Truss element opensees The command to create an element recorder is: element truss 1 1 4 10. 14. For backward compatability the command 'element corotTruss See full list on opensees. 0 1 In the first line, the “wipe” command deletes all existing FE models in OpenSees, including nodes, elements, materials, boundary conditions Problem Statement for TRUSS1, Analyze the truss as shown in fig below. e. out -time -node 4 -dof 1 2 disp recorder Node -file output/reaction_1. Originally developed for the truss element, these models have proliferated thanks to fiber section models. ops. Example: Then following code can be used to obtain the current state related to the forces and the material stress in element 1 , a Truss element. txt - time-ele 1 force recorder Element - file ele2. OpenSees Path. element forceBeamColumn 1 1 2 1 Lobatto 1 3 runImportanceSamplingAnalysis truss programme OpenSees, and then the numerical model has some advantages such as a few DOF, simple and intuitive, so OpenSees can be used in engineering design and analysis of prestressed concrete structure. Description $eleType. It is a resource intended for new users of OpenSees. list integer. Beam-Column Elements. This consistently gives me a singularity problem when I run the model on OpenSees. opensees as ops import opstool as opst import matplotlib. The first example is a simple truss structure. 0 The above figure shows the layout of the truss and zero-stiffness gauge elements that make up the Truss2 Element object. uniaxialMaterial(Elastic,1,200000)#弹性材料 Element:单元。Opensees单元命令有好多，经常用到的有零长度单元（zeroLength Element）、零长度截面单元（zeroLengthSection Element）、桁架单元（Truss Element）、弹性梁柱单元（Elastic Beam Column Element）、塑性铰单元（Elastic Beam Column Element）、Joint2D单元（Joint2D Element）等。 Finally, define the elements. Top. out -time -node 1 -dof 1 2 reaction Jun 1, 2022 · Then, two new self-centering materials for different design concepts of the SCED braces are developed in OpenSees. 0, 1) 33 element ("Truss", 3, 3 Basic Truss Example 4. The substructure model only includes the BRB modelled with truss element. A corotational formulation adopts a set of corotational axes which rotate with the element, thus taking into account an exact geometric transformation between local and global frames of reference. Introduction This example is of a linear-elastic three bar truss, as shown in the top figure, subject to static loads. Assigning Opensees Path Starting with the initial step to assign the opensees path same as in frame problem. Consider E = 2 x 1011 N/m2. Oct 6, 2024 · ops. Code. 5 9; # truss element with tag 1 added between nodes 2 and 4 with Aug 22, 2014 · The valid queries to a truss element when creating an ElementRecorder object are 'axialForce,' 'stiff,' deformations,' 'material matArg1 matArg2,' 'section sectArg1 sectArg2' There will be more queries after the interface for the methods involved have been developed further. cpp. Feb 11, 2024 · Now we can implement the element() method in a for loop that cycles through each member in the members array. 0, a Truss DID NOT INCLUDE Rayleigh damping, a TrussSection did. 0 element truss 1 1 4 10. out -ele 1 force Element forces in global coordinate system: recorder Element -file ele1sect1def. txt - time-ele 2 force constraints Plain numberer Plain system BandGeneral test EnergyIncr 1. As I know bar elements are under tension and compression but cable materials are just under Truss Elements Steel Uniaxial Materials OpenSees. Oct 1, 2010 · By this way, the beam-column element acts as a truss element and a flexural element in the IP and OOP directions, respectively. Details for the beam-truss model, material model Dec 5, 2021 · To build these models in OpenSees, use a stiff beam-column element with the corotational transformation for large displacements. 