Determining Lateral Deflections of Plastic Water-Filled Barriers

Jiang, T., Grzebieta, R.H. and Zhao, X.L, Determining Lateral Deflections of Plastic Water-Filled Barriers, Paper submitted to International Journal of Crashworthiness.

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Determining Lateral Deflections of Plastic Water-Filled Barriers

Jiang, T., Grzebieta, R.H. and Zhao, X.L.

Civil Engineering, Faculty of Engineering, Monash University, Wellington Road, Melbourne 3800, Australia Abstract - This paper presents two methods for determining the lateral deflection and the basic movement of a plastic water-filled barrier (PWB) system after an impact. In the first method theoretical equations are developed based on the conservation of energy while MADYMO simulations are used in the second method of estimating lateral deflections. Crash tests on various PWB systems carried out by different institutions including Monash University are used to validate the results from both the theoretical calculations and the MADYMO models. NOTATION D Lateral deflection (m) of a road safety barrier

Di Lateral deflection (m) of the ith segment of a PWB during impact

DLong. Displacement (m) of the segments that moved longitudinally during impact

dY Deflection (m) of a steel beam when yield occurs

E Young’s modulus (N/m2)

EBEAM Energy (J) dissipated by the distortion of a steel beam

EBR Energy (J) dissipated by the movement of PWB segments

EBR-Lat. Work (J) done by the friction force of the segments that moved laterally during impact

EBR-Long. Work (J) done by the friction force of the segments that moved longitudinally during impact

EL Vehicle kinetic energy resolved perpendicular to barrier, or lateral kinetic energy, or impact severity (J)

EVC Energy (J) dissipated by vehicle crush

EVR Work (J) of vehicle’s rolling friction resistance force

FBA Average force applied to the barrier (N)

FVA Average lateral force applied to the vehicle (N)

I Second moment of area of the cross-section of a steel beam (m4)

l1 Length of the cantilever beam (m)

lB Length (m) of a PWB segment

M(α) Relationship between the moment M (Nm) and the rotation angle α (rad) of the joints between PWB segments

mB Mass (kg) of an individual PWB segment filled with water

mV Vehicle mass (kg).

MY Yield moment (Nm)

NT Overall number of segments installed in a PWB system

NBEAM Number of the steal beams used to strengthen a PWB

n Number of segments that moved laterally during impact

nLong. Number of segments that moved longitudinally during impact

V Impact speed (m/s)

z Distance (m) of the point furthest from the elastic neutral axis

α Rotation angle (rad) of PWB segments and/or beam

αY Rotation angle (rad) when yield occurs

θ Impact angle (degrees)

μB Friction coefficient between a PWB and ground.

μV Vehicle rolling friction coefficient

σY Yield stress (N/m2)


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A BRIEF INTRODUCTION TO PLASTIC WATER-FILLED BARRIER SYSTEMS Temporary road safety barrier systems are designed to prevent an errant vehicle access into construction or maintenance work zones and can be erected and dismantled quickly. Conventionally, they are made of precast concrete. Since the late 1980’s, a new type of temporary safety barrier, i.e. a plastic water-filled barrier, has been developed and used worldwide. Normally, a PWB system consists of a certain number of identical segments/modules that are hollow inside with internal stiffening provided by web framing. Segments are connected together at their ends through specially designed joints to form a complete system and, once installed, are filled with water to provide ballast against movement (Grzebieta et al. 2001). Often steel cables, tubes, or W-beams are also used to connect each segment and provide extra strength for the system. Sometimes there are also pedestals and mounting straps for each section, so that the barrier’s centre of gravity can be adjusted to provide high-speed protection. Usually PWBs are made from low-density polyethylene with a wall thickness ranging from 6 mm to 9 mm. Typically each segment is about 2000mm long, 600mm wide at the base and 800mm to 1000mm high with a weight of 50 kg to 75 kg when empty and 300 kg to 1000 kg when filled with water. The major advantage of PWBs is that each segment is only 50 kg to 75 kg when empty and two people can install an entire system (Zou et al. 2000; Grzebieta et al. 2001). The first PWB system was developed in the late 1980s in the USA. With the release of NCHRP Report 350 in 1993, each PWB system needed to be assessed through full-scale crash tests, and all US certified PWB systems are listed on the website of the Federal Highway Administration (FHWA) (FHWA 2004). In Australia, however, when the first PWBs were introduced in the early 1990s, they were not required to satisfy any crash test requirements until the release of AS/NZS 3845 in December 1999. When selecting and installing PWBs for temporary construction or road works, it is very important for designers to know the barrier’s working width and how it moves when an errant vehicle crashes into it at different speeds and angles. However, most of the PWB vendors can only provide the lateral deflection under two certification crash test conditions, i.e. a small car (820C) crashing into the barrier at an angle of 20 degrees and at the speed of the PWB’s test level; and a pickup truck (2000P) impacting at an angle of 25 degrees and at the same speed as the 820C car test. Such information is important but limited for barrier designers when they face real world traffic and site conditions. It is impractical to carry out crash tests on a PWB system under all impact conditions. Therefore, methods need to be developed that can be used to determine lateral deflections of PWBs for different impact conditions. FULL-SCALE CRASH TESTS ON PWBS To develop theoretical equations and computer models for determining lateral deflections generated by such a complex impact process as a car crashing into a PWB, it is necessary to have data from a large number of crash tests. Hence, efforts have been made to search for full-scale crash test data on PWBs in the literature and online resources. A total of twenty-three crash tests were found. All of these crash tests were conducted according to either NCHRP Report 350 or AS/NZS 3845. Crash test results on various PWB systems are summarised in Table 1. The impact points for these crash tests were basically located near the centre of the installation which was between 40 m and 70 m long. For Test Level 2 and Test Level 3 PWB systems, specially-designed devices using either steel cables (the Triton barrier and the 426 Barrier) or steel tubes/beams (the Guardian 350 barrier, the Yodock barrier and the Guardliner™ Barrier) or using both steel tubes and cables (the SB-1-TL barrier), are needed to strengthen the PWBs.


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Table 1 - Summary of full-scale crash tests on PWB systems

No Manufacturer

and Product

Test level

Vehicle mass (kg)

Impact speed (km/h)

Impactangle(deg)

Test result Image ReferenceLateral

deflection (m)

Number of segments

moved laterallyVehicle response

1

Energy Absorption Systems, Inc.: Triton Dimension (mm): 1981*533*813(TL2) 1981*533*991(TL3) Weight (kg): Empty: 64; Full: 612 (TL2), 620 (TL3) Connection: pin joints, steel cables on top between joints

TL-2 807.3 72.0 20 1.0 Not available Came to rest

against the barrier

Energy Absorption

Syatems (2004);

FHWA (2004)

1970.5 72.3 25 3.9 Not available Came to rest against the barrier

TL-3

875 97.04 21 2.3 9 Not redirected, captured by the barrier

2005 97.56 25 5.8 11 Not redirected, captured by the barrier

--- 2004 95.74 7 1.4 7 Contained and redirected parallel to the barrier

2

Safety Barrier Systems: Guardian 350 Highway Kit Dimension (mm): 1830*610*1070 Weight (kg): Empty: 61; Full: 880 (including tubes) Connection: steel bars welded to the inside of the pipes on one end and slotted on the other for a bolted connection

TL-2

820 70.6 20.3 0.6 Not available Not available

FHWA (2004)

2000 71.5 25.8 1.98 Not available Not available

TL-3

820 100 20 1.1 Not available Contained and redirected

2000 100 25 3.4 Not available Contained


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Table 1 - Summary of full-scale crash tests on PWB systems (continued)

No Manufacturer

and Product

Test level

Vehicle mass (kg)

Impact speed (km/h)

Impactangle(deg)


deflection (m)

Number of segments


3

Yodock Wall Company, Inc.: Model 2001M (TL2) Model 2001 (TL3) Dimension (mm): 1830*457*813(TL2) 1830*610*1170(TL3) Weight (kg): Full: 460 (TL2), 786 (TL3) Connection: polyethylene couplers; steel tubes

TL-2 2042 68.5 24.0 3.68 Not available Contained Yodock

Wall Company (2003 - 2004);

FHWA (2004)

TL-3

896 97.7 19.8 1.23 Not available Contained

2041 98.4 24.8 4.28 Not available Contained

4

Rhino Safety Barrier LLC: Rhino Barrier Dimension (mm): 2000*690*890 Weight (kg): Empty: 54; Full: 476 Connection: see images

TL-2

917 72.6 20 1.75 9 Redirected

Connection: steel-reinforced polyethylene pins and steel bridging strips span the joint between barrier segments

Rhino Safety Barrier LLC

(2001);

FHWA (2004)

2000 69.2 25 4.0 Not available Contained and redirected

5

Creative Building Products: 426 Barrier Dimension (mm): 1830*610*1070 Weight (kg): Empty: 77; Full: 782 Connection: three steel cables threaded through three holes

TL-2

820 100.7 20 0.9 Not available Not reported

FHWA (2004)

2000 73 25 3.14 Not available Captured by the barrier


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No Manufacture

and Product

Test level

Vehicle mass (kg)

Impact speed (km/h)

Impactangle(deg)


deflection (m)

Number of segments


6

Safety Barriers, Inc.: Model SB-1-TL Dimension (mm): 2130*610*1070 Weight (kg): Empty: 74.5; Full: 835.5 Connection: two aluminium pipes cast into each side of each segment; four steel cables are threaded through these pipes to connect all segments

TL-3 2054 99.4 25.4 4.78 Not available Captured by the barrier

FHWA (2004)

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Barron & Rawson Pty Ltd: GuardlinerTM

Barrier Dimension (mm): 2000*600*925 Weight (kg): Empty: 50; Full: 655 (including W-beam and brackets) Connection: see images

TL-2

891 70 20.5 0.78 12 Contained

Connection: four short steel stripes at each joint; W-beam supported by steel brackets which are secured to every segment join by two bolts

Zou and Grzebieta

(2004)

2170 70 25 2.64 16 Redirected


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No Manufacturer

and Product

Test level

Vehicle mass (kg)

Impact speed

(km/h)

Impactangle (deg)

Test result

Image ReferenceLateral deflection

(m)

Number of segments

moved laterally

Vehicle response

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Barron & Rawson Pty Ltd: Roadliner 2000™ S Dimension (mm): 2000*600*925 Weight (kg): Empty: 50; Full: 630 Connection: four short steel stripes and two bolts at each joint (see images)

