STRUCTURAL ANALYSIS OF EDGE STIFFENED CANTILEVER DECK SLAB OVERHANG SUBJECTED TO HORIZONTAL BRIDGE RAILING LOAD SIMULATING VEHICLE IMPACT

10th International Conference on Short andMedium Span Bridges Quebec City, Quebec, Canada, July 31 – August 3, 2018 STRUCTURAL ANALYSIS OF EDGE STIFFENED CANTILEVER DECK SLAB OVERHANG SU

10th International Conference on Short and

Medium Span Bridges Quebec City, Quebec, Canada, July 31 – August 3, 2018

STRUCTURAL ANALYSIS OF EDGE STIFFENED CANTILEVER DECK SLAB OVERHANG SUBJECTED TO HORIZONTAL BRIDGE RAILING LOAD SIMULATING VEHICLE IMPACT

Sayed-Ahmed, Mahmoud1,3, and Sennah, Khaled2

1 Ryerson University, Megastone Inc and Doug Dixon & Associates Inc., Canada

2 Ryerson University, Toronto, Canada

Abstract: The Canadian Highway Bridge Design Code of 2014 specifies values applied loads on bridge

railing to determine the applied moment and tension force for the design of the deck slab cantilever However, these moment and tensile force values are as yet unavailable This research investigates the geometrical variables and load locations effect on the structural performance of the edge stiffened cantilever slab, which are subjected to horizontal line load Finite Element Modeling software was utilized

to conduct linear elastic analysis of concrete barrier rigidly connected to deck slab cantilevers The geometrical properties include the linearly varying slab thickness, the transverse cantilever length, the longitudinal barrier length, and the varying wall thickness Edge and mid-span loading at variable heights were determined based on the type of the barriers Three-dimensional finite element models were constructed to extract design data for the shear and moment values for the wall, and tensile force and moment for the cantilever slab Design data were analyzed using nonlinear regression analysis to provide simplified expressions, which can be used to determine the factored forces and moments needed for the structural design of the bridge barrier-deck joint as well as the deck slab cantilever due to vehicle impact forces

1 Introduction

Semi-rigid barrier is a free-standing structure, Tric-Bloc precast concrete barrier – concrete median barrier CMB - is an example of the semi-rigid barrier (Turbell, 1981), and rigid traffic barrier which is a fixed to foundation structure, where both are made out of reinforced concrete (RC) The shape of the concrete barrier is designed to redirect the impacted vehicle into a path parallel to the barrier (Ross et al 1993) Impact energy is dissipated through the redirection and deformation impacts that may be sufficient to redirect the impacted vehicle without damaging the vehicle’s bodywork and the traffic barrier Impact forces are resisted by a contribution of the rigidity and mass of the barrier The shape of the concrete single-faced or double-faced roadside barriers include constant-slope barriers, concrete step barriers, F-shape barriers, New Jersey F-shape and inverted F-shape (Dhafer et al 2007) as shown in Figure 1 Design development of the roadside barriers included testing such barriers under static to-collapse loading and crash-testing Static testing provides load-deformation info while crash testing provides velocity-time and vertical displacement-time histories The performance evaluation is assessed for (1) structural adequacy where impact vehicle should not penetrate, underride, or override the barrier; and (2) occupant risk including vehicle to remain upright, protecting occupant compartment, protecting hazard to traffic,

be increased by an “Impact Factor” in order to obtain a good approximation of the maximum dynamic deflection and stress The structural adequacy for the concrete barriers is subjected to horizontal railing load that is assessed to 2 load locations: (1) inner-load location; and (2) edge-load location The elevated horizontal railing load disperses into 2 dimensions: vertically over the height of the barrier into vertical ratio (2:1) or vertical angle towards the base; and horizontally in arching or compressive membrane action (CMA) The Canadian Highway Bridge Design Code (CHBDC) specifies transverse, longitudinal and vertical service loads for varies traffic test level (TL) barriers, and minimum barrier heights

Figure 1 Typical shapes of double-face concrete barriers, Dhafer et al 2007

a) Traffic Test Level

Barrier b) View for bridge concrete parapets

Figure 2 Single-face concrete traffic rigid barrier connected to the slab deck

Transverse moment due to live loading consists from one or more of partially distributed loads, in the concrete deck slab overhang of slab-on-girder and other similar structures Such transverse loads are larger than the loads in the longitudinal directions As a result cracks in the longitudinal direction become more significant than the transverse cracks Reduction of the flexural rigidity in transverse direction becomes higher than that of the longitudinal direction due to uneven distribution of cracks Figure 2 shows the application of the single-traffic rigid barrier over the bridge deck

