Simply Supported Beam

Problem introduction and Model specifications

A simply supported beam having a pin support at left end and a roller support at the right end. The beam is carrying a uniformly distributed transverse shear load of 5 KN/m. The material properties used are: Elastic modulus (E) = 200 GPa and Poisson ratio (ν) = 0.3.

The Model specifications are as below: The length of the beam is 6 m, width of 250 mm and height of 350 mm.

The video below contains the description about the problem introduction, model description (geometry, material, loads and constraints), analytical calculations and the expected results.

Video link: https://www.youtube.com/embed/D9S260okCmU?rel=0

Learning outcome and Output requests

This example is an introduction of how to model 1D beam element problems in NX Nastran. Solving this problem in NX Nastran, we will be able to find the location of maximum bending moment and thus the maximum bending stress in the beam. We can see how the bending stress is distributed along the beam cross section i.e. locations of tensions and compression.

Also we can identify the beam deflection at any location in the beam along with shear force and bending moment graphs in the results.

The following will be requested as output:

  1. Reaction forces at supports
  2. Shear force distribution
  3. Bending moment distribution
  4. Beam deflection
  5. Bending stress

Analytical results

Let’s calculate the reaction forces, maximum values of shear force and bending moment, maximum deflection and maximum bending stress in the beam so that we can compare them with the results given by NX Nastran.

Note: The beam deflection and bending stress is calculated using Euler Bernoulli beam theory therefore deflection and stress are calculated considering bending moment only and not shear force.

Reaction forces

Shear force distribution

Shear force distribution equation

Bending moment distribution

Bending moment distribution equation

Beam Deflection & Bending Stress

Steps

  1. CAD Modeling
  2. Meshing and Material
  3. Loading and Boundary Conditions
  4. Results post processing
  5. Results verification and validation

CAD Modeling

The first step of simulation is to create a CAD model using NX 12.0. The CAD model for this problem consists of only a line representing the neutral axis of the beam. The video below describes the following operations:

  • Creating a new part file
  • Creating a sketch
  • Sketch dimensioning
Video link: https://www.youtube.com/embed/FEDJPlpuLOI?rel=0

Meshing and Material

Next step is to create a Fem file. Fem file consists of information regarding the material properties and type of meshing to be done.

The video below describes the following operations:

  • Creating fem and sim files
  • Solver and solution type
  • Output requests
  • Material properties
  • Beam properties: Material properties and beam cross section
  • Meshing info: Element type and size

Loading and Boundary conditions

Next step is to create a sim file. Sim file consists of information about the loading and constraints to be applied. It also has information about any contacts defined in the model.

The video below describes the following operations:

  • User defined constraints: constraining dof at two ends
  • Loading applied: Pressure on beams
  • Model setup check
  • Solve the Fem model
  • Check for any errors or warnings in Analysis job information

Results post processing

After the solution is done, a result file is created that has all the output results requested. Nastran will always calculate displacement and stress as default, other output parameters are to be predefined.

The video below describes the following post processing operations:

  • Contour plots of reaction force, shear force and bending moment distribution
  • Graph of Shear force distribution in the beam
  • Contour plot of beam deflection and bending stress
  • Cross section view of bending stress
  • Identify results at any specific node and nodes having max and min values

Results verification and validation

Since we now have both the analytical and simulation results, we can easily cross check both the results to see how close the results are given by NX Nastran in comparison to the analytical results. We will also see that the results are independent of the mesh.

Note that the analytical results are calculated using Euler Bernoulli beam theory. NX Nastran uses Timoshenko beam theory by default. So, the magnitude for beam deflection and bending stress might be slightly different in both the cases.

The video below describes the following operations:

  • Comparison of analytical Vs Fem results for: Reaction force, max. shear force and bending moment, max. values of beam deflection and bending stress
  • Error calculation between analytical and Fem results
  • Mesh independence of results
Video link: https://www.youtube.com/embed/i-owSary4NA?rel=0

Reference: Mechanics of materials by R.C. Hibbeler, Ninth Edition 

Example By: Ashwani Thakur