TL-0

920 49 20 0.54 9

Contained and redirected with moderate pitching and rolling Grzebieta

and Zou

(1998-2000)

1570 48 25 1.2 10 Contained and redirected

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Barrier Systems Pty Ltd: Dimension (mm): 2000*600*940 Weight (kg): Empty: 50; Full: 950 Connection: see images

TL-0

910 50 20 0.49 8 Redirected

Grzebieta and Zou

(1998-2000)

1560 49 25 1.51 9 Contained and came to rest parallel against the barrier


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THEORETICAL EQUATIONS FOR DETERMINING LATERAL DEFLECTIONS OF PWBS To develop theoretical equations for calculating the lateral deflection and the basic movement of a PWB, it has to be assumed that a) the PWB installation is long enough and the vehicle hits the middle of the installation; b) the PWB redirects the vehicle and the vehicle does not roll over or ride over the barrier; c) energy dissipated as a result of tearing of the PWB barrier is neglected and d) the lateral deflection of a PWB caused by a vehicle impacting it at a speed of V and an angle of θ is taken to be equivalent to that generated by the vehicle crashing with the PWB laterally at a resolved speed of V·sin θ. According to the crash test results, the deformation of a PWB after an impact can be approximated in simplistic form as shown in Figure 1. Based on the theory of energy conservation, the vehicle’s lateral kinetic energy (EL) is approximately equal to the work done by the movement of the PWB segments, the crush of the impacting vehicle, the rolling friction resistance of the vehicle and the energy dissipated by the distortion of the beam (if fitted). Thus,

BEAMVRVCBR2

VL )sin(21 EEEEVmE +++== θ [1]

where EL is the vehicle’s lateral kinetic energy (J), mV is the mass of the vehicle (kg), V is the impact speed (m/s), θ is the impact angle (degrees), EBR is the energy dissipated by the movement of the PWB segments (J), EVC is the energy dissipated by the vehicle crush (J), EVR is the work of the vehicle’s rolling friction resistance force (J) and EBEAM is the energy (J) dissipated by the distortion of the beam. If EBR, EVC, EVR and EBEAM can all be determined as a function of the lateral deflection (D), the lateral deflection D can then be estimated using Equation 1.

Figure 1 - Assumed deformation of a PWB Determining EVC and EVR In the case of a car crashing into a PWB, the impact load is low because a PWB is a flexible system. Hence, the energy dissipated by the crush of vehicle EVC can be neglected. This is evident from the crash test result where a 1600 kg car crashed into a PWB system at a speed of 50 km/h and an angle of 25 degrees (Grzebieta and Zou 1998-2000). Figure 2 shows that only minor crush was observed after the impact.

lB

…... ……

CAR

Before impact

1st 2nd …… Centralsegment2

)1( −n

α D.…. ……

After impact

DLong. DLong. l

Vsinθ


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Figure 2 - Vehicle frontal crush after impact

The work done by the vehicle’s rolling friction resistance force EVR as it is being redirected can be determined as

DgmE VVVR μ= [2] where g is 9.81 (m/s2), μV is the rolling friction coefficient of the vehicle and D is the lateral deflection (m). Generally, the rolling friction coefficient μV is less than 0.1 (Bauer et al. 2000). Thus, EVR is small compared to the impact energy EL and can be ignored as well. Hence, Equation 1 can be further expressed as

BEAMBR2

V )sin(21 EEVm +=θ [3]

Determining EBR Figure 1 shows that whilst some segments were pushed and moved laterally, the other segments were dragged and displaced longitudinally towards the impact point. Hence, the energy dissipated by the movement of segments of a PWB (EBR) can be approximately considered as comprising of two parts; the work done by the friction force of the segments that moved laterally and the work done by the friction force of the segments that moved longitudinally. Thus

.LongBRLat.BRBR −− += EEE [4] where EBR-Lat. is the work (J) done by the friction force of the segments that moved laterally and EBR-Long. is the work (J) done by the friction force of the segments that moved longitudinally. However, to determine EBR-lat. and EBR-Long., the number of segments that moved laterally during impact (n) needs to be estimated first. Estimating the number of PWB segments that moved laterally during impact The process of a car crashing into a PWB is very complicated. Many time dependant factors are involved in the whole dynamic process, such as the impacting force and angle, the interaction among segments, the movement of segments both laterally and longitudinally, the friction between the


9

vehicle and the PWB, the deformation of the vehicle and barrier, and even the movement of water inside the barrier (Jiang et al. 2002). It is a challenge to develop a theoretical method for determining the number of segments that moved laterally during impact. Nevertheless, a simplified method was developed and reported as follows. If the initial lateral impact speed of the vehicle is assumed as (Vsinθ) and its final lateral speed is zero at the maximum lateral displacement D, the average lateral force applied to the vehicle can be calculated as

DVmF

2)sin( 2

VVAθ

= [5]

where FVA is the average lateral force applied to the vehicle (N). The average force applied to the PWB (FBA) is equal but opposite to FVA. The load required to move the barriers can be directly equated to the sliding resistance of the plastic barriers themselves. Thus

BB

2

VVABA 2)sin( μθ gmn

DVmFF ⋅=== [6]

where n is the number of segments that moved laterally during impact, mB is the mass (kg) of an individual PWB segment filled with water and µB is the friction coefficient between the PWB and the ground. Hence, the number of segments that moved during impact can be estimated using Equation 6 as

BB

2V

2)sin(μθ

gmDVm

n⋅

= [7]

To validate Equation 7, the numbers of segments that moved laterally during impact calculated using Equation 7 were compared to those observed in the crash tests. Table 1 shows ten crash tests where the number of segments that moved laterally during impact is available. The friction coefficient μB was assumed being the result of a laboratory test performed by Grzebieta and Zou (1998-2000) where they dragged a New Jersey type PWB over a concrete floor. As PWBs are basically made from a similar polyethylene material, the friction coefficient of PWBs placed on dry bitumen surfaces was also assumed to be 0.4. Hence, for the 820C Test Level 3 test of the Triton barrier (No. 1 in Table 1), the estimated number of segments that moved laterally during impact was calculated using Equation 7 as

74.081.96203.22

)21sin6.304.97(875

2)sin(

2

BB

2V ≈

××××

°××=

⋅=

μθ

gmDVm

n

Similarly, the estimated number of segments that moved laterally during impact for the other nine tests are summarised in Table 2. Results in Table 2 show that Equation 7 basically underestimates n by an average number of two segments. Hence, the equation for determining n is empirically adjusted by adding 2 to Equation 7 as

22

)sin(

BB

2V +⋅

=μθ

gmDVm

n [8]


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Table 2 - Comparison of n from the calculations and the crash tests

No No. in Table 1

Vehicle mass (kg)

Impact speed (km/h)

Impact angle (deg)

PWB segment

mass (kg)

Lateral deflectionfrom test

D (m)

Number of segments that moved laterally, n Difference

(=nCalculated - nTest)Crash test result, nTest

Calculated result, nCalculated

1 1 (TL-3)

875 97.04 21 620 2.3 9 7 -2

2 2005 97.56 25 620 5.8 11 9 -2

3 1 2004 95.74 7 620 1.4 7 3 -4

4 4 917 72.6 20 470 1.75 9 7 -2

5 7 (TL-2)

891 70 20.5 655 0.78 12 12 0

6 2170 70 25 655 2.64 16 12 -4

7 8 (TL-0)

920 49 20 630 0.54 9 7 -2

8 1570 48 25 630 1.2 10 8 -2

9 9 (TL-0)

910 50 20 950 0.49 8 6 -2

10 1560 49 25 950 1.51 9 5 -4 Determining EBR-Lat. Figure 1 indicates that the energy dissipated by the segments that moved laterally during impact can be approximately divided into the work done by the friction force of every segment that moved laterally (without rotation), which is symbolised as EBR-Lat.-NR, and the work required to rotate these segments to an angle α, which is symbolised as EBR-Lat.-R. Thus

R-Lat.-BRNR-Lat.-BRLat.-BR EEE += [9] (a) Determining EBR-Lat.-NR According to the crash test results, the deformation of the barriers on either the left hand or the right hand side of the central segment can be considered as approximately symmetrical (see Figure 1). Thus, EBR-Lat.-NR can be determined as

) ( 22

1

1BBBB

1BBNR-Lat.-BR ∑∑

−

==

+==

n

ii

n

ii DgmDgmDgmE μμμ [10]

where Di is the lateral displacement (m) of the ith segment. Figure 1 shows that the lateral displacement D1 of the 1st segment that has moved can be approximated as

αsin21

B1 lD = [11]

where lB is the length (m) of a PWB segment. Similarly, the lateral displacement D2 of the 2nd segment is

αsin23

B2 lD = [12]

and so on, where finally the lateral displacement of the barrier next to the central segment

21−nD is


11

αsin2

)2(B

21 lnDn

−=− [13]

The angle α can be calculated from Figure 1 using trigonometry as

2

B2

2)1(

sin

⎥⎦⎤

⎢⎣⎡ −

+

==

ln

D

DlD

α [14]

Substituting Equations 11 to 14 into Equation 10 results in

2

B2

2BBB

BB

2

B2

2BBB

BB

BBBBB

BBBBBBB

21

1BBBBNR-Lat.-BR

2)1(4

)1(

2)1(4

)1(

sin2

2)1(

2)2(

21

2

)sin2

)2(sin23sin

21(2

)(2

⎥⎦⎤

⎢⎣⎡ −

+⋅

−+=

⎥⎦⎤

⎢⎣⎡ −

+

⋅−

+=

⋅

−⋅⎟⎠⎞

⎜⎝⎛ −

++=

−+⋅⋅⋅⋅⋅⋅+++=

+= ∑−

=

lnD

DnlgmDgm

lnD

DnlgmDgm

nn

lgmDgm

lnllgmDgm

DgmDgmE

n

ii

μμ

μμ

αμμ

αααμμ

μμ

[15]

where n is as given in Equation 8. (b) Determining EBR-Lat.-R The work required to rotate one PWB segment to an angle α can be determined from Figure 3 as

∫

∫

⋅+=

⋅+=−

α

α

αμ

αα

αμα

0

BBB

0 B

BB1-R-Lat.RBR

2d)(

]d2

)([

lgmM

lgmME

[16]

where EBR-Lat.-R-1 is the work (J) required to rotate one PWB segment to an angle α, and M(α) represents the relationship between the moment M (Nm) and the rotation angle α (rad) of the joint.