The simplified analysis method was used to consider the transvers, vertical and longitudinal loads as point loads, isotropic materials for the cross section, and the linear elastic analysis method to determine the appropriate reinforcement for the section of study Added edge-beam, curbs or traffic barriers to the overhangs provide extra edge-stiffness to the longitudinal free edge of the overhang due to enhancing of load dispersion At transvers loading point, edge beam becomes subjected to sagging moment for certain distance and to hogging moment at others The moment of inertia Is for the edge-stiffened infinite

cantilever slab for a slab of linearly varying from t2 (max thickness) to t1 (min thickness), and which is of width a is given by Equation [1], and as shown in Figure 2 (Bakht, B., and Jaeger, L 1985)

[1]

This research investigates the geometrical variables, partial load distribution on the transverse direction, known as railing load, and load dispersion over the three-dimensional edge-stiffened infinite cantilever slab, while using linear elastic method Design by analysis (DBA) data extracted from the 3D finite element models will be used to propose design by formula (DBF) for different traffic rigid barriers known

as Test Levels TL as required by the CHBDC while proposing new geometry for new barriers Non-linear regression analysis (NLREG) was used to build-up the structural equation models (SEM)

1.1 Parametric Study

The parametric study is to include the transverse railing load listed in Table 1, with shape of the stiffened-edge infinite overhang shown in Figure 3 Table 2 lists the geometric variables set for this investigation, where is the minimum thickness at the edge of the cantilever slab, is the maximum thickness of the overhang slab, is the transverse length of the cantilever slab, is the longitudinal length of the overhang slab and is the thickness of the traffic barrier The concrete has compressive strength, , of 30 MPa (good rounded number for the commonly used 4000 psi concrete, which is approximately

28 MPa), while the modulus of elasticity, , and the passion ratio, , are shown in Equation [2]

Table 1 Traffic Barrier Anchorage Loads Test Level Transverse

Load (kN) LongitudinalLoad (kN) Vertical Load(kN) Vertical Height(mm) Length (mm)Horizontal

Table 2 Investigated geometrical values Barrier

TL-2 200, 275, 350 1, 1.25, 1.5 0, 0.5, 1, 1.5, 2, 2.5 5, 6, 7, 8 180, 215, 265 TL-4 CT* 200, 250, 300 1, 1.25, 1.5 0, 0.5, 1, 1.5, 2, 2.5 5, 6, 7, 8 175, 225, 275 TL-4 200, 250, 300 1, 1.25, 1.5 0, 0.5, 1, 1.5, 2, 2.5 5, 6, 7, 8 175, 225, 275 TL-5 200, 250, 300 1, 1.25, 1.5 0, 0.5, 1, 1.5, 2, 2.5 5, 6, 8, 12 175, 250, 275 (*) CT means constant thickness

The moment of inertia (MoI) for the edge-stiffened infinite cantilever slab is taken as per Equation 1, whiles the moment of inertia of the edge beam or traffic rigid barrier is calculated using the parallel axis theorem to its base and through its center of mass, as shown in Figure 2 The ratio of the flexural stiffness

of longitudinal edge beam to slab is measured by and is used to determine the relative edge beam size to the thickness of the slab The flexural stiffness and are for the edge beam and slab respectively where Ec is the modulus of elasticity of the concrete and I is the moment of inertia The stiffness ratio should be not less than 0.80 otherwise the slab thickness has to increase or the slab will not act with the edge beam to resist the load and generated deflections (ACI 318-14 Clause

thickness exceeds 0.80 which means that portion of this overhang slab will act with the beam in resisting the loads

Figure 3 Geometrical parameters for the slab-overhang with rigid barrier wall

1.1.1 Finite Element Modeling

The linear elastic finite element method (LEFEM) is the mathematical study of how solid objects deform and becomes internally stressed due to prescribed loading conditions Three dimensional models were constructed using quadrilateral shell elements with mesh size of 50x50-mm (Azimi et al., 2014) and with aspect ratio of 1 ~ 1.3 (Logan, 2011) The transverse uniform distributed loads were placed perpendicularly at the nodes connecting the shell elements All shell elements for the overhang slab at the maximum thickness where the end joints were fixed for their six-degree of freedom (6 DoF) to create fixed support In other words it forms cantilever slab with inverted edge beam (barriers)

