MD Nastran Elements 3

THE BEAM ELEMENT

1Copyright© 2010 MSC.Software CorporationCopy For Politecnico of Milano


THE CBEAM ELEMENT

● CBEAM Element Overview● Connected to two grid points● Force components:

● Axial force P

● Shear forces in 2 planes V1 and V2

● Bending moments in 2 planes M and M


● Bending moments in 2 planes M1 and M2

● Total torque T

● Warping torque Tw

● Displacement components:● ui , θi , and

ix

θdd

THE BEAM ELEMENT (Cont.)

● The beam includes all capabilities of the CBAR element plus several additional capabilities, including:● Variable cross-section - the cross-sectional properties may be specified at as

many as nine interior points and at both ends.● The neutral axis and shear center axis need not be coincident (correctly

accounts for sections which are not doubly-symmetric).● The effect of cross-sectional warping on the torsional stiffness.


● The effect of cross-sectional warping on the torsional stiffness.● The effect of taper on the transverse shear stiffness (shear relief).● K1 and K2 (Shear stiffness factors) of PBEAM have default values of 1.0. To

neglect shear deformation (as is the case with BAR elements), the values of K1 and K2 should be set to 0.0.


● Input format:



Field Contents● EID Element identification number (integer > 0)● PID Identification number of PBEAM, PBEAML, PBCOMP

or PBMSECT property entry● GA,GB Grid point identification numbers of connection

points


points● X1,X2,X3 Components of vector v at End A, measured at

the offset point for End A, parallel to the components of the displacement coordinate system for GA

● G0 Grid point identification number to optionally supply X1, X2, and X3

● OFFT Orientation Vector and offset vector interpretation

THE BEAM ELEMENT (Cont.)Field Contents

● PA,PB Pin flags for beam Ends A and B, respectively (in the element coordinate system)

● W1A,W2A,W3AW1B,W2B,W3B Components of offset vectors, measured in the

displacement coordinate systems at Grid Points A


displacement coordinate systems at Grid Points Aand B, from the grid points to the end points of the axis of shear center (real or blank)

● SA,SB Scalar or grid point identification numbers for the Ends A and B, respectively. The degrees of freedom at these points are the warping variables dq/dx



BEAM PROPERTIES


BEAM PROPERTIES (Cont.)

FIELD CONTENTS DEFAULT

PID Property identification number Required

MID Material identification number Required

A(A) Area of beam cross section at point A Required

I1(A) Area Moment of inertia of Beam cross Required


I1(A) Area Moment of inertia of Beam cross section in plane 1 (about element Z axis) at point A

Required

I2(A) Area Moment of inertia of Beam cross section in plane 2 (about element Y axis) at point A

Required

I12(A) Area product of inertia at end A (I1*I2-I12>0)

0.0



J(A) Torsional stiffness constant at end A (if warping is present, J>0) (real)

0.0

NSM(A) Nonstructural mass per unit length at end A (real)

0.0

Ci(A), Di(A), Ei(A), Fi(A)

The locations (element Y and Z) at end 0.0


Ei(A), Fi(A) The locations (element Y and Z) at end A for stress data recovery (real)

0.0

SO Stress output option (BCD) Required

YES = Stresses recovered at points C,D,E,F on next continuation entry

YESA = Stresses recovered at points with same y,z locations as end A

NO = no stress output



X/XB Distance from end A in the element coordinate system (X) divided by the length (XB)

Required

A, I1, I2, J, NSM

Properties at current cross-section See following pages

Ci, Di, Ei, Y,Z (element coordinate system)


Ci, Di, Ei, Fi

Y,Z (element coordinate system) locations for stress calculation on the current cross-section

K1, K2 Shear stiffness factor K for Plane 1 and 2

1., 1.

S1, S2 Shear relief coefficient due to taper for plane 1 and 2

0., 0.



NSI(1), NSI(2)

Nonstructural mass moment of inertia per unit length about nonstructural mass center of gravity at ends A and B (real)

0., same as end A

CW(A), CW(B)

Warping coefficient for ends A and B (real)

0., same as end A


CW(B) (real) as end A N1(A), N2(A), N1(B), N2(B) Y and Z coordinates (offsets) of the

neutral axis for ends A and B 0., same as end A

M1(A), M2(A), M1(B), M2(B) Y and Z coordinates (offsets) of the

center of gravity of nonstructural mass at ends A and B

0.0, same as end A


● A(I), J(I), I1(I), I2(I), I12(I)

● These properties must be specified for end A (except I12, which defaults to 0.0)

● By default, end B will have the same properties as end A● Unless properties are specified for Intermediate sections,


● Unless properties are specified for Intermediate sections, these properties will be found by linearly interpolating between those of end A and end B


● Shear Relief coefficient due to Taper (S1, S2)● The shear relief factor accounts for the fact that in a tapered flanged beam,

the flanges sustain a portion of the transverse shear load. This situation is illustrated below:



● The value of the shear coefficient for a tapered beam withheavy flanges that sustain the entire moment load may thenbe written as:


● For additional information, see the MSC/NASTRANReference Manual, Section 5.2.1.


