BEAM188


3D 2-Node Beam

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BEAM188 Element Description

BEAM188 is suitable for analyzing slender to moderately stubby/thick beam structures. The element is based on Timoshenko beam theory which includes shear-deformation effects. The element provides options for unrestrained warping and restrained warping of cross-sections.

The element is a linear, quadratic, or cubic two-node beam element in 3D. BEAM188 has six or seven degrees of freedom at each node; these include translations in the x, y, and z directions and rotations about the x, y, and z directions. A seventh degree of freedom (warping magnitude) is optional. This element is well-suited for linear, large rotation, and/or large strain nonlinear applications.

The element includes stress stiffness terms, by default, in any analysis with large deflection. The provided stress-stiffness terms enable the elements to analyze flexural, lateral, and torsional stability problems (using eigenvalue buckling, or collapse studies with arc length methods or nonlinear stabilization).

Elasticity, plasticity, creep and other nonlinear material models are supported. A cross-section associated with this element type can be a built-up section referencing more than one material. Added mass, hydrodynamic added mass and loading, and buoyant loading are available.

For more detailed information about this element, see BEAM188 - 3D 2-Node Beam in the Theory Reference.

Figure 188.1: BEAM188 Geometry

BEAM188 Geometry

BEAM188 Element Technology and Usage Recommendations

BEAM188 is based on Timoshenko beam theory, which is a first-order shear-deformation theory: transverse-shear strain is constant through the cross-section (that is, cross-sections remain plane and undistorted after deformation).

The element can be used for slender or stout beams. Due to the limitations of first-order shear-deformation theory, slender to moderately thick beams can be analyzed. Use the slenderness ratio of a beam structure (GAL2 / (EI) ) to judge the applicability of the element, where:

G

Shear modulus

A

Area of the cross-section

L

Length of the member (not the element length)

EI

Flexural rigidity

Calculate the ratio using some global distance measures, rather than basing it upon individual element dimensions. The following illustration shows an estimate of transverse-shear deformation in a cantilever beam subjected to a tip load. Although the results cannot be extrapolated to any other application, the example serves well as a general guideline. A slenderness ratio greater than 30 is recommended.

Figure 188.2: Transverse-Shear Deformation Estimation

Transverse-Shear Deformation Estimation

Slenderness Ratio (GAL2/(EI)) δ Timoshenko / δ Euler-Bernoulli
251.120
501.060
1001.030
10001.003

The element supports an elastic relationship between transverse-shear forces and transverse-shear strains. You can override default values of transverse-shear stiffnesses (SECCONTROL).

BEAM188 does not use higher-order theories to account for variation in distribution of shear stresses. Use solid elements if such effects must be considered.

When KEYOPT(5) = 1, BEAM188 deforms in the XY plane only. It has three degrees of freedom at each node (translations in the x and y directions, and rotation about the z direction).

BEAM188 in 3D space (KEYOPT(5) = 0) supports restrained-warping analysis by making available a seventh degree of freedom at each beam node. By default, BEAM188 elements assume that the warping of a cross-section is small enough that it can be ignored (KEYOPT(1) = 0). You can activate the warping degree of freedom by using KEYOPT(1) = 1 or 2. With the warping degree of freedom activated, each node has seven degrees of freedom: UX, UY, UZ, ROTX, ROTY, ROTZ, and WARP. When KEYOPT(1) = 1 or 2, bimoment and bicurvature are output. BEAM188 in the XY plane (KEYOPT(5) = 1) does not support restrained-warping analysis.

When KEYOPT(3) = 0 (linear, default), BEAM188 is based on linear shape functions. It uses one point of integration along the length; therefore, all element solution quantities are constant along the length. For example, when SMISC quantities are requested at nodes I and J, the centroidal values are reported for both end nodes. This option is recommended if the element is used as stiffener and it is necessary to maintain compatibility with a first-order shell element (such as SHELL181). Only constant bending moments can be represented exactly with this option. Mesh refinement is generally required in typical applications.

When KEYOPT(3) = 2 (quadratic), BEAM188 has an internal node in the interpolation scheme, effectively making this a beam element based on quadratic shape functions. Two points of integration are used, resulting in linear variation of element solution quantities along the length. Linearly varying bending moments are represented exactly.

When KEYOPT(3) = 3 (cubic), BEAM188 has two internal nodes and adopts cubic shape functions. Quadratically varying bending moments are represented exactly. Three points of integration along the length are used, resulting in quadratic variation of element solution quantities along the length. Unlike typical cubic (Hermitian) formulations, cubic interpolation is used for all displacements and rotations.

Quadratic and cubic options are recommended when higher-order element interpolations are desired in situations where:

  • The element is associated with tapered cross-sections.

  • Nonuniform loads (including tapered distributed loads) exist within the element; in this case, the cubic option gives superior results over the quadratic option.

    (For partially distributed loads and non-nodal point loads, only the cubic option is valid.)

  • The element may undergo highly nonuniform deformation (for example, when individual frame members in civil engineering structures are modeled with single elements).

