FLEXURAL CAPACITY OF STEEL-REINFORCED CONCRETE TL-5 BRIDGE BARRIER USING MODIFIED TRAPEZOIDAL YIELD-LINE FAILURE EQUATIONS

10th International Conference on Short andMedium Span Bridges Quebec City, Quebec, Canada, July 31 – August 3, 2018 FLEXURAL CAPACITY OF STEEL-REINFORCED CONCRETE TL-5 BRIDGE BARRIER USI

10th International Conference on Short and

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

FLEXURAL CAPACITY OF STEEL-REINFORCED CONCRETE TL-5 BRIDGE BARRIER USING MODIFIED TRAPEZOIDAL YIELD-LINE FAILURE

EQUATIONS

4morteza.fadaee@ryerson.ca

Abstract: Reinforced concrete bridge barriers are designed based on the specifications of the test levels

provided in the bridge design codes The Canadian Highway Bridge Design Code (CHBDC) introduces barrier crash test levels for various cases of traffic conditions on bridges, in the form of vehicle speed, impact angle and the mass of the vehicle CHBDC specifies equivalent vehicle impact loading for barrier design in the form of vertical, transverse and longitudinal impact loads, distributed over a specified barrier length and at a specified height from the deck slab In order to evaluate the flexural resistance of a barrier due to these impact loads, AASHTO-LRFD Bridge Design Specifications specify triangular yield line pattern within the barrier height Most recently, researchers developed trapezoidal yield-line failure equations based on the recorded crack pattern on TL-5 bridge barriers tested to-collapse, resulting in lower barrier capacity than that obtained from AASHTO-LRFD triangular yield-line failure equations In this study, the trapezoidal as well as the triangular yield line equations were utilized for designing TL-5 bridge barrier The analysis was conducted for both interior and end locations of the barrier Barrier flexural capacities were determined for different spacing between the vertical steel bars as well as horizontal steel bars in the barrier wall (i.e 100 to 300 mm spacing) The research outcome will assist design engineers in better understanding possible failure modes and crack patterns in TL-5 barriers

1 INTRODUCTION

Reinforced concrete barriers are one type of barriers specified in the Canadian Highway Bridge Design Code, CHBDC, (CSA 2014) to be utilized in bridges to resist impact load resulting from vehicle collision and to prevent overturning of vehicles and falling over traffic under the bridge AASHTO-LRFD Bridge Design Specifications (AASHTO 2017) specify impact loads for the design of steel-reinforced bridge barriers CHBDC has similar load configurations but with reduced values, taking into account concrete behavior under dynamic loading AASHTO-LRFD Specifications considers the yield-line theory to determine the transverse capacity of the barrier wall under vehicle impact loading The theory is based on considering a failure pattern due to the impact load, and the capacity is calculated with the equality of the internal and external work (Fadaee et al 2013) The concept of the yield-line method is based on assuming a failure pattern that is evaluated using experimental analysis Figures 1 and 2 show the AASHTO-LRFD yield line failure patterns due to vehicle collision at interior and end locations, respectively

Figure 1: AASHTO-LRFD yield line failure pattern due to vehicle collision at interior region of the barrier (adopted from AASHTO 2017)

Figure 2: AASHTO-LRFD yield line failure pattern due to vehicle collision at end location of the barrier

(adopted from AASHTO 2017) Recent studies (Jeon et al 2008 & 2011, Khederzadeh and Sennah 2014a & 2014b) have shown that the triangular failure pattern shown in Figures 1 and 2 did not exist in the tested steel-reinforced concrete Instead, a trapezoidal crack pattern exists at barrier failure The trapezoidal failure pattern for yield-line analysis was initially suggested by Jeon et al (2008, 2011) and later developed by Khederzadeh (2014)

It was shown that the trapezoidal failure pattern provides with a lower impact resistance of the barrier that the AASHTO-LRFD triangular yield-line pattern Bridge barriers are classified in different test levels as provided in bridge design codes CHBDC defines the Test Levels 1 through 5 as 1, 2, 4 and

TL-5 that were formerly known as performance levels (PL) Fadaee and Sennah (2018) investigated the modified yield-line analysis for steel-reinforced concrete bridge barrier design for TL-1 and TL-2 configurations

This paper presented the analysis of TL-5 bridge barrier based on the developed trapezoidal yield line failure patterns and compare the results with those obtained using the triangular AASHTO-LRFD yield line failure pattern The analysis was conducted considering different steel bar spacing in both the horizontal and vertical directions at the interior and end locations of the TL-5 barrier wall Recommendation for the optimum amount of reinforcement was deduced based on the findings of this research

