Monday, September 23, 2013

Rolling Loads- maximum shear force, bending moments

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  • Rolling Loads- 

  • Rolling loads are those loads which roll over the given structural element from one end to the another. You can see many live examples of rolling loads, like a train on the railway track, vehicles on the bridges or roads are rolling loads.

Now to analyse the given structural element for the rolling loads, which classify these rolling loads into the following classes:
(1) Single point rolling loads
(2) Uniformly distributed rolling loads, - a) shorter than span  b) Longer than span.
(3) Two point loads at a fixed distance apart.
(4) Several point loads at fixed distance apart.



  •  Single point load: If a single point concentrated load moves from one end of a girder to another end of it, it becomes necessary to find out the maximum values of the shear forces and bending moments at every section of the girder to produce an economical and safe design.

 Now if we analyse the girder then you will find that at any section on the girder maximum 
negative shear force induces when the point load is just on the left of that section, and maximum

positive shear force is induced if the load is just on the right of the section.

Absolute maximum negative shear force is produced at the right end of the girder and absolute maximum shear force is produced at the left end of the section.

Bending moment is positive for any position of the load, but maximum bending moment at a section occurs when the load is on the section itself and absolute maximum bending moment is produced at the central section when load is also at the center.



  •  Uniformly distributed Loads:

(a) Longer than span: When the given udl(uniformly distributed load) is longer than the given span, it is easy to find out the maximum negative shear force , positive shear force and bending moment values on the section.
Rolling Loads(udl) on bridge
 
Maximum negative shear force is induced when the udl is on the left part of the span and right end of the udl is just on the section itself.

So, maximum negative shear force is induced at the right most end of the span when the end of the load is just to the left of the section.

Similarly, maximum positive shear force is induced at the left end of the girder when left end of the load is just on the right of the left end.

Maximum bending moment at a section is induced when whole of the span is loaded with the udl, and the value of the absolute maximum bending moment is induced at the center of the span and its value is given by (w.l^2)/8.


to be continued...\


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