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Figure 3 - Rotation of a PWB segment

It was observed from crash test videos that the segments that moved laterally during impact rotated similarly to an angle α (Grzebieta and Zou 1998-2000; Zou and Grzebieta 2004). Thus, EBR-R can be estimated as

2d)( BBB

0 1-R-Lat.-BRR-Lat.-BRαμ

ααα lgnm

MnnEE +== ∫ [17]

Substituting Equations 15 and 17 into Equation 9, EBR-Lat. can be calculated as

2d)(

2)1(4

)1( BBB

0 2

B2

2BBB

BB

R-Lat.-BRNR-Lat.-BRLat.-BR

αμαα

μμ

α lgnmMn

lnD

DnlgmDgm

EEE

++

⎥⎦⎤

⎢⎣⎡ −

+⋅

−+=

+=

∫

[18]

Using trigonometry, the value of α (rad) approximately equals to sinα with a difference of less than 1% when α < 14°(Rosenbach et al. 1961; Bauer et al. 2000). Hence, the rotation angle α can be approximated using Figure 1 and Equation 14 as

2

B2

2)1(

sin

⎥⎦⎤

⎢⎣⎡ −

+

=≈

lnD

Dαα [19]

Substituting Equation 19 into Equation 18 gives

2

B2

BBB

0 2

B2

2BBB

BBLat.-BR

2)1(2

d)(

2)1(4

)1(

⎥⎦⎤

⎢⎣⎡ −

+⋅

++

⎥⎦⎤

⎢⎣⎡ −

+⋅

−+= ∫

lnD

Dlgnm

Mn

lnD

DnlgmDgmE

μ

ααμ

μα

[20]

Determining EBR-Long. The number of segments that moved longitudinally during impact can be estimated as

nNn −= TLong. [21]

lB

α

mBgμB M(α)

F


13

where nLong. is the number of segments that moved longitudinally during impact, n is the number of segments that moved laterally during impact and NT is the total number of segments installed in the PWB system. The displacement of the segments that moved longitudinally during impact, which is expressed as DLong., can be approximately determined from Figure 1 as

B

2

B2

BLong. 2)1(

2)1(

2)1( lnlnDlnlD −

−⎥⎦⎤

⎢⎣⎡ −

+=−

−= [22]

Thus, EBR-Long. can be calculated as

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−⎥⎦

⎤⎢⎣⎡ −

+−=

=

B

2

B2

BBT

Long.BBLong.Long.-BR

2)1(

2)1( )( lnlnDgmnN

DgmnE

μ

μ [23]

Substituting Equations 20 and 23 into Equation 4, the energy dissipated by the movement of the segments of a PWB (EBR) can be calculated such that

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−⎥⎦

⎤⎢⎣⎡ −

+−

+

⎥⎦⎤

⎢⎣⎡ −

+⋅

++

⎥⎦⎤

⎢⎣⎡ −

+⋅

−+

=+=

∫

−−

B

2

B2

BBT

2

B2

BBB

0 2

B2

2BBB

BB

.LongBRLat.BRBR

2)1(

2)1( )(

2)1(2

d)(

2)1(4

)1(

lnlnDgmnN

lnD

DlgnmMn

lnD

DnlgmDgm

EEE

μ

μαα

μμ

α

[24] where n is as given in Equation 8. Determining EBEAM With regard to PWBs where steel beams are used to strengthen the barrier, as illustrated in Figure 4, the energy dissipated by the distortion of the steel beam (EBEAM) during impact needs to be determined. To do so, it is assumed that the beam distorts in a manner similar to a beam with fully fixed ends as shown in Figure 5. That the distortion of the steel beam is similar to a beam restrained by fully fixed ends is clearly visible in the overhead photograph (Figure 6) of the PWB crash test performed by Grzebieta and Zou (2003).

Figure 4 - Assumed deformation of a PWB with steel beams

D

nlB

Steel beam Segments of a PWB


14

To analyse the energy dissipated by the distortion of the steel beam as shown in Figure 5, it is convenient to adopt a rigid-plastic material model. Hence the steel beam bending characteristics and thus the relationship between the bending moment M(α) and the rotation angle α can generally be simplified as bi-linear as shown in Figure 7 (Megson 1996), where MY is the yield moment (Nm) and αY is the rotation angle (rad) when yield occurs.

Figure 5 - Distortion of a steel beam

Figure 6 - Overhead view of a PWD crash test (Grzebieta and Zou 2003)

Figure 7 - Bending moment versus rotation angle for a steel beam

Figure 8 - A cantilever steel beam

D

B2)1( ln −

Steel beam

α

αY α

MY

α (rad)

M (Nm)


15

Figure 8 shows a cantilever steel beam where the deflection is D. The energy required to push the beam to a deflection D can be estimated using the curve shown in Figure 7 as

YYY

0 1-BEAM 21d)( αααα

α⋅−⋅== ∫ MMME [25]

where the rotation angle α can be approximated using Equation 19 and Figure 8 as

21

2sin

lDD+

=≈ αα [26]

where l1 is the length of the cantilever beam. With regard to the beam shown in Figure 5, the energy dissipated by the distortion of the steel beam can be considered as double of the energy dissipated by the beam shown in Figure 8. Hence

YYY1-BEAMBEAM 22 αα ⋅−⋅== MMEE [27] MY can be calculated as

zI

M YY

σ= [28]

where σY is the yield stress of the steel (N/m2), I is the second moment of area of the cross-section of the steel beam (m4) and z is the distance of the point furthest from the elastic neutral axis (m) (Megsson, 1996). Once MY is determined, the deflection of the beam when yield occurs can also be calculated as

EIlM

EIllF

EIlF

d33

)(3

21Y

211Y

31Y

Y =⋅

== [29]

where dY is the deflection (m) of the beam when yield occurs and E is the Young’s modulus (N/m2) (Megsson, 1996). Generally, dY is small compared to l1. Hence, αY can be approximated using trigonometry and Equation 29 as

EIlM

ld

31Y

1

YY =≈α [30]

Data from a laboratory test performed by Cichowski et al. (1961) was used to validate Equation 27. Figure 9 shows the test set-up and the test result, where a load was placed in the centre of a 3810 mm long W-beam rail and the load-deflection curve was recorded. The yield strength for this steel (σY) was 350 MPa and the furthest point from the neutral axis (z) was 40 mm (Cichowski et al. 1961). The second moment of area of the cross-section of the W-beam was determined as 970000 mm4 or 970.0E-09 m4 (Deleys and McHenry 1967; Reid et al. 1997). Thus, MY for the W-beam steel was calculated using Equations 28 as

(Nm) 5.84871040

10970103503

96Y

Y =×

×××== −

−

zI

Mσ


16

0

1000

2000

3000

4000

5000

0 1 2 3 4 5 6 7 8 9 10 11 12Deflection (inches)

Loa

d (lb

s)

.

W-beam length: 150" (3810 mm)

Figure 9 - W-beam laboratory test set-up and test result (Cichowski et al. 1961)

For the case shown in Figure 9, l1 was (mm) 19052

3810= . E can be taken as 210.0E+09 N/m2. Thus,

the rotation angle when yield occurs αY was calculated using Equation 30 as

(rad) 0265.010970102103

905.15.84873 99

1YY =

×××××

=≈ −EIlM

α

If the deflection was assumed as 152.4 mm (6 in.), α can be estimated using Equation 26 as

(rad) 08.0905.11524.0

1524.0222

12

=+

=+

≈lD

Dα

Thus, when the deflection was 152.4 mm (6 in.), the energy dissipated by the W-beam was calculated by substituting αY and α into Equation 27 as

(Nm) 11330265.05.848708.05.848722 YYYBEAM =×−××=⋅−⋅= αα MME The energy dissipated by the W-beam when the deflection was 152.4 mm (6 in.) was also determined using the test data as about 1300 Nm, which was the shadow area shown in Figure 9. The energy dissipated by the W-beam calculated using Equation 27 compares reasonably well with the test result.

Hence, with regard to the beam distorted as shown in Figure 5 where B1 2)1(

ln

l−

= , the energy

dissipated by the beam can be determined by substituting Equations 26 and 30 into Equation 27 as

EIlMn

lnD

DMEI

lMM

lDDM

MME

6)1(

2)1(

23

2

2

B2Y

2

B2

Y1YY2

12Y

YYYBEAM

−−

⎥⎦⎤

⎢⎣⎡ −

+

=−+

=

⋅−⋅= αα [31]


17

For PWBs where more than one steel beam is used to strengthen the PWB system, such as the Guardian 350 Highway Kit (No. 2 in Table 1) and the Yodock barrier (No. 3 in Table 1), the energy dissipated by the distortion of the beams during impact can be estimated using Equation 31 as

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−

⎥⎦⎤

⎢⎣⎡ −

+

=EI

lMn

lnD

DMNE6

)1(

2)1(

2 B2Y

2

B2

YBEAMBEAM

[32]

where NBEAM is the number of the steal beams used to strengthen the PWB barrier. Determining D Substituting Equations 24 and 32 into Equation 3, the following equation is obtained.

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−

⎥⎦⎤

⎢⎣⎡ −

+

+⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−⎥⎦

⎤⎢⎣⎡ −

+−

+

⎥⎦⎤

⎢⎣⎡ −

+⋅

++

⎥⎦⎤

⎢⎣⎡ −

+⋅

−+

=+=

∫

EIlMn

lnD

DMN

lnlnDgmnN

lnD

DlgnmMn

lnD

DnlgmDgm

EEVm

6)1(

2)1(

2

2)1(

2)1( )(

2)1(2

d)(

2)1(4

)1(

)sin(21

B2Y

2

B2

YBEAM

B

2

B2

BBT

2

B2

BBB

0 2

B2

2BBB

BB

BEAMBR2

V

μ

μαα

μμ

θ

α

[33]

where n and MY is as given in Equation 8 and Equation 28, respectively. Although Equation 33 is in a complicated form, D, which is the only unknown factor, can be calculated using the numerical solution for non-linear equations in a single unknown (Bronshtein et al. 2004). Comparison with crash test results To validate the equations for calculating the lateral deflection and the number of segments that moved laterally during impact, the calculated results were compared to the results from full-scale PWB crash tests listed in Table 1. To do so, M(α) and MY in Equation 33 had to be determined first. M(α) and MY were either determined using data of quasi-static laboratory tests or calculated using Equation 28. Details regarding the derivation of M(α) and MY are presented in Appendix A. Using the results of M(α) and MY determined, D and n can be calculated using Equations 33 and 8, respectively. The results are summarised in Table 3. Details of how these results were calculated are reported in Appendix B.


