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.

 

[piercas]

for reaching out. I can provide some guidance on how to approach these questions.

Firstly, for calculating support reactions for a beam with an increasing UDL, you can use the area under the load curve to determine the total load on the beam. This total load can then be divided by the length of the beam to get the UDL at each support. This UDL can then be used to calculate the reactions at each support using the standard equations for static equilibrium.

To show the increasing UDL on a bending moment and shear force diagram, you can use the concept of "area under the curve". The area under the shear force curve will give you the bending moment at any point along the beam. For an increasing UDL, the shear force diagram will show a linearly increasing curve, while the bending moment diagram will show a curved shape with the maximum bending moment occurring at the point where the UDL ends.

For non-increasing UDLs, it is best to divide the UDL into smaller sections and treat each section as a separate UDL. This will give you more accurate results when calculating the reactions at each support.

To calculate the maximum bending moment, you can use the equation Mmax = wl^2/8, where w is the UDL and l is the length of the beam. Points of inflection can be found by setting the second derivative of the bending moment equation to zero and solving for the corresponding x-value.

I hope this helps. Best of luck with your calculations and diagrams!