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Hollow rectangular shear formula
- Thread starter yusf
- Start date
scottiesei
Structural
You could always use VQ/I. I don't have a specific hollow section formula.
This site explains the theory
corus
corus
scottiesei
Structural
Good point Stephen. Determination of allowable V does vary from code to code. BUT, the tau's he stated are from engineering mechanics.
civilperson
Structural
tau= VQ/Ib for rectangle beam:
tau= VQ/It for thin walled open cross-section (t= wall thickness)
tau= VQ/It for thin walled open cross-section (t= wall thickness)
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
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
- Thread starter
- #9
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)
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)
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.
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.
- Thread starter
- #12
- Thread starter
- #13
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..
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..
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