Written by salar delavar qashqai www.Salardqashqai.blogfa.com

1. >> IN THE NAME OF GOD <<
Moment‐Curvature Analysis Unconfined Concrete Section with
Different Tension Steel Reinforcement in MATLAB
This program is written by Salar Delavar Ghashghaei ‐ Date of Publication: July/20/2015
E‐mail: salar.d.ghashghaei@gmail.com

2. Section Properties:
%% Section Properties
b=500;% [mm]
h=500;% [mm]
%As:As1 As2
As=[2500 2500]; % for m=0.0
As=[2500 4005.2]; % for m=0.2
As=[2500 5510.4]; % for m=0.4
As=[2500 7015.6]; % for m=0.6
As=[2500 8520.8]; % for m=0.8
As=[2500 1002.6]; % for m=1.0
%d:d1 d2
d=[75 425];
Concrete Properties:
fc =25;% [N/mm^2] Unconfined concrete strength
ecu=0.004;% Ultimate concrete strain
Ec=5000*sqrt(fc);
ec0=(2*fc)/Ec;
fct=-0.7*sqrt(fc);% Concrete tension stress
ect1=(2*fct)/Ec;ect2=(2.625*fct)/Ec;ect3=(9.292*fct)/Ec;% Concrete tension
strain
Steel Reinforcing Properties:
fy =400;% [N/mm^2] Yield strength of reinforcing steel
Es =2e5;% [N/mm^2] Modulus of elasticity of steel
fu=1.5*fy;% Ultimate steel stress

3. ey=fy/Es;% Yeild steel strain
esh=0.01;% Strain at steel strain-hardening
esu=0.09;% Ultimate steel strain
Esh=(fu-fy)/(esu-esh);
w=Es*ecu;
%calculate the beta1
if or((fc< 30),(fc== 30))
beta1=0.85;
elseif (fc> 30)&&(fc< 55)
beta1=0.85-.008*(fc-30);
else or((fc> 55),(fc== 55))
beta1=0.65;
end
%calculate the ro-bal
robal=0.85*beta1*(fc/fy)*(w/(w+fy));
robar=0.01;ro=robal*m+robar;m=[0.0;0.2;0.4;0.6;0.8;1.0];
%As: As1 As2 As3 As4 As5 As6
As=[robar 0 0 0 0 ro]*b*h;
Note: m ∴ 0.85 ∴
Analysis Report:
##########
# m = 0.00 #
##########
(+)Increment 1 : It is converged in 8 iterations ‐ strain: 0.000042 ‐ x: 215.74 ‐ Phi: 0.00019 ‐ Moment: 23.80
(+)Increment 2 : It is converged in 7 iterations ‐ strain: 0.000092 ‐ x: 216.19 ‐ Phi: 0.00043 ‐ Moment: 52.07
(+)Increment 3 : It is converged in 8 iterations ‐ strain: 0.000188 ‐ x: 217.05 ‐ Phi: 0.00086 ‐ Moment: 104.64
(+)Increment 4 : It is converged in 10 iterations ‐ strain: 0.000280 ‐ x: 207.01 ‐ Phi: 0.00135 ‐ Moment: 139.15
(+)Increment 5 : It is converged in 11 iterations ‐ strain: 0.000367 ‐ x: 187.68 ‐ Phi: 0.00196 ‐ Moment: 164.10
(+)Increment 6 : It is converged in 11 iterations ‐ strain: 0.000429 ‐ x: 178.06 ‐ Phi: 0.00241 ‐ Moment: 181.01
(+)Increment 7 : It is converged in 14 iterations ‐ strain: 0.000872 ‐ x: 152.01 ‐ Phi: 0.00573 ‐ Moment: 316.47
(+)Increment 8 : It is converged in 14 iterations ‐ strain: 0.001041 ‐ x: 150.77 ‐ Phi: 0.00690 ‐ Moment: 372.03
(+)Increment 9 : It is converged in 23 iterations ‐ strain: 0.001171 ‐ x: 139.40 ‐ Phi: 0.00840 ‐ Moment: 384.38
(+)Increment 10 : It is converged in 23 iterations ‐ strain: 0.001301 ‐ x: 127.00 ‐ Phi: 0.01024 ‐ Moment: 384.04
(+)Increment 11 : It is converged in 25 iterations ‐ strain: 0.001600 ‐ x: 109.29 ‐ Phi: 0.01464 ‐ Moment: 384.96
(+)Increment 12 : It is converged in 27 iterations ‐ strain: 0.002000 ‐ x: 97.13 ‐ Phi: 0.02059 ‐ Moment: 386.51