1 Example Analysis: •Static Nonlinear Analysis with LoadControl constraints Transformation numberer RCM system BandGeneral test NormDispIncr 1. Truss Element. Contribute to OpenSees/OpenSees development by creating an account on GitHub. (2013) are somewhat new in the OpenSees library, I am looking for anyone who has experience with the application of this element in 上記のページは、OpenSeesの最新版を例とした本にまとめました OpenSees ユーザーズガイド. The OpenSees interpreter enables finite element analysis commands to be 1 from openseespy. g Mar 6, 2022 · OpenSees evolves. The response recorded is element-dependent and also depends on the arguments which are passed to the setResponse() element method. The continuous multi-node truss element formulation enables simulation of a continuous cable/rope/wire with angular deviations while maintaining a uniform axial strain/force over its entire length. EXAMPLE: element elasticBeamColumn 1 2 4 5. Coupling OpenSees with Other Software Using the Client–Server Technique; Response Sensitivity Analysis Based on Direct Differentiation Method (DDM) Structural Analysis Based on Bond-Based Peridynamics (BPD) A Wheel–Rail Interaction Element for High-Speed Railway System; Reliability Analysis; Introduction to OpenSees Programming: Nov 26, 2013 · For the corresponding beam-truss model, shown below, the vertical and horizontal elements represent the respective reinforcing bars and their surrounding concrete in the respective direction. Beam-Column Elements 14 15 from openseespy. Statics of a 2d Portal Frame (ops_vis) # define elements element ("Truss", 1, 1, 4, A, 1 A finite element model of a simple truss is created, and static analysis is performed. Jan 14, 2010 · A software framework for simulation applications in earthquake engineering using finite element methods. The purpose of this example is to show that model generation in OpenSees can resemble typical finite element analysis programs with the definition of nodes, materials, elements, loads and constraints. 0e-6 200 algorithm Newton integrator LoadControl 1 analysis element truss 3 3 4 5. element tag. Schematic representation of distributed plasticity OpenSees model with element number labels and [node number] labels. integer. The truss element part behaves identically to the Truss Element object (or the CorotTruss Element object for the case of CorotTruss2). IS-A (Truss is an Element) 2. Nonlinear beam-truss elements Apr 7, 2021 · However, I am trying to run an analysis with Beam-Column elements in the deck, and the remaining elements as truss elements. OpenSees is not a code. UC Davis Soil Elements. 0. Elastic Beam Column Element converted from OpenSees wiki and documentation originally developed Dec 1, 2022 · DM-MVLEM cannot be modeled in OpenSees by connecting two modified MVLEMs horizontally, and modified MVLEMs should be modeled in detail using rigid beam–columns and truss elements. element type. KeyWord Prestressed concrete, Fiber model, Nonlinear finite element method, OpenSees 一、引言 This is a repository for the source codes associated with the implementation of the continuous multi-node truss element formulation in OpenSees. Nov 26, 2013 · For the corresponding truss model, shown in Figure 1(c), the vertical and horizontal trusses (Truss Elements) represent the respective reinforcing bars and their surrounding concrete in the respective direction. Uniaxial, or one-dimensional, material models are the work horses of OpenSees. A fully functional finite element analysis software, OpenSees, the Open System for Earthquake Engineering Simulation, was created in the late 1990s as the simulation platform for the Pacific Earthquake Engineering Research (PEER) Center. Now, let’s go ahead to perform a cyclic analysis using a displacement-controlled integrator. Copy path. 0 1 このelement(要素）コマンドで設定したMaterial番号は、uniaxialMaterial コマンドで設定した element Blog内初出のページは「 ここ 」 OpenSees内は、element 参照 Element の定義を行います。 element コマンドで使用する「elementの種類」は、さまざまなものが定義されており、どんどん増えているようです。 Dec 9, 2020 · OpenSees Cloud OpenSees AMI Uniaxial Multi-Tool. Corotational Truss Element; 4. The model has four nodes, labelled 1 through 4, and three elements, labelled 1 through 3. // with the truss element, we set matrix and vector pointers, // allocate space for t matrix Truss element Response¶ [1]: import openseespy. OpenSeesで紹介されているサンプル 一覧 ; OpenSeesで紹介されているサンプルで使用するtclスクリプトやデータの取得方法; PowerShell で OpenSeesコマンドを実行するには Truss Element; 4. When constructed with a UniaxialMaterial object, the truss element considers strain-rate effects, and is thus suitable for use as a damping element. pyplot as plt % matplotlib inline [2]: ops. The syntax for creating the truss element requires the following arguments: the element name, in this case always "Truss", the element tag, in this case 1 through 3, the nodes that the element is connected to, the cross-sectional area, in this case 10. Here, the members are connected at their ends via pin joints. Nov 10, 2012 · A leaning column with gravity loads is linked to the frame by truss elements to simulate P-Delta effects. ShallowFoundationGen. Corotational Truss Element. Type. Jun 20, 2023 · 01ZeroLength element我经常收到很多同学问我关于零长度单元和两节点单元，这篇推文我想讲一讲我个人的理解。 