First let’s see the forces acting on rail bridges,
There are three kinds of forces are acting on any bridge;
In above the first term refers to the weight of bridge itself. MLike any of the other structure, the bridge has a tendency to collapse simply because of gravitational forces acting on materials of which the bridge is constructed (i.e., the concrete, steel etc.).
The second term refers to the traffic that moves across the bridge as well as the normal environmental factors such as changes in the temperature, precipitation,& wind.
The third factor refers to the environmental factors that goes beyond the normal weather conditions, factors such as sudden gusts of wind & earthquakes. Above three factors are must be taken into account in the design of a bridge.
There are two ways a brigde can fail;
Hence, if bridge is weaker in the shear, then it will fail in the shear at a instant when the most of the weight of train is at one support.
And, if bridge is weaker in the flexure (i.e. bending strength), then it will fail at the centre when the centre of mass of train will be exactly at the centre of the bridge(i.e. location of max. Bending moment)
But what if the length of train is more than the span of deck? Then it will fail in the any of the above condition in which it is weak.
Now coming back to our questions,
In which case bridge will fail earlier :
Case 1 : When the train is standing still on bridge
In this case, there is only two loads are acting on the bridge deck.i.e. Dead Load (weight of deck itself) & Live Load (weight of the train).
Case 2 : When the train is moving with some speed
Now in this case, some additional loads are come into play. So there is DL, LL, Impact Load (i.e. jerks given by the train on the bumpy joints of the rails) and Traction load (if train is accelerating) / Braking Load (if train is retarding).
Thus the rail bridge will fail earlier in second case as the load acting on the bridge deck will be more in second case.
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