Steel Composite Girder Flexural Capacity: AASHTO vs Eurocode

November 26, 2021
BLOG BRIDGE INSIGHT

 

Steel Composite Girder Flexural Capacity: AASHTO vs Eurocode

 

 

Table of Contents

 

1. Introduction

2. Flexural Resistance as per AASHTO LRFD

3. Flexural Resistance as per Eurocode

4. Comparison of AASHTO vs Eurocode Flexural Resistance

5. Conclusion


 

1. Introduction

 

Steel composite bridges are widely used due to the proper utilization of tensile strength of steel girder and the compressive strength of concrete deck, thereby bending resistance is greatly enhanced, making it more efficient and economical. Multi-girder system or ladder deck forms of steel composite bridges are the main forms of construction having simply supported or continuous girders.

 

In this article, design provisions for ultimate flexural resistance as per AASHTO LRFD and Eurocode are detailed. Flowcharts are shown for better understanding.

 


 

2. Flexural Resistance as per AASHTO LRFD

 

The procedure of calculating flexural capacity of steel composite I section is outlined in Figure 1, where four cases are established. 

 

Case 1: Flexural Resistance of Positive Flexure Moment in Compact Section.

Case 2: Flexural Resistance of Positive Flexure Moment in Non-Compact Section.

Case 3: Flexural Resistance of Negative Flexure Moment.

Case 4: Flexural Resistance of Negative Flexure Moment by using Appendix A6.

 

 

Picture1

Figure 1. Flowchart for calculation of Positive Moment Flexural Capacity as per AASHTO LRFD
 
 
 
 
 

Picture2

Figure 2. Flowchart of the flexural resistance of Positive Flexure Moment in Compact Section
 
 

 

 

Picture3

Figure 3. Flowchart of the flexural resistance of Positive Flexure Moment in Noncompact Section
 
 
 

 

Picture4

Figure 4. Flowchart of the flexural resistance of Negative Flexure Moment
 
 
 

 

Picture5

Figure 5. Flowchart of the flexural resistance of Negative Flexure Moment by using Appendix A6
 
 

 

3. Flexural Resistance as per Eurocode

 

Bending resistance, MRd, can be calculated as follows based on its class.

 

Class 1 or 2 cross‐sections can be checked by using the plastic or elastic bending resistance.

 

Class 3 cross‐sections are checked with the elastic bending resistance, or possibly reclassified as effective Class 2 cross‐section and then checked with the plastic bending resistance.

 

Class 4 cross‐sections are also checked with the elastic bending resistance but by using the effective cross‐section, reduced to take account of buckling.

 

Picture6

Figure 6. Flowchart of flexural resistance as per Eurocode
 
 

 


 

4. Comparison of AAHSTO vs Eurocode Flexural Resistance

 

Let's take a 2-Span Steel Composite I girder Curved bridge for comparison.

 

Number of main girder: Four, Steel Composite I girder

Curvature radius: 4.318 m

Construction Stage Analysis: Yes

 

The bridge is modeled in midas Civil as shown below:

 

Picture7

Figure 7. Two-span Steel Composite I girder curved bridge model
 
 

 

Keeping the materials, sections, and loading the same, the positive bending region was designed as per AASHTO LRFD-17 and Eurocode (EN1994-2). The results are illustrated in figure 8 where the flexural resistance checks are satisfied as per the codes.

 
 

 

AASHTO LRFD

Eurocode

Section

 

Materials

Steel      

fsk= 355.000 MPa

Es=210000.000    MPa       

 

Concrete                                  

fck= 30.000 MPa 

Ecm = 33000.000 MPa        

 

Reinforcement    

fyk = 400.000 MPa

Er = 210000.000 MPa         

 

Steel      

fsk= 355.000 MPa

Es=210000.000    MPa       

 

Concrete                                  

fck= 30.000 MPa 

Ecm = 33000.000 MPa        

 

Reinforcement    

fyk = 400.000 MPa

Er = 210000.000 MPa         

 

Region

Positive Bending

Positive Bending

Demand Forces

Steel only moment

MD1 =2462 KNm

 

Long-term moment

MD2 =1045 KNm

 

Short-term moment

MD3 =1457 KNm

 

 

Before Composite Moment

Ma,Ed =2462 KNm

 

After Composite Moment

Mc,Ed =2502 KNm

 

MEd = 4964 KNm

 

Section Classification

Non-compact section for Curved Bridge

Class 1

Flexural Resistance

▪ Check Flexural Resistance of Composite noncompact section (AASHTO LRFD Bridge, 2018, 6.10.7.2)                 

                             

i. Check compression flange            

Fnc = Rb · Rh · Fyc = 355.000 MPa

Fbu = 67.858 MPa

             ≤ Фf · Fnc = 355.000 MPa HENCE OK    

                 

ii. Check tension flange                     

Fnt = Rh · Fyt = 355.000 MPa

fbu + (1/3) fl = 99.115 MPa

             ≤ Фf · Fnt = 355.000 MPa

 

HENCE OK                                            in which :

Rb = 1.000

Rh = 1.000

Фf = 1.000

▪ Check Flexural Resistance

(EN 1994-2:2005)

 

 

 

- Plastic resistance moment, Mpl, Rd

 

Plastic NA = 1812.6 mm

 

 Nslab  = 11221.020 kN                      

 Ng,top  = 5348.875 kN                          (Upper side of PNA)

 Ng,bot =16569.895 kN                       (Lower side of PNA)

 

 Mpl,Rd = 22842.225 kNㆍm         

 xpl = 330.327 mm                                                           

MRd = βMpl,Rd = 22842.2kNㆍm                                    

here, β =1.000                                                                                         

MRd  = 22842.22 kNㆍm            

         >MEd = 4965.21 kNㆍm

HENCE OK                                                                                     

Figure 8. Flexural resistance comparison between AASHTO LRFD and Eurocode
 
 

 

5. Conclusion

 

 

The bending resistance of a steel composite girder can be calculated using the plastic stress distribution method. AASHTO LRFD uses load and resistance factor design where resistance factors(Фf) are multiplied with the actual bending resistance, whereas Eurocode uses partial safety factors for materials(γ) and reduction factors(β). The reduction factor β is applied only when high-strength steels of Fyk = 420 and 460 MPa are used.

 

In both the codes, based on section classification the moment capacity will be affected by the demand moments. So designer must prepare the load combinations in midas Civil carefully. AASHTO LRFD suggests moment resistance checks for compact sections in positive moment regions and for non-compact and negative bending regions, a stress check approach is performed. Whereas Eurocode suggests a moment resistance check approach only.

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About the Author
Suman Dhara | Senior Bridge Engineer | MIDAS IT India

Suman has pursued his Master's Degree in Structural Engineering from IIT Hyderabad and has 6+ years of extensive Technical Consulting experience for Bridge & Building Projects. He enjoys providing solutions to engineers on sophisticated projects ranging from bridge engineering, building engineering, and special mechanics problems. 

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