也欢迎大家补充。 零长度单元大概是因为被用的频率较高，而很多时候我们对其并不是很熟悉，所以会有一些不确定的问题。 Jan 1, 2018 · Developing new simulation models requires a flexible software framework where developers can build off of existing, interchangeable modules. The valid queries to an InertiaTruss element when creating an ElementRecorder object are 'force' and ‘relAccel’, which output the axial force or relative acceleration between two end-nodes in local coordinates (along the element) Specifically, the beam and columns are modelled with a truss element and two elasticBeam elements, respectively, in the integration model. 0 fix 1 1 1 Nov 13, 2021 · Just like a regular truss element, the InertiaTruss element, merged with PR #619, computes inertial force between two nodes with a linear basic force-acceleration relationship \(f_I=b\ddot{u}_b\), where b is the inertance and \(\ddot{u}_b\) is the relative acceleration along the element. 5 100. 1. The diagonal elements (Truss2 Elements with ConcretewBeta material) span between each node in the model. Argument. Most users will conduct a simulation with a scripting language that has been extended to incorporate the features of OpenSees. Examples Manual; The OpenSees Basic Examples Manual contains examples for new users. Nonlinear Truss Analysis¶. , end releases) OpenSees Source Code Repository. 0 Oct 10, 2013 · The Element recorder type records the response of a number of elements at every converged step. Jun 1, 2022 · Then, two new self-centering materials for different design concepts of the SCED braces are developed in OpenSees. Jul 3, 2023 · The valid queries to an elastic beam-column element when creating an ElementRecorder object are 'force'. n s Material, Element y, s OpenSees is a Software Framework element truss 2 2 4 5. edu 1 from openseespy. For each element, we’re specifying: The element type (Truss) Element id; Node number at node i; Node number at node j; Cross-sectional area (A, defined above) Material id (the id of the uniaxial material we just defined) When constructed with a UniaxialMaterial object, the truss element considers strain-rate effects, and is thus suitable for use as a damping element. 4. As new features are developed, such as material models, elements, solution methods, etc. EXAMPLE: element truss 1 2 4 5. OpenSees / SRC / element / truss / InertiaTruss. Use a mesh of corotational truss elements with elastic uniaxial material. Once the model has been created OpenSees provides methods to perform the analysis* of the model, that is the determination of the response of the model (nodal and elemental) to the applied loads given the constraints. Communication between the two models is endabled through the SubStructure elements in the OpenSees integration and substructure models. Height of the truss is 4m. Truss elements do not transfer any moment at the connections. In this figure, the vector used to define the local-coordinate system in OpenSees, “vecxz”, is (0 0 -1) corresponding to the global axes shown in Figure 1. 0 and an Iz of 1e6 which uses the geometric transformation object with a tag of 9 This primer examines a few typical examples. Although this post might be a stretch for an LBU (least bloggable unit), the blogging equivalent of an LPU, there are important factors to consider for structural models comprised of truss and frame elements. 0 1 uniaxialMaterial Elastic 1 3000. . Beam-Column Elements 这个分析类似于OpenSees官网上的小例子简化版，主要是熟悉一下OpenSees的求解过程。 分析模型如下图所示，是由两个铰支节点相连的简单静定结构,杆件截面积为10，弹性模量为200000，整体模… Like any finite element application ever written, OpenSees provides for the creation of nodes, elements, constraints and loads. Blame. It was developed at UC Berkeley. 2梁单元. Of course, you can use any uniaxial material you like. 5 9; # truss element with tag 1 added between nodes 2 and 4 with Jan 4, 2000 · Contribute to OpenSees/OpenSeesDocumentation development by creating an account on GitHub. 7. , the scripting language can be extended to include them. 0e5 1 element truss 2 0 1 500. out -ele 1 section 1 fiber 0. Truss Element; A Procedure to Render 2D or 3D OpenSees Model and Mode Shapes ” after defining all the nodes and elements. 0 1e6 9; # elastic element tag 1 between nodes 2 and 4 with area 5. 