Second moments of area Izz and Ixx

on1591

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

A vertical column has the horizontal cross sectional area shown in the attached image. The column carries a vertical compressive point load of 30kN applied at d. calculate the following:

a) The second central moments of area IZZ and Ixx
b) The maximum values of compressive and tensile stresses
c) The position on the cross section where the stress is zero

2. Relevant equations



3. The attempt at a solution

I have done part a and got:

Ixx = 5.48E+5
IZZ = 1.75E+5


for part b i know the formulas for compressive stress and tensile stress. However they require a bending moment number. How do i calculate this?

Tensile = Mzc/Ixx
Compressive M(zmax-Zc)Ixx

Compressive stress due to point load F/A

C) Im not sure how to complete this part

Any help would be much appreciated

Attached Thumbnails

 

SteamKing

Hint: Neutral Axis

on1591

zc = 46.75mm and xc = 22.5mm. Is the bending moment calculated from these?

I have been trying to work out the bending moment for a while now and cant seem to get the answer of 3.97E+5 Nmm

SteamKing

Remember, take your moments about the neutral axis.

nicknack111

I am also stuck on a very similar question and i don't know how to calculate the moment. I assume the neutral axis was at the centroid of the shape which I would work out to be 46.3 mm. I have been looking for days for help on this and I'm getting nowhere

nicknack111

Do you need to draw a bending moments diagram??

fonfon1210

Bending moment is M= mass x distance between the (load point D - Zc).

fonfon1210

The position of zero stress (Zo) is basically,

Zo=total tensile stress x total length of z-direction( I beam)/total tensile stress + total compressive stress.