In practice, when two elements with restrained warping come together at a sharp angle, you must couple the displacements and rotations but leave the out-of-plane warping decoupled (typically by having two nodes at a physical location and using appropriate constraints). The process is made easier or automatic, as follows:

  • If KEYOPT(1) = 1, issue ENDRELEASE to decouple the out-of-plane warping for any adjacent elements with cross-sections intersecting at an angle > 20 degrees (default). Other ENDRELEASE options are also available.

  • If KEYOPT(1) = 2, the program performs pre-solution checks automatically (after issuing SOLVE) and decouples the out-of-plane warping for any adjacent elements as necessary. For more information, see BEAM188 Pre-Solution Checks when KEYOPT(1) = 2.

BEAM188 allows change in cross-sectional inertia properties as a function of axial elongation. By default, the cross-sectional area changes such that the volume of the element is preserved after deformation. The default is suitable for elastoplastic applications. By using KEYOPT(2), you can choose to keep the cross-section constant or rigid. Scaling is not an option for nonlinear general beam sections (SECTYPE,,GENB).

Two limitations are associated with the quadratic and cubic options in BEAM188:

  • Although the elements employ higher-order interpolations, the initial geometry of BEAM188 is treated as straight.

  • Because the internal nodes are inaccessible, no boundary/loading/initial conditions are allowed on these internal nodes.

As a result of the limitations associated with the quadratic and cubic options, you will notice discrepancies in the results between BEAM189 and the quadratic option of BEAM188 if the midside nodes of the BEAM189 model have specified boundary/loading/initial conditions and/or the midside nodes are not located exactly at the element midpoint. Similarly, the cubic option of BEAM188 may not be identical to a traditional cubic (Hermitian) beam element.

For the mass matrix and evaluation of consistent load vectors, a higher order integration rule than that used for stiffness matrix is employed. The elements support both consistent and lumped mass matrices. Issue LUMPM,ON to activate lumped mass matrix. Consistent mass matrix is used by default. You can add mass per unit length via the SECCONTROL command's ADDMAS values. See "BEAM188 Input Summary".

When ocean loading is applied, the loading is nonlinear (that is, based on the square of the relative velocity between the structure and the water). Accordingly, the full Newton-Raphson option (NROPT,FULL) may be necessary to achieve optimal results. (Full Newton-Raphson is applied automatically in an analysis involving large-deflection effects (NLGEOM,ON).)

The St. Venant warping functions for torsional behavior are determined in the undeformed state, and are used to define shear strain even after yielding. No options are available for recalculating in deformed configuration the torsional shear distribution on cross-sections during the analysis and possible partial plastic yielding of cross-sections. As such, large inelastic deformation due to torsional loading should be treated and verified with caution. Under such circumstances, alternative modeling using solid or shell elements is recommended.

BEAM188 Input Data

The geometry, node locations, coordinate system, and pressure directions for this element are shown in Figure 188.1: BEAM188 Geometry. BEAM188 is defined by nodes I and J in the global coordinate system.

Node K is a preferred way to define the orientation of the element in 3D space. For information about orientation nodes and beam meshing, see Generating a Beam Mesh With Orientation Nodes in the Modeling and Meshing Guide. See LMESH and LATT for information about generating the K node automatically.

BEAM188 in 3D space can also be defined without the orientation node K. In this case, the element x axis is oriented from node I (end 1) toward node J (end 2). If no orientation node is used, the default orientation of the element y axis is automatically calculated to be parallel to the global X-Y plane. For the case where the element is parallel to the global Z axis (or within a 0.01 percent slope of it), the element y axis is oriented parallel to the global Y axis (as shown). To control the element orientation about the element x axis, use the orientation-node option. If both are defined, the orientation-node option takes precedence. The orientation node K, if used, defines a plane (with I and J) containing the element x and z axes (as shown). If using this element in a large-deflection analysis, be aware that the location of the orientation node K is used only to initially orient the element.

The orientation of BEAM188 in the XY plane (KEYOPT(5) = 1) is determined by the location of nodes I and J. The element x axis is oriented from node I (end 1) toward node J (end 2). The element y axis is oriented along the negative global Z axis. Orientation node K is not needed.

The number of degrees of freedom depends on the value of KEYOPT(1). When KEYOPT(1) = 0 (default), six degrees of freedom occur at each node; these include translations in the x, y, and z directions and rotations about the x, y, and z directions. When KEYOPT(1) = 1 or 2, a seventh degree of freedom (warping magnitude) is also considered. Warping is not supported for BEAM188 in the XY plane (KEYOPT(5) = 1).

The beam element is a one-dimensional line element in space. The cross-section details are provided separately via the SECTYPE and SECDATA commands. (See Beam and Pipe Cross Sections in the Structural Analysis Guide for details.) A section is associated with the beam elements by specifying the section ID number (SECNUM). A section number is an independent element attribute. In addition to a constant cross-section, you can also define a tapered cross-section by using the TAPER option on the SECTYPE command. (See Defining a Tapered Beam or Pipe in the Structural Analysis Guide.)

BEAM188 ignores any real constant data. See the SECCONTROL command for defining the transverse-shear stiffness and added mass.

A summary of the element input is given in "BEAM188 Input Summary".

BEAM188 Cross-Sections

BEAM188 can be associated with these cross-section types (SECTYPE,,Type):

  • Standard library section types or user meshes which define the geometry of the beam cross-section (SECTYPE,,BEAM). The material of the beam is defined either as an element attribute (MAT), or as part of section buildup (for multi-material cross-sections). BEAM188 in the XY plane (KEYOPT(5) = 1) supports only section types that are symmetric about the XY plane.