2 DEVELOPED ANALYSIS METHOD USING TRAPEZOIDAL FAILURE

The current triangular yield-line failure pattern for barrier design available in AASHTO-LRFD Bridge Design Specifications, shown in Figure 1, consists of (i) diagonal yield-lines meeting at the barrier-deck connection with tension crack on the traffic side of the wall and (ii) a vertical yield line at the back face of the barrier wall centered at the vehicle impact point Jeon et al (2008 & 2011) suggested a trapezoidal failure pattern with an additional horizontal yield-line at the bottom of the barrier as shown in Figure 3 for vehicle collision with the barrier at interior locations This trapezoidal yield line pattern is characterized by two diagonal yield-lines, one on each side of the transverse line loading, meeting with the horizontal yield

line at the barrier-deck connection, all with tension cracks on the traffic side of the barrier wall This is in addition to two vertical yield lines, one on each side of the loaded length of the barrier, with tension cracks

on the back side of the barrier wall

Figure 3: Proposed trapezoidal yield line pattern for bridge barrier by Jeon et al (2011) at interior location The study by Jeon et al (2008 & 2011) assumed that the horizontal yield line length, X, at the barrier deck

on the study by Khederzadeh and Sennah (2014b), three different scenarios may be assumed, namely:

Khederzadeh and Sennah (2014b) developed modified trapezoidal yield-line capacity equations to

analysis of bridge barriers are explained as follows:

Yield Line Pattern with X ≥ L t (Interior Location)

of the barrier is showed with X As mentioned in the three scenarios, the first case is where the length of the base horizontal yield-line to be considered larger that the applied load length This can be assumed

external work is produced by the applied load and the lateral displacement The deformed shape is shown

fact that the external work is equal to the internal work (produced from yielding moment of the

[1]

2

,

c w

M

[2]

1

1

M Lc n L L M M n L L n L

for 1 ≤ n1 ≤ 2 where the variables are defined as follows (Khederzadeh et al., 2014; LRFD Bridge Design Manual, 2016):

Mc, w: Flexural capacity of the barrier about its horizontal axis at the wall

Mc, base: Flexural capacity of the barrier about its horizontal axis at the base H: Height of the transverse impact load application

2014)

Yield Line Pattern with X < L t (Interior Location)

With the similar concept, the equations for the second and third yield line failure scenarios can also be

horizontal yield line at the base of the wall (X) is less than the length of the applied load, as shown in

n2.Lt, 0 ≤ n2 < 1)

2

2 2

2 2 2

,

2

t

c w

M

for 0 ≤ n2 < 1 [4]

2 2

1

for 0 ≤ n2 < 1

2014)

Yield Line Pattern with X ≥ L t (End Location)

The same scenarios should be also applied to the exterior location of bridge barriers As mentioned above, the same trapezoidal yield-line pattern is applied, however, there will not be an inclined yield-line

at the end location of the barrier (Figure 6) The basis of the pattern was provided by Hirsch (1978) with a triangular scheme at the end location of the barrier His work concluded with the AASHTO-LRFD current

equations as mentioned above However, in recent studies (Khederzadeh et al 2014) the modified yield-line pattern and formulas for determining the barrier resistance was provided as follows:

[5]

2

,

c w

M H M H M n L

L n L n L

M

[6]

1

1

Yield Line Pattern with X < L t (End Location)

The last series of equations are derived for end location and when the length of the horizontal yield line at the base of the wall (X) is less than the length of the applied load (Figure 7) In this case the following

2

0.5 (1 )

L  L n 

2 2

2 2 2

,

2

t

c w

M

for 0 ≤ n2 < 1 [8]

2 2

1

for 0 ≤ n2 < 1

3 ANALYSIS PROCEDURE Analysis Cases

The provided equations in the previous section is applied to the TL-5 RC bridge barriers as per defined in CHBDC In order to evaluate all possible cases for the analysis, various parameters are changed and considered in the analysis The parameters for the analysis process include the rebar spacing in both horizontal and vertical directions ranging from 100 to 300 mm (5 iterations), interior or exterior location of

from top of the barrier to top of asphalt (full-height) or from top of the barrier to top of the tapered part of the barrier (top-height) All cases and parameters are given in Table 1 The analysis was conducted for all

Table 1: Breakdown of analysis cases and parameters

Item Level Test Location Evaluated Height n

(n 1 or n 2 )

Horizontal Rebar Spacing - S h

(mm)

Vertical Rebar Spacing - S v

(mm)

Total Cases

TL-5

Full-n1: 0.05 increments from 1 to 2 (21 cases)

portion

n2: 0.05 increments from 0 to 1 (21 cases)

No of

Analysis Results

The analysis results of the trapezoidal yield-line equations for TL-5 barrier include the minimum impact

(Tables 2 through 5) It was concluded that the full-height gives lower values for the impact resistance

following tables

Table 2: Impact load resistance (Rw) of TL-5 barrier at interior location

S v (mm)

100 1270 1145 1070 1020 985

Table 3: Corresponding n values of TL-5 barrier at interior location

100 150 200 250 300

S v (mm)

100 0.20 0.25 0.25 0.25 0.25

150 0.20 0.20 0.25 0.25 0.25

200 0.20 0.20 0.25 0.25 0.25

250 0.20 0.20 0.25 0.25 0.25

300 0.20 0.20 0.20 0.20 0.25

S v (mm)