0 1 recorder Node -file output/disp_4. eleType . Fenves, Three comprehensive video tutorials are available below to get you familiar with OpenSees Navigator. The discretization of the cross section is shown in Figure 2a. Sep 17, 2019 · In this case STKO generates trussSection or corotTrussSection elements, that are the same as truss or corotTruss, but instead of using an area and an uniaxial, they use a fiber cross section. Mar 4, 2010 · The arguments are specific to the type of element being used and are the same as those that are used in Element Recorder. PEER Center - 325 Davis Hall, University of California, Berkeley, CA 94720-1792 - (510) 642-3437 - peer_center@berkeley. NonLinear Beam-Column Elements. Fig. The location of the outer vertical truss coincides with the position of the outer longitudinal reinforcements with the location of the 这里是OpenSees官方网站的第一个例题，根据例题来学习OpenSees。 参考教程《OpenSees实用教程》-古泉 注意：这里使用英制单位，1 feet = 12 inch 代码部分： # 单位： inch-pound-second # =====[系统… May 19, 2017 · Truss is a solid structure that consists of triangular elements. 0 14 element truss 1 1 4 10. gid\OpenSees c) Output Jul 1, 2022 · A special truss element formulation, termed Truss2 and allowing the definition of the additional pair of nodes for measuring the transverse strain at each step of an analysis, is available in OpenSees. I'd like to analyze a cabled truss structure with opensees which includes both bar and cable elements. 那么在opensees中怎么进行预应力筋参数的设置呢？ 在opensees中，我们采用 桁架（truss）单元+steel02材料 进行模拟预应力筋的力学行为。 （1）steel02材料 命令格式如下图所示： 材料定义属性如下图所示（ 预应力的施加采用初始应力的方法 ）： （2）桁架（truss）单元 The valid queries to an elastic beam-column element when creating an ElementRecorder object are ‘force’. Jun 8, 2018 · The following contain information about eleType? and the args required for each of the available element types: Zero-Length Elements zeroLength Element; zeroLengthND Element; zeroLengthSection Element; CoupledZeroLength Element; zeroLengthContact Element; zeroLengthContactNTS2D; zeroLengthInterface2D; zeroLengthImpact3D ; Truss Elements Truss Create a OpenSees element. element(Truss,1,1,2,100,1)#创建杆单元，连接节点1和2，截面积为100，材料. Scott, Gregory L. Feb 18, 2024 · Still, it's definitely a step up from a truss - and sufficiently common that having a quick way to perform the analysis with OpenSeesPy will actually be a real asset to you! So, in this build, we’re dealing with elements that can develop a resistance to transverse shear forces and bending moments, in addition to axial forces. 2 recorder Node - file node. stress Stress in a fiber at a specific location: Sectional deformation (axial strain and curvature): recorder Element -file ele1force. File metadata and controls. The valid queries to a truss element when creating an ElementRecorder object are 'axialForce,' 'stiff,' deformations,' 'material matArg1 matArg2,' 'section sectArg1 sectArg2' There will be Corotational Truss Element. wipe () Contribute to OpenSees/OpenSees development by creating an account on GitHub. A Procedure to Render 2D or 3D OpenSees Model and Mode Shapes; 14. Here, the members are Jan 14, 2010 · A software framework for simulation applications in earthquake engineering using finite element methods. Figure 2. TRUSS 1. 0 1 pattern Plain 1 “Linear” { load 4 100. element Truss [ element の番号 ] [ 片方の node 番号] [片方の node 番号] [ 断面積] [Material番号] element Truss 1 1 4 10. stress / Chapter17--Adding a corotational truss element in OpenSees / corotTruss2D. OpenSees does not apply stiffness proportional damping to zeroLength elements. 梁单元在OpenSees中用于模拟结构中的弯曲和剪切力。它适用于模拟桥梁、 梁和柱等结构部件。 代码示例 #创建一个梁单元. 5 9; # truss element with tag 1 added between nodes 2 and 4 with Elements Element 1 (Linear elastic truss element) Element 2 (Truss element with path-dependent material) Element 3 (Truss element with moderate displacements) Element 5 (Linear elastic frame element) Element 6 (Frame element with P-delta) Element 7 (Concentrated plasticity frame element: Elastic-perfectly-plastic, i. opensees import * 16 17 import numpy as np 18 import The RCB structure in the advanced power reactor 1400 (APR1400) nuclear power plant (NPP) is modeled using beam-truss elements in OpenSees, a finite element platform. Nodes 1, 2,and 3 are fixed and a loads of 100kip and -50kip are imposed at node 4. 0 -50. # Create truss elements - command: element truss trussID node1 node2 A matID. An idealized schematic of the model is presented in Figure 1. Sep 7, 2013 · The above figure shows the layout of the truss and zero-stiffness gauge elements that make up the Truss2 Element object. tcl. Visit Structural Analysis Is Simple on Substack. It contains very simple examples on how to perform analysis of truss, frame and continuum models. 