  • Generalized beam cross-section (SECTYPE,,GENB), where the relationships of generalized stresses to generalized strains are input directly. Not available for BEAM188 in the XY plane (KEYOPT(5) = 1) and ocean loading.

  • Tapered beam cross-section (SECTYPE,,TAPER), where a standard library section or user mesh defines each end of the beam. Not available for ocean loading.

  • Preintegrated composite beam cross section (SECTYPE,,COMB,MATRIX), abstract cross section type for defining a fully populated but symmetrical cross-section stiffness and mass matrix directly. Not available for ocean loading.

Standard Library Sections

BEAM188 elements are provided with section-relevant quantities (area of integration, position, etc.) automatically at a number of section points using SECTYPE and SECDATA. Each section is assumed to be an assembly of a predetermined number of nine-node cells. Each cross-section cell has four integration points and each can be associated with an independent material type.

Figure 188.3: Cross-Section Cells

Cross-Section Cells

The number of cells in the cross-sections influences the accuracy of section properties and ability to model nonlinear stress-strain relationship through the cross-section. The element has a nested structure of integration (along the length and in the cross-section).

When the material associated with the elements has inelastic behavior or when the temperature varies across the section, constitutive calculations are performed at the section integration points. For more common elastic applications, the element uses precalculated properties of the section at the element integration points; however, the stresses and strains are calculated in the output pass at the section integration points. Element output is available at the integration points, as well as values extrapolated to the element and section nodes.

If the section is assigned the subtype ASEC, only the generalized stresses and strains (axial force, bending moments, transverse shears, curvatures, and shear strains) are available for output. 3D contour plots and deformed shapes are not available. The ASEC subtype is displayed only as a thin rectangle to verify beam orientation.

BEAM188 is helpful for analyzing built-up beams (that is, those fabricated of two or more pieces of material joined together to form a single, solid beam). The pieces are assumed to be perfectly bonded together; therefore, the beam behaves as a single member.

The multi-material cross-section capability is applicable only where the assumption of beam behavior (Timoshenko or Bernoulli-Euler beam theory) holds.

Therefore, the element models a simple extension of a conventional Timoshenko beam and can be used in applications such as:

  • Bimetallic strips

  • Beams with metallic reinforcement

  • Sensors where layers of a different material has been deposited

BEAM188 does not account for coupling of bending and twisting at the section stiffness level. The transverse shears are also treated in an uncoupled manner. This can have a significant effect on layered composite and sandwich beams if the lay-up is unbalanced.

Always validate the application of BEAM188, either with experiments or other numerical analysis. Use the restrained warping option with built-up sections after due verification.

KEYOPT(15) specifies the format of the .rst results file. For KEYOPT(15) = 0, the format gives only one averaged result at each section corner node; therefore, this option typically applies to homogeneous sections. For KEYOPT(15) = 1, the format gives one result for each section integration point; therefore, this option typically applies to built-up sections with multiple materials (and generates a larger results file).

Generalized Beam Cross-Sections

When using nonlinear general beam sections, neither the geometric properties nor the material is explicitly specified. Generalized stress implies the axial force, bending moments, torque, and transverse-shear forces. Similarly, generalized strain implies the axial strain, bending curvatures, twisting curvature, and transverse-shear strains. (For more information, see Using Nonlinear General Beam Sections in the Structural Analysis Guide.) This is an abstract method for representing cross-section behavior; therefore, input often consists of experimental data or the results of other analyses.

Generally, BEAM188 supports an elastic relationship between transverse-shear forces and transverse-shear strains. You can override default values of transverse-shear stiffnesses via the SECCONTROL command.

When the beam element is associated with a generalized beam (SECTYPE,,GENB) cross-section type, the relationship of transverse-shear force to the transverse-shear strain can be nonlinear elastic or plastic, an especially useful capability when flexible spot welds are modeled. In such a case, the SECCONTROL command does not apply.

Tapered Beam Cross-Sections

A linearly tapered beam is defined by specifying a standard library section or user mesh at each end of the beam. The section geometries are specified at global coordinates, then linear interpolated and evaluated at the element. The sections at the end points must be topologically identical. (For more information, see Defining a Tapered Beam or Pipe in the Structural Analysis Guide.)

BEAM188 Loads

Forces are applied at the nodes (which also define the element x axis). If the centroidal axis is not colinear with the element x axis, applied axial forces will cause bending. Applied shear forces cause torsional strains and moment if the centroid and shear center of the cross-section are different. The nodes should therefore be located at the desired points where you want to apply the forces. Use the OFFSETY and OFFSETZ arguments of the SECOFFSET command appropriately. By default, the program uses the centroid as the reference axis for the beam elements.

Element loads are described in Element Loading. Pressures can be input as surface loads on the element faces as shown by the circled numbers in Figure 188.1: BEAM188 Geometry. Positive normal pressures act into the element. Lateral pressures are input as force per unit length. End "pressures" are input as forces.

