- #1
steve321
- 25
- 0
Homework Statement
there's a composite beam that's wood on top (150mm along the x axis, 250 along the y) and a little piece of steel along the bottom (150mm along the x, only 10 along the y). Ew is 10,000MPa, Es is 200,000MPa (these are the elastic moduluseseses). the beam is to be analyzed for strong axis bending using the principle of transformed sections.
1. if the transformed section is considered as being wood, what is the transformed width of the steel plate.
2. in the transformed section, what is the distance between the centroid and the bottom surface of the beam.
3. what is the moment of inertia of the transformed section.
4. if this beam is sub ject to a strong axis bending moment of 30kn.m, what is the max tensile stress in the wood
5. if this beam is subjected to a strong axis bending moment of 30kn.m, what is the max tensile stress in the steel.
Homework Equations
1. i have absolutely no idea. i also don't understand what exactly the 'neutral axis' is, or why it's important in figuring this out. if I'm understanding this chapter correctly, the strain on a composite material is the same, but the stress is different. does the 'netural axis' run through the centroid of a single material? does it run through the centroid of a composite material?
2. also drawing a blank here.
3. i think this variable is 'I'. so the little weird 'o'x thing = -My/I
I = -My / o
the o thing is stress, but i don't know why there's a little 'x' to it, and then the book starts talking about obtaining stress o1 and o2, which haven't been mentioned previously whatsoever so that's pretty useless.
i just looked up o1 in the back of the book, and it says it's equal to - E1y/p. so that's -200,000 (assume E1 is wood, i have no idea if i can arbitrarily assign either material to it)(y) [i have no idea what 'y' is], / p, which apparently is the radius of an arc, something that i highly doubt is in the square diagram I've been presented with. I'm going to skip to 4 because i have no idea what's going on.
4. now we're talking - there's actually an example of this in the book! hopefully i can follow along.
weird 'o' of wood = Mc2/I = (30 x 10^3 N.m)(apparently this wood farthest from the neutral axis) / I
the neutral axis is apparently Y = EyA / EA and there's a bunch of lines over some of the letters. I'm totally lost again.
5. i assume this is going to be a lot like 4.
i'm going to read up some more on this and see if i can't get a little further in the next 25 minutes, but if anyone can shed some light on these ridiculous questions or give me some firm ground to stand on by way of basic explanation of what I'm even trying to find out, i'd appreciate it.
thanks!