4.60 PIPE60 Plastic Curved Pipe (Elbow)

The element has plastic, creep and swelling capabilities. If these effects are not needed, the elastic curved pipe element, PIPE18, may be used. Options are available for including a flexibility factor and for printing the forces and moments acting on the element in the element coordinate system. See Section 14.60 of the ANSYS Theory Reference for more details about this element. A plastic straight pipe element (PIPE20) is described in Section 4.20.

Figure 4.60-1 PIPE60 Plastic Curved Pipe (Elbow)

4.60.1 Input Data

Although the curved pipe element has only two end points (nodes I and J), the third node (K) is required to define the plane in which the element lies. This node must lie in the plane of the curved pipe and on the center of curvature side of line I-J. A node belonging to another element (such as the other node of a connecting straight pipe element) may be used.

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 4.60-1. Internal pressure (PINT) and external pressure (POUT) are input as positive values. The transverse pressures (PX, PY, and PZ) may represent wind or drag loads (per unit length of the pipe) and are defined in the global Cartesian directions. Positive transverse pressures act in the positive coordinate directions. See Section 14.16.7 of the ANSYS Theory Reference for more details.

Temperatures and fluences may be input as element body loads at the nodes. The first temperature (TAVG at node I) defaults to TUNIF. If all temperatures after the first are unspecified, they default to the first. If all 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. For any other pattern of input temperatures, unspecified temperatures default to TUNIF. Similar defaults occurs for fluence except that zero is used instead of TUNIF.

The KEYOPT(2) and KEYOPT(3) options control the flexibility and stress intensification factors as follows:

ANSYS Flexibility Factor = 1.65/(h(1 + PrX_k/tE)) or 1.0 (whichever is greater)
(used if KEYOPT(3)=0 or 1)

Karman Flexibility Factor = (10 + 12h²)/(1 + 12h²) (used if KEYOPT(3)= 2)

User Defined Flexibility Factors = FLXI (in-plane) and FLXO (out-of-plane) (must be positive) (used if KEYOPT(3)=3)

Reference Stress Intensification Factor (SIF) = 0.9/h^2/3 or 1.0 (whichever is greater) used for SIFI or SIFJ if KEYOPT(2)=0 or if user supplied SIF's are less than 1.0 (user supplied values must be positive)

User Defined Stress Intensification Factors = SIFI, SIFJ (must be positive) (used if KEYOPT(2)=4)

where:

h = tR/r²

P = P_i-P_o

P_{i =} internal pressure

P_{o =} external pressure

r = average radius

t = thickness

E = modulus of elasticity

X_{k =} 6 (r/t)^4/3(R/r)^1/3 if KEYOPT(3)=1 and R/r >= 1.7, otherwise X_k=0

R = radius of curvature

KEYOPT(3)=1 should not be used if the included angle of the complete elbow is less than 360/((R/r)) degrees.

A summary of the element input is given in Table 4.60-1. A general description of element input is given in Section 2.1.

Table 4.60-1 PIPE60 Input Summary

Element Name	PIPE60
Nodes	I, J, K (K is a node in the plane of the elbow, on the center of curvature side of line I-J)
Degrees of Freedom	UX, UY, UZ, ROTX, ROTY, ROTZ
Real Constants	OD, TKWALL, RADCUR, SIFI, SIFJ, FLXI, (Blank), (Blank), (Blank), (Blank), (Blank), FLXO
Material Properties	EX, ALPX, PRXY or NUXY, DENS, GXY, DAMP
Surface Loads	Pressures: 1-PINT, 2-PX, 3-PY, 4-PZ, 5-POUT
Body Loads	Temperatures: TAVG (I), T90 (I), T180 (I), TAVG (J), T90 (J), T180 (J) Fluences: FLAVG (I), FL90 (I), FL180 (I), FLAVG (J), FL90 (J), FL180 (J)
Special Features	Plasticity, Creep, Swelling, Large deflection, Birth and death
KEYOPT(2)	0 - Include reference stress intensification factors (SIF) 4 - Include stress intensification factors at nodes I and J as input with SIFI and SIFJ real constants
KEYOPT(3)	0 - Do not include pressure term in ANSYS flexibility factor 1 - Include pressure term in ANSYS flexibility factor 2 - Use Karman flexibility factor 3 - Use input flexibility factors (FLXI, FLXO)
KEYOPT(6)	0 - No printout of member forces or moments 1 - Print member forces and moments in the element coordinate system

4.60.2 Output Data

• nodal displacements included in the overall nodal solution
• additional element output as shown in Table 4.60-2

Figure 4.60-3 PIPE60 Printout Locations

The following notation is used in Table 4.60-2:

