huangyhg

analysis model of creep and shrinkage of a reinforced concre
i try to design of a long continuous reinforced concrete beam (about 100m long) which is supported by the bored piers (8m high) at 5m span. i am not sure the way to check shrinkage of the beam.
i worked out the axial displacement of 25mm due to shrinkage and input it into the computer model, i end up very bending moment at the top of pier (say 800knm). axial force is more than 24000kn.
is it the right way to do by input pre-displacement due to shrinkage into the beam model ?

i am currently designing a prestressed concrete
don't know, but did you try with temperature load?
i did try temperature of 20 degree centigrade.
i think i gonna do the equivalent temperature due to shrinkage. say shrinkage strain =500 micro strain is equivalent to 45 degree. then i add temperature and shrinkage effects (20+45=65 degree) into the computer model to analyse the beam.
axial force due to 20 degree temperature is anout 100kn
with concrete shrinkage it is generally much more feasible to attempt to allow the movement rather than restrain it. with this arrangement the piers are unlikely to have the strength/stiffness to restrain the shrinkage movements and will crack/rotate and allow the movement to occur. the large moments you are getting in your beam are basically due to the beam/pier link being modeled as rigid. the 'induced' deflection from the shrinkage bends the column (which tries to resist the deflection) resulting in large moments – which are probably beyond the capacity of the pier.
so, i would recommend the following:
pour breaks / joints – to allow some movement
pinned connection to piers – to allow them to rotate (and not throw moment back into the beam)
small pier size as possible – this reduces the restraint (cracks/rotates pier) and limits the maximum moment that can be induced in the beam (if a rigid connection) to the section capacity of the pier.
don't forget the 25mm shrinkage you have determined is total (ie 12.5mm each side).
cheers

ozeng80 comments are great. here're a few more:
1. equivalent thermal load or axial distortion/pre-strain (if your software has this option) will be most appropriate.
2. reduce modulus of elasticity to ect = ec/(1+ct), where ct is the creep factor. safely ect = ec/2.
3. do not overestimate ultimate shrinkage strain.
4. specify a couple of construction joints, so initial shrinkage will be less restrained.
5. nominally post-tension if crack control is very important.
now that you have brought it up, i also modelled shrinkage as a temperature load (25deg c with a thermal cooefficent of 0.000011 as5100.5), i didn't write anything for the sake of sounding like a cowboy, but it seems to be a widely accepted method for modelling shrinkage.
yakpol,
i will disagree on the 5 and last item. prestress is not good at providing crack control for restraint effects. you are much better to provide closely spaced reinforcement.
pt is great for crack control until the concrete cracks and then it is awful and the cracks are basically unrestrained.
as the amount of pt to stop the concrete cracking is normally very large, and in the case of rigid end restraints (cores) is basically infinite, normal reinforcement at about 200mm centres is normally much more effective.
what i did are:
- put more expansion joint and the beam is now 22m long with. piers are 5m spacing and 1m cantilever each end.
- use equivalent temperature to check shrinkage (thermal coefficient=11x10^-6), then combined live load+shrinkage+temperature (shrinkage just like permanent load). the results give reasonable axial forces (about 100kn not like 24000kn due to pre_displacement).
- the piers will take bending moment at the top and compression then check the pier capacity. if pier is not strong enough, we may increase the pier diameter or reinforcement etc. or maybe put more expansion joints.
we end up 450-600mm diameter of the pier with 8-11m long.
i agree with rapt that pt maybe not a good option becasue it's expensive.
if you increase pier diameter it will attract more load, you may end up wagging the tail.

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