18

Table 3 – Comparison of the results from the crash tests and the calculations

No Manufacturer

and Product

Test level

PWB segment data MY and M(α)

Vehiclemass

mV (kg)

Impactspeed

V (km/h)

Impactangleθ (deg)

Test result Calculated result Difference * Length (lB) ×

Width (at base) × Height (mm)

Full weight mB (kg)

Lateral deflection

D (m)

Number of segments

that moved laterally, n

Lateral deflection

D (m)

Number of segments


Lateral deflection

(%)

Number of segments

that moved laterally

1

Energy Absorption Systems, Inc: Triton

TL-2 1981×533×813 612

MY = 0

M(α) = 0

807.3 72.0 20 1.0 Not available 1.033 10 +3.3 ---

1970.5 72.3 25 3.9 Not available 3.03 12 -22.3 ---

TL-3 1981×533×991 620 875 97.04 21 2.3 9 1.917 11 -16.6 +2

2005 97.56 25 5.8 11 4.945 13 -14.7 +2

--- 1981×533×991 620 2004 95.74 7 1.4 7 0.556 10 -60.3 +3

2

Safety Barrier Systems: Guardian 350 Highway Kit

TL-2 1830×610×1070 880 MY = 2202.2 (Nm)

M(α) = 0

820 70.6 20.3 0.6 Not available 0.708 10 +17.9 ---

2000 71.5 25.8 1.98 Not available 2.16 12 +9.1 ---

TL-3 1830×610×1070 880 820 100 20 1.1 Not

available 1.221 11 +11.0 ---

2000 100 25 3.4 Not available 3.546 14 +4.3 ---

3

Yodock Wall Company, Inc: Model 2001M (TL2) Model 2001 (TL3)

TL-2 1830×457×813 460 MY = 6046.8 (Nm)

M(α) = 0

2042 68.5 24.0 3.68 Not available 3.267 13 -11.2 ---

TL-3 1830×610×1170 786

896 97.7 19.8 1.2 Not available 1.430 11 +19.2 ---

2041 98.4 24.8 4.02 Not available 4.215 13 +4.9 ---


19

Table 3 – Comparison of the results from the crash tests and the calculations (continued)

No Manufacturer

and Product

Test level

PWB segment data MY and M(α)

Vehiclemass

mV (kg)

Impactspeed

V (km/h)

Impact angleθ (deg)

Test result Calculated result Difference * Length (lB) ×

Width (at base) × Height (mm)

Full weight mB (kg)

Lateral deflection

D (m)

Number of segments


Lateral deflection

D (m)

Number of segments


Lateral deflection

(%)

Number of segments

that moved laterally

4

Rhino Safety Barrier LLC: Rhino Barrier

TL-2 2000*690*890 476

MY = 0

M(α)= 12835 α

917 72.6 20 1.75 9 1.377 11 -21.3 +2

2000 69.2 25 4.0 Not available 3.082 14 -22.9 ---

5

Creative Building Products: 426 Barrier

TL-2 1830*610*1070 782 MY = 0

M(α)=0

820 100.7 20 0.9 Not available 1.431 11 +59.0 ---

2000 73 25 3.14 Not available 2.452 12 -21.9 ---

6 Safety Barriers, Inc: Model SB-1-TL

TL-3 2130*610*1070 835.5MY = 0

M(α)=0

2054 99.4 25.4 4.78 Not available 4.91 11 +2.7 ---

7

Barron & Rawson Pty Ltd: GuardlinerTM Barrier

TL-2 2000*600*925 655

MY = 8487.5 (Nm)

M(α)=

31880 α

891 70 20.5 0.78 12 0.925 11 +18.6 -1

2170 70 25 2.64 16 2.503 14 -5.2 -2

8

Barron & Rawson Pty Ltd: Roadliner 2000™ S

TL-0 2000*600*925 630

MY = 0

M(α)= 31880 α

920 49 20 0.54 9 0.541 10 +0.2 +1

1570 48 25 1.2 10 1.133 11 -5.6 +1

9 Barrier System Pty Ltd:

TL-0 2000*600*940 950 MY = 0

M(α) = 0

910 50 20 0.49 8 0.443 8 -9.7 0

1560 49 25 1.51 9 0.987 9 -34.6 0

Note: *: ‘-’ underestimate; ‘+’ overestimate.

20 Jiang, T., Grzebieta, R.H. and Zhao, X.L, Determining Lateral Deflections of Plastic Water-Filled Barriers, Paper submitted to International Journal of Crashworthiness.

Discussion Comparison between the calculated and the test results in regards to the number of segments that moved during impact indicates that the differences are on average within two segments. The calculated lateral deflections also compare reasonably well with the crash test results, except for three tests; the 95.74 km/h at 7 degrees test for the Triton barrier, the 820C TL-2 test for the 426 Barrier and the 1600C TL-0 test for the Barrier System barrier where the differences were -60.3%, +59.0% and -34.6%, respectively. For the 95.74 km/h and 7 degrees impact test on the Triton barrier, the impact severity, defined as

2V )sin(

21 θVm , was 10.5 kJ. The test result for the lateral deflection was 1.4 m and the calculated

lateral deflection was 0.556 m. The manufacturer has provided two curves showing the impact severity versus lateral deflection in Figure 10, which were obtained from crash test data (Energy Absorption Systems Inc. 2004; FHWA 2004). Curve A was derived from crash tests where the impact point was located between 10 to 20 metres from the upstream end whereas Curve B was obtained for crash tests where the impact point was at least 20 m away from the upstream end. From Curve B, the lateral deflection is about 0.6 m when the impact severity is 10 kJ, to which the deflection (0.566 m) calculated using the methodology outlined in this paper correlated well. The test result for the lateral deflection of a 820C car crashing into the 426 Barrier at 100.7 km/h and an angle of 20 degrees was 0.9 m. The calculated deflection was 1.43 m. A check of the test report found that “the barrier segment that was struck first shattered, but the internal cables successfully contained the small car and minimized the deflection” (Power, pers. comm., October 26, 2004). In addition, when comparing the above test to the 820C Test Level 3 test for the Triton barrier, where a 875 kg car crashes into the barrier at a speed of 97.04 km/h and an angle of 21 degrees, these two tests can be considered similar in terms of impact severity and barrier joint stiffness. However, the lateral deflection recorded in the Triton barrier test was 2.3 m as opposed to 0.9 m for the 426 Barrier. Hence it would seem that the 426 Barrier test was possibly an anomaly because of the tearing of the struck barrier. The theory in this paper assumes the barriers do not tear or shatter on impact. With regard to the 1600C TL-0 test for the Barrier System barrier, the calculated lateral deflection underestimated the test result by about 35%. This is because the theory in this study assumes the car is redirected, whereas in the crash test the car was contained and came to rest parallel against the barrier (Grzebieta and Zou 1998-2000).

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 100Impact severity (kJ)

Lat

eral

def

lect

ion

(m)

Obtained from crash tests where impact points are 10 to 20 mfrom the upstream endObtained from crash tests where impact points are at least 20 maway from the upstream end

Curve A

Curve B

0.6 m


Figure 10 - Impact severity versus lateral deflection for the Triton barrier That the calculated lateral deflection underestimated the test result when the car was captured rather than directed by the barrier is also evident from the tests for the Triton barrier, the Rhino barrier and the 426 Barrier. The comparison of the results in Table 3 for these tests indicates that the calculated lateral deflection underestimated the test result by on average 20%. Hence, for PWBs where the joint stiffness is small and no steel beams are used to strengthen the barrier, such as the Triton barrier, the Rhino barrier, the 426 Barrier and the Barrier System barrier, the possible maximum lateral deflection, which is denoted as DM, can be determined empirically by multiplying a factor of 1.2 to the deflection calculated using Equation 33.

DD 2.1M = [34] Figure 11 shows the plots of the impact severity versus lateral deflection for the Triton barrier, which were obtained using crash test data (Curve B), using Equation 33 (Curve C) and using Equation 34 (Curve D), respectively. Details of how the lateral deflections for different impact severities were calculated are given in Appendix C. Also shown in Figure 11 is Curve B' which represents the 80% value of Curve B or the -20% data band of Curve B. As can be observed in Figure 11, the results from Equation 33 (Curve C) is within the data band between Curve B' and Curve B, which indicates a reasonably well comparison, whereas the results from Equation 34 (Curve D) closely agrees with the curve representing the test result for Curve B. In conclusion, comparisons between the calculated values and the test results indicate that the equations developed in this paper can be used to determine the PWB lateral deflection and the number of segments that move with reasonable accuracy, so long as the PWB installation is long enough, the impact point is close to the middle of the installation, the barrier does not overly tear apart, and the car does not roll over or ride over the barrier. With regard to PWBs where the joint stiffness is small and no steel beams are used to strengthen the barrier, the possible maximum lateral deflection can be determined by multiplying to the lateral deflection by a factor of 1.2 calculated using Equation 33.

0

1

2

3

4

5

0 10 20 30 40 50 60 70 80 90 100Impact severity (kJ)

Lat

eral

def

lect

ion

(m)

Obtained from crash tests where impact points are at least 20 m awayfrom the upstream end-20% of Curve B

Obtained using Equation 33

Obtained by multiplying 1.2 to theresult from Equation 33

Curve B

Curve D

Curve C

Curve B'


Figure 11 - Comparison of the plots of impact severity versus lateral deflection from the crash test and the calculations for the Triton barrier

DETERMINING THE LATERAL DEFLECTION OF A PWB SYSTEM USING MADYMO SIMULATIONS Two computer codes, LS-DYNA3D and MADYMO have been extensively used in road safety barrier research and designs since the 1990s. This section describes how MADYMO was used to simulate a PWB crash test where a 2000 Chevrolet C2500 pickup was impacted into the GuardlinerTM Barrier at a speed of 70 km/h and an angle of 25 degrees (Zou and Grzebieta 2004). Figure 12 shows the test setup. A total of 30 segments (60 m) were installed for the test.

