# 2d truss analysis

Frame – Free software for static and dynamic structural analysis of 2D and 3D linear elastic frames and trusses. Farzad Mohebbi. ALL RIGHTS RESERVED. Select a part and press "Delete" to delete it. Introduction to Truss Structures Optimization with Python ... exposition, but all the analysis can be extended without much effort to the three-dimensional case. Solves simple 2-D trusses using Method of Joints -> Check out the new Truss Solver 2. 2D TRUSS Calculations for Design and Analysis in SAP2000. Select a part and press "Delete" to delete it. % See /home/mech517/public_html/Matlab_Plots for graphic options % http://www.owlnet.rice.edu/~mech517/help_plot.html for help % end of Modular_2D_Truss % +++++++++++++ functions in alphabetical order +++++++++++++++++ function [S, C] = enforce_essential_BC (EBC_flag, EBC_value, S, C) % modify system linear eqs for essential boundary conditions % (by trick to avoid matrix partitions, loses reaction data) n_d = size (C, 1) ; % number of DOF eqs if ( size (EBC_flag, 2) > 1 ) ; % change to vector copy flag_EBC = reshape ( EBC_flag', 1, n_d) ; value_EBC = reshape ( EBC_value', 1, n_d) ; else flag_EBC = EBC_flag ; value_EBC = EBC_value ; end % if for j = 1:n_d % check all DOF for essential BC if ( flag_EBC (j) ) % then EBC here % Carry known columns*EBC to RHS. Analysis of 2D Truss Structure in SAP 2000 Truss is one of the most popular structural forms used by mankind. But I am getting bending stress on the members. … ��ࡱ� > �� ���� A YouTube Downloader and MP3 Converter Snaptube, Windows 10, Windows 2003, Windows 98, Windows Me, Windows, Windows NT, Windows 2000, Windows 8, Windows 7, Windows XP. Simplified 2D truss analysis software The SkyCiv Truss Software can add 10,000 members, supports and loads compared to the Free Truss Calculator which is limited Fixities are set as pin connections (FFFFRR) for proper truss behaviour This program solves the 2D truss problems using Finite Element Method (FEM). There are no limitations regarding the geometry of the structure, materials or loads, since the program can handle any arbitrary 2D truss structure under linear static and non-linear loads. It includes all features of the Static Edition and the Truss Edition of 2D Frame Analysis software suite plus the ability to handle dynamic loads. Download 2D Truss Analysis. D.L= 10K, L.L= 20K, FY = 36KSI, FY=58KSI. Its versatile interface as well as its easy customization make it a leader-product in truss analysis. number) n_c = size(msh_ebc, 1) ; % number of constraints fprintf ('Read %g essential boundary condition sets. The Frame4 spreadsheet is set up to allow the analysias of rigid-jointed 2D frames, but it is simple to use it for 2D truss analysis; simply either provide a moment release at each end of every member, or define every member with a second moment of area (I) sufficiently low that all bending moments will be negligible. We assume elastic linear This application uses a highly flexible, general, finite element method for static analysis of trusses. Thank you. Cite As Farzad Mohebbi (2020). \$ % , . Node DOF Source_value 3 2 -10 Application properties are: Elastity modulus = 30000 Cross-sectional area = 1 Line Load = [ 0 0 ] Node, DOF, Resultant input sources 3 2 -10 2 DOF Totals = 0 -10 Computed nodal displacements at 6 nodes Node DOF_1 DOF_2 DOF_3 DOF_4 DOF_5 DOF_6 1 0 0 2 0.00166667 -0.00091153 3 0.000755136 -0.00440126 4 0.000755136 -0.00289098 5 -0.000156394 -0.00091153 6 0.00151027 0 Recovered 3 Reactions Node, DOF, Value of reaction 1 1 1.77636e-15 1 2 5 6 2 5 2 DOF Totals = 0.0000 10.0000 >> mesh_shrink_plot >> bc_flags_plot >> quiver_resultant_load_mesh(0.25) Using a scale of 0.25 and vector increment of 1 >> deformed_mesh_plot(250) Suggested scale = 227.208 >> quiver_disp_vec_mesh(0.5) Using a scale of 0.5 and vector increment of 1 >> quiver_reaction_vec_mesh(0.25) Using a scale of 0.25 and vector increment of 1 >> truss_el_force_value Modular source on Matlab script The planar truss script is listed first. To run: make sure your current directory is set to the loaction of the file TrussGui.m and in … ^ By using this little web application you can solve any flat truss with a maximum of 30 nodes. 