Composite Section Analysis
Finally we came to the composite section analysis. One of the best examples is from Dr. Gilbert and Dr. Ranzi (Example 5.10, Time-dependent behavious of concrete structures, CRC Press, 2010.)
Next Steps
The proposed example is AS5100.5 Type 3 girder with 2400×150 CIP deck.
![Next Steps[1]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Next%20Steps%5B1%5D.jpg?width=412&height=615&name=Next%20Steps%5B1%5D.jpg)
![Next Steps[2]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Next%20Steps%5B2%5D.jpg?width=734&height=176&name=Next%20Steps%5B2%5D.jpg)
![Next Steps[3]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Next%20Steps%5B3%5D.jpg?width=672&height=281&name=Next%20Steps%5B3%5D.jpg)
The Different Steps
Step 0)
At age 7, the girder is released with PT=1000 kN/tendon. DL moment at span center is M=550 kN-m. Ducts have not been grouted yet.
Ec(7)=25 GPa.
A duct = (1/4)?(60mm)2 = 0.00283 mm2
=25%20GPa.jpg?width=702&height=237&name=Ec(7)=25%20GPa.jpg)
Due To DL Moment
Due To Post Tensioning
N = -2000 kN
M = (-1000 kN)(1.03m+1.16m) = -2190 kN-m
Summary
![Summary[1]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Summary%5B1%5D.jpg?width=690&height=296&name=Summary%5B1%5D.jpg)
![Summary[2]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Summary%5B2%5D.jpg?width=690&height=129&name=Summary%5B2%5D.jpg)
![Summary[3]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Summary%5B3%5D.jpg?width=690&height=352&name=Summary%5B3%5D.jpg)
Part 9
Step 1)
Calculate strain and stress at age 40. The structural system is the same as step 0) and the differences are only the time effects.
General equation for the time-dependent analysis is as follows.
For step 1), the equation can be simplified as below.
%2c%20the%20equation%20can%20be%20simplified%20as%20below.jpg?width=621&height=98&name=For%20step%201)%2c%20the%20equation%20can%20be%20simplified%20as%20below.jpg)
Ec(40)=32 GPa
Section property
Restraining force and strain
Due to creep
Φ(40,7)=0.8
![Due to creep[1]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Due%20to%20creep%5B1%5D.jpg?width=701&height=221&name=Due%20to%20creep%5B1%5D.jpg)
![Due to creep[2]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Due%20to%20creep%5B2%5D.jpg?width=701&height=155&name=Due%20to%20creep%5B2%5D.jpg)
Due to shrinkage
εsh(40)=-100×10-6
Due to relaxation
![Due to relaxation[1]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Due%20to%20relaxation%5B1%5D.jpg?width=701&height=398&name=Due%20to%20relaxation%5B1%5D.jpg)
![Due to relaxation[2]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Due%20to%20relaxation%5B2%5D.jpg?width=701&height=216&name=Due%20to%20relaxation%5B2%5D.jpg)
Unrestrained strain summary
Stress caused by unrestrained strain summary (MPa)
%20-%20Stress%20caused%20by%20unrestrained%20strain%20summary%20(MPa).jpg?width=701&height=280&name=Step%204)%20-%20Stress%20caused%20by%20unrestrained%20strain%20summary%20(MPa).jpg)
Restrained strain summary 0
Restrained strain diagram
Stress caused by unstrained and restrained strain summary (MPa)
.jpg?width=701&height=233&name=Stress%20caused%20by%20unstrained%20and%20restrained%20strain%20summary%20(MPa).jpg)
Step 2)
At this step deck is poured and the moment is M40 = 620 kN-m. The structural system is the same as step 1).
Due to deck moment
Step 2) - Restrained strain summary and diagram
%20-%20Restrained%20strain%20summary%20and%20diagram.jpg?width=701&height=525&name=Step%202)%20-%20Restrained%20strain%20summary%20and%20diagram.jpg)
Step 2) - Stress caused by restrained strain summary (MPa)
%20-%20Stress%20caused%20by%20restrained%20strain%20summary%20(MPa).jpg?width=701&height=256&name=Step%202)%20-%20Stress%20caused%20by%20restrained%20strain%20summary%20(MPa).jpg)
Step 2) - Stress caused by unstrained and restrained strain summary (MPa)
%20-%20Stress%20caused%20by%20unstrained%20and%20restrained%20strain%20summary%20(MPa).jpg?width=701&height=255&name=Step%202)%20-%20Stress%20caused%20by%20unstrained%20and%20restrained%20strain%20summary%20(MPa).jpg)
Step 3)
Duct grouting and deck composite commencement at day of 40.
Ec deck = 18 GPa
.jpg?width=701&height=421&name=Step%203).jpg)
Step 4)
Calculate strain and stress at age of 60.
.jpg?width=701&height=422&name=Step%204).jpg)
Strain summary
Due to creep
![Due to creep[N,M]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Due%20to%20creep%5BN%2cM%5D.jpg?width=701&height=125&name=Due%20to%20creep%5BN%2cM%5D.jpg)
![Due to creep[N,M]2](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Due%20to%20creep%5BN%2cM%5D2.jpg?width=701&height=136&name=Due%20to%20creep%5BN%2cM%5D2.jpg)
Due to shrinkage
Girder
Deck
Due to relaxation
![Due to relaxation[3]](https://resource.midasuser.com/hs-fs/hubfs/MOTIVE_Image/Expert%20Tip%20Creep%20Analysis%20-%20Next%20Steps/Due%20to%20relaxation%5B3%5D.jpg?width=701&height=553&name=Due%20to%20relaxation%5B3%5D.jpg)
Step 4) - Unrestrained strain summary
%20-%20Unrestrained%20strain%20summary.jpg?width=701&height=280&name=Step%204)%20-%20Unrestrained%20strain%20summary.jpg)
Step 4) - Stress caused by unrestrained strain summary (MPa)
-2.png?width=701&height=281&name=Stress%20caused%20by%20unrestrained%20strain%20summary%20(MPa)-2.png)
Step 4) - Restrained strain summary with diagram
%20-%20Restrained%20strain%20summary%20with%20diagram.jpg?width=701&height=519&name=Step%204)%20-%20Restrained%20strain%20summary%20with%20diagram.jpg)
Step 4) - Stress caused by restrained strain summary (MPa)
%20-%20Stress%20caused%20by%20restrained%20strain%20summary%20(MPa).jpg?width=701&height=277&name=Step%204)%20-%20Stress%20caused%20by%20restrained%20strain%20summary%20(MPa).jpg)
Step 4) - Stress caused by unstrained and restrained strain summary (MPa)
%20-%20Stress%20caused%20by%20unstrained%20and%20restrained%20strain%20summary%20(MPa).jpg?width=701&height=253&name=Step%204)%20-%20Stress%20caused%20by%20unstrained%20and%20restrained%20strain%20summary%20(MPa).jpg)
He is a Senior Supervising Engineer with a high level of expertise in the design and analysis of suspension bridges. He has a solid fundamental understanding of structures and can apply his knowledge exceptionally well to the design and analysis of highly complex structures. He is also a strong communicator, able to identify and distill the key information that is relevant to the task at hand and present it in a clear and quickly understandable manner.