# City Bridge – Pt IV

 Let’s Design a Deck Girder Bridge I will be doing a lot of jumping back and forth here. I’m researching via Google Books – using writing by Engineers from the late 19th and early 20th century on constructing plate girder bridges. When finished I will probably go back and clean up everything – putting like elements together but for now .. it is .. what it is Girder Height With the 54′-6″ (13.625″) span I tried using the one-fifteenth of that span for the girder height. Ratios greater then one-fifteenth were viewed with deep suspicion and normally a one-twelfth ratio or smaller was used. Since the On18 locomotives are lighter than standard gauge locomotives I went went ahead and tried this one-fifteenth ratio. It ended up at 0.908″ which comes out to 43.5″ FS (Full Size). .. and .. it just didn’t “look” right to me. I dropped back to the suggested ratio of one-twelfth .. and for me the proportions worked better. This time, the girder height ended up as 1.135″ which comes out to 54-1/2″ FS. One of the sources made a simple statement that – the web plate should be in even feet or half-feet. For the 1.135 in./54-1/2 in. plate .. that means it should be 4-1/2 ft./54 in. even. That’s 1.125 in O scale. If I went with the one-tenth ratio (seems most common) then the girder height would be 13.625/10) = 1.363 in./65.424 in. Rounding up to 5-1/2 ft./66 in. would give an O scale measurement of 1.375 in. Results: I went with the one-twelfth ratio – and the 1.250″ girder height. This is the upper limit for use with standard gauge locomotives -but- the narrower profile should work fine as a narrow gauge bridge structure. The economical depth of plate girders for railroad bridges has been established by practice. For the heavier loadings the following formula gives close results:1 $h=\frac{l}{12}+1.5 ft.$, where l = span length in feet. Since it says “For the heavier loadings..“ the 1.250″ I came up with works fine for narrow gauge.
 Bridge Width First Try Width. The distance center to center of deck plate-girders shall not be less than 8 ft.2 Width, 8 feet c. to c. of girders.3 Deck plate girders not over 75 feet long will generally be spaced 6 feet 6 inches center to center, except where greater width is required on curves.4 – it would seem from [1] that the ‘Unknown’ I show for my Bridge Width should therefore be 8ft. [2] Gives 6′-6″. It seemed to me that the smaller width might be more applicable to a deck girder bridge we are designing is supporting narrow gauge track. 6′-6″ is 1.635″ in O Scale. .. and .. it didn’t “look right”. Too wide when you compare it to the track that it will support. Remember this is On18 .. 9mm gauge or about 17″ FS. (I keep having to remind myself that the bridge was originally designed for a 3 ft. line) Second Try So – slightly irritated .. I pushed the side in until the new width looked .. well .. right. I then had a thought (occasionally I do). With a 56-1/2″ standard gauge and 8′ center to center on the girders it works out to 19-3/4″ from the track gauge to the center line of the girder. Ok. Just playing with numbers here .. but stay with me. If I took that 6′-6″ center to center distance then from the track gauge to the center of the girder works out to 10-3/4″. The center to center that I got from just pushing in until it looked right is 1.250″. That is 5ft FS. On18 is 17″ FS. If I add that 19-3/4″ to either side of that gauge .. I get 17″+19-3/4″+19-3/4″ = 56-1/2″. Dang close to the 5’/60″ I got above. This only works if the bridge was designed for the On18 gauge Taking a look at the 6′-6″ spacing – adding the 10-3/4″ to either side of the On18 gauge I get – 17″+10-3/4″+10-3/4″ = 38-1/2″.again – this only works if the bridge was designed for the On18 gauge Umm. IF .. this bridge had originally designed for a 3ft gauge line then .. I get 36″+19-3/4″+19+3/4″ = 75-1/2″ .. and .. 36″+10-3/4″+10-3/4″ = 57-1/2″ That last one works pretty well as it is close to the 1.250″/5′ I came up with earlier. Does this REALLY mean anything? Shrug. Don’t know .. but it works for me! 🙂 Results: Went with my 1.250″ width.
 Girder Width Width of Flange Plates – The width of the flange plates is generally made a proportion of the span, and must be sufficient to prevent lateral buckling of the compression flange. A usual proportion is to make the width from one-thirtieth to one-fortieth of the span .. Using these numbers on my 54′-6″/13.625″ span I get – 1/30 = 21.8″ and 1/40 = 16.35″ In one of the books they go into depth about the sizes of the steel used for the web, the angle iron used .. based on complicated mathematics for a 60 ft. deck girder bridge. They used 6 in. angle (1/8″ Evergreen angle). The REAL girders had a web thickness of 7/16-1/2 in. In O scale that is only about 0.010 in. – I’ll use 0.040 in. styrene instead. That’s close to 2 in. thick full size but that thickness won’t be seen as it will be hid by the steel plates covering the web and angles – and .040 in. in a lot stronger .. and will work fine. The sizes of the main angles should be made as large as possible, consistent with the flange width (…) The sizes of main angels used for ordinary girderwork range from 3″ by 3″ to 6″ by 6″5 With those dimensions I can construct the girder. I’ll draw up two versions – one using the 6″ by 6″ angle (.125″ Evergreen #294) and the other 4″ by 4″ angle (.080 Evergreen #292)”
 Girder Dimensions This then gives me the dimensions for the two bridge girders – as imagineered with information from the books [1][2][3] and Evergreen styrene in my grubby paws. This was my original try where I just pushed and pulled until it looked right. I made the flange extend about the width of the angle Here, left everything the same but reduced the flange width to the 21.8″ (1/30th span) Finally this girder uses the .080″ angle (4″) and the 16.32″ flange width (1/40th span) This is of course .. all just a fantasy .. but is fun! I rather like the last one (C) with the .080″ angle and the smaller flange width
 Cross-Girders Spacing Since “The spacing of web stiffeners depends on (beyond theory) practical considerations, e.g. pitch of rivets, position of cross-girders ..“6 – let’s wander over to the cross-girders then. The book goes into some detail – that each girder at some point carries the axle load of the locomotive traversing the bridge and that no advantage is gained by spacing the cross-girders closer together than the spacing of the heaviest axles. That was interesting I suppose but what caught my eye was the sentence – “For plate girder underbridges up to 100 ft. span, the usual practice is to space cross-girders from 8 to 10 ft. apart ..”

1. Design of Steel Bridges: Theory and Practice for the Use of Civil …, Volume 1, F. C. Kunz, 1915 – Pg.147 []
2. The Design of Typical Steel Railway Bridges – An Elementary Course for Engineering Students and Draftsmen , William Chase Thomson, 1908 – Pg.10 []
3. The Design of Typical Steel Railway Bridges – An Elementary Course for Engineering Students and Draftsmen , William Chase Thomson, 1908 – Pg.18 []
4. General Specifications for Steel Railroad Bridge and Structures: With a Section Making Them Applicable to Highway Bridges and Buildings, Virgil G. Bogue, 1906 – Pg.19 []
5. The Practical Design of Plate Girder Bridges, Harold Hughes Bird, 1920 – Pg.80 []
6. The Practical Design of Plate Girder Bridges, Harold Hughes Bird, 1920 []