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 4.60-2 PIPE60 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 TAVG(I), T90(I), T180(I), TAVG(J), T90(J), T180(J)	Y	Y
FLUE	Fluences FLAVG(I), FL90(I), FL180(I), FLAVG(J), FL90(J), FL180(J)	Y	Y
PRES	Pressures PINT, PX, PY, PZ, POUT	Y	Y
FFACT	Element flexibility factor	-	Y
SFACTI, SFACTJ	Stress intensification factors at nodes I and J	-	Y
MFOR(X, Y, Z)	Member forces for nodes I and J (in the element coordinate system)	1	1
MMOM(X, Y, Z)	Member moments for nodes I and J (in the element coordinate system)	1	1
SDIR	Direct (axial) stress	-	2
SBEND	Maximum bending stress at outer surface	-	2
ST	Shear stress at outer surface due to torsion	-	2
SSF	Shear stress due to shear force	-	2
S1MX, S3MN, SINTMX, SEQVMX	Maximum principal stress, minimum principal stress, maximum stress intensity, maximum equivalent stress all at the outer surface (based on SDIR, SBEND, ST, SSF but also accounting for the values of S1, S3, SINT, SEQV given below)	2	2
S(AXL, RAD, H, XH)	Axial, radial, hoop, and shear stresses	3	3
S(1, 3, INT, EQV)	Maximum principal stress, minimum principal stress, stress intensity, equivalent stress	3	3
EPEL(AXL, RAD, H, XH)	Axial, radial, hoop, and shear strains	3	3
EPTH(AXL, RAD, H)	Axial, radial, and hoop thermal strain	3	3
EPPL(AXL, RAD, H, XH)	Axial, radial, hoop, and shear plastic strains	3	3
EPCR(AXL, RAD, H, XH)	Axial, radial, hoop, and shear creep strains	3	3
SRAT	Ratio of trial stress to stress on yield surface	3	3
EPEQ	Equivalent plastic strain	3	3
HPRES	Hydrostatic pressure (postdata only)	-	3
SEPL	Equivalent stress from stress-strain curve	3	3
EPSWAXL	Axial swelling strain	3	3

1. If KEYOPT(6)=1

2. Initial elastic solution output before yield

3. The item repeats for THETA=0,45,90,135,180,225,270,315° at node I, then at node J, all at the mid-thickness of the wall

Table 4.60-3 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 4.60-3:

Name - output quantity as defined in the Table 4.60-2

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

Node I
Name	Item	E	Circumferential Location
			0°	45°	90°	135°	180°	225°	270°	315°
SAXL	LS	-	1	5	9	13	17	21	25	29
SRAD	LS	-	2	6	10	14	18	22	26	30
SH	LS	-	3	7	11	15	19	23	27	31
SXH	LS	-	4	8	12	16	20	24	28	32
EPELAXL	LEPEL	-	1	5	9	13	17	21	25	29
EPELRAD	LEPEL	-	2	6	10	14	18	22	26	30
EPELH	LEPEL	-	3	7	11	15	19	23	27	31
EPELXH	LEPEL	-	4	8	12	16	20	24	28	32
EPTHAXL	LEPTH	-	1	5	9	13	17	21	25	29
EPTHRAD	LEPTH	-	2	6	10	14	18	22	26	30
EPTHH	LEPTH	-	3	7	11	15	19	23	27	31
EPPLAXL	LEPPL	-	1	5	9	13	17	21	25	29
EPPLRAD	LEPPL	-	2	6	10	14	18	22	26	30
EPPLH	LEPPL	-	3	7	11	15	19	23	27	31
EPPLXH	LEPPL	-	4	8	12	16	20	24	28	32
EPCRAXL	LEPCR	-	1	5	9	13	17	21	25	29
EPCRRAD	LEPCR	-	2	6	10	14	18	22	26	30
EPCRH	LEPCR	-	3	7	11	15	19	23	27	31
EPCRXH	LEPCR	-	4	8	12	16	20	24	28	32
SEPL	NLIN	-	1	5	9	13	17	21	25	29
SRAT	NLIN	-	2	6	10	14	18	22	26	30
HPRES	NLIN	-	3	7	11	15	19	23	27	31
EPEQ	NLIN	-	4	8	12	16	20	24	28	32
S1	NMISC	-	1	6	11	16	21	26	31	36
S3	NMISC	-	3	8	13	18	23	28	33	38
SINT	NMISC	-	4	9	14	19	24	29	34	39
SEQV	NMISC	-	5	10	15	20	25	30	35	40
SBEND	NMISC	84	-	-	-	-	-	-	-	-
SSF	NMISC	85	-	-	-	-	-	-	-	-
FOUT	NMISC	-	91	-	88	-	89	-	90	-
FIN	NMISC	-	95	-	92	-	93	-	94	-
MFORX	SMISC	1	-	-	-	-	-	-	-	-
MFORY	SMISC	2	-	-	-	-	-	-	-	-
MFORZ	SMISC	3	-	-	-	-	-	-	-	-
MMOMX	SMISC	4	-	-	-	-	-	-	-	-
MMOMY	SMISC	5	-	-	-	-	-	-	-	-
MMOMZ	SMISC	6	-	-	-	-	-	-	-	-
SDIR	SMISC	13	-	-	-	-	-	-	-	-
ST	SMISC	14	-	-	-	-	-	-	-	-
TOUT	LBFE	-	4	-	1	-	2	-	3	-
TIN	LBFE	-	8	-	5	-	6	-	7	-