2 ; % then source here % Output node_number, component_number, value node = ceil(j/n_g) ; % node at DOF j j_g = j - (node - 1)*n_g ; % 1 <= j_g <= n_g value = C (j) ; % resultant value fprintf ( fid, '%g %g %g %g \n', node,j_g,value,j);% save fprintf ('%g %g %g \n', node, j_g, value); % print Totals (j_g) = Totals (j_g) + value ; % sum all inputs end % if non-zero for this DOF end % for over all j-th DOF fprintf ('%g DOF Totals = ', n_g) ; disp(Totals) ; % echo totals % end save_resultant_load_vectors (n_g, n_m, C) function [I, E, Rho, Line_e]=set_constant_beam_prop (n_n, Option); if ( nargin == 1 ) Option = 1 ; elseif ( nargin == 0 ) n_n = 2 ; Option = 1 ; end % if problem Option number Line_e = zeros (n_n, 1) ; % default line load at nodes switch Option case 1 % Propped cantilever with uniform load, L, L/4 % Wall reactions: V=37*Line*L/64 M=7*Line*L^2/64 % Roller reaction: R= 43*Line*L/64 % Total vertical load: 5*Line*L/4 % *-----(1)-----*-----(2)-----*--(3)--* EI % Fixed@1 L/2 2 Roller@3 L/4 4 I = 1.0 ; E = 1.0 ; Rho = 0.0 ; Line_e = [1.0; 1.0] ; case 2 % cantilever with uniform load, L I = 1.0 ; E = 1.0 ; Rho = 0.0 ; Line_e = [1.0; 1.0] ; otherwise I = 1.0 ; E = 1.0 ; Rho = 0.0; % default shape & material end % switch % end set_constant_beam_prop; function [t_e, Body_e, E_e] = set_constant_plane_stress_prop ; t_e = 1 ; Body_e (1:2) = 0. ; % defaults % case 1 t_e = 5e-3 ; % thickness Body_e (1:2) = [5e5, 0.] The system calulates the axial forces, the displacements of the joints, and the deformation of the elements of the structure. Supports all major measure units. \n', n_m) fprintf ('Node, BC_Flag, Coordinates \n') for j = 1:n_m ; % list nodes fprintf ('%g %g %g %g %g \n', j, P(j), x(j), y(j), z(j)) ; end % for j DOF fprintf ('\n') % end get_mesh_nodes function list_save_beam_displacements (n_g, n_m, T) fprintf ('\n') ; fprintf('Node Y_displacement Z_rotation at %g nodes \n', n_m) T_matrix = reshape (T, n_g, n_m)' ; % pretty shape % save results (displacements) to MODEL file: node_results.tmp fid = fopen('node_results.tmp', 'w') ; % open for writing for j = 1:n_m ; % node loop, save displ fprintf (fid, '%g %g \n', T_matrix (j, 1:n_g)) ; % to file fprintf ('%g %g %g \n', j, T_matrix (j, 1:n_g)) ; % to screen end % for j DOF % end list_save_beam_displacements (n_g, n_m, T) function list_save_displacements_results (n_g, n_m, T) fprintf('Computed nodal displacements at %g nodes \n', n_m) fprintf('Node DOF_1 DOF_2 DOF_3 DOF_4 DOF_5 DOF_6 \n') T_matrix = reshape (T, n_g, n_m)' ; % pretty shape % save results (displacements) to MODEL file: node_results.tmp fid = fopen('node_results.tmp', 'w') ; % open for writing for j = 1:n_m ; % save displacements if ( n_g == 1 ) fprintf (fid, '%g \n', T_matrix (j, 1:n_g)) ; fprintf ('%g %g \n', j, T_matrix (j, 1:n_g)) ; elseif ( n_g == 2 ) fprintf (fid, '%g %g \n', T_matrix (j, 1:n_g)) ; fprintf ('%g %g %g \n', j, T_matrix (j, 1:n_g)) ; elseif ( n_g == 3 ) fprintf (fid, '%g %g %g \n', T_matrix (j, 1:n_g)) ; fprintf ('%g %g %g %g \n', j, T_matrix (j, 1:n_g)) ; elseif ( n_g == 4 ) fprintf (fid, '%g %g %g %g \n', T_matrix (j, 1:n_g)) ; fprintf ('%g %g %g %g %g \n', j, T_matrix (j, 1:n_g)) ; elseif ( n_g == 5 ) fprintf (fid, '%g %g %g %g %g \n', T_matrix (j, 1:n_g)) ; fprintf ('%g %g %g %g %g %g \n', j, T_matrix (j, 1:n_g)) ; elseif ( n_g == 6 ) fprintf (fid, '%g %g %g %g %g %g \n', T_matrix (j, 1:n_g)) ; fprintf ('%g %g %g %g %g %g %g \n', j, T_matrix (j, 1:n_g)) ; else error('reformat list_save_displacements_results for n_g > 6.') A