Bending and Stress

Altairs

1. The problem statement, all variables and given/known data
A railway bridge of 80ft span with two tracks is supported by two main steel girders of I-section. The girders are 7ft deep between the centers of the flanges. If the dead weight of the structure between the abutments is 200 tons and the weight of each train of carriages is 1.5 tonf/ft, what must be the effective girder flange area at the centre of the span? The mean stress allowable in the flanges is 7tonf/in^2 and the resistance of the web to bending may be neglected.


2. Relevant equations
I understand the I need to use f/y = M/I and relevant equation for finding second moment of are and bending moment etc


3. The attempt at a solution

The problem here with me is that I cant get to understand the question properly. To much stupid explanation. Its all ambiguous. Like how are the tracks supported by beams ? Are beams in the same direction as the tracks or are the perpendicular ? And isn't the area supposed to be constant throughout th girder ? What is meant by this "what must be the effective girder flange area at the centre of the span" ?

PhanthomJay

I agree the problem should have been worded more clearly. It appears that there are 2 main girders (I beams) that run parallel to the tracks, one running along one side of the near track, and the other along the side of the far track. The tracks are supported on 'beams' that run perpendicular to the tracks, which frame into the main girders. You are not concerned about these 'beams', only the main girders that support them. So assume each girder takes half the structure dead load and half the train live load. That is, each is subject to a uniformly distributed live load of 1.5tons/ft, plus a uniformly distributed dead load of 100/80 = 1.25 tons/ft. Max moment occurs at the center of the span; theoretically, the girder could be of diffferent cross section towards the ends.

nvn

Altairs: You must assume both trains are longer than the railway bridge. The girders are parallel to the rail tracks. You are asked to compute the girder bending stress only at the girder midspan. To compute bending stress, you must compute second moment of area, I, of the girder (I-beam) flanges.