Table 4.60-3a PIPE60 Item and Sequence Numbers for the ETABLE and ESOL Commands

Node J
Name	Item	E	Circumferential Location
			0°	45°	90°	135°	180°	225°	270°	315°
SAXL	LS	-	33	37	41	45	49	53	57	61
SRAD	LS	-	34	38	42	46	50	54	58	62
SH	LS	-	35	39	43	47	51	55	59	63
SXH	LS	-	36	40	44	48	52	56	60	64
EPELAXL	LEPEL	-	33	37	41	45	49	53	57	61
EPELRAD	LEPEL	-	34	38	42	46	50	54	58	62
EPELH	LEPEL	-	35	39	43	47	51	55	59	63
EPELXH	LEPEL	-	36	40	44	48	52	56	60	64
EPTHAXL	LEPTH	-	33	37	41	45	49	53	57	61
EPTHRAD	LEPTH	-	34	38	42	46	50	54	58	62
EPTHH	LEPTH	-	35	39	43	47	51	55	59	63
EPPLAXL	LEPPL	-	33	37	41	45	49	53	57	61
EPPLRAD	LEPPL	-	34	38	42	46	50	54	58	62
EPPLH	LEPPL	-	35	39	43	47	51	55	59	63
EPPLXH	LEPPL	-	36	40	44	48	52	56	60	64
EPCRAXL	LEPCR	-	33	37	41	45	49	53	57	61
EPCRRAD	LEPCR	-	34	38	42	46	50	54	58	62
EPCRH	LEPCR	-	35	39	43	47	51	55	59	63
EPCRXH	LEPCR	-	36	40	44	48	52	56	60	64
SEPL	NLIN	-	33	37	41	45	49	53	57	61
SRAT	NLIN	-	34	38	42	46	50	54	58	62
HPRES	NLIN	-	35	39	43	47	51	55	59	63
EPEQ	NLIN	-	36	40	44	48	52	56	60	64
S1	NMISC	-	41	46	51	56	61	66	71	76
S3	NMISC	-	43	48	53	58	63	68	73	78
SINT	NMISC	-	44	49	54	59	64	69	74	79
SEQV	NMISC	-	45	50	55	60	65	70	75	80
SBEND	NMISC	86	-	-	-	-	-	-	-	-
SSF	NMISC	87	-	-	-	-	-	-	-	-
FOUT	NMISC	-	99	-	96	-	97	-	98	-
FIN	NMISC	-	103	-	100	-	101	-	102	-
MFORX	SMISC	7	-	-	-	-	-	-	-	-
MFORY	SMISC	8	-	-	-	-	-	-	-	-
MFORZ	SMISC	9	-	-	-	-	-	-	-	-
MMOMX	SMISC	10	-	-	-	-	-	-	-	-
MMOMY	SMISC	11	-	-	-	-	-	-	-	-
MMOMZ	SMISC	12	-	-	-	-	-	-	-	-
SDIR	SMISC	15	-	-	-	-	-	-	-	-
ST	SMISC	16	-	-	-	-	-	-	-	-
TOUT	LBFE	-	12	-	9	-	10	-	11	-
TIN	LBFE	-	16	-	13	-	14	-	15	-

Table 4.60-3b PIPE60 Item and Sequence Numbers for the ETABLE and ESOL Commands

Name	Item	E
SFACTI	NMISC	81
SFACTJ	NMISC	82
FFACT	NMISC	83
PINT	SMISC	17
PX	SMISC	18
PY	SMISC	19
PZ	SMISC	20
POUT	SMISC	21

4.60.3 Assumptions and Restrictions

The element is limited to having an axis with a single curvature and a subtended angle of 0° < 90° since there are integration points only at each end of the element. When loaded with an in-plane strain gradient (thermal, plastic, creep, or swelling) a very fine mesh of elements is recommended. If there are effects other than internal pressure and in-plane bending, the elements should have a subtended angle no larger than 45°. The elbow should have a large radius-to-thickness ratio since the integration points are assumed to be located at the mid-thickness of the wall.

The pipe element is assumed to have "closed ends" so that the axial pressure effect is included. Shear deflection capability is also included in the element formulation. The element temperatures are assumed to be linear along the length. The average wall temperature at =0° is computed as 2 * TAVG - T(180) and the average wall temperature at =-90° is computed as 2 * TAVG - T(90).

If this element is used in a large deflection analysis, it should be noted that the location of the third node (K) is used only to initially orient the element. Stress intensification factors input with values less than 1.0 are set to 1.0. The element formulation is based upon thin-walled theory. The elastic stiffness matrix is used in plasticity analyses (no tangent matrix is formed) and plasticity convergence may be slow. Only the lumped mass matrix is available.

4.60.4 Product Restrictions