO LRFD specifications model, the reliability indices of normalweight concrete are generally less than the target reliability index of., while the reliability indices of lightweight concrete are generally greater. The reliability index plane of normalweight concrete is generally less than. (Fig. ), as the reliability index plane of lightweight concrete is generally greater than.. In Soltani et al. s model, the reliability indices of normalweight and lightweight concrete are both around.. The shapes and values of the reliability index planes are also similar in both categories. To compare the reliability index as just one number for each model, an example of a critical loading scenario (DR and LR values) was chosen from the PCI Bridge Design Manual. According to Tables 9.a.- and, the maximum shear values of the wearing surface V ws, barrier weight V b, and lane load plus truck load with impact V LL + V LT were PCI Journal September October 8

8 DR LR DR LR DR LR DR LR AASHTO LRFD specifications Soltani et al. (8) Figure. Percentage of live load and dead load from wearing surface versus reliability index for normalweight concrete (top) and lightweight concrete (bottom). Note: DR = dead load ratio; LR = live load ratio; β = reliability index. equal to,, and 98 kn (,, and kip), respectively. Thus, DR and LR were calculated to be. and.8 using Eq. () and (), respectively. As previously mentioned, the resistance factor φ of the AASHTO LRFD specifications IST model is.9 for normalweight concrete and.8 for lightweight concrete. To investigate influence of the resistance factor, reliability indices were determined for a range of resistance factors (Fig. ). Following this scenario, the target reliability index of. was satisfied with the resistance factors. In Soltani et al. s model with normalweight concrete, the resistance factor should be.9 to reach to the target reliability index of.; this model with lightweight concrete needs to have the resistance factor of., which leads to the reliability index of.8. In AASHTO LRFD specifications with normalweight concrete, the resistance factor has to be equal to. to reach to the target reliability index and. for tests with lightweight concrete (it produces reliability index of.). The AASHTO LRFD specifications IST model was conservative for lightweight concrete (no need for any resistance factor PCI Journal September October 8

9 8 AASHTO LRFD specifications normalweight concrete AASHTO LRFD specifications lightweight concrete Soltani et al. normalweight concrete Soltani et al. lightweight concrete Resistance factor Figure. Reliability indices for different resistance factors. [φ equal to ]); however, it was significantly unconservative for normalweight concrete. In the latter case, a resistance factor of. was needed to satisfy the target reliability index of.. The AASHTO LRFD specifications based resistance factors led to reliability indices of.8 (p f equal to.%) and.8 (p f equal to %) for normalweight concrete and lightweight concrete, respectively. Hence, the target reliability index was not satisfied for either normalweight concrete or lightweight concrete tests. Alternatively, the resistance factors used in Soltani et al. s model successfully met the target reliability index of.. The resistance factor of.9 in Soltani et al. s model led to reliability indices of. (p f equal to.%) and. (p f equal to.%) for normalweight concrete and lightweight concrete, respectively. Parametric reliability analysis A bin analysis was also performed to evaluate the relationships between the reliability index and IST design variables, including the area of concrete interface A cv, interface shear reinforcement index ρf y, compressive strength of concrete f c, roughness amplitude of interface R, and compressive force normal to the shear plane P c. These design variables were selected for investigation because they affect IST capacity and are used in both the AASHTO LRFD specifications model and Soltani et al. s model. The interface reinforcement index ρf y is calculated using Eq. (). ρ f y = A vf A cv f y () The range of the roughness amplitude of interface R and compressive force normal to the shear plane P c were each divided into two categories. The roughness amplitude of interface categories was greater than. mm (. in.) and less than. mm. The compressive force normal to the shear plane was divided into tests with zero compressive force and tests with nonzero compressive force. These categorizations were selected based on the characteristics of tests in the database. For the rest of the design variables, the range of each variable was divided into four and three equally spaced bins for normalweight concrete and lightweight concrete, respectively. Both models had more normalweight concrete tests than lightweight concrete; thus, to