Flexural Stiffness
Flexural Stiffness
(OP)
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






RE: Flexural Stiffness
RE: Flexural Stiffness
Consider a simple beam A-B of span L. Apply a moment at point B. What is the rotation at B? Call it θB.
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.
θB = ML/3EI
or M = θB*3EI/L.
By definition, Stiffness = M when θB =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
RE: Flexural Stiffness
Consider a simple beam A-B of span L. Apply a moment at point B. What is the rotation at B? Call it θB.
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.
θB = ML/3EI
or M = θB*3EI/L.
By definition, Stiffness = M when θB =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
RE: Flexural Stiffness
BA
RE: Flexural Stiffness
RE: Flexural Stiffness
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.
RE: Flexural Stiffness
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: Flexural Stiffness
BA
RE: Flexural Stiffness
RE: Flexural Stiffness
BA
RE: Flexural Stiffness
RE: Flexural Stiffness
RE: Flexural Stiffness
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?
RE: Flexural Stiffness
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.