what is the range of period time of first mode of RC high rise buildings under seismic loads, and is this time increase with crack appearance or not?
Mostly it is 10% of the number of stories. For example 5 stories building has a time period of 0.5 seconds. If there is damages due to cracks then the structure stiffness will go down and the time period will increase.
One can not be certain of the period time range. It increases with the number of the Levels of the buildings. If also depends on the shape of the building. One should not be concentrating very much on the range. But the study can be carried out for the specific type of the building with inclusion of the parameters like variance of frequency and time period with the increase in level.
Cracks depend on the intensity of the seismic loading and effect of intensity of seismic loading varies with the height of the structure. Thus it is a three way connection between these parameters
Mostly it is 10% of the number of stories. For example 5 stories building has a time period of 0.5 seconds. If there is damages due to cracks then the structure stiffness will go down and the time period will increase.
It depends, but as a rough approximation you can use codified equations as:
T = alpha * (H^0.75)
where alpha is a constant which depends to structural system:
Steel Moment Frame ==> alpha = 0.008
R.C. Moment Frame ==> alpha = 0.007
Other ==> alpha = 0.005
On the other side, codes allow to use analytical values from modeling if they were not 1.25-1.4 times more than codified values.
About period elongation, I must say that crack appearance does not mean that structures has undergone considerable non-linearity. as you know, concrete will experience crack when stresses surpass tensile strength which is so small. Then, I believe that more deformation demands than when cracks are appeared must be forced to structure to cause a significant change in stiffness and as a consequence fundamental period.
You have loads of software even free to do this calculation. It's always better to calculate ( and know the assumptions) than guess... Those rules of thumb are mostly useless.
It is very necessary to compare between natural frequency ( DL & self weight) only and with forced frequency (Seismic loads). If NF equal or near to FF , this leads to collapse of structure.
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