Using the Beam Cross Section Interface

The Beam Cross Section interface can either be used separately or as a separate model node and geometry in the same model file where the actual beam problem is solved.


	In most cases, it is easiest to compute the beam cross section properties in a separate model.

There are some cases when using one or more Beam Cross Section interfaces and a Beam interface together in the same model file can be advantageous. For example, when changes in the cross sections can be anticipated. There are however a number of things to pay attention to in this case:

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Usually the determination of the cross section data is more computationally expensive than the actual analyses of the beam structure. Then it is best to use either separate studies or study steps for the two tasks.

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When two separate studies or study steps are used, then the must be set in the second study step where only the beam problem is solved. Under you can also click to clear the check box for the beam cross section degrees of freedom in order to save space.

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When referencing the beam cross section properties in the input fields of the Beam interface, you must use a fully qualified variable name, like mod2.bcs3.A for the area.

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If a Beam interface is added after a Beam Cross Section interface, the only study type shown when adding a physics interface is . In this case, under , select to find the other study types available for the beam analysis.


	Values of Dependent Variables and Physics and Variables Selection in the COMSOL Multiphysics Reference Manual

Since the Beam Cross Section interface is active in 2D, the cross sections are analyzed in the xy-plane. However, the Beam interface uses a notation where the local x-axis is along the beam, and the cross section is described in a local yz-plane.

In order to avoid confusion, the cross section properties are described in local x1-x2 coordinates (see Figure 9-1). When data is transferred to a Beam interface, you must keep track of the coordinates that correspond to the local y and z directions.


	Channel Beam: Application Library path Structural_Mechanics_Module/Verification_Examples/channel_beam

Computing the Cross Section Data

In a 2D model, the geometry of the cross section is drawn. If the section is simply connected (that is, has no internal holes), then usually nothing else needs to be done before running the analysis.

The default mesh density is tuned for thin-walled sections. For solid sections an unnecessarily large model is obtained when using the default mesh.

If the section is not simply connected, add one Hole node for each internal hole. In that node, select all boundaries around the hole.

The computed cross section data is stored in the variables listed in Table 9-1:

Table 9-1: Variables Containing Cross Section Data
Variable	Description	Input to beam interface	Link to Theory Section
bcs.A	Area	Area (A)	Area
bcs.CGx	Center of gravity, x coordinate	Implicit, since it affects the positioning of the beam centerline.	Center of Gravity
bcs.CGx	Center of gravity, y coordinate	As above	Center of Gravity
bcs.x1	First coordinate in principal axes system	Implicit, since it can be used for determining stress evaluation locations	Local Coordinates
bcs.x2	Second coordinate in principal axes system	As above	Local Coordinates
bcs.I1	Largest principal moment of inertia	Moment of inertia around local y/z-axis (Izz/Iyy)	Moments of Inertia
bcs.I2	Smallest principal moment of inertia	As above
bcs.Ixx	Moment of inertia around x-axis	-
bcs.Iyy	Moment of inertia around y-axis	-
bcs.Ixy	Deviatoric moment of inertia in xy system	-
bcs.rg	Radius of gyration	-
bcs.alpha	Angle from x-axis to first principal axis	Rotation of vector around beam axis (φ)	Directions of Principal Axes
bcs.mu1	Max shear stress factor, x1 direction	Max shear stress factor in local y/z direction (μy/μz)	Bending Shear Stresses
bcs.mu2	Max shear stress factor, x2 direction	As above
bcs.kappa1	Shear correction factor, x1 direction	-
bcs.kappa2	Shear correction factor, x2 direction	-
bcs.ei1	Shear center location, first local coordinate	Distance to shear center in local y/z direction.
bcs.ei2	Shear center location, second local coordinate	As above
bcs.J	Torsional constant	Torsional constant (J)	Torsion
bcs.Wt	Torsional section modulus	Torsional section modulus (Wt)	Torsion
bcs.Cw	Warping constant	-	Warping
bcs.Kw	Warping section modulus	-
bcs.sw	Nonuniform torsion parameter	-

Computing Detailed Stresses

If you have set of section forces (axial force, shear forces, bending moments, and twisting moments), it is possible to display the stresses it causes. To do this, enter the values in the section. You can also add your own acceptance criteria by adding one or more Safety nodes.

The stresses are available in the variables listed in Table 9-2.


	After changing data in this section, you do not need to compute the study for this physics interface again once is has been solved. It is sufficient to do an Update Solution to get the stress plots updated.


	Studies and Solvers in the COMSOL Multiphysics Reference Manual

Table 9-2: Variables Containing Stress Distributions
Variable	Description and	Link to Theory Section
bcs.sN	Stress from axial force	Axial Stress
bcs.sM1	Bending stress from moment around x1 axis	Bending Axial Stresses
bcs.sM2	Bending stress from moment around x2 axis	Bending Axial Stresses
bcs.tT1x	Shear stress from force in x1 direction, x component	Bending Shear Stresses
bcs.tT1y	Shear stress from force in x1 direction, y component
bcs.resT1	Shear stress from force in x1 direction, resultant
bcs.tT2x	Shear stress from force in x2 direction, x component
bcs.tT2y	Shear stress from force in x2 direction, y component
bcs.resT2	Shear stress from force in x2 direction, resultant
bcs.tMtx	Shear stress from twisting moment, x component	Torsional Shear Stresses
bcs.tMty	Shear stress from twisting moment, y component
bcs.resMt	Shear stress from twisting moment, resultant
bcs.mises	von Mises equivalent stress	Equivalent Stress
bcs.spN	Principal stresses; N=1,2,3
bcs.INs	N:th invariant of stress tensor; N=1,2,3
bcs.IINs	N:th invariant of stress tensor deviator; N=2,3
bcs.thetaL	Lode angle for stress tensor

Computing Warping Displacement

You can also compute the axial warping displacement by entering the axial twist of the beam in the section. The theory is described under Warping. The axial displacement is stored in the variable bcs.u.