Upload
qw23qw
View
225
Download
0
Embed Size (px)
Citation preview
7/22/2019 MAE 656 - 03-D01
1/24
MAE 656 - AdvancedComputer Aided Design
03. Beams and Trusses
Solution of Beams and Trusses
Problems
7/22/2019 MAE 656 - 03-D01
2/24
Introduction
If our structure is made of multiple elements that can becharacterized as beams or trusses, the best approach to the
problem is with these elements. These should be usedwhenever it is possible.
Beams: Each node has three possible displacements andthree 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.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
3/24
Beam Simulations
The simulation of a structure made of beam elements ismade with linear elements that represent the beam axis.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
4/24
Beam Simulations
The beams can have any possible shape:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
5/24
Beam Simulations
Or cross section:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
6/24
Beam Simulations
If we only have one beam, although a first beam study maybe 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
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
7/24
Simplification of the problem
We want to study the following crane:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
8/24
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 worstscenario:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
9/24
Simplification of the problem
We must know the problem dimensions:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
10/24
Simplification of the problem
We must locate the axis of the different beams, as thestructure will be defined according to these axis.
Notice that we have some distortions of reality by having to attach thedifferent bar elements along their axis. In this case, the piston becomeslarger.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
11/24
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.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
12/24
Simplification of the problem
Finally we have to define the structure dimensions and thedimensions of all cross sections of the structure:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
13/24
Variable Cross Section
Ansys Workbench does not allow to define a variable crosssection along the beam axis.
A possible solution to this problem is to divide the beam inseveral shorter beams, each one with a different crosssection.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
14/24
Cross Section Excentricity
There are some structures where the beam axis are notaligned:
The cross section of this structure looks like:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
15/24
Cross Section Excentricity
If we draw the axis of the structure we get:
Which means that the beams are placed:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
16/24
Cross Section Excentricity
We have to give an initial excentricity to the beams in orderto recover the original position
In Ansys Design Modeler:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
17/24
Previous knowledge of the problem
It is necessary a good knowledge of Strength of Materials,in order to define some structural elements:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
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!
7/22/2019 MAE 656 - 03-D01
18/24
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, whichis a first order shear deformation theory: transverse shear strainis constant through the cross-section; that is, cross-sectionsremain plane and undistorted after deformation.
It is not a TRUSS element. We will have to release nodeconnectivities in order to get a truss performance.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
19/24
Body to body connections
It is possible to define the degreesof freedom that are fixed and free in
the connection of two differentbodies. This is done with body tobody connections.
In order to get a Trussperformance we have to create arevolute joint, which frees the
rotation along z axis.The bodies to be connected must beindependent.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
20/24
Body to body connections
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
In beams elements, arevolute joint is applied
to the vertex that isshared by the twoelements that areconnected.
While a revolute jointfrees z rotation. A
General joint allowsdefining the degrees offreedom that are free.
7/22/2019 MAE 656 - 03-D01
21/24
MESHING
The performance of BEAM 188 element is such that itprovides 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 todefine enough elements to have a good representation ofthe structure geometry
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
22/24
RESULTS
The main results in which we will be interested whensolving a beam structure are the following:
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
23/24
Results
Direct stress is the stress produced by the axial load
Bending stress (maximum and mnimum) is the stressproduced by the bending moments
Combined stress is the stress result of the linear
combination of the stresses produced by the axial load andthe stresses produced by the bending moments.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01
7/22/2019 MAE 656 - 03-D01
24/24
Exercise
Obtain the displacement, efforts and stresses of the structural steelcrane drawn in the following picture. The load applied has a magnitudeof 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.
MAE656 cba Dr.XavierMartinez,2012 03.Beams&Trusses Doc01