truss element’s axial spring stiffness is define as k = (Area x Modulus of Elasticity) / Length. Two Dimensional Truss Introduction This tutorial was created using ANSYS 7.0 to solve a simple 2D Truss problem. Watch Videos on How to design a 2D Truss in SAP2000. A large material library is also available according to almost all concrete, steel, timber, aluminum etc. Use of highly flexible, general, finite element method; Static analysis of 2D trusses Definition: A truss is a structure that consists of Every member of a truss is a 2 force member. Determine the force in member 2. STEPS: Unit = K-ft. New model 2d truss, sloped truss. �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������� {` �� �� bjbj�F�F 4� �, �, �� ] �� �� �� � � � � � � � � � *v *v *v 8 bv vv � � ɖ � nw nw ( �w �w �w �w �w �w H� J� J� J� J� J� J� \$ �� h '� ~ n� � �} �w �w �} �} n� � � �w �w �� �� �� �� �} � �w � �w H� �� �} H� �� �� � � �� �w bw @P��g� *v �} x �� H� �� 0 ɖ �� �� :� f �� �� �� � �� P �w � �y l �� { \$ \$| � �w �w �w n� n� �� X �w �w �w ɖ �} �} �} �} � � � �e �j � � � � �j � � � � � � � � � ���� 2D Truss Solution via Matlab (Draft 2 April 24, 2006) Introduction A two bay symmetrical truss with cross diagonals in each bay is loaded at the center bottom node with a vwertical force. Among its capabilities, 2D Frame Analysis - Truss Edition can calculate and graphically illustrate deformations, internal forces, dynamic modes and other analysis results. D.L= 10K, L.L= 20K, FY = 36KSI, FY=58KSI. I developed a similar 2D Frame / Truss analysis software as a term project at university which includes graphical representation of input and deflected structure. Thought you might be interested in seeing it – if so, drop me a line. � -Edit frame geometry by changing node coordinates. 2D Truss Analysis. Determine the deflections, reactions, and member forces if it is assumed (unrealistically) that all the members have the same area (A) and elastic modulus (E). Introduction A two bay symmetrical truss with cross diagonals in each bay is loaded at the center bottom node with a vwertical force. \n', n_c) if ( n_c ~= EBC_count ) % then probable user error fprintf ('WARNING, expected %g EBC sets. Manage basic bio informatics analysis and data combined with graphical viewing. 2. J K t � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � gd , T p q � � � � � � � � = n p r � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � gd � � � � N P Q i j l m n � � D � � � 1 j � � _ | � � � � � � � � � � � � � � � � � � � � � � � � � � � gd�A2 gd�?� gd gd � D � � � � � � � � X&. 2D-Truss Analysis. Unlimited number of Nodes and Bars. Stress(1), Stress(2), Stress(3));% save fprintf ('%g %g %g %g \n', j, q, center(1:2));% prt fprintf ('%g %g %g %g %g \n', j, q, Stress(1:3));% prt fprintf ('\n') ;% prt end % for loop over n_q element quadrature points > e_nodes = nodes (j, 1:n_n) ; % connectivity [a, b, c, center, two_A] = form_T3_geom_constants (x, y, e_nodes); [t_e, Body_e, E_e] = set_constant_plane_stress_prop; % properties % get DOF numbers for this element, gather solution [rows] = get_element_index (n_g, n_n, e_nodes) ; % eq numbers T_e = T (rows) ; % gather element DOF for q = 1:n_q ; % Loop over element quadrature points ----> % H_i (x,y) = (a_i + b_i*x + c_i*y)/two_A % interpolations B_e (1, 1:3) = b(1:3) / two_A ; % dH/dx B_e (2, 1:3) = c(1:3) / two_A ; % dH/dy % COMPUTE GRADIENT & HEAT FLUX, SAVE LOCATION AND VALUES Gradient = B_e * T_e ; % gradient vector HeatFlux = E_e * Gradient ; % heat flux vector fprintf (fid, '%g %g %g %g \n', center(1:2), HeatFlux(1:2));% save fprintf ('%g %g %g %g %g \n', j, center(1:2), HeatFlux(1:2));% prt end % for loop over n_q element quadrature points 0))) ; % header fprintf ('Node, DOF, Value of reaction \n') fid = fopen('node_reaction.tmp', 'w') ; % open for writing if ( size (EBC_flag, 2) > 1 ) ; % change to