Structures with Prof. H

This video presents the theory and purpose of shear and moment (i.e., internal force) diagrams. The internal forces represent the stresses in the beam caused by beam bending or by axial forces. These internal forces may be calculated by hand using equilibrium. However, it is more common to draw the shear and moment diagrams that represent these internal forces along the entire length of the structure. Both the derivative and integral (area) forms for the internal force equations are given. Then the diagrams are created for an example determinate beam.

This video shows an example of how to compute the reaction forces and internal (axial) forces in a determinate truss. The unknown reaction forces are solved using the equations of equilibrium (i.e., statics). Then the method of joints or the method of sections are used to solve for the axial forces in each element - both methods work similarly by considering equilibrium of some component of the truss. Using a consistent sign convention, we can differentiate between elements in tension and compression, which will later aid us in design of trusses.

This video defines determinate and indeterminate structural systems, and how to tell the difference. The unknown reaction forces and internal forces of determinate systems can be solved using only the equations of equilibrium (i.e., statics). Indeterminate systems have more unknowns than can be solved using statics alone, and therefore new structural analysis techniques are required. The number of unknowns can be counted and compared to the number of equilibrium equations. Examples are shown for how to do this with trusses and frames (or beams, which work the same as frames).

This video introduces the two main categories of gravity load systems: one-way systems and the two-way systems. Tributary area is defined as the floor (or roof) area from which a structural element directly "collects" the load to transfer it down to the foundation. The influence area is defined as the total area that is in some way supported by a structural element. Examples are shown for how to compute these two areas for beams and columns. An example use for both tributary area and influence area is in the ASCE/SEI 7 live load reduction factor. A load combination example (U = 1.2D + 1.6L) for a one-way slab system is presented in detail. For reference, please see ASCE/SEI 7 - Minimum Design Loads and Associated Criteria for Buildings and Other Structures.

This first video in structural analysis introduces the forces of nature (loads) that structural engineers use to compute the demands on a building. These loads are considered in three different design contexts: - Serviceability - Strength - Extreme Events The Load and Resistance Factor Design (LRFD) method for Strength design is discussed in more detail, including how the variety of loads are combined and factored. For reference, please see ASCE/SEI 7 - Minimum Design Loads and Associated Criteria for Buildings and Other Structures. Load combinations are also discussed in the relevant material-based code requirements, for example ACI 318 - Building Code Requirements for Structural Concrete.

This tutorial shows how to use the Microplane model to simulate a concrete cube and reinforced concrete beam. This implementation incorporates coupled plasticity-damage and nonlocal behavior. This is the first tutorial in this series incorporating Mechanical APDL commands into the analysis. Learning objectives: 1. Sketch the Drucker-Prager yield surface and locate key points and features. 2. Explain the various parameters for the Microplane model and their typical values. 3. Add APDL commands to model complex material behavior and change element types. === Downloads === Drucker-Prager Yield Surface (Excel): https://docs.google.com/spreadsheets/d/19H-HMY3dhsJIyrzjqSg7fzgGihHGja_s/edit?usp=sharing&ouid=116718473101577906015&rtpof=true&sd=true (Link does not have edit access, but you may download a copy of the Excel file to edit it locally) Microplane APDL Commands for psi (text file): https://drive.google.com/file/d/1PToSbzrCqu3WDLy1VZcAzSTvuBbf3rg1/view?usp=sharing Microplane APDL Commands for MPa (text file): https://drive.google.com/file/d/1XC4uspetbG45U57VfNnYk8W22HMI08_W/view?usp=sharing === References === This particular implementation in ANSYS is based on the following references: Zreid, I. & Kaliske, M. (2018). A gradient enhanced plasticity-damage microplane model for concrete. Computational Mechanics. 10(1007), s00466-018-1561-1. https://doi.org/10.1007/s00466-018-1561-1 Zreid, I. & Kaliske, M. (2016). An implicit gradient formulation for microplane Drucker-Prager plasticity. International Journal of Plasticity. 83, 252-272. https://doi.org/10.1016/j.ijplas.2016.04.013 Zreid, I. & Kaliske, M. (2014). Regularization of microplane damage models using an implicit gradient enhancement. International Journal of Solids and Structures. 51(19), 3480-3489. https://doi.org/10.1016/j.ijsolstr.2014.06.020 The original microplane model was developed by Z.P. Bazant and others: Bažant, Z. P., & Gambarova, P. G. (1984). Crack shear in concrete: Crack band microplane model. Journal of structural engineering, 110(9), 2015-2035. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:9(2015) Bazant, Z. P. & Oh, B. H. (1985). Microplane model for progressive fracture of concrete and rock. Journal for Engineering Mechanics. 111, 559-582. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:4(559) Carol I, Jirásek M, & Bažant Z (2001). A thermodynamically consistent approach to microplane theory. Part I. Free energy and consistent microplane stresses. International Journal of Solids and Structures. 38:2921–2931. https://doi.org/10.1016/S0020-7683(00)00212-2

