This tower is a direct application of the Eiffel principle, that each piece should be supported by another. For that reason, each major beam is supported by alternate, smaller beams.  The same principle was used in building the late gothic cathedrals.

This is surely the tallest Lego tower ever published on the Internet!   It is 30,000 pixels high!   It is actually at two inches of the ceiling.  I couldn't make it any taller, even if I wished.   You can notice the outside elevator on the right.  It goes up to the discotheque level, after a stop at the restaurant.   This tower is so strong I can grab it with one hand in the middle, and go around like if I was transporting a briefcase.

Well, it seems that building an Eiffel tower is an interesting challenge. How can we build a structure using Lego bricks that can support a very large weight? Below, I suggest a structure that can support 50 kg (100 lbs). I made a seat with it! Sadly, I don't have enough pieces to complete it (the design requires 6000 pieces, for a total height of 3 meters - near 9 feet tall). This is the resulting plan. It does not include a balcony on the first level, nor a second floor. For this, I would need to actually build the bottom of the tower, but I only have enough pieces to build 2 of the four legs...     The basic architecture is very simple, as seen on this picture of a leg. Beams are connected with chevrons at regular interval. The beam, the core of the structure, is made of four 1 X 16 bump beams.   Although it does not look exactly like the real Eiffel tower, this structure is very robust, and I estimate that I can make an enlarged version reaching 25 meters, and suspend underneath it a swing for the younger.