● Cross-Sectional Warping - Coefficients CW(A), CW(B)

● Open section members, such as channels, undergo torsion as well as bending when transverse loads act anywhere except at the shear center of a cross section.


● This torsion produces warping of the cross section so that plane sections do not remain plane, and as a result, axial stresses are produced. This situation can be represented in the differential equation for the torsion of a beam about the axis of shear centers (in the following slide)






● Note: The warping constant Cw has units of (length)6. The development of the differential equation and methods for the numerical evaluations of the warping constant are available in the literature. (See, for example, Timoshenko and Gere,


in the literature. (See, for example, Timoshenko and Gere, Theory of Elastic Stability, McGraw Hill Book Company, 1961. Also see Roark & Young, Formulas for Stress and Strain, for values for different sections)


● Neutral Axis Offset from Shear Center (N1, N2)


BEAM PROPERTIES (Cont.)● Neutral Axis Offset from Shear Center (N1, N2)


● N1 and N2 allow you to specify the offset between the shear center and the neutral axis

BEAM PROPERTIES - THE PBEAML

● The PBEAML defines the properties of a BEAM element by using the dimensions of the cross section


BEAM PROPERTIES - THE PBEAML

Field Contents

PID Property identification number

MID Material identification number

Group Cross-section group (default = "MSCBML0")

TYPE Cross-section shape. (Character: "ROD", "TUBE",


TYPE Cross-section shape. (Character: "ROD", "TUBE", "L", "I", "CHAN", "T", "BOX", "BAR", "CROSS", "H", "T1", "I1", "CHAN1", "Z", CHAN2", "T2", "BOX1", "HEX", "HAT", “HAT1” and “DBOX” for GROUP="MSCBMLO")

DIMi(A)… DIMi(B)

Cross-section dimensions at end A and B. (Real > 0.0 for GROUP="MSCBMLO")

NSM(A)… NSM(B)

Nonstructural mass per unit length

BEAM PROPERTIES - THE PBEAML (Cont.)

Field Contents

SO(j) Stress output request option for section (j) YES = Stress recovered at this section NO = no stress output for this section

X(j)/XB Distance from end A to intermediate section (j) divided by the length of the element


divided by the length of the element NSM(j) Nonstructural mass per unit length at section (j)

DIMi(j) Cross-section dimensions at section (j)

For more information, including section information, see the MD.Nastran R3 QRG, Bulk Data Entries

BEAM ELEMENT OUTPUT● BEAM element forces and moments


BEAM ELEMENT OUTPUT (Cont.)

● The forces and moments in plane 1 can also be viewed as:


BEAM ELEMENT OUTPUT (Cont.)

● The forces and moments in plane 2 can also be viewed as:


MODELING THE TAPERED

● Use the CBEAM element● The outer radius of the pole tapers from R = 4.0” to R = 3.0”● The inner radius of the pole tapers from R = 3.5” to R = 2.5”


FIELDS

● The linearly varying outer and inner radii of the beam will be modeled by using Fields.

● Fields in PATRAN are used to define variations in● Loads


● Loads● Boundary Conditions● Material Properties● Element Properties● There are three types of fields:● Spatial Fields● Non Spatial Fields● Material Property Fields● Use Spatial Fields to model the beam tapers in this

case study.

CREATING FIELDS

Create a field for the taper in beam outer radius from 4” to 3”


radius from 4” to 3”

Create a second field for the taper in beam inner radius

from 3.5” to 2.5”

CREATING FIELDS (Cont.)


Verify the two fields by plotting

them

CREATING FIELDS (Cont.)


Create 1D element properties

CREATING ELEMENT PROPERTIES


Input properties

CREATING ELEMENT PROPERTIES (Cont.)

Select the steel material created


material created earlier

Enter the beam orientation vector



Select the circular tube section from

the Beam Library and

name it



name it “circular tube

section”

Enter R1 and R2 by

selecting the fields created

earlier



Select curve 1 and click

calculate/display to show cross section at one end of curve

Slide the parametric



location dial from End A to End B

and click Calculate/Display

to view cross section at the other end of

curve

Select OK to accept the beam library section.

Select OK to accept the input



accept the input properties.

Click Apply to create the element property.

Change from 1D to 3D display to



display to visually inspect

the cross section

3D display of tapered beam

EXAMINE THE f06 FILE


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MD Nastran Elements 3

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