This tutorial models a concrete beam reinforced with mild steel. The concrete is modeled using a Menetrey-Willam strain softening model, while the steel has bilinear hardening. Learning objectives: 1. Define a strain-softening geo-material that has different compressive and tensile behavior. 2. Embed reinforcing elements within a concrete solid. 3. Describe the stresses and strains in the concrete and steel composite structure.

This tutorial adds material plasticity into nonlinear analysis, illustrating this behavior in a steel coupon tested in tension. Learning objectives: 1. Define bilinear and multilinear plasticity properties. 2. Apply symmetry constraints to reduce the size of the model. 3. Describe the phenomenon of necking and why it occurs for plastic materials.

This tutorial focuses on conducting large displacement (also known as nonlinear geometry) analysis, and what scenarios this type of analysis is merited. Learning objectives: 1. Change analysis settings so large displacements are taken into account. 2. Identify when large displacement analysis is required. 3. Define time-stepping and iteration settings in order to conduct nonlinear analysis. 4. Describe P-Delta effects and how large displacement analysis incorporates these effects into the solution.

This tutorial focuses on using predefined materials or creating new materials for a model. An example viscoelastic material is defined and used in a time-dependent structural analysis. Learning objectives: 1. Import predefined materials from the Engineering Data Sources. 2. Create a new custom material. 3. Conduct a viscoelastic analysis with time-varying load. 4. Contrast the necessary and allowable material properties for different ANSYS analysis objects.

This tutorial focuses on defining the mesh for a model, and the types of elements that can be used to solve the finite element method. Learning objectives: 1. Contrast linear elements with quadratic elements. 2. Interrogate the mesh statistics and quality to ensure the elements are well-formed. 3. Refine a mesh locally to properly capture stress concentrations. 4. Automatically refine a mesh using a convergence criteria.

This video illustrates how to conduct a two-dimensional beam/frame analysis using Static Structural analysis. Learning objectives: 1. Create beam geometry in SpaceClaim. 2. Assign a standard AISC steel section from the library and re-orient the section for strong-axis bending. 3. Define end releases and boundary conditions for frames. 4. Generate shear and bending moment diagrams for columns and beams.

This video illustrates how to conduct a two-dimensional truss analysis using Static Structural analysis. Learning objectives: 1. Create an independent Geometry object to link to multiple analyses objects. 2. Create beam or truss geometry in SpaceClaim. 3. Assign and define cross-sections for line elements. 4. Examine beam results for axial forces.

The follow-up video tutorials on using ANSYS to perform finite element analysis, this time performing 2-D plane stress analysis on a fixed-fixed beam. Learning objectives: 1. Create a 2-D analysis. 2. Differentiate plane stress, plane strain, and axisymmetric analyses. 3. Compute reaction forces and moments. 4. Evaluate results along a specified path.

The first in a series of video tutorials on using ANSYS to perform finite element analysis. In this introduction, we will model a fixed-fixed beam with a midspan load using Static Structural analysis. Learning objectives: 1. Define simple geometry using SpaceClaim. 2. Create a mesh with a specified element size. 3. Apply boundary conditions and loads. 4. Examine deformation and stress results.