I'm writing about a setting where building technology is quite advanced, but elevators have not yet been invented, so the limiting factor on height is ergonomic.
What would be the maximum practical height for a building where the people going up the stairs are expected to be pretty fit, and where it's deemed acceptable to need to stop for a rest on the way up?
A large part of the problem is how big do you want to build without an elevator of some sort.
The earliest elevators were made in the third century BC. The basic technology is simple with a platform below a hoist. If you are going to be building something more than a few stories you will have a hard carrying everything up and down stairs or ladders and eventually will just throw a rope down and pull stuff up.
Once you are pulling stuff up on a rope its a short step to a loop to stick your foot in and then a board to stand on.
Gravy on the whole scheme is a pulley at the top so the lifting can be done from the bottom.
The elevators may not look like modern elevators but once you start building high, it is almost inevitable. You need to get things up to build, and moving 100kg of person up and down in order to move 50kg of concrete up just sucks.
Pretty much once you have a way of lifting stuff up, people will try to ride it.
The only reasons elevators wouldn't be ubiquitous in tall buildings would be political or social.
This society has a strong focus on physical fitness where there is a strong shame associated with not moving under your own power.
Elevators were invented but a tragic accident in the past instilled a cultural bias against them
If elevators are highly taxed, then there won't be many of them except for the very rich where they would almost be a status symbol.
According to http://urbansome.com/how-many-calories-does-walking-up-the-stairs-burn/ humans burn 10 calories climbing up one floor. This means that climbing up a 20 story building means you will burn a tenth of your daily calories.
New York City used to be limited to 8 story buildings due to hydraulic concerns, they couldn't get the water up to the higher floors through pressure alone. Most of these didn't have elevators.
Of course there is also this modern building in Spain. http://www.spiegel.de/international/europe/architect-forgets-elevator-for-47-floor-skyscraper-in-spain-a-916082.html
If tall building without elevators are normal, then there will be a strong desire to tie buildings together at higher floors with elevated walkways. Commuting from the 13th floor to the 12th of a building a mile away isn't so bad if every building in between is connected at the 10th floor. There is less energy expended walking the extra mile than up the 10 extra floors.
Someone on Quora asked the same question six years ago.
https://www.quora.com/How-many-floors-did-the-tallest-buildings-have-before-elevators
In ower[sic] Manhattan in New York City, in the late 1860s some office buildings were taller than five stories, but these buildings did not have elevators and apparently the top floors generally were not used for offices. In addition, some hotels were taller than five stories. Around 1870, construction of seven to ten story office buildings with elevators began. Except in lower Manhattan, until 1885 few U.S. office buildings exceeded five stories.
Third, prior to the development of practical passenger elevators, no one would pay much for offices located above the fifth floor of a building.
Thus, 5-6 floors (just like @JBH said).
The practical height wouldn't be measured in terms of human fitness — it would be measured in terms of the ability to get water and furniture to the higher stories
Elevators move more than humans. In fact, elevators move a lot more than humans. They move food, equipment, furniture, etc. Walking up stairs is easy by comparison. Let's see Rocky run up ten flights of stairs with a desk on his back.
In the good old days (and still today) buildings had pulleys (like barns) used specifically to haul material up in a way that didn't involve all those flights. But there's only so far you can do this with practicality.
I'm wholly lacking in detailed research, but I'd be somewhat surprised to hear of a pulley system that lifted 10 floors (about 100 ft or 30.5 meters). The problem isn't the technology, but the basic safety. The first time a building owner had to pay out for the death of a person smashed under a \$10,000 desk (or, perhaps, just the \$10,000 desk...) would be the last time a 10 story building would be built. (And let's see you lift a big dest 100 feet in the wind! I supppose it could be inside the building... expensive...)
Therefore, I'm going with 4–6 floors
And that's assuming your water pressure is high enough to push water through a 2" vertical pipe for 60 feet.
I can imagine a building about 100 feet (30.48 meters) wide and 1,000 feet (304.8 meters) high (almost 100 floors) and 1,000 to 10,000 feet (304.8 to 3,048 meters) long. It has widows in the rooms on both sides and broad corridors down the long middle of the building. And the broad corridors might have relatively steep stairs for the athletic and relatively gentle ramps for others. Some of the ramps might be used by pack animals to bring supplies up and some of the ramps could be broad enough to drive carts with supplies up.
I thinks that horses, etc. would usually fear steps and would have good chances of stumbling on steps and falling. The Scarlet Empress (1934) has horses charging up stairs, but that is a scene in a movie. But gentle ramps should be okay for horses.
The Abbasid Caliph al-Muktafi (reigned 902-908) built the Palace of the Taj and many other buildings at Baghdad.
