-
Notifications
You must be signed in to change notification settings - Fork 2
Expand file tree
/
Copy pathSpring_PZ.tcl
More file actions
139 lines (112 loc) · 6.5 KB
/
Spring_PZ.tcl
File metadata and controls
139 lines (112 loc) · 6.5 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
##################################################################################################################
# Spring_PZ.tcl
#
# SubRoutine to construct a rotational spring with a trilinear hysteretic response representative of steel
# panel zone response with/without the consideration of composite action
#
# References:
#--------------
# Elkady, A. and D. G. Lignos (2014). "Modeling of the Composite Action in Fully Restrained Beam-to-Column
# Connections: Implications in the Seismic Design and Collapse Capacity of Steel Special Moment Frames."
# Earthquake Eng. & Structural Dynamics 43(13). DOI: 10.1002/eqe.2430.
#
# Skiadopoulos, A., Elkady, A. and D. G. Lignos (2020). "Proposed Panel Zone Model for Seismic Design of
# Steel Moment-Resisting Frames." ASCE Journal of Structural Engineering. DOI: 10.1061/(ASCE)ST.1943-541X.0002935.
#
##################################################################################################################
#
# Input Arguments:
#------------------
# SpringID Spring ID
# NodeI Node i ID
# NodeJ Node j ID
# E Young's Modulus
# mu Poisson's Ratio
# fy Yield Stress (Expected, measured or nominal)
# tw_Col Column Web Thickness
# tdp Doubler Plate(s) Total Thickness
# d_Col Column Depth
# d_Beam Beam Depth
# tf_Col Column Flange Thickness
# bf_Col Column Flange Width
# Ix_Col Column second-moment-of-interia about the strong axis
# n Axial load ratio (P/Py)
# trib Steel deck rib depth
# ts Concrete slab depth above the rib
# Response_ID ID for Panel Zone Response: 0 --> Interior Steel Panel Zone with Composite Action
# 1 --> Exterior Steel Panel Zone with Composite Action
# 2 --> Bare Steel Interior/Exterior Steel Panel Zone
# transfTag Geometric Transformation ID
#
# Written by: Dr. Ahmed Elkady, University of Southampton, UK
#
##################################################################################################################
proc Spring_PZ {SpringID NodeI NodeJ E mu fy tw_Col tdp d_Col d_Beam tf_Col bf_Col Ix_Col n trib ts Response_ID transfTag} {
set tpz [expr $tw_Col + $tdp]; # total PZ thickness
set G [expr $E/(2.0 * (1.0 + $mu))]; # Shear Modulus
# Beam's effective depth
if {$Response_ID==2} {
set d_BeamP $d_Beam;
} else {
set d_BeamP [expr $d_Beam + $trib + 0.5 * $ts]; # Effective Depth in Positive Moment
}
set d_BeamN $d_Beam; # Effective Depth in Negative Moment
# Stiffness Calculation
set Ks [expr $tpz * ($d_Col - $tf_Col) * $G]; # PZ Stiffness: Shear Contribution
set Kb [expr 12 * $E * ($Ix_Col + $tdp * pow(($d_Col - 2*$tf_Col),3)/12.) /pow($d_Beam,3) * $d_Beam]; # PZ Stiffness: Bending Contribution
set Ke [expr ($Ks * $Kb) / ($Ks + $Kb)]; # PZ Stiffness: Total
set Ksf [expr 2 * ($bf_Col * $tf_Col) * $G]; # Flange Stiffness: Shear Contribution
set Kbf [expr 2 * 12 * $E * $bf_Col * pow($tf_Col,3)/12. /pow($d_Beam,3) * $d_Beam]; # Flange Stiffness: Bending Contribution
