Advanced Composite Section Analysis in Structural Design

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)

About the Editor

Seungwoo Lee PhD, P.E., S.E.

Senior Supervising Engineer at WSP USAs (Tampa, FL)

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.