Question

strenghts

Answer 1

I am working on the next problem for now.

Answer 2

The first image was hard to read because of the long exposure time.
If you could, try to take the picture with more illumination to reduce exposure time.

The composite beam is based on compatibility of deformations.
So, again, I would subdivide load P=2.7 into two components, Pt for timber, and Ps for steel where Pt+Ps=2.7, or using simply one unknown Pt for timber, and 2.7-Pt for steel.

Now you can load the two separately and equate the strains.
You have probably done the following,
It=2(bd^3/12), St=It/(d/2)
calculate similarly Ss.
Since M=P*L1 (L1=48"), we have
Mt=Pt*L1, sigma_t=Mt/St, epsilon_t=sigma_t/Et.
Calculate similarly epsilon_s.
Equate epsilon_t=epsilon_s to solve for Pt.
With known Pt and Ps, you can calculate sigma_t and sigma_s.

If you can confirm the same procedure, you can post a few intermediate values for verification.
I have Pt=1.577, and Ps=2.7-Pt.
We'll worry about part (b) once we have solved part (a).

Answer 3

Let me work on it a bit.

Answer 4

what is wrong with my solution thoug?

Answer 5

Oh, by the way, it seems that my values of the stresses are both about 80% of yours. So you could check the bending moments (M=P*48"). Are the units right?

Answer 6

Did you split P into timber and steel components?
I could not quite make out the first image, so didn't know what your strategy is.

Answer 7

For n = 16.145

b2, trans = 4.843

I_total = 3304

M_max = 162 kip in

Answer 8

M_max = (2.7 kip)*(5ft) = 162 kip-in

Answer 9

timber is 1 and steel is 2

Answer 10

*129.6 kip-in

Answer 11

That's where the 80% came from!

Answer 12

I think you have the rest correct! lol

Answer 13

Oh I see.. lol I am so burnt out today.

Answer 14

for stress 1 = 0.2353 psi

Answer 15

This time there is a factor of two, I have double that.

Answer 16

I suppose you mean ksi.

Answer 17

I meant ksi but it won't accept that as an answer.

Answer 18

won't accept .2353?
I have .4638

Answer 19

I have stress = (129.6*6in)/(3304)

Answer 20

For It I have 2(bd^3/12)=2(3.4*12^3/12)=979.2

Answer 21

for wood I have that and for steel I have 2324

Answer 22

I don't understand the 3304 above. I would have put 979.2.
In addition, 129.6 is the total bending moment for both steel and wood.
You need to use the compatibility condition to separate 129.6 into the wood and steel components.

Answer 23

I for steel is much smaller, (0.3*12^3/12)=43.2 in^4

Answer 24

so for steel it's (129.6*6)/(43.2)

Answer 25

As I said, P is split into two components such that the total is 129.6 kip-in.
Pt for wood and Ps for steel, such that both timber and steel have equal strains, epsilon.

Answer 26

Btw, how did you get your first attempt? they seem to be in the right proportions! lol

Answer 27

I am getting 3304 because I added the (I) for timber and steel together and used it

Answer 28

Sorry, P is split into two components, Pt and Ps such that Pt+Ps=2.7.
The corresponding moments components Mt and Ms add up to 129.6.
The strains are equal, so
(Mt/St)/Et=(Ms/Ss)/Es to solve for Mt and Ms.

Answer 29

If you do that, the two are not working together, and they have different strains (slip between the two materials).

Answer 30

what are you doing? A system of equations? What is St and Ss?

Answer 31

I don't understand your notation.

Answer 32

St=It/(d/2), similarly for Ss.
t for timber, s for steel.
sigma=M/S in general.

Answer 33

can we just start from the beginning? So I got I_wood = 979.2in^4

Answer 34

I think that's a good idea. But I think the main problem is you need to ensure the two materials are bonded together.

Answer 35

for stress in wood?

Answer 36

It=979.2 in^4 is good for me.
You cannot calculate stress in wood before you know how much each material shares the load of 2.7 kips.

Answer 37

okay

Answer 38

How do you propose to find the share of each one, bearing in mind that they are bonded together by bolts/rivets.

Answer 39

The bolts ensure that the beams have the same strain, i.e.
\(\epsilon=\sigma\)/E is the same for both materials.

Answer 40

Ok, would you like me to explain a little about composite beams?

Answer 41

I don't know. Honestly I want to get this homework assignment done. I have 4 problems left and the last problem has 25 parts to it. I might call a classmate up and see what his solutions were and discuss with him.

Answer 42

Don't worry about it. I will figure it out. Thanks.

Answer 43

ok!

Answer 44

Okay I got it.

stress 1 = 0.463 ksi

stress 2 = 7.488 ksi

P = 6.17 kips

I had to go back and carefully analyze it.

Answer 45

Yes, they are correct, well done!

Answer 46

By the way, what I did was from first principles.
You probably did it in terms of transformed sections, and that works too, and easier!