Figure 12 - Test setup for the GuardlinerTM Barrier

Vehicle model The vehicle was modelled using a multi-body system. The basic dimensions (width, length, wheelbase and track), mass and centre of gravity of the vehicle model were basically the same as those measured from the test vehicle. Ellipsoids were used to model the bumper, front body and side body. Force-displacement functions were assigned to these ellipsoids to reflect the crush characteristics of the bumper, front body and side body, respectively. A frontal rigid barrier crash test found in the NHTSA’s crash test database (NHTSA 2003) were used to derive the force-displacement function for the frontal and bumper ellipsoids. In the frontal rigid barrier crash test (NHTSA Test No. 2809), a 1998 model Chevrolet pickup truck, which is essentially the same as the pickup truck used in the GuardlinerTM Barrier test, collided with a rigid barrier at a speed of 56.1 km/h. The vehicle mass was 2328 kg, the vehicle width was 1950 mm and the average crush depth was 690 mm (NHTSA 2003). Thus, using the results from studies of vehicle frontal crush characteristics (Campbell 1974; Strother et al. 1986; Jiang et al. 2003), the coefficients A and B for this vehicle can be determined as follows.


)(N/m 449316950.1

40.194.192328

)(N/m 50953950.1

40.192.22328

)m

m/s( 40.19690.0

2.2)6.3/1.56(

2

0

21V

0

10V

01

=××

==

=××

==

=−

=−

=

wbm

B

wbbm

A

CbV

b

Hence, the force-crush equation for this vehicle’s front body was obtain as (Jiang et al. 2004):

)44931650953(950.1)( CCBAWF +×=⋅+= The force-displacement function for the bumper and the front body ellipsoids was determined by evenly distributing the above equation to each ellipsoid modelling the bumper and the front body. Barrier model The barrier segment model was developed based on a previous study performed by Zou et al. (2000). Each segment of the water barrier system was modelled using a multi-body system. Planes were attached to each segment to model the barrier shape. These planes were also used for contact definitions. A translational joint and two revolute joints were modelled between every two adjacent segments to account for barrier elongation, torsion and rotation, respectively. The joint stiffness for the rotational joints was determined using the results shown in Appendix A (Figure A.3). The joint stiffness for the elongation and torsion joints were also determined using the results of quasi-static laboratory component tests carried out by Zou et al. (2000). As shown in Figure 13, the W-beam and the water barrier segments are connected in such a way that “two bolts securing the segment joins are passed through the feet of a steel linkage bracket fitted into the two apertures and are fixed to and tightened by a washered nut in the aperture on the opposite side. A deformable C section is welded to the outer face of the linkage brackets to which a 4200 mm long W-beam is attached by a single mushroom head keyed bolt. The beams are connected by overlapping 280mm end sections and spliced by using eight 19mm diameter - 60mm long mushroom head bolts. The centreline height of the W-beam is fixed at 600mm.”(Zou and Grzebieta 2004).

Figure 13 - Connection between the W-beam and the segments of the GuardlinerTM

Barrier

C section Linkage bracket


Figure 14 - Barrier segment and W-beam models

As illustrated in Figure 14, the W-beam was modelled as a 2 m long section and each section consisted of four identical bodies. An ellipsoid was attached to each body to approximately model the W-beam shape. Moreover, a force-displacement function was assigned to these ellipsoids so that the crush characteristics of the W-beam could be simulated. The force-displacement function for the W-beam ellipsoids was derived using Reid et al.’s data, where 300 mm long W-beam sections were compressed until flattened (Reid et al. 1997). Reid et al. (1997) found that the average peak crush force from eight such compressing tests was 31 kN. Figure 15 shows the average force versus displacement curve of the W-beam flattening tests (Reid et al. 1997). A translational joint and two revolute joints were modelled between adjacent bodies of the W-beam section to replicate W-beam elongation, torsion and bending (rotation) characteristics, respectively. The translational joint and two revolute joints were also used to model the continuity of the whole W-beam installation. The stiffness of the rotational (bending) joints was determined using the results presented in Appendix A. The stiffness of the elongation and torsion joints was assumed as 3.0E+04 N/mm and 3.0E+05 Nm/rad, respectively. At each segment join bolt location, a point-restraint was used to model the connection between the W-beam and the segments. Figure 16 shows the whole model setup.

0

10

20

30

40

0 20 40 60 80Displacement (mm)

Forc

e (k

N)

Figure 15 - Force versus displacement of W-beam flattening test


Figure 16 - MADYMO model setup for the GuardlinerTM Barrier impact Contact definitions To simulate the GuardlinerTM Barrier crash test, contact between the vehicle and the ground, between the barrier segments and the ground, between the vehicle and the W-beam, and between the vehicle and the barrier segments had to be defined. Key parameter values and MADYMO contact functions between the ellipsoids and the planes that were used are detailed in Table 4. The friction coefficients was determined using the data provided by Bauer et al. and ROYMECH (Bauer et al. 2000; ROYMECH 2004).

Table 4 - Contact characteristics No Contacts MADYMO function Key parameter values

1 Vehicle and ground PLANE-ELLIPSOID

Vehicle mass mV = 2170 kg;

Impact speed: 70 km/h;

Impact angle: 25 degrees

Rolling friction between vehicle

wheels and ground: μV = 0.02

2 Barrier segments and

ground PLANE-ELLIPSOID

Segment mass mB = 630 kg;

Friction between barrier segments

and ground μB = 0.40

2 Vehicle and W-beam ELLIPSIOD-ELLIPSOID

W-beam section (2m) mass: 25 kg;

Friction between vehicle body and

W-beam: 0.15

Friction between vehicle tyres and

W-beam: 0.3

3 Vehicle and barrier

segments

PLANE-ELLIPSOID

ELLIPSIOD-ELLIPSOID

Friction between vehicle body and

barrier segments: 0.2

Friction between vehicle tyres and

barrier segments: 0.3


Comparison with the crash test The model was run on a 1.8 GHz PC requiring only 5 minutes computation for a 1.5 s impact event. Altair MotionView was used to view the model animation. Figure 17 compares the sequential overhead views obtained from the crash test and the simulation. Figure 17 shows that the simulation basically replicates the impact test and the response of the barrier. In addition, the lateral deflection, the number of segments that moved laterally during impact and the barrier up-stream end movement between the crash test and the simulation were also compared. Figure 18 shows the barrier up-stream end movement in the simulation. Figure 19 shows the barrier lateral deflection. In the crash test, the lateral deflection was measured as 2.64 m, the number of segments that moved laterally during impact was 16 segments and the up-stream end movement was about 0.52 m (Zou and Grzebieta 2004). Table 5 summarises these comparisons.

Time Comparison

0.000 s

Test

Simulation

0.170 s

Test

Simulation

0.370 s Test


Simulation

0.770 s

Test

Simulation

Figure 17 - Sequential overhead views comparing the crash test and simulation

Before test

After test

Figure 18 - Simulated barrier up-stream end movement


Figure 19 - Simulated barrier lateral deflection

Table 5 - Comparison of the barrier response between the crash test and the simulation

Lateral deflection

Number of segments moved laterally

Up-stream end movement

Crash test 2.64 m 16 segments 0.52 m

MADYMO simulation 2.50 m 14 segments 0.53 m

Discussion Comparison of the results presented above indicates that the MADYMO models developed in this study can be used to determine the lateral deflection and the number of segments that move during impact for the GuardlinerTM Barrier. To further validate the MADYMO models, the impact speed and angle were changed and the models were re-run. A total of 17 cases were simulated where the impact speed ranged from 28 km/h to 100 km/h, the impact angle ranged from 15 degrees to 45 degrees. The

impact severity, which is defined as 2V )sin(

21 θVm , ranged from 10 kJ to about 150 kJ. For each

case, the lateral deflection and the number of segments that moved laterally during impact were also calculated using Equations 33 and 8, respectively. Details of how the lateral deflections for different impact severities were calculated are given in Appendix D. Results obtained from the MADYMO simulations and the calculations are compared in Table 6. Data from the two crash tests for this barrier are also listed in Table 6. Comparison of the results from the MADYMO analyses and the theoretical calculations are also illustrated as a plot of the impact severity versus lateral deflection in Figure 20.

Table 6 - Comparison of the results from the simulations and the calculations

No Impact parameters Impact

severity a (kJ)

Theoretical results MADYMO results Impact speed (km/h)

Impact angle, θ

(degrees)

Lateral deflection (m)

Number of segments that

moved laterally

Lateral deflection

(m)

Number of segments that

moved laterally

1 25.86 25 10.0 0.523 10 0.45 8

2 36.57 25 20.0 0.902 11 0.75 11

3 b 70.0 20.5 20.7 0.80 13 --- ---

4 73.14 15 30.0 1.241 12 1.39 12

5 51.72 25 40.0 1.556 12 1.49 12

6 71.45 20 50.0 1.854 13 2.00 14


7 48.88 30 50.0 1.854 13 1.54 13

8 63.35 25 60.0 2.140 13 2.08 14

9 84.54 20 70.0 2.415 14 2.66 14

10 44.99 40 70.0 2.415 14 2.64 13

11 b 70.0 25 73.3 2.503 14 2.50 14

12 86.50 20 73.3 2.503 14 2.80 15

13 59.17 30 73.3 2.503 14 2.30 13

14 73.14 25 80.0 2.682 14 2.63 14

15 57.16 35 90.0 2.943 14 2.70 14

16 46.37 45 90.0 2.943 14 3.00 13

17 81.78 25 100.0 3.198 14 3.31 15

18 91.43 25 125.0 3.816 15 3.96 16

19 100.0 25 149.5 4.401 15 4.70 16

Note: a: Impact severity (kJ) is calculated as 2V )sin(

20001 θVm . mV is 2170 kg for all cases except

for No. 3 where mV is 891 kg. b: No. 3 and No. 11 are the same impact parameters as in the case of the two crash tests.

0.0

1.0

2.0

3.0

4.0

5.0

0.0 30.0 60.0 90.0 120.0 150.0Impact severity (kJ)

Lat

eral

def

lect

ion

(m)

Test dataTheoretical curve (Eq. 33)MADYMO dataMADYMO dataMADYMO data

(θ = 25°) (15°< θ <25°) (25°< θ <45°)

Figure 20 - Impact severity versus lateral deflection for the GuardlinerTM barrier

As can be observed in both Table 6 and Figure 20, the results from the MADYMO simulations correlated well to the test data and the theoretical data. It can be concluded that the MADYMO models developed here can be used to determine the lateral deflection and the number of segments that move for the GuardlinerTM Barrier under different impact conditions with reasonable accuracy. The modelling techniques developed can also be used to model other PWB systems listed examples of which are presented in Table 1.