(+)Increment 13 : It is converged in 29 iterations ‐ strain: 0.002400 ‐ x: 90.97 ‐ Phi: 0.02638 ‐ Moment: 387.19
(+)Increment 14 : It is converged in 30 iterations ‐ strain: 0.002800 ‐ x: 87.75 ‐ Phi: 0.03191 ‐ Moment: 389.27
(+)Increment 15 : It is converged in 31 iterations ‐ strain: 0.003200 ‐ x: 86.01 ‐ Phi: 0.03720 ‐ Moment: 393.21
(+)Increment 16 : It is converged in 33 iterations ‐ strain: 0.003600 ‐ x: 84.92 ‐ Phi: 0.04239 ‐ Moment: 396.89
(+)Increment 17 : It is converged in 34 iterations ‐ strain: 0.004000 ‐ x: 84.20 ‐ Phi: 0.04751 ‐ Moment: 400.38
## Unconfined Concrete Strain Reached to Ultimate Strain: 0.0040 ##
+=====================+
= Unconfined curve fitted =
Curvature Moment
(1/m) (kN.m)
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
0 0
0.0029 352.6904
0.0475 400.3800
+=====================+
##########
# m = 0.20 #
##########
(+)Increment 1 : It is converged in 7 iterations ‐ strain: 0.000042 ‐ x: 226.84 ‐ Phi: 0.00019 ‐ Moment: 25.12
(+)Increment 2 : It is converged in 7 iterations ‐ strain: 0.000092 ‐ x: 227.30 ‐ Phi: 0.00041 ‐ Moment: 54.95
(+)Increment 3 : It is converged in 8 iterations ‐ strain: 0.000188 ‐ x: 228.19 ‐ Phi: 0.00082 ‐ Moment: 110.41
(+)Increment 4 : It is converged in 9 iterations ‐ strain: 0.000280 ‐ x: 225.71 ‐ Phi: 0.00124 ‐ Moment: 159.62

4. (+)Increment 5 : It is converged in 10 iterations ‐ strain: 0.000367 ‐ x: 211.15 ‐ Phi: 0.00174 ‐ Moment: 188.46
(+)Increment 6 : It is converged in 11 iterations ‐ strain: 0.000429 ‐ x: 203.75 ‐ Phi: 0.00211 ‐ Moment: 210.76
(+)Increment 7 : It is converged in 14 iterations ‐ strain: 0.000872 ‐ x: 182.36 ‐ Phi: 0.00478 ‐ Moment: 374.75
(+)Increment 8 : It is converged in 13 iterations ‐ strain: 0.001041 ‐ x: 180.93 ‐ Phi: 0.00575 ‐ Moment: 437.90
(+)Increment 9 : It is converged in 13 iterations ‐ strain: 0.001171 ‐ x: 180.78 ‐ Phi: 0.00648 ‐ Moment: 485.55
(+)Increment 10 : It is converged in 14 iterations ‐ strain: 0.001301 ‐ x: 181.10 ‐ Phi: 0.00718 ‐ Moment: 531.80
(+)Increment 11 : It is converged in 29 iterations ‐ strain: 0.001600 ‐ x: 168.88 ‐ Phi: 0.00947 ‐ Moment: 591.79
(+)Increment 12 : It is converged in 33 iterations ‐ strain: 0.002000 ‐ x: 142.12 ‐ Phi: 0.01407 ‐ Moment: 595.56
(+)Increment 13 : It is converged in 36 iterations ‐ strain: 0.002400 ‐ x: 127.62 ‐ Phi: 0.01881 ‐ Moment: 597.24
(+)Increment 14 : It is converged in 39 iterations ‐ strain: 0.002800 ‐ x: 118.79 ‐ Phi: 0.02357 ‐ Moment: 597.73
(+)Increment 15 : It is converged in 42 iterations ‐ strain: 0.003200 ‐ x: 112.83 ‐ Phi: 0.02836 ‐ Moment: 597.72
(+)Increment 16 : It is converged in 42 iterations ‐ strain: 0.003600 ‐ x: 108.81 ‐ Phi: 0.03308 ‐ Moment: 599.52
(+)Increment 17 : It is converged in 43 iterations ‐ strain: 0.004000 ‐ x: 106.20 ‐ Phi: 0.03766 ‐ Moment: 604.53
## Unconfined Concrete Strain Reached to Ultimate Strain: 0.0040 ##
+=====================+
= Unconfined curve fitted =
Curvature Moment
(1/m) (kN.m)
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
0 0
0.0039 535.0500
0.0377 604.5336
