Tie beams are constructed to support the differential settlement among the isolated footings other than the vertical loads of the block works.
With reference to ACI 318-08 section 18.104.22.168, grade beams which are built up to function as horizontal ties among pile caps or footings should be proportioned in such a way so that the smallest cross-sectional dimension is identical to or exceeding the clear spacing among associated columns divided by 20 but should not be over 18 inches. Closed ties should be arranged at a gapping not surpassing the lesser of one half the lowest orthogonal cross-sectional dimension and 12 inches.”
But, it becomes difficult to understand that what force these tie beams are required. In this regard, IBC 2009 section plays an important role.
IBC2009 section 1809.13 for shallow foundations and 1810.3.13 for deep foundations.
For SDC C, D, E or F, ties have the capacity to bear, in tension or compression, a force similar to the smaller of the product of the larger pile cap or column design gravity load times the seismic coefficient, Sds, divided by 10, and 25 percent of the smaller pile or column design gravity load.
In brief, Tie beam force; FT = Larger of ( Pu_large x Sds /10 , Pu_small x 25%)