Structural Analysis - basic beam question

[Munt]

1. The problem statement, all variables and given/known data

See attachment

2. Relevant equations

Im using sigma(max) = -EKy where y is the dist from neutral axis

.: sigma(max) = -(M.y)/I ----------(1)

plus the standard statical equil. equations.

3. The attempt at a solution

I use y = 170mm
"I" is given as 301.3x10^-6 m4

so i just need to find the moment on the highest -stress particle in the beam?

reaction at end supports = 15kN
So Sum.M(x=3m) = 0 = (-15kN.3m) + M(particle)
.: M(particle) = 45kN.m

plug all into eqN (1) gives me a maximum stress of 25390 kPa (comp).

Is this correct?

Cheers
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[PhanthomJay]

Your stress equation (1) is not quite correct, in that you should lose that minus sign. The bending moment produces both tensile and compressive stresses in the beam (tension on bottom fibers, compression on top fibers). And the problem then asks you to determine the distribution of the streses across that section of maximum moment.
Your calculation for the max bending moment, which you apparently correctly have determined is at x=3m, is incorrect, and it is not the moment on a particle, but rather, an internal moment that acts on the beam at that section. You have included the moment from the reaction force, but have neglected to include the moment from the distributed load. Draw a FBD that encircles the left support and cuts through the beam at x=3m. Then sum moments = 0 about that cut section. Your equilibrium equation must account for the distributed load contribution to the moment.