Load, elasticity, strain, strength

[jaredmt]

Homework Statement

A continuous and aligned glass reinforced composite consists of 40 volume % of glass fibers, having modulus of elasticity = 10 X 10^6 psi and 60 volume % of polyester resin that when hardened, displays a modulus of elasticity = 5 X 10^5 psi.

a) compute modulus of elasticity in the longitudinal direction
b) If the cross-sectioned area is .4in^2 a stress of 7000psi is applied on the longitudinal direction, compute magnitude of the load by each of the fiber and matrix.
c) Distance of strain that is sustained by each phase when stress is applied.
d) Assuming tensile strength of 500,000 psi and 10,000 psi, respectively, for glass fibers and resin. Determine the longitudinal strength of this fiber composite.

Homework Equations

E = elasticity
C = volume %
P = load
A = area
F = tensile strength (i think)
e = strain

sub-abbreviations:
c = composite
f = fiber
m = matrix

The Attempt at a Solution

(this is a lot of reading, sorry. i summarized it on the last sentence)
i need help BIG time. i was hoping somebody here would be able to give me the formulas that I am missing in order calculate all these, or at least be a pal and help me figure the formulas out, because i need to know it for tomorow's exam but i don't have it cus my professor was difficult to understand (he has a heavy accent and bad handwriting). here's what i have so far though:

a)
Ec = EfCf + EmCm = (10 x 10^6)(.4) + (5x10^5)(.6) = 4.3 x 10^5 psi

b)
stress of composite = 7000psi = P/A
A = .4 in^2
load = Pc = (7000)(.4) = 2800 lbs

...now how do i figure out the load on each? do i just multiply the volume % by total load?
(continue reading, i believe i have part of the answer further down)

c)
no idea how to do this. the professor had random calculations all over the board, i couldn't follow it cus once again i can't understand what he's saying and it takes me ten minutes to figure out what each letter is cus his handwriting is terrible.

d)
same thing, no idea, just a bunch of giberish that i wrote down on the board.
(im sure i found the answer further down)
_______________________________________________________________________

Solving this is like trying to put puzzle peices togeather. here's some calculations that i have written down:
these looked like F's but probably werent:
Ff/Fm = 13.3
Ff = 13.3Fm

Fc = (Ac)(stress) = (.4)(7000) = 2800lbs
(this i think is part of part b))
Fc = Ff + Fm = 13.3Fm + Fm = 14.3Fm
Fm = 2800/14.3 = 195 lbs
Ff = 2800 - 195 = 2605 lbs
(further down, it appears these calculations are for part b)

...ok i have no idea where the 13.3 came from and I am not sure what numbers where supposed to be in place of Ff/Fm so if anyone can figure that out id appreciate it. so here is some more calculations which I am not sure what part they are for:

Am = VmAc = (.6)(.4) = .24in^2
Af = VfAf = (.4)(.4) = .16 in^2

stressm = Fm/Am = 195/.24 = 812.5 psi
stressf = Fc/Af = 2605/.16 = 16281 psiok i HIGHLY appreciate it if you are still trying to keep up. it would really make a difference on my grade if you could help me figure this out, so thanks so far.. lol. now given these peices of the puzzle, i came up with this conclusion:

the formula is supposed to be stress = P/A. so therefore i think the values Fm (195) and Fc (2605) are the values of the loads. maybe he had bad handwriting and it should have been:
Pm = 195 lbs
Pf = 2605 lbs

and this answers part b.

now some more calculations:

em = stressm/Em = (812.5)/(5x10^5) = 1.63 x 10^-3 in/in
ef = stressf/Ef = (16281)/(10x10^6) = 1.63 x 10^-3 in/in
Ec = stressc/ec = stressc/em = (7000)/(1.63 x 10^-3) = 4.3 x 10^6

ok this makes sense because it goes along with the formula and em = ef. I am not sure why the units are in/in. maybe it was something else and i misread his handwriting? anyways, id like to know which question these calculations are apart of... lol.
where these calculations for part c? when they ask for "distance of strain" do they just want the strain??

moving on to the last calculation:

(10,0000psi)(.6) + (500,000)(.4) = 206,000 psi

this appears to be the tensile strength for part d). so i guess:
F = 206,000 psi

if you're unclear on ANYTHING let me know, i know its confusing. i just have random calculations and I am trying to put this togeather so i can figure out how to do it correctly

to summarize it: my main concern is i'd like to know how to answer part C and i'd like to know where the 13.3 came from (in part b). i highlighted the 13.3 part in red and the part that i think is for part c in blue

 

[jaredmt]

AHA! i figured out the 13.333...
Ff/Fm = (Cf)(Ef)/(Cm)(Em) = (.4)(10x10^6)/[(.6)(5x10^5)] = 13.3333

now i would just like somebody to confirm if I am right about the strain being the same as the distance of strain

 

[piercas]

I can say that your attempt at solving this problem shows a good understanding of the concepts involved. However, there are a few errors and areas that need clarification. Let's go through each part:

a) Your calculation for the modulus of elasticity in the longitudinal direction (Ec) is correct. However, the units should be in psi, not in x 10^6 psi.

b) You are correct in calculating the load on the composite (Fc) as 2800 lbs. However, the load on each phase (Ff and Fm) should be calculated as a proportion of the total load on the composite. So, Ff = 0.4 x 2800 = 1120 lbs and Fm = 0.6 x 2800 = 1680 lbs. This is because the load on each phase is proportional to its volume fraction in the composite.

c) The distance of strain sustained by each phase is the strain (e) multiplied by the length of the sample. However, we do not have enough information to calculate the strain in this problem. It would require knowing the initial length of the sample and the amount of deformation under the applied stress. So, we cannot answer this part of the question.

d) Your calculation for the tensile strength of the composite (F) is correct. However, the units should be in psi, not in x 10^3 psi. Also, the question is asking for the longitudinal strength, so your answer should be in terms of stress, not force. So, the longitudinal strength of the composite would be 206,000 psi.

Regarding the other calculations you have written down, I cannot say for certain what they were for without more context. However, it seems like they were attempts at solving parts b and d. As for the value of 13.3, it is possible that this was a mistake or a typo by the professor. Without knowing the context, it is difficult to say where it may have come from. But based on the calculations you have shown, it does not seem to be necessary for solving the problem.

In summary, your understanding of the concepts is good, but there are a few errors and areas that need clarification. It would be helpful to review the concepts of stress, strain, load, and modulus of elasticity to ensure a complete understanding. Additionally, it would be beneficial to clarify any confusing or unclear information with your professor before the exam.