CONCLUSIONS This study investigated two methods that can be used to calculate the lateral deflection and the number of segments that move in a PWB after a vehicle has struck the barrier. In the first method theoretical equations were developed based on the conservation of energy whereas the second method used MADYMO simulations to calculate how the barrier deformed. The theoretical equations and the MADYMO simulation models developed in this study were validated against full-scale crash tests. A total of 23 full-scale crash tests were used to validate the theoretical equations. Comparison of the results indicate that both the theoretical method and MADYMO modelling simulation can be used to determine the PWB’s lateral deflection and the number of segments that move during impact with reasonable accuracy. The significance of this study is that cost-effective methods developed in this research can be used so that lateral deflections of almost all certified PWB systems under different impact conditions can be determined, as confirmed in Figure 20. Had full-scale crash tests been used to obtain the curve as shown in Figure 20, the cost would have been considerable. The findings of this study would be useful for both PWB providers and users. PWB designers can now provide more information about their PWB products such as the possible working width and the number of segments that would most likely move for different impact severities. Highway engineers can also use the findings of this study to properly select and install a PWB system for different site and traffic conditions.

ACKNOWLEDGEMENTS The authors would like to thank the Australian Research Council for providing funds to investigate roadside barrier crashes.


REFERENCES ASTM (2002). A53/A53M-01: Standard Specification for Pipe, Steel, Black and Hot-Dipped, Zinc-coated, Welded and Seamless. Annual Book of ASTM Standards 2002: Section One - Iron and Steel Products Volume 01.01. West Conshohocken, PA, USA, American Society for Testing and Materials.

Bauer, H., K. H. Dietsche, J. Crepin and F. Dinkler (2000). Automotive Handbook (5th ed.). Stuttgart, Robert Bosch GmbH.

Bronshtein, I. N., K. A. Semendyayev, G. Musiol and H. Muehlig (2004). Handbook of Mathematics. New York, Springer.

Campbell, K. L. (1974). "Energy Basis for Collision Severity." SAE Technical Paper 740565.

Cichowski, W. G., P. C. Skeels and W. R. Hawkins (1961). Appraisal of Guardrail Installations by Car Impact and Laboratory Tests. In: Highway Research Board Proceedings Vol. 40, Highway Research Board, Washington, D.C.

Deleys, N. J. and R. R. McHenry (1967). NCHRP Report 36: Highway Guardrails-A Review of Current Practice. Washington, D.C., Highway Research Board, National Research Council.

Energy Absorption Systems Inc. (2004). Workzone Products. Energy Absorption Syatems, Inc. [online] Available: http://www.energyabsorption.com/products/workzone/workzone_safety.htm.

FHWA (2004). Longitudinal Barriers and Miscellaneous Items. Federal Highway Administration (http://safety.fhwa.dot.gov/fourthlevel/hardware/listing.cfm?code=long). [online] Available: http://safety.fhwa.dot.gov/fourthlevel/hardware/listing.cfm?code=long.

Grzebieta, R. H., J. Cameron, A. Carey and R. Zou (2001). "Water-Filled Plastic Safety Barrier Systems." Road & Transport Research Vol 10(No 3): pp. 66-83.

Grzebieta, R. H. and R. Zou (1998-2000). Water-filled Barrier Crash Test Reports. Melbourne, Australia, Department of Civil Engineering, Monash University.

Grzebieta, R. H. and R. Zou (2003). NCHRP Report 350 Test 2-10 of a 920 mm High Barron & Rawson Barrier Model 2000S, Reinforced with W-Beam. Melbourne, Australia, Department of Civil Engineering, Monash University.

Jiang, T., R. H. Grzebieta, G. Rechnitzer, S. Richardson and X. L. Zhao (2003). Review of Car Frontal Stiffness Equations for Estimating Vehicle Impact Velocities. 18th International Technical Conference on the Enhanced Safety of Vehicles, Nagoya, Japan.

Jiang, T., R. H. Grzebieta and X. L. Zhao (2004). "Predicting impact loads of a car crashing into a concrete roadside safety barrier." International Journal of Crashworthiness Vol 9(No. 1): 45-63.

Jiang, T., R. H. Grzebieta, X. L. Zhao, R. Zou, G. Rundle and C. Powell (2002). Methods to Predict Dynamic Performance of Water-Filled Plastic Barriers. International Crashworthiness Conference - ICrash2002, Melbourne, Australia.

Megson, T. H. G. (1996). Structural and Stress Analysis. London, Arnold.

NHTSA (2003). Vehicle Crash Test Database. National Highway Traffic Safety Administration. [online] Available: http://www-nrd.nhtsa.dot.gov/database.

Powers, D. (26 October, 2004). Test Results for the 426 Water-Filled Plastic Barrier (FHWA List Code B111).

Reid, J. D., D. L. Sicking, R. K. Faller and B. G. Pfeifer (1997). Development of a New Guardrail System. Transportation Research Record No. 1599. Washington, D.C., Transportation Research Board, National Academy Press.

Rhino Safety Barrier LLC (2001). Testing Videos and Technical Documentation. Rhino Safety Barrier LLC. [online] Available: http://www.rhinobarriers.com/testing.cfm.

Rosenbach, J. B., E. A. Whitman and D. Moskovitz (1961). Essentials of Trigonometry, with tables. Boston, GINN AND COMPANY.

ROYMECH (2004). Friction Factors. Roy Beardmore. [online] Available: http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm.


Standards Australia (1992). AS 1594 -1992 Hot-rolled steel flat rpoducts. Sydney, Standards Australia.

Standards Australia and Standards New Zealand (1999). AS/NZS 3845:1999 - Road safety barrier systems. Sydney/Wellington, Standards Australia/Standards New Zealand.

Strother, C. E., R. L. Woolley, M. B. James and C. Y. Warner (1986). "Crush Energy in Accident Reconstruction." SAE Technical Paper 860371.

Yodock Wall Company (2003 - 2004). Highway Safety & Traffic Control. Yodock Wall Company. [online] Available: http://www.waterbarrier.com/applications/highHome.asp.

Zou, R. and R. H. Grzebieta (2004). NCHRP REPORT 350 Crash Test Results for the GuardlinerTM Barrier System (Prepared for: WTG Aussindo Inc., 5 Carol Ave, Springwood, Qld 4127, Australia and Barron & Rawson Pty Ltd, 35-37 Marigold Street Revesby, NSW 2212, Australia). Melbourne, Australia, Department of Civil Engineering, Monash University.

Zou, R., R. H. Grzebieta, G. Rundle and C. Powell (2000). Development of a Temporary Water-filled Plastic Barrier System. International Crashworthiness Conference, London, UK.


APPENDIX A: DETERMINING M(α) AND MY M(α) and MY for every PWB listed in Table 1 were determined and reported as follows. Triton barrier, 426 Barrier, SB-1-TL barrier and Barrier System barrier With regard to the Triton barrier (test No. 1 in Table 1), the 426 Barrier (test No. 5 in Table 1), the SB-1-TL barrier (test No. 6 in Table 1) and the Barrier system barrier (test No. 9 in Table 1), images of these barriers given in Table 1 show that the joints of these PWBs consist of pins (the Triton barrier and the Barrier system barrier) or use steel cables (the 426 Barrier and the SB-1-TL barrier) to connect segments. M(α) for these PWBs are small and thus can be assumed as negligible. As no steel beams are used to strengthen these PWBs, EBEAM or MY for these barriers is zero. Roadliner 2000™ S barrier With regard to the Roadliner 2000™ S barrier (test No. 8 in Table 1), bolts and short steel latches are used to connect segments (see Table 1). Data of two quasi-static laboratory tests performed by Grzebieta and Zou (Grzebieta and Zou 1998-2000; Zou et al. 2000; Grzebieta et al. 2001) were used to determine M(α). Figure A.1 shows the two joints that were tested. The barriers were empty when tested. Joint 1 and Joint 2 are quite similar except that Joint 2 has two additional short steel latches at the bottom. Figure A.2 shows the test data from both Joint 1 and Joint 2 tests and the associated plots.

Joint 1

Joint 2

Figure A.1 - Test set-up for determining the joint stiffness of a PWB


0

1000

2000

3000

4000

5000

6000

7000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8Rotational angle, α (rad)

Mom

ents

, M

(Nm

)

Joint 1

Joint 2

Figure A.2 - Joint stiffness test data for Joint 1 and Joint 2

Although the PWB used in the joint rotational stiffness tests was a modified design as shown in test No. 8 of Table 1 (Roadliner 2000™ S), the joint design of the Roadliner 2000™ S barrier still remained similar to Joint 2 except that two more short steel latches are added to the top of the barrier (see test No. 8 in Table 1). Hence, the joint rotational stiffness of the Roadliner 2000™ S barrier was determined as

)]()([)()( 1Joint 2Joint 2Joint S 2000Roadliner iiii MMMM αααα −+=™ [A.1] where MRoadliner 2000™ S (αi) is the moment required to rotate the joint of the Roadliner 2000™ S barrier to an angle αi (Nm), MJoint 2 (αi) is the moment required to rotate Joint 2 to an angle αi (Nm) and MJoint 1 (αi) is the moment required to rotate Joint 1 to an angle αi (Nm). As shown in Figure A.3, M(α) of the Roadliner 2000™ S barrier was determined as

degrees) 12or rad 0.2 (when 31880)( S 2000Roadliner ≤=™ αααM [A.2] No steel beams are used to strengthen the Roadliner 2000™ S barrier. Thus, EBEAM or MY for this barrier is also zero.

