calculating the shear area of an rectangle 9

[danieldovale]

Please help on the calculation of the shear area of an rectangular area

thanks

daniel

 

[fishercd]

it can vary depending on the system, but my guess is that it is simply the geometric area that the shear force is acting over. For a rectangle simply base*height. If this isn't it then describe the situation a bit more.

 

[rlflower]

Wrong!

Let me refer you to "Design of Wood Structures" 2nd edition by Donald E. Beyer. On page 185, a comparrison is made of the shear stress of a wide flange beam vs. that of a rectagnular cross-section. I cannot show you the diagrams here, but here is the logic: For rectangular beams, the theoretical maximum "horizontal" shear must be used. The following development shows that the maximum shear is 1.5 times the average:

avg. fv = V/A
max. fv = VQ/Ib = VA'y/IB = V(b * d/2)(d/4)/((bd^3/12)b)
max. fv = 3V/(2bd) = 1.5V/A

 

[JimParks]

RL,

The question wasn't about the maximum shear stress now was it? The shear stress you refer to is correct, I have the Beyer book myself, though that isn't the only place to find out that max shear on a timber beam is 1.5 fv ave. (The Code springs to mind.)

Daniel asked about calculating the shear area of a rectangular area. In the equation you cite,
max. fv = 1.5V/b*d. Like Fisher said.

What have you been using for area?

Jim

 

[whyun]

Cool site... I enjoyed reading this thread.
By the way, author is Breyer.

 

[rceng]

I think shear area means, or should mean, the effective area for shear stress i.e. the area by which you would divide the shear force to get maximun shear stress. This would be 1/1.5 for a rectangular area because the max. shear stress is 1.5 times the average shear stress.

 

[Mattman]

Shear area represents the area of the cross section that is effective in resisting shear deformation.
It is mainly used in finite element analysis to calculate a member's deformation due to shear stress.

Substituting SA for A, in effect, reduces the effective cross sectional area to reflect the parabolic
distribution of shear stress in the section, resulting in a better approximation of the maximum shear
stress.

It can be of significance in short, deep beams and can usually be ignored for long, slender beams where
deflections due to shear stress are negligible compared to bending stress deflections.

The shear area (SA) is as follows:

SA = I^2 / [Integral over the area of (Q/b)^2 dA], where I= moment of inertia, b= width of cross section
at a distance z from the neutral axis, Q= 1st moment of area at z, taken about neutral axis

The shear area is often expressed in terms of the actual cross sectional area as approximately
SA=A/K, where K has the following values:

Wide Flange Section (X-X): K=1.2
Rectangular cross-section: K=1.5
Solid circular cross-section: K=1.1
Thin-walled hollow cross-section: K=2

Other approximations for SA of Wide Flange Sections:

Wide Flange Section (X-X): SA=Web Area
Wide Flange Section (Y-Y): SA=0.83*Flange Area

I didn't remember all this off the top of my head; it is an amalgam from a few of my finite element
references.

 

[SauliusV]

I have compared shear area of HE100A (ARBED)with shear area calculated according SA = I^2 / [Integral over the area of (Q/b)^2 dA] and have got results, what have nothing common with mentioned ARBED cross section. May be formula is wrong ?

 

[Giuseppe01]

(be patient with my english)
You must diferentiate the following concepts:
Shear Area: The area subjected to shear
Average shear stress: The shear force divided by the shear area
Theoretical (engineering) shear stress distribution: In the case of a rectangular area: the parabolic distribution from tau= VQ/It
With those in mind we can say: "The maximum shear stress in the theoretical shear stress distribution is 3/2 times the average shear stress"
best regards

 

[camux]

Please help on the calculation of an example rectangular area (shear Area)

thanks

camux

 

[mrtwo]

Then, what is the form factor for rectangular K=1.2?