![Figure(3) Simply support beam model in SAP2000
Define Parameters:
P4=0; % [kN]
P5=1; % [kN]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Pushover analysis of simply support steel section beam based on plastic hinge concept in matlab and sap2000
- 3. P6=0; % [kN.mm] L = 1800; % [mm] a1=1500; b1=L-a1; a2=300; b2=L-a2; U5max=20;% ultimate displacement[mm] [dof(5)] %% Section Properties tf1=12;% [mm] I section thickness on Top flange bf1=200;% [mm] I section width on Top flange tw=6;% [mm] I section thickness of Web hw=876;% [mm] Height of web tf2=12;% [mm] I section thickness on Bottom flange bf2=200;% [mm] I section width on Bottom flange fy =372.3;% [N/mm^2] Yield strength of steel section Es =2e5;% [N/mm^2] Modulus of elasticity of steel section fu=511.4;% Ultimate steel stress ey=fy/Es;% Yield steel strain esh=0.02;% Strain at steel strain-hardening esu=0.14;% Ultimate steel strain Esh=(fu-fy)/(esu-esh); h=ptf1+ptf2+tf1+tf2+hw;% [mm] Height of Section Ie=((tw*hw^3)/12)+2*(((bf1*tf1^3)/12)+(bf1*tf1)*(0.5*h-0.5*tf1- ptf1)^2)+2*(((pbf1*ptf1^3)/12)+(pbf1*ptf1)*(0.5*h-0.5*ptf1)^2); A=2*tf1*bf1+tw*hw; E = 200; % [kN/mm^2] Ny= 0.3; % Poisson's ratio EI = E*Ie; % [kN.mm^2] EA = E*A; % [kN] As = 5400;% [mm^2] G = E/(2*(1+Ny)); % Shear modulus fi = (12*EI)/(G*As*L^2);% Timoshenko beam coefficient m = 3500; % number of calculation itermax = 5000;% maximum number of iterations tolerance = 1e-12; % specified tolerance for convergence lanX=1;lanY=0; % Element stiffness coefficient A=((4+fi)*EI/L)*(1/(1+fi));B=(6*EI/L^2)*(1/(1+fi));C=((2fi)*EI/L)*(1/(1+fi)); D=(12*EI/L^3)*(1/(1+fi));G=(EA/L); Plastic Hinge Properties: Lp=0.1*L; % Plastic hinge length Cur=[0;0.0041;0.3111]*10^-3; % [1/mm] Curvature M=[0;1.0610;1.6405]*10^6; % [kN.mm] Moment t=Cur*Lp; % [rad] Rotation MATLAB Analysis Report: (+)It is converged in 2 iterations for increment 1 (+)It is converged in 2 iterations for increment 2 (+)It is converged in 2 iterations for increment 3 (+)It is converged in 2 iterations for increment 4 (+)It is converged in 2 iterations for increment 5 (+)It is converged in 2 iterations for increment 6 (+)It is converged in 2 iterations for increment 7 (+)It is converged in 2 iterations for increment 8 (+)It is converged in 2 iterations for increment 9 (+)It is converged in 2 iterations for increment 10 . . .
