4.3 BEAM3 2-D Elastic Beam

4.3 BEAM3 2-D Elastic Beam (UP19980821 ) BEAM3 is a uniaxial element with tension, compression, and bending capabilities. The element has three degrees of freedom at each node: translations in the nodal x and y directions and rotation about the nodal z-axis. See Section 14.3 of the ANSYS Theory Reference for more details about this element. Other 2-D beam elements are the plastic beam (BEAM23) and the tapered unsymmetric beam (BEAM54).

Figure 4.3-1 BEAM3 2-D Elastic Beam



4.3.1 Input Data

Figure 4.3-1 shows the geometry, node locations, and the coordinate system for this element. The element is defined by two nodes, the cross-sectional area, the area moment of inertia, the height, and the material properties. The initial strain in the element (ISTRN) is given by /L, where is the difference between the element length, L (as defined by the I and J node locations), and the zero strain length. The initial strain is also used in calculating the stress stiffness matrix, if any, for the first cumulative iteration.

You can use the element in an axisymmetric analysis if hoop effects are negligible, such as for bolts, slotted cylinders, etc. The area and moment of inertia must be input on a full 360° basis for an axisymmetric analysis. The shear deflection constant (SHEARZ) is optional. You can use a zero value of SHEARZ to neglect shear deflection. See Section 2.10 for details. The shear modulus (GXY) is used only with shear deflection. Properties you do not input default as described in Section 2.4. You can specify an added-mass-per-unit-length with the ADDMAS value.

Section 2.7 describes element loads. You can specify pressures as surface loads on the element faces, shown by the circled numbers in Figure 4.3-1. Positive normal pressures act into the element. You specify lateral pressures as a force per unit length. End "pressures" are input as a force. KEYOPT(10) allows tapered lateral pressures to be offset from the nodes. You can specify temperatures as element body loads at the four "corner" locations shown in Figure 4.3-1. The first corner temperature T1 defaults to TUNIF. If all other temperatures are unspecified, they default to T1. If only T1 and T2 are input, T3 defaults to T2 and T4 defaults to T1. For any other input pattern, unspecified temperatures default to TUNIF.

KEYOPT(9), used to request output at intermediate locations, is not valid if

Table 4.3-1 summarizes the element input. Section 2.1 contains a general description of element input.

Table 4.3-1 BEAM3 Input Summary

Element Name

BEAM3

Nodes

I, J

Degrees of Freedom

UX, UY, ROTZ

Real Constants

AREA, IZZ, HEIGHT, SHEARZ, ISTRN, ADDMAS

Material Properties

EX, ALPX, DENS, GXY, DAMP

Surface Loads

Pressure:
face 1 (I-J) (-Y normal direction),
face 2 (I-J) (+X tangential direction),
face 3 (I) (+X axial direction),
face 4 (J) (-X axial direction)
(use a negative value for loading in the opposite direction)

Body Loads

Temperatures: T1, T2, T3, T4

Special Features

Stress stiffening, Large deflection, Birth and death

KEYOPT(6)

0 - No printout of member forces and moments
1 - Print out member forces and moments in the element coordinate system

KEYOPT(9)

Used to control additional output between ends I and J
N - Output at N intermediate locations (N = 0, 1, 3, 5, 7, 9)

KEYOPT(10)

Used only for tapered surface loads with the SFBEAM command.
0 - Offset for load placement is in terms of length units
1 - Offset is in terms of a length ratio (0.0 to 1.0)

Note-SHEARZ goes with the IZZ. If SHEARZ=0, there is no shear deflection in the element Y direction.

4.3.2 Output Data

The solution output associated with the element is in two forms:

Figure 4.3-2 illustrates several items. Section 2.2 gives a general description of solution output. See the ANSYS Basic Analysis Procedures Guide for ways to view results.

