4.4 BEAM4 3-D Elastic Beam

Figure 4.4-1 BEAM4 3-D Elastic Beam

4.4.1 Input Data

The element x-axis is oriented from node I toward node J. For the two-node option, the default (=0°) orientation of the element y-axis is automatically calculated to be parallel to the global X-Y plane. Several orientations are shown in Figure 4.4-1. 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). For user control of the element orientation about the element x-axis, use the angle (THETA) or the third node option. If both are defined, the third node option takes precedence. The third node (K), if used, defines a plane (with I and J) containing the element x and z axes (as shown). If this element is used in a large deflection analysis, it should be noted that the location of the third node (K), or the angle (THETA), is used only to initially orient the element. (For information about orientation nodes and beam meshing, see Chapter 7 of the ANSYS Modeling and Meshing Guide.)

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 shear deflection constants (SHEARZ and SHEARY) are used only if shear deflection is to be included. A zero value of SHEAR_ may be used to neglect shear deflection in a particular direction. See Section 2.10 for details.

KEYOPT(2) is used to activate the consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffness matrix plus the consistent stress stiffness matrix) in large deflection analyses [NLGEOM,ON]. You can often obtain more rapid convergence in a geometrically nonlinear analysis, such as a nonlinear buckling or postbuckling analysis, by activating this option. However, you should not use this option if you are using the element to simulate a rigid link or a group of coupled nodes. The resulting abrupt changes in stiffness within the structure make the consistent tangent stiffness matrix unsuitable for such applications.

KEYOPT(7) is used to compute an unsymmetric gyroscopic damping matrix (often used for rotordynamic analyses). The rotational frequency is input with the SPIN real constant (radians/time, positive in the positive element x direction). The element must be symmetric with this option (e.g., IYY=IZZ and SHEARY=SHEARZ).

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 4.4-1. Positive normal 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 eight "corner" locations shown in Figure 4.4-1. 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. If only T1 and T4 are input, T2 defaults to T1 and T3 defaults to T4. In both cases, T5 through T8 default to T1 through T4. For any other input pattern, unspecified temperatures default to TUNIF.

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

• stress stiffening is turned on [SSTIF,ON]
• more than one component of angular velocity is applied [OMEGA]
• any angular velocities or accelerations are applied with the CGOMGA, DOMEGA, or DCGOMG commands.

Table 4.4-1 BEAM4 Input Summary

Element Name	BEAM4
Nodes	I, J, K (K orientation node is optional)
Degrees of Freedom	UX, UY, UZ, ROTX, ROTY, ROTZ
Real Constants	AREA, IZZ, IYY, TKZ, TKY, THETA, ISTRN, IXX, SHEARZ, SHEARY, SPIN, ADDMAS
Material Properties	EX, ALPX, DENS, GXY, DAMP
Surface Loads	Pressures: face 1 (I-J) (-Z normal direction), face 2 (I-J) (-Y normal direction), face 3 (I-J) (+X tangential direction), face 4 (I) (+X axial direction), face 5 (J) (-X axial direction) (use negative value for opposite loading)
Body Loads	Temperatures: T1, T2, T3, T4, T5, T6, T7, T8
Special Features	Stress stiffening, Large deflection, Birth and death
KEYOPT(2)	0 - Use only the main tangent stiffness matrix when NLGEOM is ON. (Stress stiffening effects used in linear buckling or other linear prestressed analyses must be activated separately with PSTRES,ON.) 1 - Use the consistent tangent stiffness matrix (i.e., a matrix composed of the main tangent stiffness matrix plus the consistent stress stiffness matrix) when NLGEOM is ON. (SSTIF,ON will be ignored for this element when KEYOPT(2)=1 is activated.) Note that if SOLCONTROL is ON and NLGEOM is ON, KEYOPT(2) is automatically set to 1; i.e, the consistent tangent will be used.
KEYOPT(6)	0 - No printout of member forces or moments 1 - Print out member forces and moments in the element coordinate system
KEYOPT(7)	0 - No gyroscopic damping matrix 1 - Compute gyroscopic damping matrix. Real constant SPIN must be greater than zero. IYY must equal IZZ.
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 IZZ, if SHEARZ = 0, there is no shear deflection in the element Y direction

Note-SHEARY goes with IYY, if SHEARY = 0, there is no shear deflection in the element Z direction

4.4.2 Output Data

• nodal displacements included in the overall nodal solution
• additional element output as shown in Table 4.4-2.