have a comparable number of tests, more normalweight concrete bins were defined than lightweight concrete bins. Tables and show the bias factor, coefficient of variation, and number of tests for each bin. The bias factors for tests with normalweight concrete ranged from. to. in the AASHTO LRFD specifications model and from. to. in Soltani et al. s model. Tests with lightweight concrete had bias factors ranging from. to. in the AASHTO LRFD specifications model and from. to. in Soltani et al. s model. Thus, Soltani et al. s model was generally more accurate than the AASHTO LRFD specifications model. The coefficients of variation ranged from. to.9 and from. to. in the AASHTO LRFD specifications model and Soltani et al. s model, respectively. PCI Journal September October 8

10 Table. Statistical information of evaluating bins for normalweight concrete f ć, MPa ρf y, MPa A cv, mm R, mm P c, kn Source Parameter < > < >. <,, 9,8 9,8 9, >9, < > AASHTO LRFD specifications Soltani et al. (8) λ COV n.d. Number of tests λ COV Number of tests Note: A cv = area of concrete considered to be engaged in interface shear transfer; COV = coefficient of variation; f c = compressive strength of concrete; n.d. = no data in the bin; P c = permanent net compressive force normal to the shear plane; R = roughness amplitude of interface; λ = bias factor; ρf y = interface reinforcement index. mm =.9 in.; kn =. kip; MPa =. ksi. Table. Statistical information of evaluating bins for lightweight concrete f ć, MPa ρf y, MPa A cv, mm R, mm P c, kn Source Parameter <8 8 > <...8 >.8 <,, 9, >9, < > AASHTO LRFD specifications Soltani et al. (8) λ COV n.d... n.d Number of tests λ COV Number of tests Note: A cv = area of concrete considered to be engaged in interface shear transfer; COV = coefficient of variation; f c = compressive strength of concrete; n.d. = no data in the bin; P c = permanent net compressive force normal to the shear plane; R = roughness amplitude of interface; λ = bias factor; ρf y = interface reinforcement index. mm =.9 in.; kn =. kip; MPa =. ksi. This shows that Soltani et al. s model is consistently more accurate throughout the ranges of design variables than the AASHTO LRFD specifications model. In some bins of the AASHTO LRFD specifications model, there were no data to compare with similar bins of Soltani et al. s model. This was due to requirements in the AASHTO LRFD specifications, such as minimum compressive strength of concrete and minimum interface reinforcement of tests. These limitations do not exist in Soltani et al. s model. Figure illustrates the reliability indices related to each bin of IST design variables, including compressive strength of concrete, interface reinforcement index, area of concrete interface, roughness amplitude of interface, and compressive force normal to the shear plane. The results of this analysis will help designers and practitioners produce reliable designs. The investigation of the reliability index with respect to each design variable is discussed in the following sections. Compressive strength of concrete f ć For normalweight concrete with f c between and MPa (.9 and 8. ksi), the AASHTO LRFD specifications reliability index was. (below the target reliability index), which is significantly higher than the target reliability index when f c is greater than MPa. The reliability indices of Soltani et al. s model were more consistent than those of the AASHTO LRFD specifications IST model, and averaged around. for all bins. For lightweight concrete, the reliability indices of Soltani et al. s model for all bins ranged from. to.9. When the compressive strength of concrete was greater than 8 MPa (. ksi), the AASHTO LRFD specifications reliability indices were higher than the target reliability index of.. PCI Journal September October 8

11 AASHTO LRFD specifications Soltani et al. (8) < < Compressive strength of concrete f c, MPa < < <8 8- < Compressive strength of concrete f c, MPa < < Interface reinforcement index ρf y, MPa < Area of concrete interface A cv, mm < > Roughness amplitude of interface R, mm Compressive force normal to the shear plane P c, kn Normalweight concrete Interface reinforcement index ρf y, MPa -9 9< Area of concrete interface A cv, mm < > Roughness amplitude of interface R, mm Compressive force normal to the shear plane P c, kn Lightweight concrete Figure. Reliability indices for ranges of design variables. Note: mm =.9 in.; kn =. kip; MPa =. ksi. PCI Journal September October 8

