The tracks can curve,

The tracks can curve, supported by ties that lie on a curve, but the stringers and supporting structure below them cannot practically curve.  Instead, bridges are segmented, at least on railroads.  

Use straight bridges in a curve

It's very hard to build a curved bridge, especially for heavy trains. Real bridges are mostly built from straight sections which have a slight angle at every support. Straight sections are easier to produce. Besides, on a curved bridge the load is a bit excentric which makes a heavier construction necessary. 

Erik

Gordon Creek Trestle

The Gordon Creek Trestle in central Utah uses steel girders under a curved wooden deck.

brick and stone railway bridges

You could build a composite bridge with multiple stone arches curving at either end to get the most from a curved structure then use either a large arch span in concrete or plate Girder section over the centre to allow lower line access to other side. There are plenty of examples on Bridgehunter or U.K. Bridge wikipedia

 You could build a stone or concrete (Brick Near built up urban areas) curved viaduct bridge which can be seen in many places most commonly found in the U.K. Ken Patterson birth place one such curved bridge can be found at Arthington Viaduct, also known as Castley Viaduct and  listed as the Wharfedale Viaduc The viaduct was built, between 1845 and 1849, in a curve some 1509 feet & 2.236 inches (500 yards or 460 m) in length, with 21 semi-circular arches on high  piers

Curved deck truss bridge over North Fork of Middle Fork of American River on FDR 96-Mosquito Ridge Road although a dedicated road bridge a great example for modelling a dual  purpose rail and Road traffic

https://bridgehunter.com/ca/placer/51754000001028/

Abandoned deck plate girder bridge over Lucky Strike Canyon (Silver Bow County, Montana) on Northern Pacific Railroad Homestake Pass built 1901-2 segmented girder bridge smaller the girder the less segmented it looks

https://www.flickr.com/photos/raildudemel/9250676332

Pete

Bridges with curved

Bridges with curved trusses/girders were possible early in the 20th century for light rail traffic: https://www.flickr.com/photos/christoph_bellin/22356108430

It is the Roedingsmarkt Viaduct of the subway in Hamburg built around 1912. Or the Viaduc du Quai de la Rapée in Paris, France, a Metro bridge: https://upload.wikimedia.org/wikipedia/commons/c/ca/P1220028_Paris_XII_viaduc_du_quai_de_la_Rap%C3%A9e_rwk.jpg

For heavy freight traffic the trusses or girders are not suited. Only with the use of prestressed concrete curved railroad bridges besides viaduct got possible: https://www.welt.de/img/wirtschaft/mobile165624470/5161622707-ci23x11-w1600/ICE-Neubaustrecke-im-Bau.jpg

It is a bridge on the HSR line Munich to Berlin. One of the first curved railroad bridges was built in Germany about 1959. It crossed the river Neckar and had a radius of 2,250 ft.
Regards, Volker

Styrene Stone Sheets

Hi Chuck68,

I have two curved bridges; one built of Micro Engineering piers and girders and one built of styrene stone sheets.

If your layout has minimal temperature/humidity changes, the spindly steel trestles are fantastic.  Working the scenery materials around the trestle bases is VERY challenging.  I spent more time removing plaster, foam and paint from the girders than anything else in the area(LOL).  There were also some curved girder kits that could be bent to the correct radius before being glued permanently.  You could probably find some at swap meets or eBay.

If you're concerned about a smooth transition at the end of your helix...consider extending the roadbed material across the gorge and use styrene stone sheets to build a curved bridge.  They can be bent and easily glued to the plywood.  The arches can be tedious to install.  I made paper patterns before cutting the styrene to save time and frustration.