Partial Beam Reinforcement

[RSCBeard]

I will be partially reinforcing a beam with a WT. I am looking for guidance as to determining the length of WT to provide. I've calculated moment diagrams and know the length exceeding the moment capacity.

My question concerns the require length of WT beyond these points. How do you detrmine this length and are there code references for this?

Also, the WT would be stitch welded, but typically there is a continuous length at each end ("tail weld?"). How and where can I find information on determining this weld length?

Richard Beard, PE
Century Engineering, Inc

http://www.centuryeng.com

 

[UcfSE]

See this thread507-160349. Take a look at jike's response from 19 Jul 06 19:46 and particularly WillisV's response from 20 Jul 06 12:23.

I would extend the WT past the theoretical cut-off point at least enough to place the end weld and then more so you can have some tolerance if they place the WT in the field off from where you specify.

 

[RSCBeard]

Thanks for the quick response.

WillisV's response discusses the cover plates which are thin. Thus the design is based on the weld length to fully stress the plate.

The WT will have a much greater variation in stress levels. This would mean the WT flange would reach full stress prior to the web where the attachment is made.

How does this affect these calculations? I would assume it would be conservative to assume the force in the WT to be fs*(Area wt).


Richard Beard, PE
Century Engineering, Inc

http://www.centuryeng.com

 

[jec67]

The equation the WillisV posted in the response to the referenced thread is valid for the case of the WT reinforcement. The welds at the ends of the WT need to transfer the forces (at the end of the WT) out of the WT and into the existing beam. By using MQ/I, where M is at the theoretical cutoff, the force in the WT at the cutoff point is calculated, and this force must be resisted by the end welds.

With this formula, you will account for the stress distirbution that you have mentioned in your post.

 

[UcfSE]

I believe it would be conservative to take the WT area times the maximum stress in the WT.

I'll give it a shot for the equation. Steel stress is a function of the distance from the neutral axis. Let's call that "y". We know we can use f_s=My/I for the stress ionthe steel at a given distance "y" from the neutral axis. The variable "c" will represent the maximum value of "y", so the maximum stress would be f_{s max}=Mc/I. The stress at the top of the bottom flange of the WT would be f_s2=M(c-t_f)/I and the stress at the top of the stem of the WT would be f_s1=M(c-d)/I where t_f is the WT flange thickness and d is the depth of the WT. If we take stress times the area over which it acts we can find force. The differences in stress at each location result in a trapezoidal stress distribution. The area of a trapezoid is the average of the two heights times the base. The force in the WT then becomes F_WT=[(f_s1+f_s2)/2](d-t_f)t_w+[(f_s2+f_{s max})/2]b_ft_f. This is the average stress in the stem times the stem area plus the average stress in the flange times the flange area. The variables b_f and t_w are the flange width and the stem thickness, respectively.

Make any sense?

 

[jec67]

Yes - it would be conservative to use the maximum stress in the WT. The MQ/I formula is using the average stress at the centroid of the WT times the area of the WT to calculate the force in the WT. this is the "true" solution. Using the maximum stress in the WT will err on the side of caution - always a good thing.

 

[RSCBeard]

Thanks for the help.

Richard Beard, PE
Century Engineering, Inc

http://www.centuryeng.com