At both ends of the element, temperatures can be input at these locations:

  • At the element x axis (T(0,0))

  • At one unit from the x axis in the element y direction (T(1,0)) (not supported for (KEYOPT(5) = 1)

  • At one unit from the x axis in the element z direction (T(0,1))

Element locations (T(y,z)) are given according to the convention used in Figure 188.1: BEAM188 Geometry.

For beam elements, element body load commands (BFE) accept an element number and a list of values, 1 through 6 for temperatures TI(0,0), TI(1,0), TI(0,1), TJ(0,0), TJ(1,0), and TJ(0,1). This input can be used to specify temperature gradients that vary linearly both over the cross section and along the length of the element.

The following defaults apply to element temperature input:

  • If all temperatures after the first are unspecified, they default to the first. This pattern applies a uniform temperature over the entire element. (The first coordinate temperature, if unspecified, defaults to TUNIF.)

  • If all three temperatures at node I are input, and all temperatures at node J are unspecified, the node J temperatures default to the corresponding node I temperatures. This pattern applies a temperature gradient that varies linearly over the cross section but remains constant along the length of the element.

  • For any other input pattern, unspecified temperatures default to TUNIF.

Alternatively, temperatures at nodes I and J can be defined using nodal body loads (BF,NODE,TEMP,VAL1). When using a nodal body load to define a temperature, a uniform temperature is applied over the cross section at the specified node.

Temperature gradients across the cross-section are not allowed when the beam section has an arbitrary (ASEC) subtype, where the integrated cross-section inertia properties are user-defined (SECTYPE,,BEAM,ASEC).

You can apply an initial stress state to this element via the INISTATE command. Initial state is not available for beam sections of subtype ASEC (SECDATA,BEAM,ASEC).

The effects of pressure load stiffness are automatically included for this element. If an unsymmetric matrix is needed for pressure load stiffness effects, use NROPT,UNSYM.

Ocean Loading

Hydrodynamic added mass and loading, and buoyant loading, are available (OCDATA and OCTABLE).

The global origin is normally at the mean sea level, with the global Z axis pointing away from the center of the earth; however, the vertical location can be adjusted via Zmsl (Val6) on OCDATA (following OCTYPE,BASIC).

BEAM188 in the XY plane (KEYOPT(5) = 1) does not support ocean loading.

For more information, see Applying Ocean Loads in the Basic Analysis Guide.

BEAM188 Input Summary

Nodes
I, J, and K (an optional but recommended orientation node) if KEYOPT(5) = 0
I, J if KEYOPT(5) = 1
Degrees of Freedom
UX, UY, UZ, ROTX, ROTY, ROTZ if KEYOPT(1) = 0 and KEYOPT(5) = 0
UX, UY, UZ, ROTX, ROTY, ROTZ, WARP if KEYOPT(1) = 1 or 2 and KEYOPT(5) = 0
UX, UY, ROTZ if KEYOPT(5) = 1
Section Controls
TXZ, TXY, ADDMAS (See SECCONTROL)
(TXZ and TXY default to A*GXZ and A*GXY, respectively, where A = cross-sectional area)
Material Properties

TB command: See Element Support for Material Models for this element.

MP command: EX, (PRXY,or NUXY), GXY, GXZ, ALPX, (or CTEX, or THSX), DENS, ALPD, BETD, DMPR, DMPS

Surface Loads
Pressure -- 
face 1 (I-J) (-z normal direction)
face 2 (I-J) (-y normal direction) (not applicable if KEYOPT(5) = 1)
face 3 (I-J) (+x tangential direction)
face 4 (I) (+x axial direction)
face 5 (J) (-x axial direction)
---
I and J denote the end nodes.
Use a negative value for loading in the opposite direction.
Issue the SFBEAM command to specify surface loads.
For faces 1, 2, and 3, offsets apply only if you are using the cubic option (KEYOPT(3) = 3).
Body Loads
Temperatures -- 

T(0,0), T(1,0), T(0,1) at each end node

Special Features
KEYOPT(1)

Warping degree of freedom:

0 -- 

Six degrees of freedom per node, unrestrained warping (default)

1 -- 

Seven degrees of freedom per node (including warping). Bimoment and bicurvature are output.

2 -- 

Seven degrees of freedom per node (including warping), but with automatic pre-solution checks. (See BEAM188 Pre-Solution Checks when KEYOPT(1) = 2.) Bimoment and bicurvature are output.

KEYOPT(2)

Cross-section scaling, applies only if NLGEOM,ON has been invoked:

0 -- 

Cross-section is scaled as a function of axial stretch (default)

1 -- 

Section is assumed to be rigid (classical beam theory)

KEYOPT(3)

Shape functions along the length:

0 -- 

Linear (default)

2 -- 

Quadratic

3 -- 

Cubic

KEYOPT(4)

Shear stress output:

0 -- 

Output only torsion-related shear stresses (default)

1 -- 

Output only flexure-related transverse-shear stresses

2 -- 

Output a combined state of the previous two types

KEYOPT(5)

Deformation occurs in 3D space or XY plane:

0 -- 

3D space (default)

1 -- 

XY plane

KEYOPT(6), KEYOPT(7), and KEYOPT(9)

active only when OUTPR,ESOL is active:

KEYOPT(6)

Output control for section forces/moments and strains/curvatures:

0 -- 

Output section forces/moments and strains/curvatures at integration points along the length (default)

