4.54 BEAM54 2-D Elastic Tapered Unsymmetric Beam

4.54 BEAM54 2-D Elastic Tapered Unsymmetric Beam (UP19980821 ) BEAM54 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. This element allows a different unsymmetrical geometry at each end and permits the end nodes to be offset from the centroidal axis of the beam. If these features are not desired, the uniform symmetrical beam element, BEAM3 (described in Section 4.3), may be used. This element does not have plastic, creep, or swelling capabilities. These effects are included in BEAM23, the two-dimensional, untapered, plastic beam element. Stress stiffening capability is also included. A 3-D tapered unsymmetrical beam (BEAM44) is described in Section 4.44.

Shear deformation and elastic foundation effects are available as options. Another option is available for printing the forces acting on the element in the element coordinate directions. See Section 14.54 of the ANSYS Theory Reference for more details about this element.

Figure 4.54-1 BEAM54 2-D Elastic Tapered Unsymmetric Beam



4.54.1 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 4.54-1. The element x-axis is oriented in the global X-Y plane (or a parallel plane) from node I (end 1) toward node J (end 2). The element real constants describe the beam in terms of the cross-sectional areas, the area moments of inertia, the extreme fiber distances from the centroid, the offset distances, and the shear deflection constant. The moments of inertia (IZ_) are about the principal axis of the beam. The element may be used in axisymmetric analyses if hoop effects are negligible, such as for bolts, slotted cylinders, etc. The areas and moments of inertia must be input on a full 360° basis for an axisymmetric analysis.

The shear deflection constant (SHEARZ) is optional. A zero value of SHEARZ may be used to neglect shear deflection. The shear modulus (GXY) is used only with shear deflection. See Section 2.10 for details. Properties not input default as described in Section 2.4. The offset constants (DX_, DY_) define the centroid location of the section relative to the node location. Offset distances are measured positive from the node in the positive element coordinate directions. The shear areas (AREAS_) are used only for the shear stress computation. The shear areas are generally less than the actual cross-sectional area.

The AREA_, IZ_, HY__, and AREAS_ real constants for end 2 of the beam default to the corresponding end 1 values if zero. Furthermore, the "top" height at end 1, HYT1, defaults to the "bottom" height at end 1, HYB1, and the "top" height at end 2, HYT2, defaults to the "top" height at end 1, HYT1. The heights are measured from the centroid of the section. The elastic foundation stiffness (EFS) is defined as the pressure required to produce a unit normal deflection of the foundation. This capability is bypassed if EFS equals zero. 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. An added mass per unit length may be input with the ADDMAS value.

Element loads are described in Section 2.7. Pressures may be input as surface loads on the element faces as shown by the circled numbers on Figure 4.54-1. The circled number represents the load key for the indicated face. Positive pressures act into the element. Lateral pressures are input 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. Temperatures may be input as element body loads at the four "corner" locations shown in Figure 4.54-1. 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

A summary of the element input is given in Table 4.54-1. A general description of element input is given in Section 2.1.

Table 4.54-1 BEAM54 Input Summary

Element Name

BEAM54

Nodes

I, J

Degrees of Freedom

UX, UY, ROTZ

Real Constants

AREA1, IZ1, HYT1, HYB1, AREA2, IZ2, HYT2, HYB2, DX1, DY1, DX2, DY2, SHEARZ, AREAS1, AREAS2, EFS, ISTRN, ADDMAS

Material Properties

EX, ALPX, DENS, GXY, DAMP

Surface Loads

Pressures:
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 negative value for loading in opposite direction)

Body Loads

Temperatures: T1, T2, T3, T4

Special Features

Stress stiffening, Large deflection, Birth and death

KEYOPT(6)

0 - No member force printout
1 - Print 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-If SHEARZ = 0.0, there is no shear deflection in the element y direction.
AREAS1 and AREAS2 are used only for the shear stress calculation.

4.54.2 Output Data

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

Several items are illustrated in Figure 4.54-2. At each cross-section, the computed output consists of the direct (axial) stress and two bending components. Then these three values are combined to evaluate the maximum and minimum stresses. If KEYOPT(6)=1 for this element, the 6 member forces and moments (3 at each end) are also printed (in the element coordinate system). The element x-axis is defined through the center of gravity of the cross-section. Additional results at intermediate locations between the ends may be output with KEYOPT(9). A general description of solution output is given in Section 2.2. See the ANSYS Basic Analysis Procedures Guide for ways to view results.

