Nonlinear Moment Rotation Hinge

[Araj]

Hello,

Is there any material class or anything that can simulate the Moment Rotation Hinge as defined in ATC-40 to be used in Beam-Column elements.

I wish to work on a pushover anlaysis and would like to use it. If somebody has used such a thing, I shall be glad if you can post the commands and give some idea about it.

Thank you,

Regards,
Aloke

[aemmons]

I am using nonlinear rotaional springs (hinges) in an analysis. However, my model is a steel moment resisting frame, not concrete. If you are interested in my code let me know.

andrew

[berktaftali]

You can use elastic and steel materials in series and parallel to obtain the desired moment-rotation curve. The procedure below is old and NOT FULLY WORKING. I guess the syntax of some of the commands that I used in this procedure has changed in the newer versions. This will give you an idea. Use it a your own risk ...

PS. I would use Steel01 instead of Hardening material that's used in the procedure....

Code: Select all

# femamomentrotation.tcl
#
# Procedure which creates a uniaxial material to be used in defining 
# moment-rotation curves in FEMA-273 for pushover analysis.
#
# Written: BT
# Date: Dec 2002
#
# Formal arguments
#    eleID - unique uniaxial material ID for this material
#    E     - rotational stiffness (My/EI)
#    My    - yield moment
#    h     - % hardening
#    c,d,e - FEMA values (see figure below)
#    index - defines the dummy material tags
#
#          Q/Qce
#            ^
#            |<-------------- e ------->
#            |<------ d ------>
#            |       __________
#            |      /          |
#            |     /           |
#            |    /            |
#            |   /             |
#            |  /              |_______    ^
#            | /                        |  c            
#            |/                         |  v
#            L-------------------------------> rot/roty
#
#            Q    - generalized component load
#            Qce  - generalized component expected strength
#            rot  - plastic rotation of beam or column
#            roty - rotation at yield
#
# Returns
#    Nothing
#
# Notes
#    - Won't work in OpenSees versions > 1.3

proc FEMAMomentRotation {eleID E My h c d e} {

    # calculate internal values
    set M1   [expr (1-$c)*$My];
    set M2   [expr $c*$My];
    set roty [expr $My/$E];
    set k1   [expr $M1/$roty];
    set k2   [expr $M2/$roty];
    
    # define uniaxial materials
    #                           tag                 E     fy  h_iso               h_kin
    uniaxialMaterial Hardening  [expr $eleID*100+1] $k1   $M1 [expr $h*($k1+$k2)] 0.0
    uniaxialMaterial Hardening  [expr $eleID*100+2] $k2   $M2 0.001               0.0
    uniaxialMaterial Elastic    [expr $eleID*100+3] 1e-5

    # combine in parallel
    #                           tag                 tag1                tag2                max			    min
    uniaxialMaterial Parallel   [expr $eleID*100+4] [expr $eleID*100+1] [expr $eleID*100+3] -max [expr $roty * $d] -min [expr -1* $roty * $d];
    uniaxialMaterial Parallel   [expr $eleID*100+5] [expr $eleID*100+2] [expr $eleID*100+4] -max [expr $roty * $e] -min [expr -1* $roty * $e];
    uniaxialMaterial Parallel   $eleID              [expr $eleID*100+5] [expr $eleID*100+3]
}