Hello,
I am attempting to verify the flange lateral stresses that I am seeing in my model (I have the analysis toggle for "Compute flange lateral bending per NCHRP 725" selected).
Per LEAP Bridge Steel Help, "The cross frame end moments are used to determine the flange lateral bending moments and stresses as described in Report 725, Section 3.2.4."
However, when reading Section 3.2.4 I see that they adopt an approach of using the cross frame forces, not cross frame ended moments.
This is further backed up by the NCHRP Project 12-79 Task 8 Report (Appendix C of Report 725) stating that "It should be emphasized that to predict the flange lateral bending stresses... it is necessary to first have an accurate prediction of the cross frame forces" (Section 6.4, shown below).
As I continued with additional testing, it was clear that the diaphragm forces are not impacting the flange lateral moments because when performing a sensitivity analysis, I was given results of diaphragm forces over 500kips (seen below)... and yet my flange lateral stress was exactly the same! And sure enough, my cross frame end moments were the same throughout all incremental changes.
So, from all this, here are my questions:
1. How is the Timoshenko beam element representing the diaphragm member calculating member axial forces from the equivalent member end moments and shears?
2. Why does LBS use cross frame end moments to calculate flange lateral moments when NCHRP Report 725 Section 3.2.4 says to use the cross frame lateral forces?
3. Can a user hand verify how the program computes flange lateral stresses from the cross frame end moments?
Thank you
The following is the formulation to be used by LBS for computation of flange lateral bending moments when grillage models are employed. This procedure follows Section 3.2.4 of NCHRP report 725.
- Cross frame Model- Recap conversion to equivalent cross frame beam (CFB) model- Forces from equivalent beam model to flange- Convert CFB end moments into force couples using moment from the STAAD analysis and the cross frame height- Cross frame end forces Mz and Fy for the various load cases need to be stored in the database for each dead load and live load case.- Translate these forces to the T and B flange using dcf/h as described in NHRP Report 725- Computation of lateral flange moment per Report 725, page 60.- Please check AASHTO simplified approach equation C4.6.1.2.4b-1 for use in curved bridges
Computing flange lateral bending moments from Cross Frame Forces
The example below shows how these moments are computed:
Equation 1: Mz_lat(interior) = Pab/2L (2ab/L^2 +1)Equation 2: Mz_lat(exterior) = Pab/2L (ab/〖2L〗^2 +b/L+1)
Where a and b are unbraced lengths and L = a+b
The cross-frames are modeled (represented) as single beams in grillage models. By using the end moments (M_L or M_R) of this beam element and the distance center to center of flanges (h), the lateral force (P) on the flange is calculated. By using lateral force (P) and unbraced lengths (a, b and L), lateral moment on the flange (Mz_Lat) is calculated. Then, using Mz_Lat and section modulus of the flange (S_flange), the lateral bending stress on the flange is calculated.This method can be conservative and would to use FEM method and find out the flange lateral stresses.