12 Interface reinforcement index ρf y In the tests with normalweight concrete using Soltani et al. s model, more interface reinforcement led to higher values of reliability index. The lowest reliability index was. in the AASHTO LRFD specifications model, when the interface reinforcement index was between.8 and. MPa (. and.8 ksi). The reliability indices for the tests with lightweight concrete in all bins of the AASHTO LRFD specifications model were too high compared with the target reliability index. However, the reliability indices were consistent, with an average of approximately. for Soltani et al. s model. Area of concrete interface A cv For normalweight concrete, when the area of concrete interface was between, and 9,8 mm ( and in. ), the AASHTO LRFD specifications reliability index was the lowest (β equal to.98). In Soltani et al. s model, the highest reliability index was obtained when the area of concrete interface was less than, mm ( in. ). For the tests with lightweight concrete, the minimum AASHTO LRFD specifications reliability index was.99. However, the minimum reliability index of Soltani et al. s model was.9 when the area of concrete interface was between, and 9, mm ( and in. ). Roughness amplitude of interface R For the tests with normalweight concrete, the AASHTO LRFD specifications reliability index was. for a roughness amplitude of interface greater than mm (. in.) and. for a roughness amplitude of interface less than mm. Thus, the AASHTO LRFD specifications model was. times more reliable when the interface was roughened compared with smooth interfaces. However, Soltani et al. s model showed consistent reliability index values for both interface roughness scenarios (β of about.). The minimum reliability index for the tests with lightweight concrete using the AASH- TO LRFD specifications model was., which is higher than the target reliability index. Compressive force normal to the shear plane P c The AASHTO LRFD specifications reliability indices do not relate to the compressive force normal to the shear plane. The reliability index for tests with normalweight concrete was less than.8, with or without the presence of a normal force. However, for tests with normalweight concrete using Soltani et al. s model, the reliability index was around. in both P c scenarios. Considering lightweight concrete with no normal force applied, the reliability index of Soltani et al. s model was.9. The AASHTO LRFD specifications reliability index was higher than the target reliability index in both P c scenarios. The results of the parametric study show that the AASHTO LRFD specifications reliability index values depend on the values of the design variables. However, the reliability indices of Soltani et al. s model were more consistent for different ranges of the design variables compared with the AASHTO LRFD specifications model and also averaged around the target reliability index of.. Conclusion Reliability analyses were performed on the IST model of the AASHTO LRFD specifications and on Soltani et al. s revised IST model to evaluate and determine their respective resistance factors. The analyses considered members with normalweight and lightweight concrete. Source data for the analyses were from a database presented in Soltani and Ross. To perform the reliability analyses, a resistance model R and a load model Q were created for each IST model. The reliability indices were obtained under a critical load scenario in which the shear values of the wearing surface, barrier weight, and lane load plus truck load with impact were determined to be,, and 98 kn (,., and kip), respectively. The reliability index of the current AASHTO LRFD specifications IST model was reported. Considering the target reliability index of., a resistance factor was proposed for Soltani et al. s model. Finally, reliability analyses using bin analysis were performed on ranges of design variables, including the compressive strength of concrete f c, area of concrete interface A cv, interface reinforcement index ρf y, roughness amplitude of interface R, and compressive force normal to the shear plane P c. The resistance factors of.9 (normalweight concrete) and.8 (lightweight concrete) in the AASHTO LRFD specifications model led to reliability indices of.8 and.8 for normalweight and lightweight concrete, respectively. For the tests with normalweight concrete, a resistance factor of. resulted in the target reliability index of.. The reliability index of the current AASHTO LRFD specifications IST model for normalweight concrete tests is lower than the target reliability index, while the AASHTO LRFD specifications IST model for lightweight concrete is too conservative (no resistance factor needed to satisfy the target reliability index). These results showed the need to revise the AASHTO LRFD specifications IST model and the resistance factors associated with it. The resistance factor of.9 for both normalweight and lightweight concrete in Soltani et al. s model resulted in reliability indices of. and. for normalweight and lightweight concrete, respectively. This shows that Soltani et al. s model met the target reliability index requirement through applying only one resistance factor for both normalweight and lightweight concrete. Therefore, Soltani et al. s model is an appropriate alternative to the current AASHTO LRFD specifications IST model. References. Soltani, M., and B. E. Ross.. Database Evaluation of Interface Shear Transfer in Reinforced Concrete Members. ACI Structural Journal (): 8 9. PCI Journal September October 8