Ali Muktafi also constructed halls of assembly and divers cupolas in the immediate neighborhood of the Taj; one especially was known as the Cupola of the Ass (Kubbat-al-Himar), this being a tower ascended by a spiral stair, of such an easy gradient that the Caliph could ride to the summit on a donkey trained to an ambling gait. Thus without fatigue he could enjoy the view over the surrounding country, for the height of this tower is described as very great, and in plan it was semicircular.
https://books.google.com/books?id=rdcoAAAAYAAJ&pg=PA254&lpg=PA254&dq=The+cupola+of+the+ass+in+Baghdad&source=bl&ots=U_ZH093BdX&sig=W3frDQNY8omwhlqykTgxpjwrwCM&hl=en&sa=X&ved=2ahUKEwiOz_qDy4veAhVSUt8KHaIZAIoQ6AEwAXoECAgQAQ#v=onepage&q=The%20cupola%20of%20the%20ass%20in%20Baghdad&f=false1
The Rundetaarn in Copenhagen built 1635 to 1642 has a helical ramp to the top.
This design was chosen to allow a horse and carriage to reach the library, moving books in and out of the library as well as transporting heavy and sensitive instruments to the observatory.
People have ridden horses, bicycles, and motor vehicles up and/or down the ramp. It is said that Empress Catherine I of Russia rode a carriage up the ramp in 1716.
https://en.wikipedia.org/wiki/Rundetaarn2
Legend claimed that you could drive a carriage up to the top of the tower of Fonthill, but the tower was actually too narrow for a sufficiently wide spiral ramp. But a series of long straight gently sloping ramps would be fine for riding horses and driving carriages and carts hundreds or thousands of feet in the air.
The first rail roads were for hand or horse pulled carts in mines, and thus indoors. And I have read that King Louis Philippe of France (reigned 1830-1848) had a miniature steam train which he used to ride in the Grand Gallery of the Louvre - inside.
So a tall building could have railroads that hauled loads of supplies up and down long straight or wide spiral ramps. Or steam engines could power winches that pulled carts up ramps and lowered them down.
Possibly the stairs and ramps would not be in the central spine of the building but at intervals at right angles to the building. That would avoid problems with steam engines making indoors air pollution.
A system of windmills could pump water tens, hundreds or thousands of feet to the top of the building when the wind was blowing and store it in reservoirs near the top for later use.
Most of the length of ancient Roman aqueducts consisted of underground water channels. Sometimes when an aqueduct had to cross a valley it would simply go down the side of the valley and back up the other side, relying on the water pressure to drive the water back up the other side of the valley.
The Romans only put their aqueducts on top of tall arches when the ground was sloping too steeply for a steady flow of water.
And sometimes the Romans built tall arches to carry aqueducts across valleys. The tallest Roman aqueducts and viaducts (bridges) include 19 with maximum heights of 28 meters (91.8635 feet) or more, 13 with maximum heights of 100 feet (30.48 meters) or more, And 5 with maximum heights of 40 meters (131.234 feet) or more - up to 66 meters (216.535 feet).
http://www.romanaqueducts.info/aquastat/aquastatbridgeheight.htm3
Here is a link to an image of the Pont du gard aqueduct and bridge near Nimes, France.
https://en.wikipedia.org/wiki/Pont_du_Gard#/media/File:Pont_du_gard_v1_082005.JPG4
It has a maximum height of 48.77 meters (160.00656 feet).
Now picture 2, 3, 4, or 5 parallel copies of the Pont du gard across a valley, close enough together to lay floor beams between them. Fill in the arches with masonry walls and glass windows and put a roof on the top and you have a building that is up to 48.77 meters or 160 feet tall. There can be access roads that gradually rise up the sides of the valley to reach doors at each level of the building, so that people who live or work on one floor of the building have little need to use the stairs and ramps inside the building to go up or down. And that building across a valley can be built at one end of an aqueduct that carries water from higher elevation down to it - the Pont du gard that inspired it was part of an aqueduct.
One possible purpose of such a building would be to be a fortress across a valley that could be used as an invasion route.
So with advanced enough building techniques, and sufficient reasons for building a building of a great height, and sufficiently intelligent methods of getting people and materials and water up to the top and/or down to the bottom, a science fictional or fantasy building could be built several times 100 feet (30.48 meters) or several times 1,000 feet (304.8 meters) tall without using anything resembling modern elevators.
Any practical (i.e. within the troposphere) height, if there is a primary reason for people to do something on highest floors. It would be part of the duty (or pilgrimage) to ascend the tower over the course of multiple days, toiling up the supplies.
15-20 stories high, if it's a general purpose building and it should be accessed by wide population - including frail, but high-ranking members of the society. Any more than that, and carrying up a high-level bureaucrat on the stairs would became an impractical task.
40-50 stories high for a residential building in a central location. Apartments on higher floors would be priced progressively lower, until no reliable tenant would be willing to occupy the apartment and no super-fit superintendent to work on those floors.
The answers above assume that water can be pumped to any height (and then flushed down without issues).
I've walked up several tall structures - the tallest may have been Ulm Minster; at 161 m approximately the same height as 50 storey building. I'm middle-aged and quite unfit - I found it pretty tiring, needing to stop for a rest a couple of times.
