This MATLAB program analyzes the moment-curvature behavior of unconfined concrete sections with varying amounts of tension steel reinforcement. It performs an incremental analysis to determine the moment-curvature response up to the ultimate concrete strain limit of 0.004. Results are presented for sections with tension reinforcement ratios (ρ) of 0, 0.2, 0.4, etc. The analysis converges successfully for each reinforcement ratio and reports the moment and curvature at each increment.

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: