SAP155

SAP155 is a structural analysis program designed to supplement structural analysis courses (e.g., CE 155) offered at the UP Institute of Civil Engineering. Unlike conventional commercial software, this application is designed so students gain confidence in performing matrix structural analysis and gain better understanding of the direct stiffness method. It provides utility to view quantities such as, element rotation matrices or stiffness matrices in local and global coordinates, structure’s global stiffness matrix, or equivalent nodal forces of element loads, etc. This provides opportunities for researchers and structural engineers to solve problems that are otherwise difficult to solve using conventional software.

Key Features:

o Open-source, cross-platform* console application

o User-readable formatted input and output files

* Developed using Visual Studio 2010 in Microsoft

WindowsTM 10 and using Xcode in MacOS-X + Currently, after post-processing

o Utility to view quantities such as stiffness matrices, rotation matrices, used in computations

o Visualization of displacements+ o Loads industry-standard sections

(AISC Shapes Database v15.0)

matrix structural analysis for everyone

Eric Augustus J. Tingatinga, Ph.D. Professor, Institute of Civil Engineering

University of the Philippines Diliman eating@up.edu.ph, +63917-2516374

SAP155

The most important single aspect of software development is to be clear about what you are trying to build.

- Bjarne Stroustrup

SAP155 matrix structural analysis for everyone.

% ./SAP155 <-i filename> <-o filename2> [-s <filename3>] [-g <filename4> [scale] [nPoints]]

What’s included? The folder shared contains the executable files (SAP155.exe for Windows and SAP155 for MacOS), documentation files, and utility files. Please see Figure 1.

Figure 1. SAP155v1.1 Distributable Package

How to Use:

The pre-compiled console application is launched using a Command Prompt in WindowsTM or a Terminal in Linux/MacOS systems (for Windows, it is suggested to use the shortcut SAP155-Launcher.lnk). When loaded at the same directory of the executable file, the following command must be issued:

where

filename1 - is the name of the input text file containing information about the structure, loads, etc. See file format in Figure 1.

filename2 - is the output file name containing results of analysis, e.g., computed displacements, reactions, and member forces. It also contains relevant quantities such as assigned global degrees of freedoms, transformation matrices, etc. Please see format in Figure 2.

filename3 - is the name of the output file that may be used to check if inputs are correct. If filename1 is valid, filename3 is a duplicate copy of the file.

filename4 - is the name of the output file that contains coordinates of points along the members of the structure that may be used to create scatter plots of the unloaded and loaded structure. The file in CSV format may be loaded in Excel then the contents copy-and-pasted in the Plot sheet in the file _SAP155-Plot.xls.

scale - Scale factor used to exaggerate displacements on the structure. Default is 50. nPoints - Number of points that will be used to draw the elements. Defaults is 10.

[ ] optional parameters that starts with -x flags. When specified, items in < > must be given.

WindowsTM executable file Shortcut to formatted command

line tool (cmd.exe)

MacOS X executable This document

Sample data files Utility file: Scatter plot Input file template

AISC Shapes database

SAP155 matrix structural analysis for everyone.

INPUT FILE FORMAT Structure information must be inputted in a formatted text-file. The format of the file is shown below:

Figure 2. SAP155v1.1 Input File Format

# This is a line comment. Anything after this ‘#’ are ignored. Comments cannot be placed within blocks. # UNITS Block [optional] # Force units are: "kN", "N", "lbf", "kips"; Displacement units are: "mm", "m", "in", "ft" # If unspecified, units default to kN and mm. [UNITS <Force units: string> <Length units: string>] # MATERIALS Table # Properties: E = Young’s Modulus, v = Poisson’s ratio, a = Coefficient of Thermal Expansion MATERIALS <ID:string> <E=value:real> [v=value:real] [a=value:real] END-TABLE # SECTIONS Table [Optional à when using standard AISC section] [SECTIONS <ID:string> [A=value:real] [J=value:real] [Iy=value:real] [Iz=value:real] END-TABLE] # NODES Table NODES <ID:string> <X=value:real> <Y=value:real> [Z=value:real] END-TABLE # ELEMENTS Table # Element types: "Truss2D", "Beam", "Truss3D", "Frame2D", "Grid", "Frame3D" E <ID:string> <Node1 ID > <Node2 ID> <Type> <Material-ID> <Section-ID> x # LOADS Table # Type-parameters: # "Nodal" load: <Node ID:string> <PX=value> <PY=value> … <MZ=value> # "Distributed" load: <Elem-ID:string> <DOF:string> <x1=value > <w1=value > <pos2=value > w2=value > # "Concentrated" load: <Elem-ID:string> [x=value] [Px=value] [Py=value] … [Mz=value] # where: DOF = direction in local coordinates (“Dx”, “Dy”, “Dz”, “Rx”, “Ry”, “Rz”) LOADS <ID:string> <Type:string> <Type-parameters> END-TABLE # RESTRAINTS Block #. Types: "Fixed", "Pinned", "DX", "DY", "DZ". "RX", "RY", "RZ" RESTRAINTS <Node-ID: string> <Type:string> … <Type:string> END-TABLE # RELEASES Block # DOF: DOF in global coordinates "DX", "DY", "DZ", "RX", "RY", "RZ". # Force: in global coordinates RELEASES <Element-ID:string> <Node-ID:string> <DOF:String> <Force:real> END-TABLE # SUPPORT MOVEMENT Block # DOF: "DX", "DY", "DZ", "RX", "RY", "RZ". Displacement: in global coordinates DISPLACEMENTS <Node-ID: string> [DX=value:real] [DY=value:real] … [RZ=value:real] END-TABLE

