Bending Moment for Simply Supported, Overhanging Beam with two Overhangs

[benwb93]

Homework Statement

Bending Moment for Simply Supported, Overhanging Beam with
Two overhangs

Relevant Equations

Bending Moment

This formula works for a beam with one uniformly distributed load... How would I apply the same technique to get the bending moment equation in terms of x for the same type of scenario with a point load before R1 and after R2 at each end of the overhangs? Would I simply add a term for each the positive and negative bending moment to the already provided R1x-w(a+x)^2/2 ?

 

[Lnewqban]

Welcome, @benwb93 !

What formula (which works for a beam with one uniformly distributed load) are you referring to?
Could you post an image with better quality for us to be able to see its details?
Could you also post a handmade diagram of the situation that you describe?

 

[benwb93]

I am looking to solve the Mx moment equation in terms of x for the same scenario in the situation posted above, but with the uniform load replaced by two point loads at each end of the overhangs. This is what I am trying to formulate:

these two point loads are overhanging the same distance from each furthest bearing, instead of using the uniformly distributed load, I want to apply this formula to this situation with 2 point loads.

Formula above originated from here: https://www.linsgroup.com/MECHANICAL_DESIGN/Beam/beam_formula.htm

 

[benwb93]

Essentially, I want the sum of moments about this shaft

My assumptions is it would be something like:

Summing moments at 0
M=-Fp(a)+R1(b)+R2(c)-R3(d)+Fg(e)

but instead I want to formulate it as a function of x where I can write it as shown in the formulas above, M(x)=R1x-w(a+x)^2/2

If I do this and sum up the moments this is what I get:

for some reason im not positive that this is correct as I havent done much CE/strengths of materials in awhile
try to ignore the smudges from my scanner and the random change into meters in the final solution

there would be another orthogonal set of planes with another moment reaction obviously but is this formulation correct as it stands so far?

 

[Lnewqban]

This shaft is over-supported, meaning it works as a statically indetermined beam.
That situation requires a slightly different approach.
Please, see:
https://mathalino.com/reviewer/mechanics-and-strength-of-materials/statically-indeterminate-members