+=====================+
##########
# m = 0.40 #
##########
(+)Increment 1 : It is converged in 7 iterations ‐ strain: 0.000042 ‐ x: 236.73 ‐ Phi: 0.00018 ‐ Moment: 26.20
(+)Increment 2 : It is converged in 7 iterations ‐ strain: 0.000092 ‐ x: 237.21 ‐ Phi: 0.00039 ‐ Moment: 57.32
(+)Increment 3 : It is converged in 8 iterations ‐ strain: 0.000188 ‐ x: 238.12 ‐ Phi: 0.00079 ‐ Moment: 115.12
(+)Increment 4 : It is converged in 8 iterations ‐ strain: 0.000280 ‐ x: 238.28 ‐ Phi: 0.00118 ‐ Moment: 169.25
(+)Increment 5 : It is converged in 10 iterations ‐ strain: 0.000367 ‐ x: 228.43 ‐ Phi: 0.00161 ‐ Moment: 198.63
(+)Increment 6 : It is converged in 10 iterations ‐ strain: 0.000429 ‐ x: 222.32 ‐ Phi: 0.00193 ‐ Moment: 231.05
(+)Increment 7 : It is converged in 13 iterations ‐ strain: 0.000872 ‐ x: 205.00 ‐ Phi: 0.00425 ‐ Moment: 415.82
(+)Increment 8 : It is converged in 13 iterations ‐ strain: 0.001041 ‐ x: 203.47 ‐ Phi: 0.00511 ‐ Moment: 483.51
(+)Increment 9 : It is converged in 13 iterations ‐ strain: 0.001171 ‐ x: 203.31 ‐ Phi: 0.00576 ‐ Moment: 534.54
(+)Increment 10 : It is converged in 14 iterations ‐ strain: 0.001301 ‐ x: 203.66 ‐ Phi: 0.00639 ‐ Moment: 584.40
(+)Increment 11 : It is converged in 16 iterations ‐ strain: 0.001600 ‐ x: 205.61 ‐ Phi: 0.00778 ‐ Moment: 692.02
(+)Increment 12 : It is converged in 36 iterations ‐ strain: 0.002000 ‐ x: 198.91 ‐ Phi: 0.01005 ‐ Moment: 787.70
(+)Increment 13 : It is converged in 42 iterations ‐ strain: 0.002400 ‐ x: 175.01 ‐ Phi: 0.01371 ‐ Moment: 793.43
(+)Increment 14 : It is converged in 47 iterations ‐ strain: 0.002800 ‐ x: 159.82 ‐ Phi: 0.01752 ‐ Moment: 796.52
(+)Increment 15 : It is converged in 50 iterations ‐ strain: 0.003200 ‐ x: 149.15 ‐ Phi: 0.02145 ‐ Moment: 798.40
(+)Increment 16 : It is converged in 53 iterations ‐ strain: 0.003600 ‐ x: 141.16 ‐ Phi: 0.02550 ‐ Moment: 799.62
(+)Increment 17 : It is converged in 56 iterations ‐ strain: 0.004000 ‐ x: 134.90 ‐ Phi: 0.02965 ‐ Moment: 800.41
## Unconfined Concrete Strain Reached to Ultimate Strain: 0.0040 ##
+=====================+
= Unconfined curve fitted =
Curvature Moment
(1/m) (kN.m)
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
0 0
0.0047 691.8680
0.0297 800.4104
+=====================+
##########
# m = 0.60 #
##########
(+)Increment 1 : It is converged in 6 iterations ‐ strain: 0.000042 ‐ x: 245.62 ‐ Phi: 0.00017 ‐ Moment: 27.11
(+)Increment 2 : It is converged in 7 iterations ‐ strain: 0.000092 ‐ x: 246.11 ‐ Phi: 0.00038 ‐ Moment: 59.29

5. (+)Increment 3 : It is converged in 8 iterations ‐ strain: 0.000188 ‐ x: 247.04 ‐ Phi: 0.00076 ‐ Moment: 119.07
(+)Increment 4 : It is converged in 8 iterations ‐ strain: 0.000280 ‐ x: 247.93 ‐ Phi: 0.00113 ‐ Moment: 175.77
(+)Increment 5 : It is converged in 10 iterations ‐ strain: 0.000367 ‐ x: 242.14 ‐ Phi: 0.00152 ‐ Moment: 211.25
(+)Increment 6 : It is converged in 10 iterations ‐ strain: 0.000429 ‐ x: 236.94 ‐ Phi: 0.00181 ‐ Moment: 237.33