1 -- 

Same as KEYOPT(6) = 0 plus current section area

2 -- 

Same as KEYOPT(6) = 1 plus element basis directions (X,Y,Z)

3 -- 

Output section forces/moments and strains/curvatures extrapolated to the element nodes

KEYOPT(7)

Output control at integration points (not available when section subtype = ASEC):

0 -- 

None (default)

1 -- 

Maximum and minimum stresses/strains

2 -- 

Same as KEYOPT(7) = 1 plus stresses and strains at each section point

KEYOPT(9)

Output control for values extrapolated to the element and section nodes (not available when section subtype = ASEC):

0 -- 

None (default)

1 -- 

Maximum and minimum stresses/strains

2 -- 

Same as KEYOPT(9) = 1 plus stresses and strains along the exterior boundary of the cross-section

3 -- 

Same as KEYOPT(9) = 1 plus stresses and strains at all section nodes

KEYOPT(11)

Set section properties:

0 -- 

Automatically determine if preintegrated section properties can be used (default)

1 -- 

Use numerical integration of section

KEYOPT(12)

Tapered section treatment:

0 -- 

Linear tapered section analysis; cross-section properties are evaluated at each Gauss point (default). This is more accurate, but computationally intensive.

1 -- 

Average cross-section analysis; for elements with tapered sections, cross-section properties are evaluated at the centroid only. This is an approximation of the order of the mesh size; however, it is faster.

KEYOPT(13)

Hydrodynamic output (not available in harmonic analyses that include ocean wave effects (HROCEAN)):

0 -- 

None (default)

1 -- 

Additional hydrodynamic printout

KEYOPT(15)

Results file format:

0 -- 

Store averaged results at each section corner node (default).

1 -- 

Store non-averaged results at each section integration point. (The volume of data may be excessive. This option is typically useful for built-up sections with multiple materials only.)

BEAM188 Pre-Solution Checks when KEYOPT(1) = 2

When KEYOPT(1) = 2, the following automatic pre-solution checks occur after issuing SOLVE:

  • For beam elements using an open cross-section only (for example, section subtype CHAN, I, Z, L, T, HATS, ASEC, or MESH), the program ensures that the warping degree of freedom has been added.

    If a beam element with a closed cross-section is found (for example, section subtype RECT, QUAD, CSOLID, CTUBE, or HREC), the program assigns it a new element type with KEYOPT(1) = 0. (All other KEYOPT settings are retained from the original element type.)

  • For beam elements confirmed to have open cross-sections, the program determines whether the warping degree of freedom needs to be decoupled at any selected nodes. The warping is decoupled for the connected elements in the following cases:

    • If elements intersect at an angle > 20 degrees.

    • If the difference in any of the cross-section properties is > 20 percent.

    The automatic check is equivalent to issuing ENDRELEASE,,,WARP,,,,,1, excluding the offsets and cross-section orientation checks.

BEAM188 Output Data

The solution output associated with these elements is in two forms:

To view 3D deformed shapes for BEAM188, issue an OUTRES,MISC or OUTRES,ALL command for static or transient analyses. To view 3D mode shapes for a modal or eigenvalue buckling analysis, you must expand the modes with element results calculation active (via the MXPAND command's Elcalc = YES option).

Linearized Stress

It is customary in beam design to employ components of axial stress that contribute to axial loads and bending in each direction separately; therefore, BEAM188 provides a linearized stress output as part of its SMISC output record, as indicated in the following definitions:

SDIR is the stress component due to axial load.

SDIR = Fx/A, where Fx is the axial load (SMISC quantities 1 and 14) and A is the area of the cross-section.

SByT and SByB are bending-stress components.

SByT = -Mz * ymax / Izz
SByB = -Mz * ymin / Izz
SBzT = My * zmax / Iyy
SBzB = My * zmin / Iyy

where My, Mz are bending moments in the beam coordinate system (SMISC quantities 2,15,3,16), as shown in Figure 188.1: BEAM188 Geometry. Coordinates ymax, ymin, zmax, and zmin are the maximum and minimum y, z coordinates in the cross-section measured from the centroid. Values Iyy and Izz are moments of inertia of the cross-section. Except for the ASEC type of beam cross-section, the program uses the maximum and minimum cross-section dimensions. For the ASEC type of cross-section, the maximum and minimum in each of y and y direction is assumed to be +0.5 to -0.5, respectively.

Corresponding definitions for the component strains are:

EPELDIR = Ex
EPELByT = -Kz * ymax
EPELByB = -Kz * ymin
EPELBzT = Ky * zmax
EPELBzB = Ky * zmin

where Ex, Ky, and Kz are generalized strains and curvatures (SMISC quantities 7,8,9, 20,21 and 22).

The reported linearized stresses are strictly valid only for elastic behavior of members. BEAM188 always employs combined stresses in order to support nonlinear material behavior. When the elements are associated with nonlinear materials, the component stresses can at best be regarded as linearized approximations and should be interpreted with caution.

When using KEYOPT(7) with the cubic option (KEYOPT(3) = 3), the integration point at the middle of the element is reported last in the integration-point printout.