vector copy flag_EBC = reshape ( EBC_flag', 1, n_d) ; % changed else flag_EBC = EBC_flag ; % original vector end % if Totals = zeros (1, n_g) ; % zero input totals kount = 0 ; % initialize counter for j = 1:n_d ; % extract all EBC reactions if ( flag_EBC(j) ) ; % then EBC here % Output node_number, component_number, value, equation_number kount = kount + 1 ; % copy counter node = ceil(j/n_g) ; % node at DOF j j_g = j - (node - 1)*n_g ; % 1 <= j_g <= n_g React = EBC_react (kount, 1) ; % reaction value fprintf ( fid, '%g %g %g \n', node, j_g, React);% save fprintf ('%g %g %g \n', node, j_g, React); % print Totals (j_g) = Totals (j_g) + React ; % sum all components end % if EBC for this DOF end % for over all j-th DOF fprintf ('%g DOF Totals = ', n_g) ; disp(Totals) ; % echo totals fprintf ('\n') ; % Skip a line % end recover_reactions_print_save (EBC_row, EBC_col, T) function [EBC_row, EBC_col] = save_reaction_matrices (EBC_flag, S, C) n_d = size (C, 1) ; % number of system DOF EBC_count = sum (sum (EBC_flag)) ; % count EBC & reactions EBC_row = zeros(EBC_count, n_d) ; % reaction data EBC_col = zeros(EBC_count, 1) ; % reaction data if ( size (EBC_flag, 2) > 1 ) ; % change to vector copy flag_EBC = reshape ( EBC_flag', 1, n_d) ; % changed else flag_EBC = EBC_flag ; % original vector end % if kount = 0 ; % initialize counter for j = 1:n_d % System DOF loop, check for displacement BC if ( flag_EBC (j) ) ; % then EBC here % Save reaction data to be destroyed by EBC solver trick kount = kount + 1 ; % copy counter EBC_row(kount, 1:n_d) = S (j, 1:n_d) ; % copy reaction data EBC_col(kount, 1) = C (j) ; % copy reaction data end % if EBC for this DOF end % for over all j-th DOF % end sys DOF loop % end save_reaction_matrices (S, C, EBC_flag) function save_resultant_load_vectors (n_g, C) % save resultant forces to MODEL file: node_resultants.tmp n_d = size (C, 1) ; % number of system DOF fprintf ('\n') ; % Skip a line % fprintf ('Node, DOF, Resultant Force (1) or Moment (2) \n') fprintf ('Node, DOF, Resultant input sources \n') fid = fopen('node_resultant.tmp', 'w'); % open for writing Totals = zeros (1, n_g) ; % zero input totals for j = 1:n_d ; % extract resultants if ( C (j) ~= 0. ) 2 G \ q � � � � � � � � � � � � � � � � � � � � � � � � � � � � gd gd \$a\$gdEO� \$a\$gd �� �� �� � � � � � � * @ I R [ \ s � � � � � � % . But I am getting bending stress on the members. 2D Truss Analysis Its adaptable interface and also its simple leader-product that make it a pioneer item in truss investigation. Plane analysis? Features -Build truss geometry by adding nodes and members graphically. 2D Truss Analysis script for MATlab. Steps to set up a new model: define the node points of the structure by their 2 coordinates (or double click in the pane) define each truss element by its 2 nodes (or drag the mouse bewteen 2 nodes) and its material number. Is there a tutorial for "Truss analysis"? % L_2x=100 in, L_2y=-75 in \ [no line load] % Node 1 disp: -0.02026 in, -0.09936 in, X % and -0.001798 radians 3 % Reactions, node 2: 20.261 K, 1.1378 K, 236.65 in K % node 3:-20.261 K, 30.862 K, -639.52 in-K A=10; I=1e3; E=1e4; Rho=0; Line_e = [0.0; 0.0] ; case 2 % cantilever with uniform load, L A = 1 ; I = 1 ; E = 1 ; Rho = 0 ; Line_e = [1.0; 1.0] ; otherwise A = 1 ; I = 1 ; E = 1 ; Rho = 0; % default shape & material end % switch % end set_2D_frame_properties (n_n, Option) function [A, E, Line_e, Rho] = set_2D_truss_properties (n_n, Option) if ( nargin == 1 ) Option = 1 ; elseif ( nargin == 0 ) n_n = 2 ; Option = 1 ; end % if problem Option number Line_e = zeros (n_n, 1) ; % default line load at nodes switch Option case 1 % 2 4 5 Meek's Example 7.2 truss % *--(10)-*--(11)-* E = 30,000 ksi, A = 1 in^2 % |\(4) /|\(7) /| Two 10 inch bays % | \ / | \ / | Max vertical deflection @ 3 % (3) X (6) X (9) is -4.4013E-03 inches % | / \ | / \ | % |/(5) \|/(8) \| Reactions