- 5. ‐0.0000 0.0060 ‐0.0060 0.0000 0.0000 0.0075 ‐0.0075 ‐0.0000 ‐0.0000 0.0090 ‐0.0090 0.0000 ‐0.0000 0.0105 ‐0.0105 0.0000 ‐0.0000 0.0120 ‐0.0120 0.0000 0.0000 0.0135 ‐0.0135 ‐0.0000 0.0000 0.0150 ‐0.0150 ‐0.0000 0.0000 0.0165 ‐0.0165 ‐0.0000 ‐0.0000 0.0180 ‐0.0180 0.0000 0.0000 0.0195 ‐0.0195 ‐0.0000 ‐0.0000 0.0210 ‐0.0210 0.0000 0.0000 0.0225 ‐0.0225 0.0000 ‐0.0000 0.0240 ‐0.0240 0.0000 . . . ‐0.0000 1.0545 ‐1.0545 0.0000 0.0000 1.0560 ‐1.0560 ‐0.0000 0.0000 1.0575 ‐1.0575 0.0000 0.0000 1.0590 ‐1.0590 ‐0.0000 ‐0.0000 1.0605 ‐1.0605 0.0000 0.0000 1.0620 ‐1.0620 0.0000 0.0000 1.0635 ‐1.0635 ‐0.0000 ‐0.0000 1.0650 ‐1.0650 0.0000 0.0000 1.0665 ‐1.0665 0.0000 0.0000 1.0680 ‐1.0680 ‐0.0000 ‐0.0000 1.0695 ‐1.0695 0.0000 ‐0.0000 1.0710 ‐1.0710 0.0000 0.0000 1.0725 ‐1.0725 ‐0.0000 ============================================== SAP2000 Analysis Report: B E G I N A N A L Y S I S 2016/07/21 19:37:53 RUNNING ANALYSIS WITHIN THE GUI PROCESS USING THE ADVANCED SOLVER (PROVIDES LIMITED INSTABILITY INFORMATION) NUMBER OF JOINTS = 3 WITH RESTRAINTS = 2 NUMBER OF FRAME/CABLE/TENDON ELEMENTS = 2 NUMBER OF LOAD PATTERNS = 1 NUMBER OF ACCELERATION LOADS = 6 NUMBER OF LOAD CASES = 2 N O N L I N E A R S T A T I C A N A L Y S I S 19:37:53 CASE: 1 STARTING FROM ZERO (UNSTRESSED) INITIAL CONDITIONS LOAD CONTROL TYPE = FORCE NUMBER OF STAGES = 0 TYPE OF GEOMETRIC NONLINEARITY = NONE INCLUDE ELASTIC MATERIAL NONLINEARITY = YES INCLUDE INELASTIC MATERIAL NONLINEARITY = YES METHOD TO USE WHEN HINGES DROP LOAD = UNLOAD ENTIRE STRUCTURE SAVE POSITIVE INCREMENTS ONLY = YES RELATIVE FORCE CONVERGENCE TOLERANCE = 0.000100 RELATIVE EVENT TOLERANCE = 0.010000 E L E M E N T F O R M A T I O N 19:37:53
- 6. Saved Null Total Iteration Relative Curr Step Curr Sum Max Sum Steps Steps Steps this Step Unbalance Size of Steps of Steps ( 100 50 200 10/40 1.000000 0.100000 1.000000 1.000000) 1 0 1 Conv 1 2.17E-15 0.100000 0.100000 0.100000 2 0 2 Conv 1 4.34E-15 0.100000 0.200000 0.200000 3 0 3 Conv 1 8.67E-15 0.100000 0.300000 0.300000 4 0 4 Conv 1 8.67E-15 0.100000 0.400000 0.400000 5 0 5 Conv 1 8.68E-15 0.100000 0.500000 0.500000 6 0 6 Conv 1 2.03E-16 0.100000 0.600000 0.600000 7 0 7 Conv 1 2.37E-16 0.100000 0.700000 0.700000 8 0 8 Conv 1 2.71E-16 0.100000 0.800000 0.800000 9 0 9 Conv 1 3.05E-16 0.100000 0.900000 0.900000 10 0 10 Conv 1 3.39E-16 0.100000 1.000000 1.000000 TIME FOR INITIALIZING ANALYSIS = 0.21 TIME FOR CONTROLLING ANALYSIS = 0.02 TIME FOR UPDATING LOADS AND STATE = 0.08 TIME FOR FORMING STIFFNESS MATRIX = 0.05 TIME FOR SOLVING STIFFNESS MATRIX = 0.51 TIME FOR CALCULATING DISPLACEMENTS = 0.06 TIME FOR DETERMINING EVENTS = 0.00 TIME FOR SAVING