The Element Output Definitions table uses the following notation:

In the table below, the O column indicates the availability of the items in the file Jobname.out. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 188.1: BEAM188 Element Output Definitions

NameDefinitionOR
ELElement numberYY
NODESElement connectivityYY
MATMaterial numberYY
C.G.:X, Y, ZElement center of gravityY 1
AreaArea of cross-section 2 Y
SF:y, zSection shear forces 2 Y
SE:y, zSection shear strains 2 Y
S:xx, xy, xzSection point stresses 3 Y
EPEL:xx, xy, xzElastic strains 3 Y
EPTO:xx, xy, xzSection point total mechanical strains (EPEL + EPPL + EPCR) 3 Y
EPTT:xx, xy, xzSection point total strains (EPEL + EPPL + EPCR+EPTH) 3 Y
EPPL:xx, xy, xzSection point plastic strains 3 Y
EPCR:xx, xy, xzSection point creep strains 3 Y
EPTH:xxSection point thermal strains 3 Y
NL:SEPLPlastic yield stress- 4
NL:SRATPlastic yielding (1 = actively yielding, 0 = not yielding)- 4
NL:HPRESHydrostatic pressure- 4
NL:EPEQAccumulated equivalent plastic strain- 4
NL:CREQAccumulated equivalent creep strain- 4
NL:PLWKPlastic work/volume- 4
SEND:ELASTIC, PLASTIC, CREEPStrain energy densities- 4
TQTorsional momentYY
TETorsional strainYY
Ky, KzCurvatureYY
ExAxial strainYY
FxAxial forceYY
My, MzBending momentsYY
BMWarping bimoment 6 6
BKWarping bicurvature 6 6
EXT PRESSExternal pressure at integration point 5 5
EFFECTIVE TENSEffective tension on beam 5 5
SDIRAxial direct stress- 2
SByTBending stress on the element +Y side of the beam-Y
SByBBending stress on the element -Y side of the beam-Y
SBzTBending stress on the element +Z side of the beam-Y
SBzBBending stress on the element -Z side of the beam-Y
EPELDIRAxial strain at the end-Y
EPELByTBending strain on the element +Y side of the beam.-Y
EPELByBBending strain on the element -Y side of the beam.-Y
EPELBzTBending strain on the element +Z side of the beam.-Y
EPELBzBBending strain on the element -Z side of the beam.-Y
TEMPTemperatures at all section corner nodes.-Y
LOCI:X, Y, ZIntegration point locations- 7
SVAR:1, 2, ... , NState variables- 8
The following values apply to ocean loading only: [9]
GLOBAL COORDElement centroid location 10 Y
VXY, VZHorizontal and vertical fluid particle velocities (VXY is always > 0) 10, 11 Y
AR, AZRadial and vertical fluid particle accelerations 10 Y
PHDYNDynamic fluid pressure head 10 Y
ETAWave amplitude over center of element 10 Y
TFLUIDFluid temperature (printed if VISC is nonzero) 10 Y
VISCViscosity (output if VISC is nonzero) 10 Y
REN, RETNormal and tangential Reynolds numbers (if VISC is nonzero) 10 Y
CTInput tangential drag coefficients evaluated at Reynolds numbers 10 Y
CDY, CDZInput normal drag coefficients evaluated at Reynolds numbers 10 Y
CMY, CMZInput inertia coefficients evaluated at Reynolds numbers 10 Y
URT, URNTangential (parallel to element axis) and normal relative velocities 10 Y
ABURNVector sum of normal (URN) velocities 10 Y
ARNRelative accelerations normal to element 10 Y
FX, FY, FZHydrodynamic tangential and normal forces per unit length in element coordinates 10 Y
ARGUEffective position of wave (radians) 10 Y

  1. Available only at the centroid as a *GET item.

  2. See KEYOPT(6) description.

  3. See KEYOPT(7) and KEYOPT(9) descriptions.

  4. Available if the element has a nonlinear material.

  5. Available only if ocean loading is present.

  6. See KEYOPT(1) description.

    Warping bimoment (BM) is the torsional effect caused by the warping (torsion by the axial stress). It is added to the total torque in addition to the twist by the shear stress. Warping bicurvature (BK) defines the axial strain variation in the section that is caused by the twist of the beam.

  7. Available only if OUTRES,LOCI command is used.

  8. Available only if the UserMat subroutine and TB,STATE command are used.

  9. Values are given as the average of the hydrodynamic integration points, which are distributed along the wetted portion of the element.

  10. Applies to ocean loading only.

  11. Vector sum of wave and current velocities.

More output is described via the PRESOL and *GET,,SECR commands in POST1.

