Does Adding Multiple Point Loads on a Continuous Beam Reduce the Maximum Moment?

[student1856]

Is the moment in a continuous beam maximum when there is one point load because if you had multiple point loads they would cancel each other out since there are several pin connections along the beam?

For example, if I had a 20 kip load moving across a continuous beam and found the maximum moment in the beam, and then decided to add a second 20 kip load moving a bit behind the first load, there would be less moment in the second scenario even though there is 40 kips total moving across the beam oppose to the original 20 kips?

Also can anyone explain what the purpose is in radius of gyration oppose to just moment of inertia?

 

[SteamKing]

Is the moment in a continuous beam maximum when there is one point load because if you had multiple point loads they would cancel each other out since there are several pin connections along the beam?

For example, if I had a 20 kip load moving across a continuous beam and found the maximum moment in the beam, and then decided to add a second 20 kip load moving a bit behind the first load, there would be less moment in the second scenario even though there is 40 kips total moving across the beam oppose to the original 20 kips?

Also can anyone explain what the purpose is in radius of gyration oppose to just moment of inertia?

The gyradius relates the second moment of area to the area of the cross section. A larger value of the gyradius means that for a given cross sectional area, a beam is stiffer than a section with the same area but lower value of the gyradius.

The gyradius is explicitly used when evaluating the critical buckling load of a column.

 

[PhanthomJay]

Is the moment in a continuous beam maximum when there is one point load because if you had multiple point loads they would cancel each other out since there areMa doing ok looks not too bad considering all. several pin connections along the beam?

For example, if I had a 20 kip load moving across a continuous beam and found the maximum moment in the beam, and then decided to add a second 20 kip load moving a bit behind the first load, there would be less moment in the second scenario even though there is 40 kips total moving across the beam oppose to the original 20 kips?

if the 2nd load was just a silly millimeter behind the first, max moment would essentially double the value of the max moment with just the first.

Also can anyone explain what the purpose is in radius of gyration oppose to just moment of inertia?

The radius of gyration, r, is $r=\sqrt {I/A}$. It is convenient to use it in stability problems. It represents the distance from the reference axis where the area of the section would be concentrated to give the same moment of inertia.