13 . AASHTO (American Association of State Highway and Transportation Officials).. AASHTO LRFD Bridge Design Specifications. th ed., customary U.S. units. Washington, DC: AASHTO.. Soltani, M., B. E. Ross, and A. Khademi. Forthcoming. A Statistical Approach to Refine Design Codes for Interface Shear Transfer in Reinforced Concrete Structures. ACI Structural Journal.. Mast, R. F. 98. Auxiliary Reinforcement in Concrete Connections. Journal of the Structural Division 9 (): 8.. Birkeland, P. W., and H. W. Birkeland. 9. Connections in Precast Concrete Construction. Journal of the American Concrete Institute (): 8.. Hsu, T. T., S. T. Mau, and B. Chen. 98. Theory on Shear Transfer Strength of Reinforced Concrete. Structural Journal 8 (): 9.. Santos, P. M., and E. N. Júlio.. A State-of-the-Art Review on Shear-Friction. Engineering Structures : Jimenez-Perez, R., P. Gergely, and R. N. White. 98. Shear Transfer across Cracks in Reinforced Concrete. Report PB Ithaca, NY: Cornell University. 9. Scott, J.. Interface Shear Strength in Lightweight Concrete Bridge Girders. PhD diss., Virginia Polytechnic Institute and State University, Blacksburg, VA.. AASHTO.. AASHTO LRFD Bridge Design Specifications. th ed. Washington, DC: AASHTO.. Lang, M.. Analysis of the AASHTO LRFD Horizontal Shear Strength Equation. PhD diss., Virginia Polytechnic Institute and State University, Blacksburg, VA.. PCI Bridge Design Manual Steering Committee.. PCI Bridge Design Manual. MNL-. rd ed. Chicago, IL: PCI. Notation A cv A vf = area of concrete engaged in interface shear transfer = area of interface shear reinforcement crossing the shear plane within the area A cv Avg V exp Vn = mean value of the strength ratios c C = cohesion factor = cohesion coefficient COV DC = coefficient of variation of DC COV DW = coefficient of variation of DW COV F = coefficient of variation of F COV LL+IM = coefficient of variation of LL + IM COV M = coefficient of variation of M COV P = coefficient of variation of P COV Q = coefficient of variation of the load model COV R = coefficient of variation of the resistance model DC DR DW f c = dead load from the weight of structural components and nonstructural attachments = dead load ratio = dead load from the weight of the wearing surface = compressive strength of concrete. Nowak, A. S., and K. R. Collins.. Reliability of Structures. Boston, MA: McGraw-Hill.. Robert, E. M Structural Reliability Analysis and Prediction. Chichester, West Sussex, UK: Wiley.. Nowak, A. S., M. M. Szerszen, E. K. Szeliga, A. Szwed, and P. J. Podhorecki.. Reliability-based Calibration for Structural Concrete. Report UNLCE -. Lincoln, NE: University of Nebraska Department of Civil Engineering.. Nowak, A. S Calibration of LRFD Bridge Design Code. NCHRP (National Cooperative Highway Research Project) report 8. Washington, DC: Transportation Research Board. nchrp_rpt_8.pdf. f y F h IM k k k k = yield stress of reinforcement = fabrication factor = horizontal displacement = impact load from the forces produced by moving vehicles on the bridge = cohesion factor applied to R = cohesion factor applied to f c = shear friction factor applied to R = shear friction factor applied to f c 8 PCI Journal September October 8

14 k = normal force friction factor applied to R V ri = factored interface shear resistance k K K LL = normal force friction factor applied to f c = fraction of concrete strength available to resist interface shear = limiting interface shear resistance = live load from the forces from moving vehicles on the bridge V ui V ws Z value β = factored interface shear force due to the total load based on the applicable strength and extreme-event load combinations = wearing surface maximum shear = standard normal variable = reliability index LR = live load ratio γ DC = load factor of DC m Q = mean value of the load model γ DW = load factor of DW m RM = mean value of the resistance model γ LL = load factor of LL M = material factor λ = bias factor M M p f p s P P c Q R R m = friction coefficient for the shear-friction mechanism = friction coefficient for the normal force = failure probability = survival probability = professional factor = compressive force normal to the shear plane = load model = roughness amplitude of interface = resistance model SD V exp Vn = standard deviation of the strength ratios v V b = vertical displacement = barrier