Table 5: Corresponding n values of TL-5 barrier at exterior location

100 150 200 250 300

S v (mm)

100 0.40 0.45 0.45 0.50 0.50

150 0.35 0.40 0.40 0.45 0.45

200 0.35 0.40 0.40 0.40 0.45

250 0.35 0.35 0.40 0.40 0.40

300 0.30 0.35 0.35 0.35 0.40

4 TL-5 STEEL-REINFORCED CONCRETE BARRIER DESIGN

In barrier design, CHDBC specifies minimum impact resistance required for each of the test levels The impact load resistance given in the codes are in the form of applied static loads based on previous crash test results The minimum specified impact resistance for TL-5 bridge barrier in CHBDC is given as 210

kN without the live load factor Thus, by adding the 1.7 live load factor, a minimum impact resistance of 210x1.7 = 357 kN is required for TL-5 bridge barrier

Considering CHBDC requirements, barrier design, including the steel bar spacing for horizontal and vertical directions, can be recommended based on the modified trapezoidal yield-line analysis The analysis results (Tables 2 through 5) show that the end location of the barrier provides with lower impact resistances compared to interior locations One may observe that 15M steel bars at 300 mm spacing in the vertical and horizontal direction as depicted in Figure 8 provides the optimal design since its ultimate transverse resistance of 442 kN is greater than the 357-kN CHBDC design value At end location, considering the horizontal bar spacing maintained as 300 mm spacing, a 200 mm bar vertical spacing will provide a transverse capacity of 389 KN which is greater than the 357-kN CHBDC design value

Figure 8: Design recommendation for TL-5 concrete bridge barrier at interior location based on the

yield-line theory

5 CONCLUSIONS

This study presents the analysis of a TL-5 steel-reinforced concrete bridge barrier using the yield-line theory The developed transverse resistance of the barrier based on the trapezoidal yield-line failure pattern was considered in barrier analysis conducted in this study Results showed that to obtain the

critical transverse capacity of the TL-5 barrier wall, the length of the horizontal yield line portion of the trapezoidal yield line pattern at the barrier-deck connection should be less than the 2400 mm distributed length of the transverse line loading simulating vehicle collision with the barrier wall For a given TL-5 barrier dimensions similar to those shown in the 2014 CHBDC Commentary, 300 mm vertical and horizontal spacing for 15M steel bars at interior segments of the barrier wall is adequate to ensure that the barrier transverse resistance based on the yield-line theory is more than the CHBDC design value Also, reducing spacing of vertical bars from 300 to 200 mm at the end segment yields capacity-to-demand ratio more than 1

References

AASHTO 2017 AASHTO LRFD Bridge Design Specifications, 8th Edition American Association of State Highway and Transportation Officials, Washington D.C., USA

CSA 2014 Canadian Highway Bridge Design Code, CAN/CSA S6-14 Canadian Standards Association, Rexdale ON, Canada

Fadaee, M., Iranmanesh, A and Fadaee, M.J 2013 A Simplified Method for Designing RC Slabs under

Concentrated Loading International Journal of Engineering and Technology, IJET, 5(6): 675-679.

Fadaee, M and Sennah K 2018 Flexural Resistance of TL-1 and TL-2 Concrete Bridge Barriers using

the Yield-Line Theory 6th International Structural Specialty Conference, Canadian Society for Civil

Engineering, Fredericton NL, Canada, pp 1-10

Fadaee, M and Sennah K 2017 Investigation on Impact Loads for Test Level 4 of Concrete Bridge Barriers 6th International Conference on Engineering Mechanics and Materials Canadian Society for Civil Engineering, Vancouver BC, Canada, pp 1-10

Jeon, S.J., Choi, M.S and Kim, Y.J., 2011 Failure Mode and Ultimate Strength of Precast Concrete

Barrier ACI Structural Journal, 108(1): 99-107.

Jeon, S.J., Choi, M.S and Kim, Y.J., 2008 Ultimate Strength of Concrete Barrier by the Yield Line Theory

International Journal of Concrete Structures and Materials, 2(1), 57-62.

Khederzadeh, H 2014 Development of Innovative Designs of Bridge Barrier System Incorporating Reinforcing Steel or GFRP bars Ph.D Thesis, Civil Engineering Department, Ryerson University, Toronto, Canada

Khederzadeh, H and Sennah, K 2014a Experimental Investigation of Steel-Reinforced PL-3 Bridge Barriers Subjected to Transverse Static Loading Proceedings of the 9th International Conference on Short and Medium Span Bridges, Calgary, AL, pp 1-9

Khederzadeh, H and Sennah, K 2014b AASHTO-LRFD Yield-line Analysis for Flexural Resistance of Bridge Barrier Wall: Re-visited Proceedings of the 9th International Conference on Short and Medium Span Bridges, Calgary, AL, pp 1-10