Figure 4.3-2 BEAM3 Stress Output



Table 4.3-2 uses the following notation:

A colon (:) in the Name column indicates the item can be accessed by the Component Name method [ETABLE, ESOL] (see Section 2.2.2). The O and R columns indicate the availability of the items in the file Jobname.OUT (O) or in the results file (R), a Y indicates that the item is always available, a number refers to a table footnote which describes when the item is conditionally available, and a - indicates that the item is not available.

Table 4.3-2 BEAM3 Element Output Definitions

Name

Definition

O

R

EL

Element number

Y Y
NODES

Element nodes - I, J

Y Y
MAT

Element material number

Y Y
VOLU:

Element volume

N Y
CENT: X,Y

Center location of the element XC, YC

N Y
TEMP

Temperatures T1, T2, T3, T4

Y Y
PRES

Pressure P1 at nodes I,J; OFFST1 at I,J; P2 at I,J; OFFST2 at I, J;
P3 at I; P4 at J

Y Y
SDIR

Axial direct stress

1 1
SBYT

Bending stress on the element +Y side of the beam

1 1
SBYB

Bending stress on the element -Y side of the beam

1 1
SMAX

Maximum stress (direct stress + bending stress)

1 1
SMIN

Minimum stress (direct stress - bending stress)

1 1
EPELDIR

Axial elastic strain at the end

1 1
EPELBYT

Bending elastic strain on the element +Y side of the beam

1 1
EPELBYB

Bending elastic strain on the element -Y side of the beam

1 1
EPTHDIR

Axial thermal strain at the end

1 1
EPTHBYT

Bending thermal strain on the element +Y side of the beam

1 1
EPTHBYB

Bending thermal strain on the element -Y side of the beam

1 1
EPINAXL

Initial axial strain in the element

1 1
MFOR(X, Y)

Member forces in the element coordinate system X and Y direction

2 Y
MMOMZ

Member moment in the element coordinate system Z direction

2 Y
1. The item repeats for end I, intermediate locations (see KEYOPT(9)), and end J.

2. If KEYOPT(6)=1.

The following tables list output available through the ETABLE command using the Sequence Number method. See Chapter 5 of the ANSYS Basic Analysis Procedures Guide and Section 2.2.2.2 of this manual for more information. Tables 4.3-3 through 4.3-3e all use the following notation:

Table 4.3-3 BEAM3 (KEYOPT(9)=0) Item and Sequence Numbers for the ETABLE and ESOL Commands

KEYOPT(9)=0

Name

Item

E

I

J

SDIR

LS

- 1 4
SBYT

LS

- 2 5
SBYB

LS

- 3 6
EPELDIR

LEPEL

- 1 4
EPELBYT

LEPEL

- 2 5
EPELBYB

LEPEL

- 3 6
EPTHDIR

LEPTH

- 1 4
EPTHBYT

LEPTH

- 2 5
EPTHBYB

LEPTH

- 3 6
EPINAXL

LEPTH

7 - -
SMAX

NMISC

- 1 3
SMIN

NMISC

- 2 4
MFORX

SMISC

- 1 7
MFORY

SMISC

- 2 8
MMOMZ

SMISC

- 6 12
P1

SMISC

- 13 14
OFFST1

SMISC

- 15 16
P2

SMISC

- 17 18
OFFST2

SMISC

- 19 20
P3

SMISC

- 21 -
P4

SMISC

- - 22
Pseudo Node

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.3-3a BEAM3 (KEYOPT(9)=1) Item and Sequence Numbers for the ETABLE and ESOL Commands

