Hollow rectangular shear formula

[yusf]

hi can any one suggest me which formula is used to find transverse shear stress of hollow rectangular section

for example for hollow circular section i have

tau=2*V/A

for circular solid section

tau=(4/3)*V/A

thanks

 

[scottiesei]

You could always use VQ/I. I don't have a specific hollow section formula.

 

[JStephen]

Depends on what you need it for. The structural codes are generally set up for average shear on the web, not VQ/I.

 

[corus]

This site explains the theory

http://www.ae.msstate.edu/~masoud/Teaching/SA2/chA14.6_text.html

corus

 

[scottiesei]

Good point Stephen. Determination of allowable V does vary from code to code. BUT, the tau's he stated are from engineering mechanics.

 

[broekie]

One book that I have gives:

tau = 2.25*V/A

but this is only for a square hollow tube, not a rectangular one. The book I have does not give a formula for the rectangular hollow tube.

 

[civilperson]

tau= VQ/Ib for rectangle beam:
tau= VQ/It for thin walled open cross-section (t= wall thickness)

 

[dik]

For Torsion:
Generally used V/L where L is the length of the steel cross section. If a largely rectangular, I usually neglect the length of the short sides. Depending on the mood, for the latter, I sometimes use 1.5 X shear obtained to correct for the parabolic stress distribution.

for Shear:
Generally use the length of the side affected by torsion and if the depth is greater than twice the width, use the 1.5X noted above.
Dik

 

[yusf]

thank you all

 

[rb1957]

well, i don't follow some of these posts ...

for torque, stress = T/(2[A]t)
where [A] = b*d (approximately)

for shear load = V/(2lt)
where l = the side length along the applied load.
this is approximately the average shear, neglecting the parabolic distribution and neglecting the contribution of the short sides (directly)

 

[jphs]

Hi,

I came across this post as I was trying to solve just this problem. Machine Design and Mechanics of Materials books don't do the square or rectangular tube (generally) since it is a little more difficult, an exception is Juvinall and Marshek 3rd ed. The question asked was what is the transverse shear stress (which results from a transverse applied load, i.e., bending). The general solution is tau = (V Q) / (I b), where V is the shear load, I is the second moment of area, b is the width of the beam, and Q is the integral of y dA over some cross-section of the beam {it is the first moment of area for the region of interest about the Neutral Axis}. So to get the answer for a rectangle of say b width and h height and wall thickness t, at the neutral axis where it will be maximum we need to break the integral into two parts: first from the distal fibers (h/2) to the inside of the tube wall (h/2 - t) and second integrate from the inside wall of the tube to the neural axis, i.e, (h/2 - t) to 0. Note that the "b" is not the same for these two since the b in this expression is the "width" at the top of cross-section that is being integrated. So, with the help of Mathematica here is the maximum transverse shear stress (at the neutral axis) for a hollow rectangular tube of width b, height h, and wall thickness t.

tauTransverse = 2 t^4 - 2 h t^3 +(1/2) (h^2 - b^2) t^2 + (1/2) b^2 t

Hope this helps.

 

[yusf]

Thank you for your valuable contribution JPHS..

 

[yusf]

JPHS..

while i am checking the formula you have given i noticed that in this formula there is not shear force term...are you agree with me that above formula maight be the Q term instead of tauTransverse..then by using tau=VQ/Ib we are able to find shear stress right?

i would be glad if you correct me

thanks..

 

[rb1957]

h=overall height of tube
b=overall width of tube
t=thickness

I = 2*th^3/12 + 2*(b-2t)*t*(h/2-t/2)^2

Q = 2*h/2*t*h/4 + (b-2t)*t*(h/2-t/2)

tau = V*Q/(I*t)