(+)Increment 7 : It is converged in 13 iterations ‐ strain: 0.000872 ‐ x: 222.61 ‐ Phi: 0.00392 ‐ Moment: 446.20
(+)Increment 8 : It is converged in 13 iterations ‐ strain: 0.001041 ‐ x: 221.37 ‐ Phi: 0.00470 ‐ Moment: 518.17
(+)Increment 9 : It is converged in 13 iterations ‐ strain: 0.001171 ‐ x: 221.20 ‐ Phi: 0.00529 ‐ Moment: 571.74
(+)Increment 10 : It is converged in 14 iterations ‐ strain: 0.001301 ‐ x: 221.56 ‐ Phi: 0.00587 ‐ Moment: 623.77
(+)Increment 11 : It is converged in 16 iterations ‐ strain: 0.001600 ‐ x: 223.60 ‐ Phi: 0.00716 ‐ Moment: 736.38
(+)Increment 12 : It is converged in 18 iterations ‐ strain: 0.002000 ‐ x: 227.77 ‐ Phi: 0.00878 ‐ Moment: 868.55
(+)Increment 13 : It is converged in 42 iterations ‐ strain: 0.002400 ‐ x: 230.19 ‐ Phi: 0.01043 ‐ Moment: 969.17
(+)Increment 14 : It is converged in 52 iterations ‐ strain: 0.002800 ‐ x: 208.82 ‐ Phi: 0.01341 ‐ Moment: 977.26
(+)Increment 15 : It is converged in 57 iterations ‐ strain: 0.003200 ‐ x: 193.41 ‐ Phi: 0.01655 ‐ Moment: 983.17
(+)Increment 16 : It is converged in 80 iterations ‐ strain: 0.003600 ‐ x: 187.40 ‐ Phi: 0.01921 ‐ Moment: 983.12
(+)Increment 17 : It is converged in 87 iterations ‐ strain: 0.004000 ‐ x: 185.14 ‐ Phi: 0.02160 ‐ Moment: 980.94
## Unconfined Concrete Strain Reached to Ultimate Strain: 0.0040 ##
+=====================+
= Unconfined curve fitted =
Curvature Moment
(1/m) (kN.m)
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
0 0
0.0050 784.6939
0.0216 980.9371
+=====================+
##########
# m = 0.80 #
##########
(+)Increment 1 : It is converged in 6 iterations ‐ strain: 0.000042 ‐ x: 253.67 ‐ Phi: 0.00017 ‐ Moment: 27.88
(+)Increment 2 : It is converged in 7 iterations ‐ strain: 0.000092 ‐ x: 254.16 ‐ Phi: 0.00036 ‐ Moment: 60.97
(+)Increment 3 : It is converged in 7 iterations ‐ strain: 0.000188 ‐ x: 255.10 ‐ Phi: 0.00074 ‐ Moment: 122.41
(+)Increment 4 : It is converged in 8 iterations ‐ strain: 0.000280 ‐ x: 256.02 ‐ Phi: 0.00109 ‐ Moment: 180.70
(+)Increment 5 : It is converged in 9 iterations ‐ strain: 0.000367 ‐ x: 253.47 ‐ Phi: 0.00145 ‐ Moment: 230.60
(+)Increment 6 : It is converged in 10 iterations ‐ strain: 0.000429 ‐ x: 248.97 ‐ Phi: 0.00172 ‐ Moment: 249.24
(+)Increment 7 : It is converged in 13 iterations ‐ strain: 0.000872 ‐ x: 236.86 ‐ Phi: 0.00368 ‐ Moment: 469.67
(+)Increment 8 : It is converged in 13 iterations ‐ strain: 0.001041 ‐ x: 236.00 ‐ Phi: 0.00441 ‐ Moment: 545.39
(+)Increment 9 : It is converged in 12 iterations ‐ strain: 0.001171 ‐ x: 235.94 ‐ Phi: 0.00496 ‐ Moment: 601.18
(+)Increment 10 : It is converged in 13 iterations ‐ strain: 0.001301 ‐ x: 236.31 ‐ Phi: 0.00550 ‐ Moment: 655.03
(+)Increment 11 : It is converged in 16 iterations ‐ strain: 0.001600 ‐ x: 238.39 ‐ Phi: 0.00671 ‐ Moment: 770.99
(+)Increment 12 : It is converged in 18 iterations ‐ strain: 0.002000 ‐ x: 242.65 ‐ Phi: 0.00824 ‐ Moment: 906.95
(+)Increment 13 : It is converged in 20 iterations ‐ strain: 0.002400 ‐ x: 247.97 ‐ Phi: 0.00968 ‐ Moment: 1017.63
