Sstan builds the global equation R = KG*r starting at the element level just like you did by hand

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Amberlynn Lyons
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1 CES - Stress Analysis Spring 999 Ex. #, the following -D truss is to be analyzed using Sstan (read the online stan intro first, and Ch- in Hoit) k k 0 ft E= 9000 ksi A= 0 in*in 0 ft Sstan builds the global equation R = KG*r starting at the element level just like you did by hand Let s pull out element and look at all the information Sstan needs to find its contribution to KG Coordinates of nodes let s call node the origin x=0 y=0 z=0 x=0* y=0* Boundaries DOF = R,R,F,F,F,F DOF = F,F,F,F,F,F R - released F - fixed for a -D truss, only (x,y) exist, so all other DOF are fixed i j i - near end node j - far end node for this element TRUSS, M= M= will describe the material properties A=0, E=9000 Loads there are no loads on either node of this member This information: where are the nodes what are their boundary conditions how are they attached by the member what are the material properties what are the loads Is needed for every element. Some of it will be repetitive (we only need to define the coordinates of a node once, no matter how many elements are touching it). Now let s look at the complete input file for the whole structure. of /9/99 Ex. #,

2 CES - Stress Analysis Spring 999 k k 0 ft E= 9000 ksi A= 0 in*in 0 ft NOTE: All the stuff in BLUE does not actually appear in the input file, its for me to comment on the contents The file is named stanex.inp example -D truss # The first line in the file must be a title,, : NODES, ONE ELEMENT TYPE (TRUSSES), ONE LOAD CASE COORDINATES Be careful to spell headings correctly X=0 Y=0 Z=0 node, converting to inches as we go X=0* y and z not defined, so previous line is used Y=0* X=0 y and z not defined, so previous line is used BOUNDARY,, DOF=R,R,F,F,F,F define nodes to in steps of DOF=F,R,F,F,F,F A -D truss is always fixed in z, Ixx, Iyy, Izz DOF=F,F,F,F,F,F make sure EVERY node is defined TRUSS here we define the truss properties and connectivity with nodes, : MEMBERS, SET OF PROPERTIES A=0 E=9000 material set, and its values C------DEFINE THE TRUSS CONNECTIVITY, M= truss # connects nodes and, uses material set, truss # connects nodes and, no material set defined, so use previous, truss # connects nodes and, no material set defined, so use previous,,, LOADS Be careful to spell headings correctly (including plural) L= F=,- node #, used in load case #, in x, - in y : forces in other d.o.f. are not defined, so they = 0 NOTE: the software will decide how to label the degrees of freedom. IT WILL REPORT RESULTS IN TERMS OF THE NODE NUMBERING YOU GAVE. of /9/99 Ex. #,

3 CES - Stress Analysis Spring 999 the RED portions in the output files are highlights I made to point them out the BLUE portions are my own additions OUTPUT FILE => automatically named stanex.out, and placed in same director as input file ******************************************************** SSTAN - Simple Structural Analysis Program Copyright 99 By Dr. Marc Hoit, University of Florida File Compression and Equation Parser By Dr. G Consolazio Nodal Renumbering using the PFM algorithm Static and Dynamic Version Version.0 November, 99 ******************************************************** Input File = "C:\Program Files\Sstan and Cal90\CES\stanex.inp" Analysis Run on at 0: THIS PART REPEATS THE INPUT INFORMATION (ALWAYS VERIFY THAT ITS CORRECT!!!) example truss # NUMBER OF JOINTS = NUMBER OF DIFFERENT ELEMENT TYPES = NUMBER OF LOAD CONDITIONS = NUMBER OF LOAD COMBINATIONS = 0 TOLERANCE FOR NONLINEAR SOLUTION = E-0 Truss has Non-Compression/Tension = NO Frames/Beams Include P-Delta Effects = NO Sequential Loads Active = NO NODE BOUNDARY CONDITION CODES NODAL POINT COORDINATES NUMBER X Y Z XX YY ZZ X Y Z R R F F F F F R F F F F F F F F F F R R F F F F EQUATION NUMBERS N X Y Z XX YY ZZ ***** TRUSS MEMBERS ***** NUMBER OF DIFFERENT MEMBER PROPERTIES = MEMBER PROPERTY NUMBER--= AXIAL AREA = 0.00 MODULUS OF ELASTICITY, E= 0.900E+0 *** ZC or ZT in T/C column means Zero compression or Tension *** MEMB CONNECT. CASE MAT END ECCENTRICITIES NUM. ACTV SET ***** I-END **** **** J-END ***** ZERO I J X-VALUE Y-VALUE Z-VALUE X-VALUE Y-VALUE Z-VALUE T/C of /9/99 Ex. #,

4 CES - Stress Analysis Spring THE NODE NUMBERING USED PRODUCED A HALF BANDWIDTH OF TOTAL STORAGE REQUIRED = TOTAL STORAGE AVAILABLE = 0000 *** CONCENTRATED NODAL LOADS *** NODE LOAD X Y Z XX YY ZZ 0.0E+0-0.0E E E E E+00 SOLUTION CONVERGED IN ITERATION(S) THIS PART PROVIDES THE OUTPUT DISPLACEMENTS, INTERNAL FORCES, AND REACTIONS *** PRINT OF FINAL DISPLACEMENTS *** DISPLACEMENTS FOR LOAD CONDITION NODE X Y Z XX YY ZZ 0.9E-0-0.0E E E E E E E E E E E E E E E E E E-0-0.E E E E E+00 Do these displacement results make sense w.r.t. boundary cond. and forces? CHECK IT OUT FORCE"S TRUSS MEMBERS ASTERISK (*C or *T) MEANS COMPRESSION OR TENSION SET TO ZERO FOR THIS MEMBER ASTERISK (*SQ) MEANS SEQUENCED MEMBER AND NOT ACTIVE MEMBER LOAD IEND JEND AXIAL AXIAL # # # # FORCES STRESS REACTIONS FOR LOAD CONDITION NODE X Y Z MX MY MZ E E E E E E E E E E E E E E E E E E E E E E E E+00 UNITS NOTE: You have to be consistent with units yourself, and figure out final units yourself. Here we gave material properties in inches^ and ksi, node locations in inches, loads in kips, so final units are: displacement - inches. Internal forces and reactions - kips If E is in ksi, and loads are in kips, the 000 factor is built in. We converted the nodal locations to inches in the input file by using feet*. of /9/99 Ex. #,

5 CES - Stress Analysis Spring 999 Interpretation of results We can use the output file to create F.B.D of each member and each joint. the figure has reactions on it. k k k k k 0 ft E= 9000 ksi A= 0 in*in 0 ft -.99 (compression). (tension) -.99 (compression) -. (compression) 0.0 (tension).0 (tension) Now the joints...hey wait, you do it... of /9/99 Ex. #,

k 21 k 22 k 23 k 24 k 31 k 32 k 33 k 34 k 41 k 42 k 43 k 44

k 21 k 22 k 23 k 24 k 31 k 32 k 33 k 34 k 41 k 42 k 43 k 44 CE 6 ab Beam Analysis by the Direct Stiffness Method Beam Element Stiffness Matrix in ocal Coordinates Consider an inclined bending member of moment of inertia I and modulus of elasticity E subjected shear