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MAE 656 - AdvancedComputer Aided Design

03. Beams and Trusses

Solution of Beams and Trusses

Problems

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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

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Beam Simulations

The simulation of a structure made of beam elements ismade with linear elements that represent the beam axis.


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Beam Simulations

The beams can have any possible shape:


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Beam Simulations

Or cross section:


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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


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Simplification of the problem

We want to study the following crane:


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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:


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We must know the problem dimensions:


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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.


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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.


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Finally we have to define the structure dimensions and thedimensions of all cross sections of the structure:


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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.


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Cross Section Excentricity

There are some structures where the beam axis are notaligned:

The cross section of this structure looks like:


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If we draw the axis of the structure we get:

Which means that the beams are placed:


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We have to give an initial excentricity to the beams in orderto recover the original position

In Ansys Design Modeler:


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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!

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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.


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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.


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Body to body connections


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.

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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


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RESULTS

The main results in which we will be interested whensolving a beam structure are the following:


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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.


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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.


MAE 656 - 03-D01

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