Reactions And bending moment and shear force diagrams

[Stacyg]

Hi.
I've been given this to calculate the support reactions but I'm not sure how to handle the increasing udl. And how would this be shown on a Bending moment and shear force diagram??
Also with non increasing Udl's when calculating the reaction is it best to change the udl to one force mid-span of the udl or two forces one at each end of the udl??
And how do you calculate maximum bending moment and points of inflection ?

Thanks

 

[PhanthomJay]

Hi.
I've been given this to calculate the support reactions but I'm not sure how to handle the increasing udl.

In calculating support reactions from a triangularly distributed laod, replace the distributed load with a single force acting at the center of gravity (centroid) of the triangle. What would be the magnitude of that force, and where would it be placed?

And how would this be shown on a Bending moment and shear force diagram??

The slope of the shear diagram at a given point is equal to the negative value of the distributed load at that point. The slope of the moment diagram at a given point is equal to the shear value at that point.

Also with non increasing Udl's when calculating the reaction is it best to change the udl to one force mid-span of the udl or two forces one at each end of the udl??

either way will work, but why use two forces when one will do?

And how do you calculate maximum bending moment and points of inflection ?

in the absence of 'point' moments or couples, maximum moments occur at the point of zero shear. Inflection points , if they exist, occur at the points of zero moment.