Why is the distrance to the top of a 26 story building that as two stair cases per floor?

Question

Do not forget both the horizonal and verticle distrance of the stair cases. Please show your math.

Answer 1

Well it depends on a number of factors, but I will try and make some educated assumptions.

Assumptions:
1) each story is 3 meters
2) the rise of each step is the same as the depth
3) The width of each stair area is 1 meter
4) There is a 2x1 meter platform for changing directions at the top of each stair section.
5) you move in the middle of the stair.

Using these assumptions, for each stair case you move horizontally 1/2+1/2=1 meter on the platforms and 3 meters on the stairs. You also move 3 meters on the stairs. Therefore you move 3√2 meters on the stairs and 1 meter on the platform. Once you get to the next platform you will move one meter over (to be aligned in the middle of the next staircase). Therefore you move 1+3√2+1=2+3√2 meters for each staircase. There are two staircases per floor so you move 4+6√2 meters per floor.

If you start on floor 1 and go to floor 26 you have gone up 25 floors, and therefore you have moved 25(4+6√2)=100+150√2≈312 meters.

If you start on a base floor (that isn't 1) and go to floor 26, you have gone up 26 floors and have moved 104+156√2≈324 meters.

This of course feels like more work than walking 324 meters because you are going up. It's much harder to work against gravity.

Whatever it is, it sounds like a good workout, especially if you do it everyday.

Answer 2

The number of staircases makes no difference to the overall height of the building.
The total height depends upon the storey height of each floor. That is the distance from top of a floor up to the top of the next floor.This storey height can vary depending upon what the building is being designed for and how many services are to be housed within any false ceiling space.
A storey height of 4metres would be reasonable for an office building with a large number of services but if there are car parking floors the storey height could be down to 2.5metres.
Assuming that all storey heights are 4m the overall height is going to be 26x4=104metres or 341.12 feet.