Figure 3-28. CBEND Element Coordinate System
Offsets of the ends of the element from the grid points are the same at both ends. The offsets are measured in the element coordinate system as shown inFigure 3-28. The element coordinate system is defined by one of four methods that you specify in the GEOM field on the CBEND entry.
• The Z -direction of the element coordinate system is defined by the cross product of the vector connecting grid point GA to grid point GB and the vector for GEOM = 1.
For GEOM = 2, 3, or 4, the Z -direction is defined by the cross product . The center of curvature and intersection of the tangent lines from end A and end B are located using the data required for each of the four options.
• The R -direction is obtained by the vector extending from the center of curvature to end A . The q -direction is the cross product of . When q = 0, end A of the element is indicated and q = qBrepresents end B. Plane 1 of the element lies in the R q plane of the element coordinates.
• Plane 1 is parallel to the plane defined by GA, GB and the vector , but it is offset by ZC in the Z -direction. Plane 2 lies in the qZ plane and is offset from GA and GB by RC in the R -direction. The subscripts 1 and 2 refer to forces and geometric properties associated with bending in Planes 1 and 2, respectively. These reference planes are the principal planes of the element cross section.
The neutral axis radial offset shown inFigure 3-28from the geometric centroid due to bending of a curved beam with a constant radius of curvature is defined as follows:
Equation 3-8.
where:
RB = the bend radius A = the cross section area Z =
r = a local variable aligned with Relemdirection
You can use the default provided with the general format or you can calculate and input a value using the above formula. For the circular section format, the neutral axis offset is automatically calculated with analytical expressions for hollow and solid circular cross-sectional elements.
Flexibility and stress intensification factors
The flexibility factors which multiply the bending terms of the flexibility matrix and the stress intensification factors are selected by the FSI field on the hollow circular section format of the property entry. The options available are as follows:
FSI = 1:
Out-of-plane
FSI = 2: ASME code Section III, NB-3687.2, NB-3685.2., 1977 In and
f = Locations of stress recovery on the cross section at the locations 0°, 90°, 180°, 270°
FSI = 3: Empirical factors from the Welding Research Council Bulletin 179, by Dodge and Moore
FSI = 4: ASME code N-319-3 (approval date of January 17,2000).
Out-of-plane
Linear interpolation of THETAB will be done for values between 180° and 0°; KZ (in-plane flexibility factor) shall not be less than 1.0
Out-of-plane
Linear interpolation with THETAB will be done, but the in-plane stress intensification factor shall not be less than interpolated for THETAB = 30° and not less than 1.0 for any THETAB.
where:
FSI = 5: ASME code B31.1 - 2001 which defines flexibility and stress intensification factors for an elbow, pipes and miter bends. These flexibility factors also apply to the class 2 (2001 edition of ASME Boiler & Pressure Vessel Code NC-3600) & class 3 (2001 edition of ASME Boiler & Pressure Vessel Code ND-3600) with the only difference being that the flexibility correction for pressure is not specified in the Figure NC/ND-3673.2(b)-1 equations but defaults to the same equation when the pressure is input as zero. All must be greater or equal to 1.0.
In and Out-of-plane flexibility factors
= Welding elbow or pipe bend:
Closely spaced miter bend:
Widely spaced miter bend:
In and Out-of-plane stress
intensification factors
= Welding elbow or pipe bend:
Closely spaced miter bend:
Widely spaced miter bend:
where:
he = (T) (RB/ (RM)2) (for welding elbow or pipe bend)
hc = (SACL) (T) cot (ALPHA) / 2 (RM)2) (for closely spaced miter bend) hw = T (1 + cot (ALPHA)) / (2 RM) (for widely spaced miter bend) FSI=6 User definable flexibility and stress intensification factors: KY =
out-of-plane flexibility factor, KZ = in-plane flexibility factor, SY = out-of-plane stress factor, SZ = in-plane stress factor. All must be greater or equal to 1.0.
Figure 3-29. Definition of SACL and ALPHA where
for a closely spaced miter
for a widely spaced miter
The positive sign conventions for internal element forces are shown inFigure 3-30. The following element forces, either real or complex (depending on the rigid format), are output on request at both ends:
• Bending moments in the two reference planes, M1and M2.
• Shears in the two reference planes, V1and V 2.
• Average axial force, Fq.
• Torque about the bend axis, Mq.
Figure 3-30. CBEND Element Internal Forces and Moments The following real element stress data are output on request:
• Real longitudinal stress at the four points which are the same at both ends for the general cross-sectional property entry format. If the circular cross-sectional property and format is used, the stress points are automatically located at the points indicated on the following figure.
• Maximum and minimum longitudinal stresses.
• Margins of safety in tension and compression for the element if you enter stress limits on the MAT1 entry.
• When you use the pipe format, NX Nastran modifies the stress data to account for stress intensification resulting from internal pressurization and curvature of the element. The internal pressure is prescribed on the property entry. The methods used to calculate the stress intensification factor are selected through the FSI parameters.
See Also
o PBEND in the NX Nastran Quick Reference Guide
Tensile stresses are given a positive sign and compressive stresses a negative sign. Only the longitudinal stresses are available as complex stresses. The stress recovery coefficients on the general form of the PBEND entry are used to locate points on the cross section for stress recovery. The subscript 1 is associated with the distance of a stress recovery point from Plane 2. The subscript 2 is associated with the distance from Plane 1. If zero value stress recovery coefficients are used, the axial stress is output.
3.5 CONROD Rod Element
The CONROD entry is an alternate form of the CROD element that includes both the connection and property information on a single entry. It has two grid points, one at each end, and supports axial force and axial torsion. Thus, stiffness terms exist for only two DOFs per grid point. All element connectivity and property information is contained directly on the CONROD entry—no separate property entry is required. This element is convenient when you’re defining several rod elements that have different properties.
Figure 3-31. CONROD Element Convention
The CONROD element x-axis (xelem) is defined along the line connecting G1 to G2. Torque T is applied about the xelemaxis in the right-hand rule sense. Axial force P is shown in the positive (tensile) direction.