Flexural Stiffness 1

[Ogrork1]

Can anyone explain to me how and what flexural stiffness as used in the AISC 13th edition on page 16.1-426 under torsional bracing is? From my understanding, flexural stiffness is just EI, how is it that they get 2EI/L for single curvature and 6EI/L for double curvature? And also, if possible, how is it that the plate attached to bottom flanges will bend in single curvature and plate attached to the top flange bend in double curvature? My problem is I'm attaching a plate to the web of a beam and it doesnt fall into either case

 

[frv]

The stiffness of a beam is affected by the end restraint conditions. Any structural analysis book should cover it pretty thoroughly.

 

[BAretired]

I don't know AISC, any edition, so I'm not sure I can help you. As I recall, the flexural stiffness of a beam is the moment required to produce unit rotation at the point of application of the moment.

Consider a simple beam A-B of span L. Apply a moment at point B. What is the rotation at B? Call it [θ]_B.

The Moment diagram is triangular, 0 at A and M at B. The area under the M/EI diagram is ML/2EI, so the rotation at A is ML/6EI and the rotation at B is ML/3EI.

[θ]_B = ML/3EI

or M = [θ]_B*3EI/L.

By definition, Stiffness = M when [θ]_B =1.

So stiffness = 3EI/L when A is hinged.

If A is fixed against rotation, the beam is stiffer. A larger moment is required at point B in order to produce unit rotation at B. In fact, the stiffness of the beam with point A fixed against rotation is 4EI/L. Check it out.

BA

 

[BAretired]

I don't know AISC, any edition, so I'm not sure I can help you. As I recall, the flexural stiffness of a beam is the moment required to produce unit rotation at the point of application of the moment.

Consider a simple beam A-B of span L. Apply a moment at point B. What is the rotation at B? Call it [θ]_B.

The Moment diagram is triangular, 0 at A and M at B. The area under the M/EI diagram is ML/2EI, so the rotation at A is ML/6EI and the rotation at B is ML/3EI.

[θ]_B = ML/3EI

or M = [θ]_B*3EI/L.

By definition, Stiffness = M when [θ]_B =1.

So stiffness = 3EI/L when A is hinged.

If A is fixed against rotation, the beam is stiffer. A larger moment is required at point B in order to produce unit rotation at B. In fact, the stiffness of the beam with point A fixed against rotation is 4EI/L. Check it out.



BA

 

[BAretired]

Didn't mean to send it twice. Sorry.

BA

 

[dhengr]

BA... That’s O.K., look at it this way, the rest of us are now twice as smart for your effort.

 

[csd72]

BAretired,

Double posting is not allowed and triple posting is heinous crime punishable by being slapped around the head with a wet fish!

Nice post though.

 

[paddingtongreen]

BA should get an "E" for effort.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

How about a "WF" for wet fish?

BA

 

[dhengr]

You mean all these years when I speced. a 24" WF beam, I was actually telling them to weld up a wet fish to support the roof?

 

[BAretired]

Amazing, isn't it dhengr?

BA

 

[Ogrork1]

Thanks BAretired, I asked 5 other engineers before resorting to this website. It is kind of weird that I have examples showing that flexural stiffness is EI. Maybe flexural stiffness can mean more than one thing?

 

[miecz]

I believe that the discusion in the Article on Torsional Bracing Stiffness accounts for the rotation at the far end of the stiffener. If the rotation at the far end of the brace were zero, then the stiffness would be 4EI/L, as shown by BA above. However, if the far end of the brace rotates the same amount as the near end, as often happens when the bracing is attached to the top flange, the stiffener requires more moment to rotate it to the unit angle. The additional moment is 2EI/L, giving an apparent stiffness of 6EI/L. If the beam at the far end rotates in the opposite direction (single curvature), then the required moment to rotate a unit angle is reduced by the 2EI/L, so the apparent stiffness is 2EI/L (4EI/L minus 2EI/L).

 

[ToadJones]

Stiffness in general is an extensive property, meaning it is directly dependent on the system one is investigating.
That is to say that it is only useful on a case-by-case basis.
"I have situation 'x' with such n' such end conditions, then beam "A" is stiffer than beam "B"" In this case beams "A" and "B" differ by EI.
Remove the system constraints and the term is relatively meaningless.

wow, this would make a really good Critical Thinking term paper, huh?

 

[csd72]

Ogork1,

The confusion is because of the question: Flexural stiffness of what?

EI is the stiffness of the section
2EI/L e.t.c. are the stiffness of the member.

Both are valid for sifferent situations.