0 for element 1 and 5. Brick Elements. pyplot as plt 5 6 32 element ("Truss", 2, 2, 4, 5. 3. So, it is possible that recent versions of OpenSees will give errors with these examples. Jan 1, 2018 · OpenSees, an open source finite element software framework, has been used broadly in the earthquake engineering community for simulating the seismic response of structural and geotechnical systems. Aug 22, 2014 · There was an inconsistency in the way damping was treated between element types before version 2. The truss is having three different sectional areas as shown in fig. By default they both DO NOT now include Rayleigh damping by default. Original Post - 09 Dec 2020 - Michael H. 3: Cold-Formed Steel Shear Wall Panel details and equivalent OpenSees finite element model Sep 19, 2021 · After posting on reasons that the solution to Ax=b fails, I realized I omitted an important case: truss nodes in a frame model. eleNodes (list ) Corotational Truss Element. The zero-stiffness gauge element is used to measure the strain in the direction of the gauge. UC San Diego Soil Elements recorder Element -file ele1sect1def. The only trick is you have to scramble the nodes up a little bit--if you try to analyze a perfectly straight cable, you'll get… Aug 22, 2014 · There was an inconsistency in the way damping was treated between element types before version 2. This corotational truss element is defined from workpoint-to-workpoint and has cross-sectional area of the BRB core and BRBMaterial_4 . The only thing I changed in my model was that I changed those selected elements May 18, 2024 · The boundary members form a mechanism and the lateral stiffness and strength are derived directly from the zeroLength element. 2. Moreover, one code-improved truss element is developed for providing a more direct way to determine the required model parameters according to the actual force-displacement relationship. opensees import * 2 3 import numpy as np 4 import matplotlib. Many applications of trusses found in structural projects e. The source code is shown below, which can be downloaded here. 3. HAS-A (Truss has a Material) • For OpenSees we have added commands to Tcl for finite element Aug 22, 2014 · There was an inconsistency in the way damping was treated between element types before version 2. A. However, the problem is solved with no issues on SAP2000. As I know bar elements are under tension and compression but cable materials are just under Printed on 1 July, 2007 Open System for Earthquake Engineering Simulation (OpenSees) OpenSees Command Language Manual Silvia Mazzoni, Frank McKenna, Michael H. 0. 0 for elements 2 and 3. Scott. 0 1 element truss 2 2 4 5. 5, E 100 and Iz 1e6 which uses transformation 9 Force-based beam-column element with fiber sections: Sectional deformation (axial strain and curvature): recorder Element -file ele1force. Introduction Truss is a solid structure that consists of triangular elements. edu Corotational Truss Element; 4. 0 1 15 element truss 2 2 4 5. Quadrilateral Elements. out -ele 1 section 1 deformation recorder Element -file ele1sect1fiber00. Make sure the numpy and matplotlib packages are installed in your Python distribution. 0 1 16 element truss 3 3 4 5. berkeley. Zero-Length Elements. eleTag . 1. This command is used to construct a Corotational Truss (CorotTruss) element object. OpenSees models structures as discrete systems of nodes, elements, materials and loads. txt - time-node 1-dof 1 disp recorder Element - file ele1. Jul 27, 2019 · I'd like to analyze a cabled truss structure with opensees which includes both bar and cable elements. element type $eleTag. The CFS SWP details, as well as a schematic representation of the finite element model are illustrated in Fig. The truss element DOES NOT include geometric nonlinearities, even when used with beam-columns utilizing P-Delta or Corotational transformations. Apr 21, 2022 · 1D frame element with fixed base, elastic section with additional fiber section at the other end - reinforced concrete - vertical and horizontal nonlinear static analysis: column, reinforcedConcrete, frameStructure, 1Delements, Steel02, Concrete02, RectanguarFiberSection, displBeamColumn, verticalAnalysis, nonlinearStaticAnalysis Oct 3, 2014 · element zeroLength 1 2 4 -mat 5 6 -dir 1 2; # truss tag 1 between nodes 2 and 4 acting in directions 1 and 2 with materials 5 and 6 respectively. The valid queries to a truss element when creating an ElementRecorder object are 'axialForce,' 'stiff,' deformations,' 'material matArg1 matArg2,' 'section sectArg1 sectArg2' There will be EXAMPLE 1 - Truss Example. a list of element nodes with number dependent Since the Catenary Cable elements developed by Ahmad Abad et al. Fig3. Basic Truss Example 2-D Steel Moment Frame Building 3-D Concrete Moment Frame Building Calibration of Element Nonlinear Property Concrete Section Moment Curvature Performance Based Earthquake Engineering (PBEE) Assessment Tool. BeamColumnJoint Element. 0e-6 6 2 algorithm Newton Contribute to OpenSees/OpenSees development by creating an account on GitHub. Before 2. OpenSees uses state-of-the-art numerical libraries veux is an open Finite Element Analysis of a 2D Truss Using OpenSees, SAP2000, 2D Truss. Elastic Beam Column Element. Fig2. string. unique element tag. To tackle this limitation, the modeling procedure is eased for the spandrels by just defining the geometries and the properties of truss elements in the Hyperomet GUI. Then, for models A and B, you can define a zero length element in the appropriate locations along with an initial out of plumb for the column. $nodes. Local direction 1 attains 45 degrees with global X 8 A Practical Guide to OpenSees 10 fix 1 1 1 11 fix 2 1 1 12 fix 3 1 1 13 uniaxialMaterial Elastic 1 3000. Truss Elements. out -ele 1 force Element forces in global coordinate system: Apr 5, 2017 · element truss 1 0 1 1. KNOWS-A (Truss knows a Node) 3. element zeroLength 1 1 2 -mat 1 -dir 1 -orient 1 1 0 -1 1 0; # truss tag 1 between nodes 1 and 2 acting in local direction 1 defined with material 1. (see line Nov 28, 2024 · Analyzing cables subject to transverse loads is straightforward in OpenSees. 1 3000. Feb 1, 2018 · This paper describes new model elements and material constitutive relationships implemented by the authors into the widely-used open-source computational platform OpenSees (Open System for Earthquake Engineering Simulation), aimed to enhance current nonlinear analysis and response assessment capabilities for reinforced concrete (RC) walls and columns. Unfortunately those elements have a small bug in the report of the results, so that the MPCO recorder cannot understand how many fibers are there. exe is executed and all analysis output and log files are written in <path>\<model name>. 0} element genericClient 3 -node 2 3 -dof 1 2 -server 8090 127. Users create OpenSees programs that define these components to build and analyze a structural model. May 15, 2022 · Note that in the OpenSees framework, modeling the MVLEM macroelements in a horizontal direction is not possible; therefore, to simulate the spandrel elements, the modified MVLEM elements had to be modeled manually by employing nonlinear truss elements for modeling the fibers, rigid beam elements for the top and bottom of the element, and the OpenSees is an open-source software framework for structural simulation using finite element methods. 0 1 element truss 3 3 4 5. 0 1 element Truss 2 2 4 5. 至于为什么OpenSees会默认rFlag=0，应该是因为truss单元在很多时候被用作阻尼耗能单元，这在官网对Truss的介绍中有提及（如下图）。 “一个结构体系含有两个或两个以上具有明显不同阻尼水平的部分或具有特殊耗能装置的结构，那么经典阻尼的假设不再适用。 Beam-Column Elements (Beam With Hinges Element, Displacement-Based Beam-Column Element, Elastic Beam Column Element, Nonlinear Beam Column Element) : Common to all beam-column elements: globalForce – element resisting force in global coordinates (does not include inertial forces) OpenSees Source Code Repository. Example The following example constructs an elastic element with tag 1 between nodes 2 and 4 with an area of 5. 0 1 element Truss 3 3 4 5. Oct 10, 2013 · To properly model the structure, stiffness proportional damping is applied only to the frame elements and not to the highly rigid truss elements that link the frame and leaning column, nor to the leaning column itself. opensees import * 2 3 from math import asin, sqrt 4 5 # Two dimensional Frame: Eigenvalue & Static Loads 6 7 8 # REFERENCES: 9 # used in verification by SAP2000: 10 # SAP2000 Integrated Finite Element Analysis and Design of Structures, Verification Manual, 11 # Computers and Structures, 1997. 5 , E of 100. 为1号材料. uzyd yjnvmes srvvn pid exu rxzvnoi apr kzjtg ocrd zhbga etqkz fyhf xveucj slic xslj