 ## 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)π(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 ## 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

Φ(40,7)=0.8

## ### Due to shrinkage

εsh(40)=-100×10-6

## Restrained strain diagram

## ### 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).

## ### 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.

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