M =31880αR 2=0.9983

M = 6962α + 5052R 2 = 0.9988

M = 12835αR 2 = 0.9988

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0.0 0.2 0.4 0.6 0.8Rotational angle, α (rad)

Mom

ents

, M

(Nm

)

M = 4548 αR ² = 0.9996

Roadliner 2000™ S

Joint 2

Joint 1

Rihno barrier

Figure A.3 - Results of joint stiffness


Rhino barrier With regard to the Rhino barrier, the joint of the Rihno barrier, as shown in test No. 4 in Table 1, consists of a steel-reinforced polyethylene pin and two short galvanized steel “bridging strips”. The joint stiffness is mainly determined by the stiffness of these two short steel strips. Hence, M(α) of the Rihno barrier can also be approximated using the data of Joint 1 and Joint 2 tests as

)()()( 1Joint 2Joint Rihno iii MMM ααα −= [A.3] where MRihno (αi) is the moment required to rotate the joint of the Rihno barrier to an angle αi (Nm). Figure A.3 shows that M(α) of the Rihno barrier can be determined as

degrees) 12or rad 0.2 (when 12835)( Rihno ≤= αααM [A.4] No steel beams are used to strengthen the Rihno barrier. Thus, EBEAM or MY for this barrier is also zero. Guardian 350 Highway Kit barrier With regard to the Guardian 350 Highway Kit barrier (test No. 2 in Table 1), four schedule 40 ASTM A120 steel tubes are used to strengthen the Guardian 350 Highway Kit barrier (FHWA 2004). The outside diameter of the tube is 60.3 mm and the thickness of the tube wall is 3.91 mm (ASTM 2002). Hence, the second moment of area for this tube is (Megson 1996):

)(m 10276647)(mm 27664764

])91.323.60(3.60[ 412444

−×==×−−

=πI

σY for the tube is 240 MPa (ASTM 2002). Thus, MY for this tube can be calculated using Equation 28 as

(Nm) 2202.210)2/3.60(

10276647102403

126Y

Y =×

×××== −

−

zIM σ

The image of the barrier shown in Table 1 indicates that M(α) of this barrier can be considered as negligible. Yodock barrier Each segment of the Yodock barrier has two 1830 mm long square steel tubes, which are spliced to the square tubes of the adjacent segment with 280 mm long 63.5 × 63.5 × 6.35 mm square steel tubes using two bolts (Yodock Wall Company 2003 - 2004; FHWA 2004). The second moment of area for this square tube is (Megson 1996):

)(m 10799945)(mm 79994512

])35.625.63(5.63[ 412444

−×==×−−

=I σY for this steel tube is also assumed as 240 MPa (ASTM 2002) and its respective MY is

(Nm) 8.604610)2/5.63(

10799945102403

126Y

Y =×

×××== −

−

zIM σ

The segments of the Yodock barrier are connected at the ends using polyethylene couplers (Yodock Wall Company 2003 - 2004; FHWA 2004). Thus, M(α) of the barrier can also be considered as negligible.


GuardlinerTM barrier As shown in test No. 7 in Table 1, the GuardlinerTM barrier is assembled by securing steel W-beam rails to the Roadliner 2000™ S barrier (test No. 8 in Table 1). As mentioned above, the second moment of area of the cross-section of the W-beam was 970000 mm4 or 970.0E-09 m4 (Deleys and McHenry 1967; Reid et al. 1997). The W-beam was formed from steel grade HA350 or equivalent in accordance with AS 1594 (Standards Australia and Standards New Zealand 1999). The yield strength for this steel (σY) is 350 MPa (Standards Australia 1992). Also according to AS/NZS 3845 (Standards Australia and Standards New Zealand 1999), the furthest point from the neutral axis (z) is 40 mm. Thus, MY for this W-beam was calculated using Equations 28 as

(Nm) 5.84871040

10970103503

96Y

Y =×

×××== −

−

zI

Mσ

M(α) of the GuardlinerTM barrier can also be determined using Equation A.2.


APPENDIX B: DERIVATION OF RESULTS IN TABLE 3 With regard to the first test of the Triton barrier (test No. 1 in Table 1), the vehicle mass mV was 807.3 kg, the impact speed V was 72.0 km/h, the impact angle θ was 20 degrees, 30 segments were installed in the crash test, the length of one segment of this barrier lB was 1.981 m and the weight of one segment filled with water mB was 612 kg (Energy Absorption Systems Inc. 2004; FHWA 2004). μB was also assumed as 0.4. As determined in the above section, M(α) and MY for this barrier can be ignored. Thus, substituting these values into Equation 33 gives

⎥⎥⎦

⎤

⎢⎢⎣

⎡×

−−⎥⎦

⎤⎢⎣⎡ ×

−+−××

+

⎥⎦⎤

⎢⎣⎡ ×

−+⋅

×××+

⎥⎦⎤

⎢⎣⎡ ×

−+⋅

−×××+××

=°××

981.12

)1(981.12

)1()30)(4.081.9612(

981.12

)1(2

)981.14.081.9612(

981.12

)1(4

)1)(981.14.081.9612()4.081.9612(

)20sin6.30.72(3.807

21

22

22

22

2

2

nnDn

nD

nD

nD

DnD

or

[ ] [ ]

[ ] ⎥⎦⎤

⎢⎣⎡ −−−+−

+−+⋅

+−+⋅

−+=

)1( 9905.0)1( 9905.0 )30( 49.2401

)1( 9905.02

35.4757 )1( 9905.04

)1( 35.475749.240123.18887

22

2222

2

nnDn

nD

nD

nD

DnD

[B.1]

where n is calculated using Equation 8 as

286.72)4.081.9612(2

)20sin6.30.72(3.807

22

)sin(2

BB

2V +=+

×××

°×=+

⋅=

DDgmDVm

nμθ [B.2]

The solution of Equation B.1 can be determined using the Iteration Method for solving non-linear equations in a single unknown (Bronshtein et al. 2004). The basic step is to assign a value for D first; then calculate n using Equation B.2; substitute the assigned value for D and the calculated n into Equation B.1 and compare the right hand side value with the left hand side value of Equation B.1; repeat the above process and D can be determined until the difference is less than 0.0001. This process can be easily done using a worksheet. D and n determined for this test was 1.033 m and 9.6 (rounded up to 10), respectively. The lateral deflection from the crash test was 1.0 m (Energy Absorption Systems Inc. 2004; FHWA 2004). The difference between the calculated lateral deflection

and the test result was determined as %3.3%1000.1

0.1033.1+=×

− . The difference between the

calculated number of segments that moved laterally during impact and the test result could not be determined because this data was not available. Similarly, the calculated lateral deflection, the calculated number of segments that moved laterally during impact and the difference between the calculated and the test result for the Triton barrier (test No. 1 in Table 1), the 426 Barrier (test No. 5 in Table 1), the SB-1-TL barrier (test No. 6 in Table 1)


and the Barrier system barrier (test No. 9 in Table 1) were obtained using the same procedure as described above. With regard to the 2000P Test Level 2 test for the GuardlinerTM barrier (test No. 7 in Table 1), the vehicle mass mV was 2170 kg, the impact speed V was 70.0 km/h, the impact angle θ was 25 degrees, 30 segments were installed in the crash test, the length of one segment of this barrier lB was 2.0 m and the weight of one segment filled with water mB was 655 kg (Zou and Grzebieta 2004). μB was determined as 0.4. NBEAM for this barrier was 1. MY of the W-beam rail was determined in the above section as 8487.5 Nm. The second moment of area of the W-beam was 970.0E-09 m4. E can be taken as 210.0E+09 N/m2. M(α) of the GuardlinerTM barrier was as given in Equation A.2. Substituting these values and Equations 19 and A.2 into Equation 33 results in

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

×××××−

−

⎥⎦⎤

⎢⎣⎡ ×

−+

××

+⎥⎥⎦

⎤

⎢⎢⎣

⎡×

−−⎥⎦

⎤⎢⎣⎡ ×

−+××−

+

⎥⎦⎤

⎢⎣⎡ ×

−+⋅

×××

++

⎥⎦⎤

⎢⎣⎡ ×

−+⋅

−×××+××

=°××

−

∫

99

2

22

22

22

0 22

2

2

10970102106)0.25.8487)(1(

0.22

)1(

)5.84872(1

0.22

)1(0.22

)1( )4.081.9655)(30(

0.22

)1(2

)0.24.081.9655(

d 18803

0.22

)1(4

)1)(0.24.081.9655()4.081.9655(

)25sin6.30.70(2170

21

n

nD

D

nnDn

nD

nD

nnD

DnDα

αα

Through some calculations of the above equation, the following equation is obtained.


[ ]

[ ]⎥⎥⎦

⎤

⎢⎢⎣

⎡−−

−++−−−+−

+−+

+−+

+−+

−+=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−

−++−−−+−

+−+⋅

++−+⋅

−+=

)1(88.117)1(

16975)1()1( )30( 22.2570

)1(

570.222 )1(

15940

)1(

)1( 285.11122.2570

)1(88.117)1(

16975)1()1( )30( 22.2570

)1(2

44.5140 )2

31880( )1(4

)1( 44.514022.25705.73268

22

22

2222

2

22

2

22

22

22

2

22

2

nnD

DnnDn

nD

nDnDnD

nD

DnD

nnD

DnnDn

nD

nDnnD

DnD α

where n is calculated using Equation 8 as

251.282)4.081.9655(2

)25sin6.3

70(21702

2)sin(

2

BB

2V +=+

×××

°×=+

⋅=

DDgmDVm

nμθ

Using the same method that was used to solve Equation B.1, the solution of the above equation was calculated as D = 2.503 (m) and n = 13.4 ≈14. The lateral deflection and the number of segments that moved laterally from the crash test was 2.64 m and 16, respectively (Zou and Grzebieta 2004). The difference between the calculated lateral

deflection and the test result was determined as %2.5%10064.2

64.2503.2−=×

− . The difference

between the calculated number of segments that moved laterally during impact and the test result was determined as: n (from the calculation) - n (from the crash test) = 14 – 16 = -2. Similarly, the calculated lateral deflection, the calculated number of segments that moved laterally during impact and the difference between the calculated and the test result for the Guardian 350 Highway Kit barrier (test No. 2 in Table 1), the Yodock barrier (No. 3 in Table 1), the Rhino barrier (No. 4 in Table 1) and the Roadliner 2000™ S barrier (test No. 8 in Table 1) were also obtained in a similar way. The worksheet that was used to calculate D and n for all of the crash tests listed in Table 1 is given in Table B.1.


