Structural Analysis - basic beam question

[Munt]

Homework Statement

See attachment

Homework 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.

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

 

[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.

 

[piercas]

it is important to always double check your calculations and assumptions to ensure accuracy in your results. In this case, it looks like you have correctly applied the relevant equations and solved for the maximum stress in the beam. However, it would be beneficial to also consider the material properties of the beam and compare the calculated stress to the yield strength of the material to determine if the beam is under safe operating conditions. Additionally, it may be helpful to provide a visual representation of the beam and its loading conditions to better understand the problem. Overall, it seems like you have successfully solved the problem and reached the correct answer, but always remember to check for any potential errors or overlooked factors.