MOTIVE

Advanced Composite Section Analysis in Structural Design

Written by Seungwoo Lee, Ph.D., P.E., S.E. | Oct 17, 2023 6:32:12 AM

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.

 

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

 

 

Due To DL  Moment

 

Due To Post Tensioning

N = -2000 kN
M = (-1000 kN)(1.03m+1.16m) = -2190 kN-m

 


Summary

 

 

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.

 

Ec(40)=32 GPa

 

Section property

 

Restraining force and strain

 

Due to creep

Φ(40,7)=0.8

 

Due to shrinkage

 

εsh(40)=-100×10-6

 

 

Due to relaxation

 

Unrestrained strain summary

 

 

Stress caused by unrestrained strain summary (MPa)

 

 

Restrained strain summary 0

 

Restrained strain diagram

 

 

Stress caused by unstrained and restrained strain summary (MPa)

 

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

 

 

Step 2) - Stress caused by restrained strain summary (MPa)

 

 

Step 2) - Stress caused by unstrained and restrained strain summary (MPa)

 

 

Step 3)

Duct grouting and deck composite commencement at day of 40.
Ec deck = 18 GPa

 

Step 4)

Calculate strain and stress at age of 60.

 

Strain summary

 

 

Due to creep

 

 

Due to shrinkage

 

Girder

 

Deck

 

 

Due to relaxation

 

Step 4) - Unrestrained strain summary

 

 

Step 4) - Stress caused by unrestrained strain summary (MPa)

 

 

Step 4) - Restrained strain summary with diagram

 

 

Step 4) - Stress caused by restrained strain summary (MPa)

 

 

Step 4) - Stress caused by unstrained and restrained strain summary (MPa)