MAE 656 - Advanced Computer Aided Design 03. Beams and Trusses Solution of Beams and Trusses Problems
Introduction If our structure is made of multiple elements that can be characterized as beams or trusses, the best approach to the problem is with these elements. These should be used whenever it is possible. Beams: Each node has three possible displacements and three possible rotations. Efforts in the node are three forces (axial and shear) and three moments (torsion and bending) Trusses: The bar element only handles axial loads. Displacement of the nodes will be along the bar axis.
Beam Simulations The simulation of a structure made of beam elements is made with linear elements that represent the beam axis.
Beam Simulations The beams can have any possible shape: MAE 656 cba Dr. Xavier Martinez, 2012 03. Beams & Trusses Doc 01
Beam Simulations Or cross section:
Beam Simulations If we only have one beam, although a first beam study may be helpful to establish preliminary dimensions, we may have to use shell or solid elements to obtain good results. On the other hand, if we have many beams: the beam analysis becomes imperative
Simplification of the problem We want to study the following crane:
Simplification of the problem The first thing we have to decide is in which configuration (or configurations) we want to study it. If we are concerned about maximum bending, this can be the worst scenario:
Simplification of the problem We must know the problem dimensions:
Simplification of the problem We must locate the axis of the different beams, as the structure will be defined according to these axis. Notice that we have some distortions of reality by having to attach the different bar elements along their axis. In this case, the piston becomes larger.
Simplification of the problem We have to define the cross sections of the beams. In this example we will approximate the beam behavior with a single beam which thickness is the mean value.
Simplification of the problem Finally we have to define the structure dimensions and the dimensions of all cross sections of the structure:
Variable Cross Section Ansys Workbench does not allow to define a variable cross section along the beam axis. A possible solution to this problem is to divide the beam in several shorter beams, each one with a different cross section.
Cross Section Excentricity There are some structures where the beam axis are not aligned: The cross section of this structure looks like:
Cross Section Excentricity If we draw the axis of the structure we get: Which means that the beams are placed:
Cross Section Excentricity We have to give an initial excentricity to the beams in order to recover the original position In Ansys Design Modeler:
Previous knowledge of the problem It is necessary a good knowledge of Strength of Materials, in order to define some structural elements: The proposed simplification can be made if forces are acting along the x axis. If forces act along the y axis, this simplification is not correct!
Beam Elements in Ansys Workbench The linear element available in ANSYS Workbench is BEAM 188: (// Element Reference // I. Element Library // BEAM188) (http://www.kxcad.net/ansys/ansys/ansyshelp/hlp_e_beam188.html) This beam element is based on Timoshenko beam theory, which is a first order shear deformation theory: transverse shear strain is constant through the cross-section; that is, cross-sections remain plane and undistorted after deformation. It is not a TRUSS element. We will have to release node connectivities in order to get a truss performance.
Body to body connections It is possible to define the degrees of freedom that are fixed and free in the connection of two different bodies. This is done with body to body connections. In order to get a Truss performance we have to create a revolute joint, which frees the rotation along z axis. The bodies to be connected must be independent.
Body to body connections In beams elements, a revolute joint is applied to the vertex that is shared by the two elements that are connected. While a revolute joint frees z rotation. A General joint allows defining the degrees of freedom that are free.
MESHING The performance of BEAM 188 element is such that it provides a correct solution if each bar is defined with a single finite element. In case of structures with curved beam elements, or with elements with a variable cross section, it is necessary to define enough elements to have a good representation of the structure geometry
RESULTS The main results in which we will be interested when solving a beam structure are the following:
Results Direct stress is the stress produced by the axial load Bending stress (maximum and mínimum) is the stress produced by the bending moments Combined stress is the stress result of the linear combination of the stresses produced by the axial load and the stresses produced by the bending moments.
Exercise Obtain the displacement, efforts and stresses of the structural steel crane drawn in the following picture. The load applied has a magnitude of 15 kn and it is applied vertical at the end of the arm If there is any beam that holds stresses larger than 90% the elastic limit (250MPa), modify it to reduce the stresses in it.