The 3D model verification took place by the construction of 1-m wide model for the overhang slab with traffic barrier having L-shape, fixed thickness, with 1 unit of transvers loading Ft Reaction, moment and deflection of the exact solution matched those obtained from the FEM program using SAP2000 version 19.0 with zero percentage of error As a result the unit load was replaced by the actual loading value and length over the investigated geometrical values listed in Tables 1 and 2 to study the effect of the 1-m strip obtained from the dispersed loads The load distribution angle in concrete is used to be 45-degree (1H:1V), while it is permitted to be up to 60-degrees (2H:1V for vertically applied load) and 70-degree for prestressed concrete (almost 3H:1V for vertically applied load) (AS3600-2009) “Section Cut” technique was used to obtain the forces and moments at two locations: first location at the beginning height of the traffic barrier (H), while the second point considers the cantilever length up to the starting point of the traffic barrier at b3 The manual 1-m drawn line for “Section Cut” in SAP2000 requires the selection of joints and the adjacent shell elements Each Test Level TL barrier fixed over the overhang slab has been constructed into 648 models to account for all geometrical variables, listed in Table 2 and for 2 times due

to load location Each TL has been loaded to one type of a load in a time for: (a) internal loading at the mid-longitudinal span, and (b) to external edge loading

1.2 Proposed Structural Equation Modeling (SEM)

Grouped data attributed to the geometrical variables, fixed boundary conditions, uniform distributed loads, and load locations Generated data attributed to the moments and forces at the designated locations of the section cuts Structural equation modeling is a multivariate statistical analysis technique that is used

to analyze structural relationships (Wright, 92) This technique is the combination of the parametric variables from the grouped data (also known as input data), generated data (also known as output data), and the non-linear least squares regression analysis NLREG to determine the unbiased predicted parameters for the developed equations and to equate the inputs to the outputs as per following:

Internal Loading:

1 Moment in inner portion of deck per metre at face of barrier [kN-m/m]

2 Tensile force at the overhang slab [kN]

3 Moment in inner portion of wall per meter at face of barrier [kN-m/m]

4 Shear force of the wall [kN]

External Loading:

1 Moment in end portion of deck per metre at face of barrier [kN-m/m]

2 Tensile force at the overhang slab [kN]

3 Moment in end portion of wall per meter at face of barrier [kN-m/m]

4 Shear force of the wall [kN]

Table 3 NLREG predicted parameters for TL-2 and TL-4 CT

Barrier

Type

Structural

Element

Load Location

Name of Reaction

Predicted Parameters

Wall External Force 0.194 0.053 0.0469 0.568 -0.3935

Cant Wall: means cantilever wall

i. Slab-Internal-Moment ii. Wall-Internal-Moment iii. Slab-External-Moment iv. Wall-External-Moment Figure 4.a TL-2 internal loading

i Slab-Internal-Force ii. Wall-Internal-Force iii. Slab-External-Force iv Wall-External-Force Figure 4.b TL-2 external loading

i Slab-Internal-Moment ii. Wall-Internal-Moment iii. Slab-External-Moment iv. Wall-External-Moment Figure 5.a TL-4 CT internal loading

i. Slab-Internal-Force ii. Wall-Internal-Force iii. Slab-External-Force iv. Wall-External-Force Figure 5.b TL-4 CT external loading

A Developed Design Models for TL-2 and TL-4 CT

Table 3 presents the NLREG predicted parameters for the TL-2 and TL-4 CT in conjunction with the proposed Equations 3 and 4 for the moment for forces respectively All units were used in N and mm then

multiplied by 10 or 10 to get values of the force and moment respectively The proposed models considered the flexural stiffness for the beam-to-slab, and transverse length of the cantilever slab to the longitudinal length of the overhang slab Equations 5 and 6 in conjunction with Table 3 present the proposed SEMs for the cantilever wall (barrier) without the slab overhang

[3]

[4]

[5]

[6]

Figures 4.a to 5.b depict the correlation of the developed structural equation models to the generated data from the 3D linear elastic FEM Upper control limit (UCL) and lower control limits (LCL) of +/- 5% were plotted on all graphs It can be seen that majority of generated data from the SEM falls within the range of +/-5%