Table 188.2: BEAM188 Item and Sequence Numbers lists output available via the ETABLE and ESOL commands using the Sequence Number method. See Creating an Element Table in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The table uses the following notation:

Name

output quantity as defined in the Table 188.1: BEAM188 Element Output Definitions

Item

predetermined Item label for ETABLE

I,J

sequence number for data at nodes I and J

Table 188.2: BEAM188 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input
ItemEIJ
FxSMISC-- 114
MySMISC--215
MzSMISC--316
TQ [11]SMISC--417
SFzSMISC--518
SFySMISC--619
ExSMISC--720
KySMISC--821
KzSMISC--922
TESMISC--1023
SEzSMISC--1124
SEySMISC--1225
BMSMISC--2729
BKSMISC--2830
SDIRSMISC--3136
SByTSMISC--3237
SByBSMISC--3338
SBzTSMISC--3439
SBzBSMISC--3540
EPELDIRSMISC--4146
EPELByTSMISC--4247
EPELByBSMISC--4348
EPELBzTSMISC--4449
EPELBzBSMISC--4550
TEMPSMISC--51-5354-56
EXT PRESS [9]SMISC--6266
EFFECTIVE TENS [9]SMISC--6367
S:xx, xy, xzLS--CI[1], DI[2]CJ[1], DJ[2]
EPEL:xx, xy, xzLEPEL--CI[1], DI[2]CJ[1], DJ[2]
EPTH:xxLEPTH--AI[3], BI[4]AJ[3], BJ[4]
EPPL:xx, xy, xzLEPPL--CI[1], DI[2]CJ[1], DJ[2]
EPCR:xx, xy, xzLEPCR--CI[1], DI[2]CJ[1], DJ[2]
EPTO:xx, xy, xzLEPTO--CI[1], DI[2]CJ[1], DJ[2]
EPTT:xx, xy, xzLEPTT--CI[1], DI[2]CJ[1], DJ[2]
NL: SEPL, SRAT, HPRES, EPEQ, CREQ, PLWKNLIN--EI[5], FI[6]EJ[5], FJ[6]
AreaNMISC--2930
The following output quantities are valid for ocean loading only and are averaged values for the element: [10]
GLOBAL COORDNMISC1, 2, 3-- --
VXY, VZNMISC4, 5-- --
AR, AZNMISC6, 7 [7]-- --
PHDYNNMISC8 [7]-- --
ETANMISC9 [7]-- --
TFLUIDNMISC10-- --
VISCNMISC11-- --
REN, RETNMISC12, 13 [8]-- --
CTNMISC14-- --
CDY, CDZ NMISC15, 16-- --
CMY, CMZNMISC17, 18 [7]-- --
URT, URNNMISC19, 20, 21-- --
ABURNNMISC22 [7]-- --
ARNNMISC23, 24 [7]-- --
FX, FY, FZNMISC25, 26, 27-- --
ARGUNMISC28 [7]-- --

  1. CI and CJ are the sequence numbers for accessing the averaged line element solution quantities (LS, LEPEL, LEPPL, LEPCR, LEPTO, and LEPTT) at RST section nodes (section corner nodes where results are available), at element Node I and J respectively. CI and CJ are applicable only when KEYOPT(15) = 0. For a given section corner node nn, CI and CJ are given as follows:

    CI = (nn - 1) * 3+ COMP

    CJ = (nnMax + nn - 1) * 3+ COMP

    Where nnMax is the total number of RST section nodes, and COMP is the stress or strain component (1 - xx, 2 - xy, 3 - xz). Locations of RST section nodes can be visualized with SECPLOT,,6.

  2. DI and DJ are the sequence numbers for accessing the non-averaged line element solution quantities (LS, LEPEL, LEPPL, LEPCR, LEPTO, and LEPTT) at RST section integration points (section integration points where results are available), at element Node I and J respectively. DI and DJ are applicable only when KEYOPT(15) = 1. For the ith integration point (i = 1, 2, 3, or 4) in section cell nc, DI and DJ are given as follows:

    DI = (nc - 1) * 12 + (i - 1) * 3 + COMP

    DJ = (ncMax + nc - 1) * 12 + (i - 1) * 3 + COMP

    Where ncMax is the total number of RST section cells, and COMP is the stress or strain component (1 - xx, 2 - xy, 3 - xz). Locations of RST section cells can be visualized with SECPLOT,,7.

  3. AI and AJ are the sequence numbers for accessing the averaged line element thermal strain quantities LEPTH at RST section nodes (section corner nodes where results are available), at element Node I and J respectively. AI and AJ are applicable only when KEYOPT(15) = 0. For a given section corner node nn, AI and AJ are given as follows:

    AI = nn

    AJ = nnMax + nn

    Where nnMax is the total number of RST section nodes. Locations of RST section nodes can be visualized with SECPLOT,,6.

  4. BI and BJ are the sequence numbers for accessing the non-averaged line element thermal strain quantities LEPTH at RST section integration points (section integration points where results are available), at element Node I and J respectively. BI and BJ are applicable only when KEYOPT(15) = 1. For the ith integration point (i = 1, 2, 3, or 4) in section cell nc, BI and BJ are given as follows:

    BI = (nc - 1) * 4 + i

    BJ = (ncMax + nc - 1) * 4 + i

    Where ncMax is the total number of RST section cells. Locations of RST section cells can be visualized with SECPLOT,,7.

  5. EI and EJ are the sequence numbers for accessing the averaged line element nonlinear solution quantities (NLIN) at RST section nodes (section corner nodes where results are available), at element Node I and J, respectively. EI and EJ are applicable only when KEYOPT(15) = 0. For a given section corner node nn, EI and EJ are given as follows:

    EI = (nn - 1) * 10 + COMP

    EJ = (nnMax + nn - 1) * 10 + COMP

    where nnMax is the total number of RST section nodes, and COMP is the nonlinear element solution component (1 - SEPL, 2 - SRAT, 3 - HPRES, 4 -EPEQ, 5 - CREQ, 6 - PLWK). Locations of RST section nodes can be visualized via SECPLOT,,6.