END-OF-FILE

SAP155 matrix structural analysis for everyone.

OUTPUT FILE FORMAT The program launched in Command prompt or Terminal will create an output file (with filename indicated after the -o flag) that will print analysis results (i.e., displacements, reactions, and member forces) along with information and quantities used in the computations. The first section lists the assigned global degrees of freedom per node and the number of unrestrained and support degrees of freedom. The next two sections are for the computed displacements and reactions at these DOFs. Information about each member follows: listing the assigned DOFs, local and global stiffness matrices, element forces, and the transformation matrix used in the computations. Computed parameters associated with the structure, e.g., Kff and Ksf matrices, are listed. The detailed format is shown below:

Figure 3. SAP155v1.1 Output File Format

GLOBAL DEGREES OF FREEDOM Node <id>: <DOF-1> <DOF-2> <DOF-3> à Assigned global DOFs of the nodes : Total number of GDOFs: <NDOF> Unrestrained [DOFs]: <ndf> Support DOFs: <nds> DISPLACEMENTS U<DOF> <Displacement> <units>

: REACTIONS P<DOF> <Reaction> <units> : MEMBERS ELEMENT <Element-ID> ------------ Nodes: (<Node1-ID>, <Node2-ID>) Length: <Length> <units> DOFs: <DOFS: Vector6D> Local Stiffness Matrix k(<Element-ID>) = <E-value> x [Matrix k] Transformation Matrix = [Matrix T] Global Stiffness Matrix K(<Element-ID>) = <E-value> x [Matrix K] à Labeled with assigned global DOFs ELEMENT <Next-Element-ID> ------------ : STRUCTURE PROPERTIES Kff [Matrix(ndf,ndf)] à with rows and columns labeled with assigned DOFs Ksf [Matrix (nds, ndf)] Kfs [Matrix (ndf, nds)] Kss [Matrix (nds, nds)] Pf <Vector(ndf)> à Nodal force vector, if non-zero PfE <Vector(ndf)> à Equivalent nodal force vector PfE of loads, if non-zero PsE <Vector(nds)> à Equiv. nodal force vector PsE at support DOFs, if non-zero

SAP155 matrix structural analysis for everyone.

POST-PROCESSING The current version of the application provides a way to visualize the deformed structure using the -g flag. The program generates a CSV file (with filename indicated after the -g flag) containing the coordinates of the nodes and the coordinates of number of points (indicated by variable nPoints) along the members. The coordinates of points in the deformed structure are computed using the scale provided to be able to visualize the actual displacements that are very small when compared with the dimensions of the structure. The output file then can be copied and then pasted into the sheet “Data” of the spreadsheet SAP155-Plot.xls provided. The “Plot” sheet then displays the unloaded and deformed structure as shown below.

EXAMPLE For example, please see sample data file for the structure in Example 5.7 of the Book by McGuire below:

Figure 4. SAP155v1.1 Output File Format

SAP155 matrix structural analysis for everyone.

Solution To solve this problem, the following steps must be carried out:

1. Create a data file using Notepad or TextEdit applications then save the file (in this example, named as E5.7Frame2D.txt) in the same directory as the executable file SAP155.

2. Launch a Terminal or Command Prompt then change directory to the same location. 3. Executable the program by typing the following command

% ./SAP155 -i E5.7Frame2D.txt -o E5.7Results.txt -g E5.7.csv 100 to produce two output files: E5.7Results.txt and E5.7.csv. The former contains analysis results while the latter is for visualization of displaced structure.

4. Review the analysis results then generate the scatter plots for the unloaded and displaced structure

The following are the (a) input file, (b) Terminal window, (c) analysis results file and the corresponding (d) scatter plot.

(a) (b)

(c) (d)