(+)Increment 14 : It is converged in 21 iterations ‐ strain: 0.002800 ‐ x: 253.58 ‐ Phi: 0.01104 ‐ Moment: 1109.51
(+)Increment 15 : It is converged in 65 iterations ‐ strain: 0.003200 ‐ x: 254.99 ‐ Phi: 0.01255 ‐ Moment: 1132.81
(+)Increment 16 : It is converged in 79 iterations ‐ strain: 0.003600 ‐ x: 249.87 ‐ Phi: 0.01441 ‐ Moment: 1129.62
(+)Increment 17 : It is converged in 89 iterations ‐ strain: 0.004000 ‐ x: 246.86 ‐ Phi: 0.01620 ‐ Moment: 1125.68
## Unconfined Concrete Strain Reached to Ultimate Strain: 0.0040 ##
+=====================+
= Unconfined curve fitted =
Curvature Moment
(1/m) (kN.m)
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
1.0e+003 *
0 0
0.0000 0.7657
0.0000 1.1257
+=====================+
##########
# m = 1.00 #
##########

6. (+)Increment 1 : It is converged in 7 iterations ‐ strain: 0.000042 ‐ x: 260.99 ‐ Phi: 0.00016 ‐ Moment: 28.54
(+)Increment 2 : It is converged in 6 iterations ‐ strain: 0.000092 ‐ x: 261.49 ‐ Phi: 0.00035 ‐ Moment: 62.41
(+)Increment 3 : It is converged in 7 iterations ‐ strain: 0.000188 ‐ x: 262.43 ‐ Phi: 0.00071 ‐ Moment: 125.29
(+)Increment 4 : It is converged in 8 iterations ‐ strain: 0.000280 ‐ x: 263.36 ‐ Phi: 0.00106 ‐ Moment: 184.91
(+)Increment 5 : It is converged in 9 iterations ‐ strain: 0.000367 ‐ x: 262.67 ‐ Phi: 0.00140 ‐ Moment: 238.19
(+)Increment 6 : It is converged in 10 iterations ‐ strain: 0.000429 ‐ x: 259.17 ‐ Phi: 0.00166 ‐ Moment: 259.08
(+)Increment 7 : It is converged in 13 iterations ‐ strain: 0.000872 ‐ x: 248.78 ‐ Phi: 0.00350 ‐ Moment: 488.57
(+)Increment 8 : It is converged in 12 iterations ‐ strain: 0.001041 ‐ x: 248.23 ‐ Phi: 0.00419 ‐ Moment: 567.22
(+)Increment 9 : It is converged in 12 iterations ‐ strain: 0.001171 ‐ x: 248.33 ‐ Phi: 0.00471 ‐ Moment: 625.08
(+)Increment 10 : It is converged in 13 iterations ‐ strain: 0.001301 ‐ x: 248.77 ‐ Phi: 0.00523 ‐ Moment: 680.54
(+)Increment 11 : It is converged in 15 iterations ‐ strain: 0.001600 ‐ x: 250.87 ‐ Phi: 0.00638 ‐ Moment: 799.39
(+)Increment 12 : It is converged in 18 iterations ‐ strain: 0.002000 ‐ x: 255.17 ‐ Phi: 0.00784 ‐ Moment: 937.70
(+)Increment 13 : It is converged in 20 iterations ‐ strain: 0.002400 ‐ x: 260.53 ‐ Phi: 0.00921 ‐ Moment: 1049.86
(+)Increment 14 : It is converged in 22 iterations ‐ strain: 0.002800 ‐ x: 266.28 ‐ Phi: 0.01052 ‐ Moment: 1140.61
(+)Increment 15 : It is converged in 24 iterations ‐ strain: 0.003200 ‐ x: 275.00 ‐ Phi: 0.01164 ‐ Moment: 1172.97
(+)Increment 16 : It is converged in 26 iterations ‐ strain: 0.003600 ‐ x: 283.01 ‐ Phi: 0.01272 ‐ Moment: 1194.81
(+)Increment 17 : It is converged in 27 iterations ‐ strain: 0.004000 ‐ x: 290.39 ‐ Phi: 0.01377 ‐ Moment: 1208.87
## Unconfined Concrete Strain Reached to Ultimate Strain: 0.0040 ##
+=====================+
= Unconfined curve fitted =
Curvature Moment
(1/m) (kN.m)
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
1.0e+003 *
0 0
0.0000 0.6806
0.0000 1.2089
+=====================+
Plot: