Monte Carlo Simulation on
Ultimate Bending Capacity ofHybrid Composite Girder
モンテカル法に基づくハイブリッド合成桁の終局曲げ耐力に関する研究

XU YIFEI
Yamamoto Lab., EME, GSSIE
University of Tsukuba

INTRODUCTION 背景
Specification-based
Design for Bridge

Updated[1]Allowable Stress
Design method (ASD)
Stress-based Design

DesignStrengthMaximum
Stress[1] Japan Road Association: Road Bridge Specifications, 2017. (in Japanese)

Performance-based
Design for Bridge
Limit State Design
Method (LSD)
Capacity-based Design
Stress-based Design
DesignCapacity

Maximum
Load1

MERIT OF CAPACITY-BASED DESIGN
Concrete SlabUltimate Limit State =Concrete Crushing or Steel BucklingSteel Girder[2] Kyosuke Yamamoto, Hitotaka Kouno, Kuniyuki Sugiura, Yoshinobu Oshima and Tarou Tonegawa, Effect of material
plastic properties on ultimate Bending Capacity of Hybrid Composite Girder, 62nd Annual Lecture of Civil Engineering
Society, 2007. (in Japanese)

2

COMPOSITE GIRDER AMELIORITON

NormalHybrid

Composite Girders

Composite Girders

Comparison
Comparison

Steel Cost

20% decrease[3]High Performance Steel

10% decrease[3] Masutsugu Nagai, Takeshi Miyashita, Cuiping Liu, Naofumi Inaba and Atsushi Homma, Design and Application ofSteel and Steel-Concrete Plate Girds Bridges with Hybrid Section, Journal of Japan Society of Civil Engineers A1,Vol68, No.1, pp.203-215, 2012. (in Japanese)3

BENDING CAPACITY CALCULATE CRITERION
Full-Plastic
Ultimate Bending Moment
Bending Momentcalculated by Fiber Method / Finite Element Method

ororEasier

The Design ValueOf Ultimate Limit State
Factor ofsafety

More Accurate

The true value ofUltimate Bending Moment
𝑀 : basic design method (easy) 𝑀
𝛼𝑀 ：design load
evaluate 𝑀 < or > 𝑀< : Failure> : Safety
Bending Capacity evaluate 𝑀 /𝑀4

PURPOSE

NCGs = Normal Composite Girders
HCGs = Hybrid Composite Girders

To verify the ultimate limit state
Compare the Reliability of NCGs and HCGs
Failure Probability
Ultimate Limit State = Concrete Crushing or Steel Buckling

Fiber Method

FEM

All Material Parameters are taken as Random Variables
5

Random Variables
 Compression Strength 𝑓 Young's Modulus 𝐸 Yield Strength 𝜎 hardening strain 𝜀 Hardening Coefficient 𝐸
 Hardening Curvature 𝜉NUMERICAL EXPERIMENT
evaluate

Bending
Capacity

Ultimate Full-Plastic
Bending Bending
Moment Moment

NormalDistribution

Log-normal
Distribution

Weibull
Distribution

900900900600600

600300300300024262830322fc(N/mm )3436024262830322fc(N/mm )34360242628303234362fc(N/mm )6

CONTENT Fiber method

Concrete crushing ultimate state② Model setup③ Results and Discussion
①

 FEM

Steel buckling ultimate state② Model setup③ Results and Discussion①

7

CONTENT Fiber method

Concrete crushing ultimate state② Model setup③ Results and Discussion
①

 FEM

Steel buckling ultimate state② Model setup③ Results and Discussion①7

SIMULATION MODEL

𝒕𝒇𝒕 =12𝒕𝒇𝒃 =24𝒕𝒇𝒕 =24𝒕𝒘 =24

𝒕𝒘 =15

𝒕𝒘 =12

slender

𝒕𝒇𝒕 =15

𝒕𝒇𝒃 =40standard

𝒕𝒇𝒃 =64

compact
8FIBER METHOD
Basic design method

Ultimate Limit State

Design Index

ConcreteCrush

UltimateBending
Moment:Full-Plastic
Bending
Moment:[4] Yukio Maeda, Yasuharu Kajikawa and Masao Ishiwata, Bending Behaviors and Maximum Load-Caring Capacity ofHybrid Composite Beams, Kawasaki Technical Report, Vol.10, No.1, pp.86-99, 1978. (in Japanese)

9RESULT OF WEIBULL DIST.
1400

Slender NCG

1400

Standard of NCG

1400

1050

1050

1050

700

700

700

350

350

350

00.7
1400

11.3

00.711.300.7

1400

1400

1050

1050

1050

700

700

700

350

350

350

00.7

1

Mu/Mp

1.300.7

1Mu/Mp11.3

Mu/Mp
Compact HCG

Mu/Mp
Standard HCG

Mu/Mp
Slender HCG

Compact NCG

1.300.7

11.3

Mu/Mp

10

DISCUSSION OF HISTOGRAMSNormalFailureComposite Girders

1400

SafetyStandard of NCG

1050
700

00.70.91

Mu/Mp

HybridFailureComposite Girders 1400

SafetyStandard HCG

1050
700
00.7

High failure probability means ,with certain factor of safety,
there are more unreliable
1.3 samples and more failurecases, with means less reliable.

Smaller quality variation
Small quality variation means aconcentrate data distribution
and is more likely to have fewer
abnormal samples.

Lower Failure Probability

350

Less than𝑀
𝛼𝑀

Large quality variation meansa disperse data distribution
and is more likely to have moreabnormal samples.

Higher Failure Probability

350

Less than𝑀
𝛼𝑀

Larger quality variation

0.9

1Mu/MpLow failure probability means ,with certain factor of safety,
there are fewer unreliable
1.3 samples and fewer failurecases, with means more 11reliable.

RELIABILITY INDEX[3]Destruction

Design Load

[3] Masatsugu Nagai, Takeshi Miyashita, Guiping Liu, Naofumi Inaba and Atsushi Homma, Design andapplicabicability of steel and steel-concrete plate girder bridges with hybrid section, Vol.68, No.1, 203215,2012. (in Japanese)

12

RESULT成果考察

既往成果
成果考察

Risky

Safe
Risky

Safe

13

RESULT成果考察
Risky

既往成果
成果考察
HybridComposite Girders

NormalComposite Girders
Safe
Risky

Safe

13

RESULT成果考察
Risky

With same section dimensions, HCGs
have lower Reliability than that of NCGs.

Compact
HCGs

because concrete was inferred to resist
against larger compress stress.

Weibull Dist.
Normal Dist.

Compact
NCGs

Log-normal Dist.

Safe
Risky

Failure Probability estimated fromthe assumption of Weibull Dist. is highest,
which means better to use for safety

Safe

14

RESULTWith same material properties, the slendermodel has a higher Reliability.

Risky

Compact
NCGs

Slender
NCGs
Standard
NCGs
Safe
Risky

Safe

15

RESULT
10000

NCGsHCGs NCGsHCGsNCGsHCGs

10000

8000

8000

6000

6000

4000

𝑆𝑙𝑒𝑛𝑑𝑒𝑟

4000

0.8

0.901.0

10000 NCGsHCGs NCGsHCGsNCGsHCGs

0.91.0

Small design load6000

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑Large design load

2000
00.8



8000

4000

𝐶𝑜𝑚𝑝𝑎𝑐𝑡

2000

2000
0

NCGsHCGsNCGsHCGsNCGsHCGs

0.8

0.9

1.016

CONTENT Fiber method

Concrete crushing ultimate state② Model setup③ Results and Discussion① FEM

Steel buckling ultimate state② Model setup③ Results and Discussion①7

FINITE ELEMENT METHOD
Concrete Crushing

Steel BucklingComparison𝛿[4] Shun-Fa Hwang, GUU-Huann Liu, Buckling Behavior of Composite laminates with multiple delaminations under
uniaxial compression, Composite Structures, 53 (2001) 235-243.

17

SIMULATION MODEL
Stiffener

Cross Girder※Restraining thedeformation ofbuckling※Restraining thelateral buckling

Two-Girder Model18

RESULT

既往成果
成果考察
Displacement

10 times scale

19

RESULT

既往成果
成果考察strain 10 times scale
Total mechanical

Upper edge ofconcrete slab

Maximum value < 𝜀 = 0.035
Steel buckling ultimate state

20

RESULT OF WEIBULL DIST.
SlenderStandard

Compact

NCGs

HCGs

21

DISCUSSION OF HISTOGRAMSNormalFailure

SafetyLarger quality variation
Large quality variation meansa disperse data distribution
and is more likely to have moreabnormal samples.

Composite Girders

Higher Failure Probability
High failure probability means ,with certain factor of safety,
there are more unreliablesamples and more failurecases, with means less reliable.

Less than𝑀
𝛼𝑀

HybridFailure

Composite Girders

SafetySmaller quality variation
Small quality variation means aconcentrate data distribution
and is more likely to have fewer
abnormal samples.

Less than𝑀
𝛼𝑀

Lower Failure Probability

Low failure probability means ,with certain factor of safety,
there are fewer unreliablesamples and fewer failurecases, with means more 22reliable.

RESULT
StandardHybrid
Composite Girders

SlenderCompact

23

RESULT

Small design load

既往成果

Large design load

Small design load

Large design load

24

SUMMARIES

既往成果

 Fiber Method: Concrete crushing ultimate state FEM: Steel buckling ultimate state

Designload

Sectiondimension

model

Large

Slender

NCGs

SmallSlender

HCGs

Large

Compact

HCGs

Small

Compact

HCGs
25

CONCLUSIONS 結論
 From the results of Fiber method, slender section shows a better performanceof bending capacity, and NCGs are proved to have a higher reliability withlarge design load. The reliability of HCGs is overvalued.
 From the results of FEM, compact section is inferred to have a better
performance of resisting buckling. And the buckling resistance performanceof HCGs are obvious. Thus, the compact HCGs are concluded to be mostreliable structure.
 To synthesize the results of Fiber method and FEM, the results of Fibermethod are not completely credible when the structure has a thin shell part,and the buckling calculation should be considered in the simulation. The
advantages of HCG could be interpreted. The compact HCGs could beconcluded to have a highest structural reliability among these situations andhave a better performance to resist buckling.

26

FUTURE WORK 今後の予定
 It is possible to improve the parameters used in numerical simulation. Dueto the different statistical data of references, materials and steel
manufacturers, it is possible to further rationalize the results by using more
realistic values.
 Due to the complexity and time-consuming of the FEM buckling analysis,
only 100 variables are generated for simulation in this research. In thefuture work, we should try to simplify the calculation process and use morevariables to make the results more reliable.
 For the structure with thin shell part, Fiber method is not enough forcalculation. In order to make the result more reliable, buckling analysis of
FEM should be added into calculation. To make fully use of performance ofeach material, a more appropriate section dimension could be found for thedesign of composite girder in the future work, which should satisfy that thestructure achieves the failure of upper edge of concrete slab and buckling
ultimate state simultaneously.

27