The maximum stress is computed as the direct stress plus the absolute values of both bending stresses. The minimum stress is the direct stress minus the absolute value of both bending stresses. 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 4.4-2 3-D BEAM4 Stress Output

The following notation is used in Table 4.4-2:

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 4.4-2 3-D BEAM4 Element Output Definitions

Name	Definition	O	R
EL	Element number	Y	Y
NODES	Element node number (I and J)	Y	Y
MAT	Material number for the element	Y	Y
VOLU:	Element volume	-	Y
CENT: X, Y, Z	Global location of the element centroid XC, YC, ZC	-	Y
TEMP	Temperatures at integration points T1,T2,T3,T4,T5,T6,T7,T8	Y	Y
PRES	Pressure P1 at nodes I,J; OFFST1 at I,J; P2 at I,J; OFFST2 at I,J; P3 at I,J; OFFST3 at I,J; P4 at I; P5 at J	Y	Y
SDI R	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
SBZT	Bending stress on the element +Z side of the beam	1	1
SBZB	Bending stress on the element -Z 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
EPELBZT	Bending elastic strain on the element +Z side of the beam	1	1
EPELBZB	Bending elastic strain on the element -Z 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
EPTHBZT	Bending thermal strain on the element +Z side of the beam	1	1
EPTHBZB	Bending thermal strain on the element -Z side of the beam	1	1
EPINAXL	Initial axial strain in the element	1	1
MFOR(X, Y, Z)	Member forces in the element coordinate system X, Y, Z directions	2	Y
MMOM(X, Y, Z)	Member moments in the element coordinate system X, Y, Z directions	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. The following notation is used in Tables 4.4-3 through 4.4-3e:

Name - output quantity as defined in the Table 4.4-2

Item - predetermined Item label for ETABLE command

E - sequence number for single-valued or constant element data

I,J - sequence number for data at nodes I and J

ILn - sequence number for data at Intermediate Location n

KEYOPT(9)=0
Name		Item	E	I	J
SDIR		LS	-	1	6
SBYT		LS	-	2	7
SBYB		LS	-	3	8
SBZT		LS	-	4	9
SBZB		LS	-	5	10
EPELDIR		LEPEL	-	1	6
EPELBYT		LEPEL	-	2	7
EPELBYB		LEPEL	-	3	8
EPELBZT		LEPEL	-	4	9
EPELBZB		LEPEL	-	5	10
SMAX		NMISC	-	1	3
SMIN		NMISC	-	2	4
EPTHDIR		LEPTH	-	1	6
EPTHBYT		LEPTH	-	2	7
EPTHBYB		LEPTH	-	3	8
EPTHBZT		LEPTH	-	4	9
EPTHBZB		LEPTH	-	5	10
EPINAXL		LEPTH	11	-	-
MFORX		SMISC	-	1	7
MFORY		SMISC	-	2	8
MFORZ		SMISC	-	3	9
MMOMX		SMISC	-	4	10
MMOMY		SMISC	-	5	11
MMOMZ		SMISC	-	6	12
P1		SMISC	-	13	14
OFFST1		SMISC	-	15	16
P2		SMISC	-	17	18
OFFST2		SMISC	-	19	20
P3		SMISC	-	21	22
OFFST3		SMISC	-	23	24
P4		SMISC	-	25	-
P5		SMISC	-	-	26

		Pseudo Node
		1	2	3	4	5	6	7	8
TEMP	LBFE	1	2	3	4	5	6	7	8

Table 4.4-3a BEAM4 (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	6	11
SBYT	LS	-	2	7	12
SBYB	LS	-	3	8	13
SBZT	LS	-	4	9	14
SBZB	LS	-	5	10	15
EPELDIR	LEPEL	-	1	6	11
EPELBYT	LEPEL	-	2	7	12
EPELBYB	LEPEL	-	3	8	13
EPELBZT	LEPEL	-	4	9	14
EPELBZB	LEPEL	-	5	10	15
SMAX	NMISC	-	1	3	5
SMIN	NMISC	-	2	4	6
EPTHDIR	LEPTH	-	1	6	11
EPTHBYT	LEPTH	-	2	7	12
EPTHBYB	LEPTH	-	3	8	13
EPTHBZT	LEPTH	-	4	9	14
EPTHBZB	LEPTH	-	5	10	15
EPINAXL	LEPTH	16	-	-	-
MFORX	SMISC	-	1	7	13
MFORY	SMISC	-	2	8	14
MFORZ	SMISC	-	3	9	15
MMOMX	SMISC	-	4	10	16
MMOMY	SMISC	-	5	11	17
MMOMZ	SMISC	-	6	12	18
P1	SMISC	-	19	-	20
OFFST1	SMISC	-	21	-	22
P2	SMISC	-	23	-	24
OFFST2	SMISC	-	25	-	26
P3	SMISC	-	27	-	28
OFFST3	SMISC	-	29	-	30
P4	SMISC	-	31	-	-
P5	SMISC	-	-	-	32