Table 4 NLREG predicted parameters for TL-4 and TL-5

Barrier

Type

Structural

Element

Load Location

Name of Reaction

Predicted Parameters

B Developed Design Models for TL-4 and TL-5

Table 4 presents the NLREG predicted parameters for the TL-4 and TL-5 in conjunction with the proposed Equations 7 and 8 for the moment for forces respectively All units were used in N and mm then multiplied by 10-3 or 10-6 to get values of the force and moment respectively The proposed models

longitudinal length of the overhang slab Equations 9.a and 9.b in conjunction with Table 4 present the proposed SEMs for the cantilever wall (barrier) TL-4 without the slab overhang Equations 10.a and 10.b

in conjunction with Table 4 present the proposed SEMs for the cantilever wall (barrier) TL -5 without the slab overhang

[7]

[8]

[9.a]

[9.b]

i. Slab-Internal-Moment ii. Wall-Internal-Moment iii. Slab-External-Moment iv. Wall-External-Moment Figure 6.a TL-4 internal loading

i. Slab-Internal-Force ii. Wall-Internal-Force iii. Slab-External-Force iv Wall-External-Force Figure 6.b TL-4 external loading

i. Slab-Internal-Moment ii. Wall-Internal-Moment iii Slab-External-Moment iv Wall-External-Moment Figure 7.a TL-5 internal loading

N.A N.A.

i. Slab-Internal-Force ii. Wall-Internal-Force iii Slab-External-Force iv Wall-External-Force Figure 7.b TL-5 external loading

[10.a]

[10.b]

Figures 6.a to 7.b depict the correlation of the developed structural equation models to the generated data from the 3D linear elastic FEM Upper control limit (UCL) and lower control limits (LCL) of +/- 5% were plotted on all graphs It can be seen that majority of generated data from the SEM falls within the range of +/-5%

1.3 Discussion

The 3D FEM reveals that the moment in the end portion of the overhang slab deck per meter at face of the rigid barrier is higher than that of the inner portion by a range of 30% to 50% The FEM reveals that the moment for the cantilever barrier (without the overhang slab) for the inner portion is higher of up to 59%, while it is higher by 43% for the end portion Generated data also may reveal extra information

Conclusions

On the basis of the numerical analysis and structural equation modeling for the stiffened-edge overhang slab with edge beam (barrier), the following conclusions can be drawn:

 The traffic barrier will add additional forces and moments to the overhang slab deck

 The proposed structural equations models for the forces and moments with the generated parameters using NLREG have good correlation to the 3D FEM results within +/- 5%

 Proposed models provide simplified structural analysis values for 1-m strip in order to facilitate the design and evaluation process

Acknowledgements

The authors acknowledge the support to this project by Ryerson University in Canada

References

AASHTO 2016 Manual for Assessing Safety Hardware, Second Edition American Association of State Highway and Transportation Officials, USA

ACI 318 2014 Building Code Requirements for Structural Concrete, ACI 31-14 American Concrete Institute, USA

AS 3600-2009 2009 Concrete Structures Australian Standard

Azimi, H., Sennah, K., Tropynina, E., Goremykin, S., Lucic, S., Lam, M 2014 Anchorage Capacity of Concrete Bridge Barriers Reinforced with GFRP Bars with Headed Ends ASCE Journal of Bridge Engineering, DOI: 10.1061/(ASCE)BE.1943-55922.0000606

CHBDC 2014 Canadian Highway Bridge Design Code, CAN/CSA S6-14 Canadian Standard Association, Ontario

Dhafer, M., Buyuk, M., Kan, S., 2007 Performance evaluation of portable concrete barriers National Crash Analysis Center, George Washington University, USA

Logan, D 2011 A First Course in The Finite Element Method, Fourth Edition Cengage Learning, USA Ross, H.E., Sicking D.L., Zimmer R.A., and Michie J.D 1993 Recommended Procedures for the Safety Performance Evaluation of Highway Features, NCHRP Report 350 Transportation Research Board National Research Council, National Academy Press, Washington, D.C

Turbell, T 1981 Crash Test of the Tric-Bloc precast concrete median barrier, Nr 252 National Road & Traffic Research Institute, Sweden

Wright, S (1921) Correlation and causation Journal of Agricultural Research, 20, 557-585