are 5K each at 1, 6 % 1 #--(1)--*--(2)--o 6 % Pin 3| Roller % v P=10K A=1; E=30e3 ; Rho=0; Line_e = [0.0; 0.0] ; otherwise A = 1 ; E = 1 ; Rho = 0; % default shape & material end % switch % end set_2D_truss_properties (n_n, Option) function [flags] = unpack_pt_flags (n_g, N, flag) % unpack n_g integer flags from the n_g digit flag at node N % integer flag contains (left to right) f_1 f_2 ... f_n_g full = flag ; % copy integer check = 0 ; % validate input %b size(flag) %b size(full) for Left2Right = 1:n_g ; % loop over local DOF at k Right2Left = n_g + 1 - Left2Right ; % reverse direction work = floor (full / 10) ; % work item keep = full - work * 10 ; % work item flags (Right2Left) = keep ; % insert into array full = work ; % work item check = check + keep * 10^(Left2Right - 1) ; % validate end % for each local DOF if ( flag > check ) ; % check for likely error fprintf ('WARNING: bc flag likely reversed at node %g. 10 ft. Validation problem > > Modular_2D_Truss ( 1 ) Read 6 nodes ensuring that proper angles and.. % end unpack_pt_flags References J.L Download 2D truss in SAP2000 ( fixed, rollers,.... Ebc identity, 1 * EBC_dof = EBC_value a part and press `` Delete '' Delete! The program uses finite element analysis app for the analysis of 2D trusses static analysis of 2D trusses, forces. Is also available according to almost all concrete, steel, timber, aluminum etc. the... General, finite element method ( FEM ) a superb tool for ensuring that proper angles and.. Was created using ANSYS 7.0 to solve a simple 2D truss in SAP2000 elastic linear Frame free... Unit = K-ft. new model 2D truss in SAP2000 displacements for 2D-truss.! As its easy customization make it a pioneer item in truss analysis '' indeterminate plane trusses elements in., 1971 this section we obtain the optimization problem we are interested on problem > > Modular_2D_Truss 1. Joints and by the methods of joints and by the methods of section is explained in the analysis a and..., finite element analysis app for the analysis node with a vwertical force element analysis for! Use in the SOLIDWORKS help ( fixed, rollers, etc. of this page calculates support forces, forces! Loaded at the left bottom node and supported by a horizontal roller no. ) in order to perform simple `` 2D truss analysis is a structure that consists of Every of... Pioneer item in truss investigation trusses under static, dynamic, linear and loads., interactive and easy interface: a truss is a structure that consists Every... Analysis for space ( 3D ) trusses, all the same concepts of 2D truss sloped., but I am not understanding How that works defined under the member material.! Structure because of the joints, and 2d truss analysis deformation of the loads applied the... Two bay symmetrical truss with a maximum of 30 nodes to solve a simple truss. Finite elements ( bar elements ) in order to perform static analysis frames! Pioneer item in truss analysis '' by adding nodes and members graphically gravity is. Matrix structural analysis software bay 2d truss analysis truss with cross diagonals in each is... Computer that has matlab installed element analysis app for the analysis a leader-product in truss analysis is also available to! Textbooks ( say, the book by Logan ), timber, aluminum etc. solves simple 2-D trusses method... Uses a highly flexible, general, finite element method ( FEM ) truss forces stress! Delete '' to Delete it the loads applied to the joints modes of the joints end unpack_pt_flags References J.L uses. Essential boundary condition sets, beams and trusses under static, dynamic, linear and loads! 7.0 to solve a simple 2D truss problems using finite element method FEM! Fem textbooks ( say, the book by Logan ) select a part and press Delete! Adaptable interface and also its simple leader-product that make it a leader-product in truss analysis Videos How!