		Pseudo Node
		1	2	3	4	5	6	7	8
TEMP	LBFE	1	2	3	4	5	6	7	8

Table 4.4-3b BEAM4 (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	6	11	16	21
SBYT	LS	-	2	7	12	17	22
SBYB	LS	-	3	8	13	18	23
SBZT	LS	-	4	9	14	19	24
SBZB	LS	-	5	10	15	20	25
EPELDIR	LEPEL	-	1	6	11	16	21
EPELBYT	LEPEL	-	2	7	12	17	22
EPELBYB	LEPEL	-	3	8	13	18	23
EPELBZT	LEPEL	-	4	9	14	19	24
EPELBZB	LEPEL	-	5	10	15	20	25
SMAX	NMISC	-	1	3	5	7	9
SMIN	NMISC	-	2	4	6	8	10
EPTHDIR	LEPTH	-	1	6	11	16	21
EPTHBYT	LEPTH	-	2	7	12	17	22
EPTHBYB	LEPTH	-	3	8	13	18	23
EPTHBZT	LEPTH	-	4	9	14	19	24
EPTHBZB	LEPTH	-	5	10	15	20	25
EPINAXL	LEPTH	26	-	-	-	-	-
MFORX	SMISC	-	1	7	13	19	25
MFORY	SMISC	-	2	8	14	20	26
MFORZ	SMISC	-	3	9	15	21	27
MMOMX	SMISC	-	4	10	16	22	28
MMOMY	SMISC	-	5	11	17	23	29
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	-	-	-	40
OFFST3	SMISC	-	41	-	-	-	42
P4	SMISC	-	43	-	-	-
P5	SMISC	-	-	-	-	-	44

		Pseudo Node
		1	2	3	4	5	6	7	8
TEMP	LBFE	1	2	3	4	5	6	7	8

Table 4.4-3c BEAM4 (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	6	11	16	21	26	31
SBYT	LS	-	2	7	12	17	22	27	32
SBYB	LS	-	3	8	13	18	23	28	33
SBZT	LS	-	4	9	14	19	24	29	34
SBZB	LS	-	5	10	15	20	25	30	35
EPELDIR	LEPEL	-	1	6	11	16	21	26	31
EPELBYT	LEPEL	-	2	7	12	17	22	27	32
EPELBYB	LEPEL	-	3	8	13	18	23	28	33
EPELBZT	LEPEL	-	4	9	14	19	24	29	34
EPELBZB	LEPEL	-	5	10	15	20	25	30	35
SMAX	NMISC	-	1	3	5	7	9	11	13
SMIN	NMISC	-	2	4	6	8	10	12	14
EPTHDIR	LEPTH	-	1	6	11	16	21	26	31
EPTHBYT	LEPTH	-	2	7	12	17	22	27	32
EPTHBYB	LEPTH	-	3	8	13	18	23	28	33
EPTHBZT	LEPTH	-	4	9	14	19	24	29	34
EPTHBZB	LEPTH	-	5	10	15	20	25	30	35
EPINAXL	LEPTH	36	-	-	-	-	-	-	-
MFORX	SMISC	-	1	7	13	19	25	31	37
MFORY	SMISC	-	2	8	14	20	26	32	38
MFORZ	SMISC	-	3	9	15	21	27	33	39
MMOMX	SMISC	-	4	10	16	22	28	34	40
MMOMY	SMISC	-	5	11	17	23	29	35	41
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	-	-	-	-	-	52
OFFST3	SMISC	-	53	-	-	-	-	-	54
P4	SMISC	-	55	-	-	-	-	-	-
P5	SMISC	-	-	-	-	-	-	-	56