Table B.1 - Worksheet used to calculate D and n for all of the crash tests listed in Table 1

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

A B C D E F G H I J K L M N O P Q R S T U m V V θ m B μ B l B N N BEAMM (α )= M Y D n D Long. E L

a E BR-Lat.-NR E BR-Lat.-R E BR-Long. E BEAM ∑E b Differencec

(kg) (km/h) (deg) (kg) (m) k J α (Nm) (m) (m) (J) (J) (J) (J) (J) (J)k J Eq. 22 Eq. 15 Eq. 17 Eq. 23 Eq. 32

Triton barrier (Nm/rad)TL-2 807 72 20.0 612 0.4 1.981 30 0 0 0 1.0331 9.613 0.0623 18887.231 13087.591 2748.95 3051.47 0 18888.01 4.123E-05TL-2 1971 72.3 25.0 612 0.4 1.981 30 0 0 0 3.026 11.77 0.421 70976.494 44902.946 7640.228 18433.3 0 70976.479 -2.109E-07TL-3 875 97.04 21.0 620 0.4 1.981 30 0 0 0 1.9165 10.76 0.1882 40825.634 26972.207 5042.328 8811.94 0 40826.476 2.061E-05TL-3 2005 97.56 25.0 620 0.4 1.981 30 0 0 0 4.945 12.93 0.9929 131498.1 78232.235 12028.3 41235.3 0 131495.86 -1.7E-05

2004 95.74 7.0 620 0.4 1.981 50 0 0 0 0.5563 9.777 0.0178 10525.397 7280.6925 1504.535 1739.97 0 10525.2 -1.875E-05Guardian 350 Highway Kit

TL-2 820 70.6 20.3 880 0.4 1.830 33 4 0 2202.2 0.7076 9.768 0.0311 18979.558 13113.495 2711.589 2498.66 655.014 18978.761 -4.204E-05TL-2 2000 71.5 25.8 880 0.4 1.830 33 4 0 2202.2 2.1595 12.02 0.2286 74721.728 47635.336 7953.33 16564.4 2566.99 74720.023 -2.283E-05TL-3 820 100 20.0 880 0.4 1.830 33 4 0 2202.2 1.2214 10.77 0.083 37006.858 24640.318 4606.385 6371.4 1388.45 37006.552 -8.255E-06TL-3 2000 100 25.0 880 0.4 1.830 33 4 0 2202.2 3.5464 13.25 0.5475 137813.42 83782.702 12628.85 37332.2 4065.11 137808.82 -3.337E-05

Yodock barrierTL-2 2042 68.5 24.0 460 0.4 1.830 25 2 0 6046.8 3.267 12.37 0.5009 61154.507 37882.9 6121.007 11418.9 5736.71 61159.465 8.107E-05TL-3 896 97.7 19.8 786 0.4 1.830 25 2 0 6046.8 1.4304 10.58 0.1159 37860.798 25272.188 4808.58 5154.83 2622.46 37858.061 -7.227E-05TL-3 2041 98.4 24.8 786 0.4 1.830 25 2 0 6046.8 4.2154 12.32 0.8251 134141.42 81143.365 13105.94 32275.2 7616.65 134141.19 -1.746E-06

Rhino barrier

TL-2 d 917 72.6 20.0 476 0.4 2.000 34 0 0 0 1.3765 10.48 0.0994 21812.776 14636.557 2812.684 4364.79 0 21814.031 5.755E-05TL-2 2000 69.2 25.0 476 0.4 2.000 34 0 12835 0 3.082 13.46 0.3754 65993.884 40582.981 11015.39 14399.2 0 65997.625 5.669E-05426 barrier

TL-3 820 100.7 20.0 782 0.4 1.830 32 0 0 0 1.431 10.55 0.1164 37526.767 25074.33 4787.293 7665.88 0 37527.499 1.95E-05TL-2 2000 73 25.0 782 0.4 1.830 32 0 0 0 2.4515 11.76 0.3005 73440.77 46805.398 7978.062 18663.9 0 73447.395 9.02E-05

SB-1-TL barrierTL-3 2054 99.4 25.4 836 0.4 2.130 22 0 0 0 4.91 10.95 1.0824 144052.71 88750.657 16073.49 39216 0 144040.16 -8.712E-05

Guardlin erTM. barrierTL-2 891 70 20.5 655 0.4 2.000 30 1 31880 8487.5 0.9253 10.69 0.0441 20658.052 13844.167 4152.204 2188.89 472.367 20657.625 -2.065E-05TL-2 2170 70 25.0 655 0.4 2.000 30 1 31880 8487.5 2.5031 13.39 0.2503 73268.504 45495.179 15185.77 10688.5 1901.46 73270.921 3.299E-05

Roadliner 2000TM. S barrierTL-0 920 49 20.0 630 0.4 2.000 30 0 31880 0 0.5413 9.45 0.0173 9968.9254 6980.1355 2109.093 879.924 0 9969.1529 2.282E-05TL-0 1570 48 25.0 630 0.4 2.000 30 0 31880 0 1.1326 10.9 0.0646 24925.486 16572.829 5306.838 3048.11 0 24927.776 9.187E-05

Barrier System barrierTL-0 910 50 20.0 950 0.4 2.000 24 0 0 0 0.4425 8.224 0.0135 10267.146 7596.7544 1874.375 796.239 0 10267.369 2.167E-05TL-0 1560 49 25.0 950 0.4 2.000 24 0 0 0 0.9874 9.012 0.0606 25809.421 18315.235 4109.164 3386.76 0 25811.159 6.734E-05

Note: a. E L = ½ m V (V sinθ /3.6)2 b. ∑E = E BR-Lat.-NR + E BR-Lat.-R + E BR-Long. + E BEAM

c. Difference = ( ∑E - E L ) / E L d. In this test, no short steel “bridging strips” were used. Thus, M (α ) was ignored.


APPENDIX C: WORKSHEET USED TO CALCULATE D AND n FOR THE TRITON BARRIER

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20




(Nm/rad)

Triton barrier

2004 95.74 7.0 620 0.4 1.981 50 0 0 0 0.5563 9.777 0.0178 10525.397 7280.6925 1504.535 1739.97 0 10525.2 -1.875E-05807 72 20.0 612 0.4 1.981 30 0 0 0 1.0331 9.613 0.0623 18887.231 13087.591 2748.95 3051.47 0 18888.01 4.123E-05

2000 47 25.0 620 0.4 1.981 30 0 0 0 1.511 10.28 0.1233 30442.984 20509.754 4018.239 5917.34 0 30445.328 7.7E-05875 97.04 21.0 620 0.4 1.981 30 0 0 0 1.9165 10.76 0.1882 40825.634 26972.207 5042.328 8811.94 0 40826.476 2.061E-05

2000 60 25.0 620 0.4 1.981 30 0 0 0 2.2433 11.09 0.2487 49612.83 32324.497 5852.936 11439.6 0 49617.052 8.51E-052000 65 25.0 620 0.4 1.981 30 0 0 0 2.552 11.38 0.312 58226.169 37476.978 6606.416 14137 0 58220.441 -9.837E-051971 72.3 25.0 612 0.4 1.981 30 0 0 0 3.026 11.77 0.421 70976.494 44902.946 7640.228 18433.3 0 70976.479 -2.109E-072000 76 25.0 620 0.4 1.981 30 0 0 0 3.2855 11.96 0.4863 79601.03 49912.142 8348.567 21346.9 0 79607.609 8.265E-052000 80 25.0 620 0.4 1.981 30 0 0 0 3.57 12.16 0.5624 88200.587 54781.939 9005.58 24417.5 0 88204.992 4.994E-052000 85.1 25.0 620 0.4 1.981 30 0 0 0 3.947 12.39 0.6703 99804.615 61239.088 9859.742 28712.7 0 99811.571 6.97E-05


c. Difference = ( ∑E - E L ) / E L


APPENDIX D: WORKSHEET USED TO CALCULATE D AND n FOR THE GUARDLINERTM BARRIER

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26




(Nm/rad)Guardlin erTM. barrier

2170 25.86 25.0 655 0.4 2.000 30 1 31880 8487.5 0.5233 9.435 0.0162 9999.5 7006.3587 2078.226 857.23 56.8574 9998.6725 -8.275E-052170 36.57 25.0 655 0.4 2.000 30 1 31880 8487.5 0.9019 10.63 0.0422 19997.291 13427.12 4021.58 2099.12 448.607 19996.423 -4.341E-052170 73.14 15.0 655 0.4 2.000 30 1 31880 8487.5 1.2412 11.4 0.0738 30000.403 19668.588 6023.033 3526.16 784.403 30002.188 5.949E-052170 51.72 25.0 655 0.4 2.000 30 1 31880 8487.5 1.556 12 0.1095 39998 25781.105 8071.629 5065.22 1080.38 39998.327 8.185E-062170 71.45 20.0 655 0.4 2.000 30 1 31880 8487.5 1.854 12.49 0.1486 49995.689 31796.107 10164.93 6686.68 1348.96 49996.679 1.98E-052170 48.88 30.0 655 0.4 2.000 30 1 31880 8487.5 1.8543 12.49 0.1486 50006.577 31802.557 10167.05 6688.27 1349.18 50007.06 9.666E-062170 63.35 25.0 655 0.4 2.000 30 1 31880 8487.5 2.1398 12.91 0.1907 60008.736 37737.924 12301.8 8374.96 1597.34 60012.025 5.48E-052170 84.54 20.0 655 0.4 2.000 30 1 31880 8487.5 2.4148 13.28 0.2352 69992.673 43589.926 14468.6 10110.5 1828.78 69997.79 7.311E-052170 44.99 40.0 655 0.4 2.000 30 1 31880 8487.5 2.4153 13.28 0.2353 70015.099 43602.7 14472.21 10112.8 1828.96 70016.689 2.271E-052170 86.5 20.0 655 0.4 2.000 30 1 31880 8487.5 2.5031 13.39 0.2503 73275.756 45498.872 15184.99 10686.8 1901.04 73271.728 -5.496E-052170 59.17 30.0 655 0.4 2.000 30 1 31880 8487.5 2.5031 13.39 0.2503 73277.032 45499.522 15184.85 10686.5 1900.96 73271.87 -7.044E-052170 73.14 25.0 655 0.4 2.000 30 1 31880 8487.5 2.682 13.6 0.2822 79989.163 49383.245 16670.84 11892.2 2047.28 79993.546 5.479E-052170 57.16 35.0 655 0.4 2.000 30 1 31880 8487.5 2.9425 13.9 0.3314 89989.485 55117.392 18903.97 13713.1 2254.83 89989.305 -1.997E-062170 46.37 45.0 655 0.4 2.000 30 1 31880 8487.5 2.943 13.9 0.3315 90005.474 55126.715 18908.71 13717.5 2255.4 90008.376 3.224E-052170 81.78 25.0 655 0.4 2.000 30 1 31880 8487.5 3.198 14.17 0.3828 100003.56 60802.294 21173.73 15578.8 2454.45 100009.27 5.713E-052170 91.43 25.0 655 0.4 2.000 30 1 31880 8487.5 3.8155 14.75 0.5197 124996.74 74752.907 26951.03 20375.7 2919.68 124999.3 2.046E-052170 100 25.0 655 0.4 2.000 30 1 31880 8487.5 4.401 15.22 0.6655 149527.56 88135.394 32774.09 25283.1 3342.93 149535.48 5.296E-05


c. Difference = ( ∑E - E L ) / E L

Determining Lateral Deflections of Plastic Water-Filled Barriers

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Transcript of Determining Lateral Deflections of Plastic Water-Filled Barriers