RESULTS = 0.12 ---------- TOTAL TIME FOR THIS ANALYSIS = 1.05 N O N L I N E A R S T A T I C A N A L Y S I S 19:37:54 CASE: PUSH CONTINUING FROM THE END OF CASE: 1 LOAD CONTROL TYPE = DISPLACEMENT NUMBER OF STAGES = 0 TYPE OF GEOMETRIC NONLINEARITY = NONE INCLUDE ELASTIC MATERIAL NONLINEARITY = YES INCLUDE INELASTIC MATERIAL NONLINEARITY = YES METHOD TO USE WHEN HINGES DROP LOAD = UNLOAD ENTIRE STRUCTURE SAVE POSITIVE INCREMENTS ONLY = NO RELATIVE FORCE CONVERGENCE TOLERANCE = 0.000100 RELATIVE EVENT TOLERANCE = 0.010000 Saved Null Total Iteration Relative Curr Step Curr Sum Max Sum Steps Steps Steps this Step Unbalance Size of Steps of Steps ( 30 50 200 10/10 1.000000 0.050000 1.000000 1.000000) 1 0 1 Conv 1 6.01E-12 0.050000 0.050000 0.050000 2 0 2 Conv 1 8.02E-12 0.050000 0.100000 0.100000 3 0 3 Conv 1 8.02E-12 0.050000 0.150000 0.150000 4 0 4 Conv 1 8.02E-12 0.050000 0.200000 0.200000 5 0 5 Conv 1 1.60E-11 0.050000 0.250000 0.250000 6 0 6 Conv 1 1.60E-11 0.050000 0.300000 0.300000 7 0 7 Conv 1 1.60E-11 0.050000 0.350000 0.350000 8 0 8 Conv 1 1.60E-11 0.050000 0.400000 0.400000 9 0 9 Conv 1 5.64E-13 0.050000 0.450000 0.450000 10 0 10 Conv 1 6.26E-13 0.050000 0.500000 0.500000 11 0 11 Conv 1 6.43E-13 0.013630 0.513630 0.513630 11 0 12 1 1.560729 0.050000 0.513630 0.513630 12 0 12 Conv 2 0.133201 0.050000 0.563630 0.563630 12 0 13 1 1.693929 0.050000 0.563630 0.563630 13 0 13 Conv 2 0.144569 0.050000 0.613630 0.613630 13 0 14 1 1.705297 0.050000 0.613630 0.613630 14 0 14 Conv 2 0.145539 0.050000 0.663630 0.663630 14 0 15 1 1.706267 0.050000 0.663630 0.663630
- 7. 15 0 15 Conv 2 0.145622 0.050000 0.713630 0.713630 15 0 16 1 1.706350 0.050000 0.713630 0.713630 16 0 16 Conv 2 0.145629 0.050000 0.763630 0.763630 16 0 17 1 1.706357 0.050000 0.763630 0.763630 17 0 17 Conv 2 0.145629 0.050000 0.813630 0.813630 17 0 18 1 1.706358 0.050000 0.813630 0.813630 18 0 18 Conv 2 0.145629 0.050000 0.863630 0.863630 18 0 19 1 1.706358 0.050000 0.863630 0.863630 19 0 19 Conv 2 0.145629 0.050000 0.913630 0.913630 19 0 20 1 1.706358 0.050000 0.913630 0.913630 20 0 20 Conv 2 0.145629 0.050000 0.963630 0.963630 20 0 21 1 1.280907 0.036370 0.963630 0.963630 21 0 21 Conv 2 0.109319 0.036370 1.000000 1.000000 TIME FOR INITIALIZING ANALYSIS = 0.02 TIME FOR CONTROLLING ANALYSIS = 0.04 TIME FOR UPDATING LOADS AND STATE = 0.03 TIME FOR FORMING STIFFNESS MATRIX = 0.18 TIME FOR SOLVING STIFFNESS MATRIX = 0.76 TIME FOR CALCULATING DISPLACEMENTS = 0.17 TIME FOR DETERMINING EVENTS = 0.00 TIME FOR SAVING RESULTS = 0.16 ---------- TOTAL TIME FOR THIS ANALYSIS = 1.36 A N A L Y S I S C O M P L E T E 2016/07/21 19:37:56 Plot : Figure(4) Steel section in SAP2000