Figure 4.54-2 BEAM54 Stress Output



The following notation is used in Table 4.54-2:

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 4.54-2 BEAM54 Element Output Definitions

Name

Definition

O

R

EL

Element number

Y Y
NODES

Nodes - I, J

Y Y
MAT

Material number

Y Y
VOLU:

Volume

- Y
CENT: X, Y, Z

Center location XC, YC, ZC

- Y
TEMP

Temperatures T1, T2, T3, T4

Y Y
PRES

Pressures 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
SXY

Average shear (Y-direction)

2 2
MFOR(X, Y)

Member forces in the element coordinate system

3 Y
MMOMZ

Member moment in the element coordinate system

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

2. Output only if real constants AREAS1 and AREAS2 are input

3. If KEYOPT(6)=1

Table 4.54-3 lists 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. The following notation is used in Table 4.54-3:

Table 4.54-3 BEAM54 (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 - -
MFORX

SMISC

- 1 7
MFORY

SMISC

- 2 8
MMOMZ

SMISC

- 6 12
SXY

SMISC

- 13 14
P1

SMISC

- 15 16
OFFST1

SMISC

- 17 18
P2

SMISC

- 19 20
OFFST2

SMISC

- 21 22
P3

SMISC

- 23 -
P4

SMISC

- - 24
SMAX

NMISC

- 1 3
SMIN

NMISC

- 2 4

Corner Location

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.54-3a BEAM54 (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 - - -
MFORX

SMISC

- 1 7 13
MFORY

SMISC

- 2 8 14
MMOMZ

SMISC

- 6 12 18
SXY

SMISC

- 19 20 21
P1

SMISC

- 22 - 23
OFFST1

SMISC

- 24 - 25
P2

SMISC

- 26 - 27
OFFST2

SMISC

- 28 - 29
P3

SMISC

- 30 - -
P4

SMISC

- - - 31
SMAX

NMISC

- 1 3 5
SMIN

NMISC

- 2 4 6

Corner Location

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.54-3b BEAM54 (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 - - - - -
MFORX

SMISC

- 1 7 13 19 25
MFORY

SMISC

- 2 8 14 20 26
MMOMZ

SMISC

- 6 12 18 24 30
SXY

SMISC

- 31 32 33 34 35
P1

SMISC

- 36 - - - 37
OFFST1

SMISC

- 38 - - - 39
P2

SMISC

- 40 - - - 41
OFFST2

SMISC

- 42 - - - 43
P3

SMISC

- 44 - - - -
P4

SMISC

- - - - - 45
SMAX

NMISC

- 1 3 5 7 9
SMIN

NMISC

- 2 4 6 8 10

Corner Location

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.54-3c BEAM54 (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 - - - - - - -
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
SXY

SMISC

- 43 44 45 46 47 48 49
P1

SMISC

- 50 - - - - - 51
OFFST1

SMISC

- 52 - - - - - 53
P2

SMISC

- 54 - - - - - 55
OFFST2

SMISC

- 56 - - - - - 57
P3

SMISC

- 58 - - - - - -
P4

SMISC

- - - - - - - 59
SMAX

NMISC

- 1 3 5 7 9 11 13
SMIN

NMISC

- 2 4 6 8 10 12 14

Corner Location

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.54-3d BEAM54 (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 - - - - - - - - -
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
SXY

SMISC

- 55 56 57 58 59 60 61 62 63
P1

SMISC

- 64 - - - - - - - 65
OFFST1

SMISC

- 66 - - - - - - - 67
P2

SMISC

- 68 - - - - - - - 69
OFFST2

SMISC

- 70 - - - - - - - 71
P3

SMISC

- 72 - - - - - - - -
P4

SMISC

- - - - - - - - - 73
SMAX

NMISC

- 1 3 5 7 9 11 13 15 17
SMIN

NMISC

- 2 4 6 8 10 12 14 16 18

Corner Location

1

2

3

4

TEMP

LBFE

1 2 3 4
Table 4.54-3e BEAM54 (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 - - - - - - - - - - -
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
SXY

SMISC

- 67 68 69 70 71 72 73 74 75 76 77
P1

SMISC

- 78 - - - - - - - - - 79
OFFST1

SMISC

- 80 - - - - - - - - - 81
P2

SMISC

- 82 - - - - - - - - - 83
OFFST2

SMISC

- 84 - - - - - - - - - 85
P3

SMISC

- 86 - - - - - - - - - -
P4

SMISC

- - - - - - - - - - - 87
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

Corner Location

1

2

3

4

TEMP

LBFE

1 2 3 4

4.54.3 Assumptions and Restrictions

The beam must not have a zero length or area and must lie in an X-Y plane. The element heights are used in locating the extreme fibers for the stress calculations and in computing the thermal gradient. Incorrect bending or thermal stresses may result if zero heights are input. The beam may have any cross-sectional sectional shape for which the moments of inertia can be computed. Tapers within an element, if any, should be gradual. If AREA2/AREA1 or I2/I1 is not between 0.5 and 2.0, a warning message is output. If the ratio is outside of the range of 0.1 to 10.0, an error message is output. The element should not taper to a point (zero thickness).

The applied thermal gradient is assumed to be linear across the thickness and along the length of the element. The flexible length of the beam is adjusted to account for the effect of the offsets. The offset lengths may be regarded as rigid portions of the beam. Unequal lateral offsets, which rotate the beam, also cause a corresponding shortening of the beam's flexible length. The difference between the lateral offsets should not exceed the length of the element. Rotational body forces resulting from an angular velocity are based upon the node locations (as if zero offsets). The shear stress is calculated independently of the shear deflection. The effect of offsets on the mass matrix is ignored if the lumped mass matrix formulation is specified [LUMPM,ON].

4.54.4 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