/sci/ - Science & Math » Thread #13813021

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Anonymous Tue 02 Nov 18:12:14 2021 No.13813021 View Reply Original Report

Quoted By: >>13813358 >>13813499

So the bottom stretches in length, the top compresses in length. Right at the middle it shrinks down. Anything not in the middle cancels out. ? y is not zero but negligible.

I need a free body diagram of a cube against that moment?

Anonymous

Anonymous Tue 02 Nov 2021 20:10:20 No.13813303 Report

Quoted By:

Timoshenko: Mechanics of Materials. Read.

Anonymous

Anonymous Tue 02 Nov 2021 20:25:44 No.13813358 Report

Quoted By:

>>13813021
Today was a very long day ok, but I really don't understand your question. You want a FBD of a cubic element under Mflex,z because you want to find the related deformation field using St.Venant solutions for the one-dimensional beam?

Anonymous

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Anonymous Tue 02 Nov 2021 21:10:09 No.13813499 Report

Quoted By: >>13814086

>>13813021
not sure if i understood it correctly.
the stress on each side is in equillibrium with itself (sums up to 0) yet still has a moment.

Anonymous

Anonymous Tue 02 Nov 2021 22:37:12 No.13813859 Report

Quoted By: >>13814074 >>13814086

I hate engineering so much
Im 1 year from graduating and still not quite sure what an integral is
Im 100% certain a bridge or building i design in the future will collapse and hurt someone
the worst part of it all is that im getting job offers with an average mark of 55% in uni while my smart friends are jobless.

Anonymous

Anonymous Wed 03 Nov 2021 00:10:37 No.13814074 Report

Quoted By: >>13816132

>>13813859
You don't need to know how integrals work in engineering. At most you only need to know the equations, and what numbers to put into the calculator.

Anonymous

Anonymous Wed 03 Nov 2021 00:15:30 No.13814086 Report

Quoted By:

>>13813859
The way I’ve always thought of integrals is that you have an object, and you have a certain variable on the object that changes value across it. Could be stress, strain, temperature or whatever. And you want to know the total impact of this variable across this object, so you integrate.
This is easily generalized for multiples variables and multiple dimensions of the object

>>13813499
This is the answer OP. The stress is 0 in the line of action

Anonymous

Anonymous Wed 03 Nov 2021 07:49:03 No.13814832 Report

Quoted By: >>13814953

Why is the neutral axis not at the midline of the beam?

Anonymous

Anonymous Wed 03 Nov 2021 09:22:49 No.13814953 Report

Quoted By: >>13816077 >>13816232

>>13814832
the neutral axis is at the geometric center of the beam (for homogeneous material), not at the half.
otherwise the stress would not only have a moment but an axial force as well.

if your superimpose axial tension/compression forces with the moment the neutral axis can sshift as well

Anonymous

Anonymous Wed 03 Nov 2021 19:08:43 No.13816077 Report

Quoted By: >>13816132 >>13816306

>>13814953
Is it correct to say that in the idealized model described in the OP, the beam segment does not change area due to the deformation?

Anonymous

Anonymous Wed 03 Nov 2021 19:24:06 No.13816132 Report

Quoted By: >>13816211 >>13816237

>>13816077
No, you do assume it changes area. It changes from a rectangle to a triangular section, above the neutral axis there is compression, below there is elongation. The total forces of the upper and lower section should equal to zero. The material and the edges is stretched/compressed more than the material at the neutral axis (which has no strain)
>>13814074
Engineers that dumb wont know what equations mean. In practice these guys dont design anything, they just make check that the crews put the rebar as called for and have meetings with city hall to get permits.

Anonymous

Anonymous Wed 03 Nov 2021 19:54:47 No.13816211 Report

Quoted By: >>13816234 >>13816237

>>13816132
>No, you do assume it changes area

Overall, does it get smaller or larger area? I can't seem to understand intuitively.

Anonymous

Anonymous Wed 03 Nov 2021 20:07:15 No.13816232 Report

Quoted By: >>13816306

>>13814953
>if your superimpose axial tension/compression forces with the moment the neutral axis can sshift as well
No, that just changes the stress diagram.

stress = M*y/I + P/A

This formula relates to the neutral axis only through the parameter "y" (distance from N.A. to top/bottom surface), and the value of the stress itself at any point does not change the N.A. value.

With a large enough axial load and small enough moment, the stress is almost constant (P/A >> M*y/I), but it doesn't mean that the N.A. of a homogeneous, symmetrical beam changes.

Anonymous

Anonymous Wed 03 Nov 2021 20:07:52 No.13816234 Report

Quoted By: >>13816240

>>13816211
There is a change in shape, i dont know if it preserves area, i dont think it does. In a beam made of reinforced concrete the part where the rebar is classically located (the part that stretches) doesnt change much in size since steel is so strong a bit of stretch has a lot of force, but concrete is weaker so at the compression zone it mechanically changes shape much more to cause an equivalent force level. Maybe a pure steel beam would preserve the volume/area, dunno.

Anonymous

Anonymous Wed 03 Nov 2021 20:09:55 No.13816237 Report

Quoted By:

>>13816132
Wrong. Straight lines remain straight, and there is no warping of the cross-section. The area of a bent cross-section equals the area of a straight cross-section.

>>13816211
It doesn't change.
The assumption for the two basic beam theories (Euler-Bernoulli, Timoshenko and others) is that the cross-section does not change length (distance from top surface to bottom surface = constant) during deformation.

Anonymous

Anonymous Wed 03 Nov 2021 20:11:59 No.13816240 Report

Quoted By:

>>13816234
> In a beam made of reinforced concrete the part where the rebar is classically located (the part that stretches) doesnt change much in size since steel is so strong a bit of stretch has a lot of force, but concrete is weaker so at the compression zone it mechanically changes shape much more to cause an equivalent force level
The strain of the cross-section in balanced failure is equal in concrete and steel.

Roughly "ec=0.35%" (concrete ultimate stain), "es = fyd/Es = 0.2174%" (steel strain at yielding) in balanced failure. For an under-reinforced section (typical in design), the steel has a higher amount of strain than concrete at ultimate; usually well above 0.2174%.

Anonymous

Anonymous Wed 03 Nov 2021 20:45:36 No.13816306 Report

Quoted By:

>>13816232
i meant that the line of zero stress can shift when additional axial loads exist.
>>13816077
in reality it changes but it is neglected often in practice.

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