Shear Centre of asymmetrical section.
Shear Centre of asymmetrical section.
(OP)
Good afternoon folks,
I am currently attempting to calculate the shear centre and shear flows in a "built-up" asymmetrical section we are using in a particular fabrication. I have not done this type of thing for quite some time and am finding it quite difficult to find any worked examples using asymmetrical sections - every text I pick up has the same old easy C channel section.
Can anyone assist me?
Some help would be much appreciated.
Regards.






RE: Shear Centre of asymmetrical section.
Draw the cross section with a shear force diagram (of the cross section, not the typical shear diagram of the beam). Using VQ/I, get the shears at the corners and the max along the vertical legs (the vert legs will be parabolic). Now draw a vertical shear outside the section and use this force to determine the "eccentricity" of the shear forces acting on the section. Now determine the value of that eccenticity such that the shear forces acting on the section have no net moment. That is your shear center.
RE: Shear Centre of asymmetrical section.
RE: Shear Centre of asymmetrical section.
RE: Shear Centre of asymmetrical section.
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BA
RE: Shear Centre of asymmetrical section.
RE: Shear Centre of asymmetrical section.
I have a copy of Gere & Timoshenko Mechanics of Materials 4th Edition and it only has the basic sections in it.
Attached is a drawing of the section. For whatever reason it has come back from the fabricators as this so we need to run with it.
Once again - any help greatly appreciated.
RE: Shear Centre of asymmetrical section.
Just out of curiosity, why do you want to know this?
BA
RE: Shear Centre of asymmetrical section.
Probably barking up the wrong tree anyhow, but originally it was requested of me as we were to do a "flange check" as we were to hang an underslung trolley and hoist off it. This has now changed however to a top running crab (running on both sides of a shipping container). We are having another section the same fabricated as I speak.
Now simply curiosity has got to me, and I would like to know a simple way of doing this in case of similar events in the future.
By the way - what is SEIT? If you have a solution handy could you please post it?
Regards.
RE: Shear Centre of asymmetrical section.
BA
RE: Shear Centre of asymmetrical section.
RE: Shear Centre of asymmetrical section.
e=3(b2-c2)/[6(b+c)+h]
with
h=section depth (at mid thickness) (200)
b=flange width on larger side (100)
c=flange width on shorter side (50)
thickness assumed constant everywhere
e=shear center distance from web (located towards the shorter flange)=20.5
The formula correctly gives zero for a doubly symmetrical section and reduces to the known (Roark) formula for a 'C' section (c=0).
prex
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RE: Shear Centre of asymmetrical section.
RE: Shear Centre of asymmetrical section.
RE: Shear Centre of asymmetrical section.
The flange check was a bending check.
SEIT could you tell me what edition of Timoshenko you have?
Prex that formula is great! Could you show me how it is derived?
Regards.
RE: Shear Centre of asymmetrical section.
RE: Shear Centre of asymmetrical section.
I = h3/12 + (b + c)(h/2)2*2
Qb = (b+c)*h/2
vb = V*Qb/I = 6V(b+c)/(h(h+6(b+c))
Ht&b = (b2-c2)vb/(2(b+c))
For no torsion, Ht&b*h = V*e
so e = 3(b2 - c2)/(h(h + 6(b+c))
BA