Aluminium - Shear in Webs

[Taimoor957]

I am seeking help using shear in web equation for calculating slenderness limit S2? it says h/t at intersection of Eq 3.4.24(2) and (3) in attached photo, I may have done something wrong however when solving the equation i got

(h/t)_intersection = -0.048467902247158*Bs^2/(Ds^2*(-0.00600421828991631*Bs^3/Ds^3 + (6.7762635780344e-21*Bs^6/Ds^6 - 0.0120084365798326*Bs^3*E*phi_v/(Ds^4*phi_vp) + E^2*phi_v^2/(Ds^2*phi_vp^2))^0.5 + E*phi_v/(Ds*phi_vp))^(1/3)) + 0.266666666666667*Bs/Ds - 1.46717946958971*(-0.00600421828991631*Bs^3/Ds^3 + (6.7762635780344e-21*Bs^6/Ds^6 - 0.0120084365798326*Bs^3*E*phi_v/(Ds^4*phi_vp) + E^2*phi_v^2/(Ds^2*phi_vp^2))^0.5 + E*phi_v/(Ds*phi_vp))^(1/3)

For E = 70000, phi_v = 0.8, phi_vp = 0.9, Dc = 0.49, Bc = 119.26, the bold part of equation turns into negative causing imaginary root. In my case actual h/t is only 14.33 and is well below S1 and doesn't govern though but still interested evaluating S2 being part of a spreadsheet, I am pretty sure simpler method should exist which I am not aware, sorry using this standard for first time.

 

[Smoulder]

Haven't tried to reproduce but e-21 term looks suspect. Self check algebra. Also solve by trial and error so you know correct answer. If spreadsheet is diferent it's wrong.

 

[Taimoor957]

but e-21 term looks suspect

I solved the equation for h/t using python, should probably try with hand, e-21 just represent "x 10 ^ -12", sorry should had elaborated that. I am trying to write a spreadsheet so avoiding other methods.

 

[Smoulder]

I understood e-21 but it's tiny. Can see it goes with 6th power and maybe that compensates. But don't see by glancing how it gets to 6th power. Probably not helpful comments as i haven't tried to solve it myself.

 

[Taimoor957]

Thanks Smoulder, standards shouldn't be leaving users for such exercises, probably a graph should had been helpful, i will for sure try to find it later when i get some time, needed to get going so found these equations which are taken from American design standards seems exactly the same in AS1664.1, following snippet is taken from 2015 manual section G.2





I have set lambda_2 >= lambda_1 and it works great for time being. Cheers

 

[Smoulder]

I did some aluminium design years ago. Company had helpful book on shelf. American but matched AS1664 so I think AS1664 was based heavily on US code. From web search think it was by Kissell and Ferry but not really sure now.