KEYOPT(9) = 1

Name

Item

E

I

IL1

J

SDIR

LS

- 1 4 7
SBYT

LS

- 2 5 8
SBYB

LS

- 3 6 9
EPELDIR

LEPEL

- 1 4 7
EPELBYT

LEPEL

- 2 5 8
EPELBYB

LEPEL

- 3 6 9
EPTHDIR

LEPTH

- 1 4 7
EPTHBYT

LEPTH

- 2 5 8
EPTHBYB

LEPTH

- 3 6 9
EPINAXL

LEPTH

10 - - -
SMAX

NMISC

- 1 3 5
SMIN

NMISC

- 2 4 6
MFORX

SMISC

- 1 7 13
MFORY

SMISC

- 2 8 14
MMOMZ

SMISC

- 6 12 18
P1

SMISC

- 19 - 20
OFFST1

SMISC

- 21 - 22
P2

SMISC

- 23 - 24
OFFST2

SMISC

- 25 - 26
P3

SMISC

- 27 - -
P4

SMISC

- - - 28
Pseudo Node

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.3-3b BEAM3 (KEYOPT(9)=3) Item and Sequence Numbers for the ETABLE and ESOL Commands

KEYOPT(9) = 3

Name

Item

E

I

IL1

IL2

IL3

J

SDIR

LS

- 1 4 7 10 13
SBYT

LS

- 2 5 8 11 14
SBYB

LS

- 3 6 9 12 15
EPELDIR

LEPEL

- 1 4 7 10 13
EPELBYT

LEPEL

- 2 5 8 11 14
EPELBYB

LEPEL

- 3 6 9 12 15
EPTHDIR

LEPTH

- 1 4 7 10 13
EPTHBYT

LEPTH

- 2 5 8 11 14
EPTHBYB

LEPTH

- 3 6 9 12 15
EPINAXL

LEPTH

16 - - - - -
SMAX

NMISC

- 1 3 5 7 9
SMIN

NMISC

- 2 4 6 8 10
MFORX

SMISC

- 1 7 13 19 25
MFORY

SMISC

- 2 8 14 20 26
MMOMZ

SMISC

- 6 12 18 24 30
P1

SMISC

- 31 - - - 32
OFFST1

SMISC

- 33 - - - 34
P2

SMISC

- 35 - - - 36
OFFST2

SMISC

- 37 - - - 38
P3

SMISC

- 39 - - - -
P4

SMISC

- - - - - 40
Pseudo Node

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.3-3c BEAM3 (KEYOPT(9)=5) Item and Sequence Numbers for the ETABLE and ESOL Commands

KEYOPT(9) = 5

Name

Item

E

I

IL1

IL2

IL3

IL4

IL5

J

SDIR

LS

- 1 4 7 10 13 16 19
SBYT

LS

- 2 5 8 11 14 17 20
SBYB

LS

- 3 6 9 12 15 18 21
EPELDIR

LEPEL

- 1 4 7 10 13 16 19
EPELBYT

LEPEL

- 2 5 8 11 14 17 20
EPELBYB

LEPEL

- 3 6 9 12 15 18 21
EPTHDIR

LEPTH

- 1 4 7 10 13 16 19
EPTHBYT

LEPTH

- 2 5 8 11 14 17 20
EPTHBYB

LEPTH

- 3 6 9 12 15 18 21
EPINAXL

LEPTH

22 - - - - - - -
SMAX

NMISC

- 1 3 5 7 9 11 13
SMIN

NMISC

- 2 4 6 8 10 12 14
MFORX

SMISC

- 1 7 13 19 25 31 37
MFORY

SMISC

- 2 8 14 20 26 32 38
MMOMZ

SMISC

- 6 12 18 24 30 36 42
P1

SMISC

- 43 - - - - - 44
OFFST1

SMISC

- 45 - - - - - 46
P2

SMISC

- 47 - - - - - 48
OFFST2

SMISC

- 49 - - - - - 50
P3

SMISC

- 51 - - - - - -
P4

SMISC

- - - - - - - 52
Pseudo Node

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.3-3d BEAM3 (KEYOPT(9)=7) Item and Sequence Numbers for the ETABLE and ESOL Commands

KEYOPT(9) = 7

Name

Item

E

I

IL1

IL2

IL3

IL4

IL5

IL6

IL7

J

SDIR

LS

- 1 4 7 10 13 16 19 22 25
SBYT

LS

- 2 5 8 11 14 17 20 23 26
SBYB

LS

- 3 6 9 12 15 18 21 24 27
EPELDIR

LEPEL

- 1 4 7 10 13 16 19 22 25
EPELBYT

LEPEL

- 2 5 8 11 14 17 20 23 26
EPELBYB

LEPEL

- 3 6 9 12 15 18 21 24 27
EPTHDIR

LEPTH

- 1 4 7 10 13 16 19 22 25
EPTHBYT

LEPTH

- 2 5 8 11 14 17 20 23 26
EPTHBYB

LEPTH

- 3 6 9 12 15 18 21 24 27
EPINAXL

LEPTH

28 - - - - - - - - -
SMAX

NMISC

- 1 3 5 7 9 11 13 15 17
SMIN

NMISC

- 2 4 6 8 10 12 14 16 18
MFORX

SMISC

- 1 7 13 19 25 31 37 43 49
MFORY

SMISC

- 2 8 14 20 26 32 38 44 50
MMOMZ

SMISC

- 6 12 18 24 30 36 42 48 54
P1

SMISC

- 55 - - - - - - - 56
OFFST1

SMISC

- 57 - - - - - - - 58
P2

SMISC

- 59 - - - - - - - 60
OFFST2

SMISC

- 61 - - - - - - - 62
P3

SMISC

- 63 - - - - - - - -
P4

SMISC

- - - - - - - - 64
Pseudo Node

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.3-3e BEAM3 (KEYOPT(9)=9) Item and Sequence Numbers for the ETABLE and ESOL Commands

KEYOPT(9) = 9

Name

Item

E

I

IL1

IL2

IL3

IL4

IL5

IL6

IL7

IL8

IL9

J

SDIR

LS

- 1 4 7 10 13 16 19 22 25 28 31
SBYT

LS

- 2 5 8 11 14 17 20 23 26 29 32
SBYB

LS

- 3 6 9 12 15 18 21 24 27 30 33
EPELDIR

LEPEL

- 1 4 7 10 13 16 19 22 25 28 31
EPELBYT

LEPEL

- 2 5 8 11 14 17 20 23 26 29 32
EPELBYB

LEPEL

- 3 6 9 12 15 18 21 24 27 30 33
EPTHDIR

LEPTH

- 1 4 7 10 13 16 19 22 25 28 31
EPTHBYT

LEPTH

- 2 5 8 11 14 17 20 23 26 29 32
EPTHBYB

LEPTH

- 3 6 9 12 15 18 21 24 27 30 33
EPINAXL

LEPTH

34 - - - - - - - - - - -
SMAX

NMISC

- 1 3 5 7 9 11 13 15 17 19 21
SMIN

NMISC

- 2 4 6 8 10 12 14 16 18 20 22
MFORX

SMISC

- 1 7 13 19 25 31 37 43 49 55 61
MFORY

SMISC

- 2 8 14 20 26 32 38 44 50 56 62
MMOMZ

SMISC

- 6 12 18 24 30 36 42 48 54 60 66
P1

SMISC

- 67 - - - - - - - - - 68
OFFST1

SMISC

- 69 - - - - - - - - - 70
P2

SMISC

- 71 - - - - - - - - - 72
OFFST2

SMISC

- 73 - - - - - - - - - 74
P3

SMISC

- 75 - - - - - - - - - -
P4

SMISC

- - - - - - - - - - - 76
Pseudo Node

1

2

3

4

TEMP

LBFE

1 2 3 4

4.3.3 Assumptions and Restrictions

The beam element can have any cross-sectional shape for which the moment of inertia can be computed. However, the stresses are determined as if the distance from the neutral axis to the extreme fiber is one-half of the height. The element height is used only in the bending and thermal stress calculations. The applied thermal gradient is assumed linear across the height and along the length. The beam element must lie in an X-Y plane and must not have a zero length or area. The moment of inertia may be zero if large deflections are not used.

4.3.4 Product Restrictions

When used in the product(s) listed below, the stated product-specific restrictions apply to this element in addition to the general assumptions and restrictions given in the previous section.

ANSYS/LinearPlus