weight maximum shear λ DC λ DW λ F λ LL+IM λ M λ P μ ρf y σ comp σ Q σ R σ stl = bias factor of DC = bias factor of DW = mean value of F = bias factor of LL + IM = mean value of M = mean value of P = friction factor = interface reinforcement index = compressive stress perpendicular to the interface = standard deviation of load model = standard deviation of resistance model = tensile stress developed in steel reinforcement due to shear-friction V exp V LL V LT = measured experimental interface shear transfer strength = lane load maximum shear = truck load maximum shear τ φ φ () = shear stress developed at the interface = shear resistance factor = inverse standard normal distribution function V n = predicted nominal interface shear transfer strength V ni = nominal interface shear resistance according to the AASHTO LRFD specifications V pre = predicted interface shear transfer strength PCI Journal September October 8 9

15 About the authors <Body>Mohamed Mahmoodreza Soltani, K. Nafadi, PhD, is a PhD, postdoctoral is an assistant researcher/lecturer professor of in structural the Glenn engineering Department at of Assiut Civil FPO University Engineering in at Assiut, Clemson Egypt. University former in Clemson, graduate S.C. research He received He is a assistant his bachelor s in the degree Department from Shahid of Civil, Beheshti Construction, University and in Tehran, Environmental Iran; his Engineering master s degree at North from the Carolina University State of Texas University at El Paso, (NCSU) in Tex.; Raleigh. and his PhD from Clemson University. His research interests include the behavior, analysis, and design of reinforced Omar and prestressed M. Khalafalla, concrete is a structures graduate and bridge engineering research and reliability and teaching analysis assistant of civil engineering FPOsystems. and PhD candidate in the Department of Civil, Construction, and Environmental Engineering at NCSU. FPO FPO Gregory W. Lucier, PhD, is a research assistant professor in the Department of Civil, Construction, and Environmental Engineering and manager of the Constructed Facilities Laboratory at NCSU. Sami H. Rizkalla, PhD, FPCI, FACI, FASCE, FIIFC, FEIC, FCSCE, is Distinguished Professor of Civil Engineering and Construction, director of the Constructed Facilities Laboratory, and director of the National Science Foundation Center on Integration of Composites into Infrastructure at NCSU. Abstract Body Interface textshear transfer (IST) is a concept that describes the mechanisms by which shear forces pass Keywords through a concrete-to-concrete interface no, or negligible, moment is present. Previous research Body has shown text that the IST model of the American Association of State Highway and Transportation Officials AASHTO policy LRFD Bridge Design Specifications Review produces inconsistent levels of accuracy for different values text of design variables, such as compressive Body strength of concrete. In this study, a reliability analysis Reader was performed comments on the AASHTO LRFD specifications model to evaluate the code s resistance factor. In addition, a text comparative reliability analysis was performed Body on a new IST model that improves the limitations of the AASHTO LRFD specifications model to calibrate its resistance factor to meet the target reliability index of.. Results showed that for a critical load combination, the reliability indices of the AASHTO LRFD specifications model with normalweight and lightweight concrete were.8 and.8, respectively, as applying a resistance factor of.9, the reliability indices of the alternative IST model for tests with normalweight concrete and lightweight concrete were. and., respectively. The results of the reliability study show that the alternative model performs better than the AASHTO LRFD specifications model. In this study, reliability indices were also scrutinized for different ranges of IST design variables, which benefits designers and practitioners. Keywords Design model, interface shear transfer design variables, lightweight concrete, load model, normalweight concrete, resistance factor, resistance model, shear friction. FPO FPO Paul Z. Zia, PhD, PE, FPCI, is a Distinguished University Professor Emeritus in the Department of Civil, Construction, and Environmental Engineering at NCSU. Gary J. Klein, PE, is executive vice president and senior principal for Wiss, Janney, Elstner Associates Inc. in Northbrook, Ill. Review policy This paper was reviewed in accordance with the Precast/Prestressed Concrete Institute s peer-review process. Reader comments Please address any reader comments to PCI Journal editor-in-chief Emily Lorenz at elorenz@pci.org or Precast/Prestressed Concrete Institute, c/o PCI Journal, W. Adams St., Suite, Chicago, IL. PCI Journal September October 8