set Kef [expr ($Ksf * $Kbf) / ($Ksf + $Kbf)]; # Flange Stiffness: Total
set ay [expr (0.58 * $Kef / $Ke + 0.88) / (1 - $Kef / $Ke)];
set aw_eff_4gamma 1.10;
set aw_eff_6gamma 1.15;
set af_eff_4gamma [expr 0.93 * $Kef / $Ke + 0.015];
set af_eff_6gamma [expr 1.05 * $Kef / $Ke + 0.020];
set r {expr sqrt(1- pow($n,2))}; # Reduction factor accounting for axial load
set Vy [expr $r * 0.577 * $fy * $ay * ($d_Col - $tf_Col) * $tpz]; # Yield Shear Force
set Vp_4gamma [expr $r * 0.577 * $fy * ($aw_eff_4gamma * ($d_Col - $tf_Col) * $tpz + $af_eff_4gamma * ($bf_Col - $tw_Col) * 2*$tf_Col)]; # Plastic Shear Force @ 4 gammaY
set Vp_6gamma [expr $r * 0.577 * $fy * ($aw_eff_6gamma * ($d_Col - $tf_Col) * $tpz + $af_eff_6gamma * ($bf_Col - $tw_Col) * 2*$tf_Col)]; # Plastic Shear Force @ 6 gammaY
set gamma_y [expr $Vy/$Ke];
set gamma4_y [expr 4.0 * $gamma_y];
set gamma6_y [expr 6.0 * $gamma_y];
set My_P [expr $Vy * $d_BeamP];
set Mp_4gamma_P [expr $Vp_4gamma * $d_BeamP];
set Mp_6gamma_P [expr $Vp_6gamma * $d_BeamP];
set My_N [expr $Vy * $d_BeamN];
set Mp_4gamma_N [expr $Vp_4gamma * $d_BeamN];
set Mp_6gamma_N [expr $Vp_6gamma * $d_BeamN];
set Slope_4to6gamma_y_P [expr ($Mp_6gamma_P - $Mp_4gamma_P) / (2 * $gamma_y) ];
set Slope_4to6gamma_y_N [expr ($Mp_6gamma_N - $Mp_4gamma_N) / (2 * $gamma_y) ];
# Defining the 3 Points used to construct the trilinear backbone curve
set gamma1 $gamma_y;
set gamma2 $gamma4_y;
set gamma3 [expr 100 * $gamma_y];
set M1_P [expr $My_P];
set M2_P [expr $Mp_4gamma_P];
set M3_P [expr $Mp_4gamma_P + $Slope_4to6gamma_y_P * (100 * $gamma_y - $gamma4_y)];
set M1_N [expr $My_N];
set M2_N [expr $Mp_4gamma_N];
set M3_N [expr $Mp_4gamma_N + $Slope_4to6gamma_y_N * (100 * $gamma_y - $gamma4_y)];
set gammaU_P 0.3;
set gammaU_N -0.3;
set Dummy_ID [expr 12 * $SpringID];
# Hysteretic Material without pinching and damage
# uniaxialMaterial Hysteretic $matTag $s1p $e1p $s2p $e2p <$s3p $e3p> $s1n $e1n $s2n $e2n <$s3n $e3n> $pinchX $pinchY $damage1 $damage2
# Composite Interior Steel Panel Zone
if { $Response_ID == 0.0 } {
uniaxialMaterial Hysteretic $Dummy_ID $M1_P $gamma1 $M2_P $gamma2 $M3_P $gamma3 [expr -$M1_P] [expr -$gamma1] [expr -$M2_P] [expr -$gamma2] [expr -$M3_P] [expr -$gamma3] 0.25 0.75 0. 0. 0.;
uniaxialMaterial MinMax $SpringID $Dummy_ID -min $gammaU_N -max $gammaU_P;
}
# Composite Exterior Steel Panel Zone
if { $Response_ID == 1.0 } {
uniaxialMaterial Hysteretic $Dummy_ID $M1_P $gamma1 $M2_P $gamma2 $M3_P $gamma3 [expr -$M1_N] [expr -$gamma1] [expr -$M2_N] [expr -$gamma2] [expr -$M3_N] [expr -$gamma3] 0.25 0.75 0. 0. 0.;
uniaxialMaterial MinMax $SpringID $Dummy_ID -min $gammaU_N -max $gammaU_P;
}
# Bare Steel Interior/Exterior Steel Panel Zone
if { $Response_ID == 2.0 } {
uniaxialMaterial Hysteretic $Dummy_ID $M1_N $gamma1 $M2_N $gamma2 $M3_N $gamma3 [expr -$M1_N] [expr -$gamma1] [expr -$M2_N] [expr -$gamma2] [expr -$M3_N] [expr -$gamma3] 0.25 0.75 0. 0. 0.;
uniaxialMaterial MinMax $SpringID $Dummy_ID -min $gammaU_N -max $gammaU_P;
}
element zeroLength $SpringID $NodeI $NodeJ -mat $SpringID -dir 6;
}