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.)
The proposed example is AS5100.5 Type 3 girder with 2400×150 CIP deck.
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.
A duct = (1/4)π(60mm)2 = 0.00283 mm2
N = -2000 kN
M = (-1000 kN)(1.03m+1.16m) = -2190 kN-m
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.
Restrained strain diagram
At this step deck is poured and the moment is M40 = 620 kN-m. The structural system is the same as step 1).
Duct grouting and deck composite commencement at day of 40.
Ec deck = 18 GPa
Calculate strain and stress at age of 60.
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