		Pseudo Node
		1	2	3	4	5	6	7	8
TEMP	LBFE	1	2	3	4	5	6	7	8

Table 4.4-3d BEAM4 (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	6	11	16	21	26	31	36	41
SBYT	LS	-	2	7	12	17	22	27	32	37	42
SBYB	LS	-	3	8	13	18	23	28	33	38	43
SBZT	LS	-	4	9	14	19	24	29	34	39	44
SBZB	LS	-	5	10	15	20	25	30	35	40	45
EPELDIR	LEPEL	-	1	6	11	16	21	26	31	36	41
EPELBYT	LEPEL	-	2	7	12	17	22	27	32	37	42
EPELBYB	LEPEL	-	3	8	13	18	23	28	33	38	43
EPELBZT	LEPEL	-	4	9	14	19	24	29	34	39	44
EPELBZB	LEPEL	-	5	10	15	20	25	30	35	40	45
SMAX	NMISC	-	1	3	5	7	9	11	13	15	17
SMIN	NMISC	-	2	4	6	8	10	12	14	16	18
EPTHDIR	LEPTH	-	1	6	11	16	21	26	31	36	41
EPTHBYT	LEPTH	-	2	7	12	17	22	27	32	37	42
EPTHBYB	LEPTH	-	3	8	13	18	23	28	33	38	43
EPTHBZT	LEPTH	-	4	9	14	19	24	29	34	39	44
EPTHBZB	LEPTH	-	5	10	15	20	25	30	35	40	45
EPINAXL	LEPTH	46	-	-	-	-	-	-	-	-	-
MFORX	SMISC	-	1	7	13	19	25	31	37	43	49
MFORY	SMISC	-	2	8	14	20	26	32	38	44	50
MFORZ	SMISC	-	3	9	15	21	27	33	39	45	51
MMOMX	SMISC	-	4	10	16	22	28	34	40	46	52
MMOMY	SMISC	-	5	11	17	23	29	35	41	47	53
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	-	-	-	-	-	-	-	64
OFFST3	SMISC	-	65	-	-	-	-	-	-	-	66
P4	SMISC	-	67	-	-	-	-	-	-	-	-
P5	SMISC	-	-	-	-	-	-	-	-	-	68

		Pseudo Node
		1	2	3	4	5	6	7	8
TEMP	LBFE	1	2	3	4	5	6	7	8

Table 4.4-3e BEAM4 (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	6	11	16	21	26	31	36	41	46	51
SBYT	LS	-	2	7	12	17	22	27	32	37	42	47	52
SBYB	LS	-	3	8	13	18	23	28	33	38	43	48	53
SBZT	LS	-	4	9	14	19	24	29	34	39	44	49	54
SBZB	LS	-	5	10	15	20	25	30	35	40	45	50	55
EPELDIR	LEPEL	-	1	6	11	16	21	26	31	36	41	46	51
EPELBYT	LEPEL	-	2	7	12	17	22	27	32	37	42	47	52
EPELBYB	LEPEL	-	3	8	13	18	23	28	33	38	43	48	53
EPELBZT	LEPEL	-	4	9	14	19	24	29	34	39	44	49	54
EPELBZB	LEPEL	-	5	10	15	20	25	30	35	40	45	50	55
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
EPTHDIR	LEPTH	-	1	6	11	16	21	26	31	36	41	46	51
EPTHBYT	LEPTH	-	2	7	12	17	22	27	32	37	42	47	52
EPTHBYB	LEPTH	-	3	8	13	18	23	28	33	38	43	48	53
EPTHBZT	LEPTH	-	4	9	14	19	24	29	34	39	44	49	54
EPTHBZB	LEPTH	-	5	10	15	20	25	30	35	40	45	50	55
EPINAXL	LEPTH	56	-	-	-	-	-	-	-	-	-	-	-
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
MFORZ	SMISC	-	3	9	15	21	27	33	39	45	51	57	63
MMOMX	SMISC	-	4	10	16	22	28	34	40	46	52	58	64
MMOMY	SMISC	-	5	11	17	23	29	35	41	47	53	59	65
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	-	-	-	-	-	-	-	-	-	76
OFFST3	SMISC	-	77	-	-	-	-	-	-	-	-	-	78
P4	SMISC	-	79	-	-	-	-	-	-	-	-	-	-
P5	SMISC	-	-	-	-	-	-	-	-	-	-	-	80

		Pseudo Node
		1	2	3	4	5	6	7	8
TEMP	LBFE	1	2	3	4	5	6	7	8

4.4.3 Assumptions and Restrictions

If you use the consistent tangent stiffness matrix (KEYOPT(2)=1), take care to use realistic (i.e., "to scale") element real constants. This precaution is necessary because the consistent stress-stiffening matrix is based on the calculated stresses in the element-if you use artificially large or small cross-sectional properties, the calculated stresses will become inaccurate, and the stress-stiffening matrix will suffer corresponding inaccuracies. (Certain components of the stress-stiffening matrix could even overshoot to infinity.) Similar difficulties could arise if unrealistic real constants are used in a linear prestressed or linear buckling analysis [PSTRES,ON].

Eigenvalues calculated in a gyroscopic modal analysis can be very sensitive to changes in the initial shift value, leading to potential error in either the real or imaginary (or both) parts of the eigenvalues.

4.4.4 Product Restrictions

ANSYS/LinearPlus

• The SPIN real constant (R11) is not available. Input R11 as a blank.
• The DAMP material property is not allowed.
• KEYOPT(2) can only be set to 0 (default).
• KEYOPT(7) can only be set to 0 (default).
• The only special features allowed are stress stiffening and large deflections.