  6. FI and FJ are the sequence numbers for accessing the nonaveraged line element nonlinear solution quantities (NLIN) at RST section integration points (section integration points where results are available), at element Node I and J, respectively. FI and FJ are applicable only when KEYOPT(15) = 1. For a given section integration point (i = 1, 2, 3, or 4) in section cell nc, FI and FJ are given as follows:

    FI = (nc - 1) * 40 + (i - 1) * 10 + COMP

    FJ = (ncMax + nc - 1) * 40 + (i - 1) * 10 + COMP

    where ncMax is the total number of RST section cells and COMP is the nonlinear element solution component (1 - SEPL, 2 - SRAT, 3 - HPRES, 4 - EPEQ, 5 - CREQ, 6 - PLWK). Locations of RST section cells can be visualized via SECPLOT,,7.

  7. Applies to ocean loading only.

  8. These quantities are output only if a Reynold's number dependency is used.

  9. External pressure (EXT PRESS) and effective tension (EFFECTIVE TENS) occur at integration points, and not at end nodes.

  10. Values are given as the average of the hydrodynamic integration points, which are distributed along the wetted portion of the element.

  11. The torsional moment (TQ) is given by , where is the torsional stiffness, and are twists at node I and J, and is the axial orientation ( at node I and at node J).

Transverse-Shear Stress Output

The BEAM188 formulation is based on three stress components:

  • one axial

  • two shear stress

The shear stresses are caused by torsional and transverse loads. BEAM188 is based on first-order shear-deformation theory, also popularly known as Timoshenko beam theory. The transverse-shear strain is constant for the cross-section; therefore, the shear energy is based on a transverse-shear force. The shear force is redistributed by predetermined shear-stress distribution coefficients across the beam cross-section, and made available for output purposes. By default, the program outputs only the shear stresses caused by torsional loading. Use KEYOPT(4) to activate output of shear stresses caused by flexure or transverse loading.

The accuracy of transverse-shear distribution is directly proportional to the mesh density of cross-section modeling (for determination of warping, shear center and other section geometric properties). The traction-free state at the edges of a cross-section is met only in a well-refined model of the cross-section.

By default, the program uses a mesh density (for cross-section modeling) that provides accurate results for torsional rigidity, warping rigidity, inertia properties, and shear-center determination. The default mesh employed is also appropriate for nonlinear material calculations; however, more refined cross-section models may be necessary if the shear stress distribution due to transverse loads must be captured very accurately. Increasing cross-section mesh size does not imply larger computational cost if the cross-section is homogeneous and the associated material is linear. Use the SECTYPE and SECDATA commands to adjust cross-section mesh density.

The transverse-shear distribution calculation ignores the effects of Poisson's ratio. The Poisson's ratio affects the shear-correction factor and shear-stress distribution slightly, and this effect is ignored. Shear-correction factors for some common sections are as follows: rectangle (5/6), solid circle (9/10), thin-walled hollow circle (1/2). For the arbitrary section (ASEC), shear-correction factors can be input directly (SECDATA).

BEAM188 Assumptions and Restrictions

  • The beam must not have zero length.

  • By default (KEYOPT(1) = 0), the effect of warping restraint is assumed to be negligible.

  • Cross-section failure or folding is not accounted for.

  • The location of an axial load on the cross-section does not affect the buckling load.

  • Initial state is not available for beam sections of subtype ASEC (SECDATA,BEAM,ASEC).

  • The element works best with the full Newton-Raphson solution scheme (that is, the default choice in solution control).

  • Only moderately "thick" beams can be analyzed. See "BEAM188 Element Technology and Usage Recommendations" for more information.

  • Stress stiffening is always included in geometrically nonlinear analyses (NLGEOM,ON). Prestress effects can be activated by the PSTRES command.

  • When the element is associated with nonlinear general beam sections (SECTYPE,,GENB), additional restrictions apply. For more information, see Considerations for Using Nonlinear General Beam Sections in the Structural Analysis Guide.

  • For a random vibration (PSD) analysis, equivalent stress is not calculated.

  • When the element is used in an ocean environment:

    • For subtype ASEC, the calculated perimeter is two times the sum of the input maximum height and width.

    • Hydrodynamic output via KEYOPT(13) is not available in harmonic analyses that include ocean wave effects (HROCEAN).

    • The three-dimensional effect of water pressure on the element is adjusted, as the element has only one direct stress. For more information, see Hydrostatic Loads in the Theory Reference.

    • Enclosed spaces used by subtypes CTUBE or HREC are assumed to have the same pressure and internal fluid density as the surrounding ocean (that is, as if the flooding option used with PIPE288 or PIPE289 is always enabled).

    • Generally, it is better to use a pipe element (PIPE288 or PIPE289) rather than beam subtype CTUBE, as the pipe element has a degree of freedom to account for cross-sectional compression and can also have an independent internal pressure applied.

    • The output axial force may not be exact when using ocean loading with nonlinear materials.

BEAM188 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 Mechanical Pro  —  

  • Birth and death is not available.

  • Initial state is not available.

  • Ocean loading is not available.