Tapered Tee Design

[cgstrucg]

Hello,

I am aware of a design manual for design of tapered tee sections. I am not aware any of any software designing tapered tee sections so that multiple combinations can be tried easily. Any help will be appreciated.

Thanks

 

[BridgeSmith]

The Wyoming DOT's BRASS-Girder bridge girder design software will analyze it; just create a plate girder with a variable-depth web and zero width bottom flange. Don't know how easy it would be to create the load combinations you're looking to use - the moving live loads it's programmed with a are multiple-axle truck wheel loads, but it has input for uniform, linearly varying, and concentrated static loads, also.

That said, I'm sure there are simpler (and cheaper) programs available...

 

[JoshPlumSE]

The CSI programs (SAP200 & ETABS) make it pretty easy to define a non-prismatic section. You just define the cross section properties of the starting section and of the ending section. This can be done, I believe, with any type of cross section. Therefore, it should be reasonably easy to get your analysis done.

I'm not sure about design checks (as I'm relatively new to these programs). But, my guess is that you'd have to do them yourself based on the forces, moments and deflections you get from the analysis.

 

[Celt83]

If its just a single span element conjugate beam approach for the slope and deflection wouldn't be too difficult with a spreadsheet, shear and moment would be the same as if it were a uniform cross section.

EDIT: Single span with pinned ends

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[ENGINEER92]

Never had to do this myself but I remember reading this article by RISA about modeling tapered pipes. If I was asked to design some tapered members, this would be my first train of thought.

https://risa.com/news/how-do-i-model-a-tapered-pipe/

 

[cgstrucg]

Design Guide only calls for W shape members. Can I use that for Tee shape too? Celt83 do you have any excel file I can compare my solution with.

 

[Celt83]

I don't I did something similar with c++ several years ago.

For a single span pin-pin beam the conjugate beam supports are the same as the real beam supports

The way I did it was use simpson rule integration along the beam loaded with the M/EI diagram to get slope and deflection diagrams, you may not get the absolute maximum deflection this way but can get close depending on how many points you use along the span.

You just need to come up with your function of I relative to X to get the right M/EI diagram.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[dhengr]

Sgstrucsg:
Take a look at Newmark’s Methods of Numerical Integration, they handle these kinds of problems fairly easily. This is essentially the conjugate beam approach which Celt83 is suggesting, done in a formalized way, and fairly easily put into a spreadsheet format. The text book I learned this from, back in the mid 60’s is a good ref. “Numerical Analysis of Beam and Column Structures,” by William G. Godden, pub. by Prentice-Hall International Series. You will find this covered in other advanced Structures and Theory of Elasticity/Strength of Materials texts too. I’ve uses this over the years on some pretty unusual structural configurations, with a very good degree of success. The calc’ed. deflections (and moments or calc’ed. stresses) were very close to those found under test. That takes care of the analysis, but of course you still have to do the code design yourself.

 

[Celt83]

here is a quickly thrown together python approach:

from __future__ import division
import scipy

iter_num = 5000
l = 10 # units are ft
length_step = l/iter_num
rl_conjugate = 0
w_conjugate = [0]*(iter_num+1)
m_conjugate = [0]*(iter_num+1)
v_conjugate =  [0]*(iter_num+1)
w_conjugate_center = [0]*(iter_num+1)
x_conv =[0]
x_conm =[0]
w_conv = [0]
w_conm = [0]

#generate the list of x coordinates
j=0        
while (j < iter_num+1):
    x = x + length_step
    if j == 0:
        x = 0
    elif x > l:
        x = l
    else:
        x=x       
    x_coord[j]=x        
    j+=1

# Fill your mx list here based on your loading

# Fill your Ix list here based on your I function

# Create the M/EI Loading diagram
j=0
while (j<iter_num+1):
    # 144 and 20736 convert E(KSI) to E(KSF) and I(in4) to I(ft4)
    # Ix[j] and mx[j] are lists of predetermined values @ the cooresponding j X coordinate
    # j just iterates over a set number of x coordinates

    w_conjugate[j]=(mx[j])/((E*144)*(Ix[j]/20736)) 
    j+=1

# Find the horizontal center of the M/EI loading curve
j=0
while (j<iter_num+1):
    w_conjugate_center[j]=w_conjugate[j]*x_coord[j] 
    j+=1

# Left Conjugate Beam Reaction or Initial Slope Value
# Statics by summing moments of the conjugate beam about the right support
rl_conjugate=(scipy.integrate.simps(w_conjugate,x_coord)*(l-((scipy.integrate.simps(w_conjugate_center,x_coord))/scipy.integrate.simps(w_conjugate,x_coord))))/l

j=0
while (j<iter_num+1):
    if j==0:
        v_conjugate[j] = rl_conjugate
    else:
        x_conv.append(x_coord[j])
        w_conv.append(w_conjugate[j])
        v_conjugate[j]= rl_conjugate - scipy.integrate.simps(w_conv,x_conv)
    j+=1

j=0
while (j<iter_num+1):
    if j==0:
        d_main[j] = 0
    else:
        x_conm.append(x_coord[j])
        w_conm.append(v_conjugate[j])
        d_main[j]= (0 - scipy.integrate.simps(w_conm,x_conm))*12 # 12 to report deflection in inches
    j+=1

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[Retrograde]

I am aware of a design manual for design of tapered tee sections.

I would be interested in getting a copy of this design manual.