Nonprismatic

Note: At least two frame sections must already be defined for the Add Nonprismatic option to be included in the Add {Section Type} drop-down list box.

Nonprismatic frame sections may be defined with the properties varying along the section length. In addition, the section length may be divided into any number of segments of unequal lengths. Most common situations can be modeled using one to five segments. The variation of the bending stiffnesses may be linear, parabolic, or cubic over each segment of length. The axial, shear, torsional, mass, and weight properties all vary linearly over each segment. Section properties may change discontinuously from one segment to the next. Click here to review figures and example input for nonprismatic frame sections.

To define a nonprismatic frame section, provide input in the following areas of the Nonprismatic Section Definition form and use the buttons to Add, Insert, Modify or Delete section definitions:

• Nonprismatic Section Name  Use the default or specify another name for the nonprismatic section to be defined. This name will appear in the Properties area of the Frame Properties form after the section has been successfully defined.

• Display Color box. The color that will be used to display the section on-screen in the model.

• 1. Click on the "Display Color" text or the small sample square of the color to access the Color form.

  2. Select the desired new color on the Color form and click the OK button.

• Section Notes Modify/Show Notes button. Click this button to access the Frame Section Property Notes form and add section notes to the model file.

• Start Section and End Section

• 1. Select the name of a previously defined/default prismatic section from the Start Section drop-down list. This defines the end closest to joint i.

  2. Select the name of a previously defined/default prismatic section from the End Section drop-down list. This defines the end closest to joint j.

The starting and ending sections may use the same named section if the properties are constant over the length of the segment. The material would normally be the same for both the starting and ending sections and only the geometric properties would differ, but this is not required.

• Length edit box and Length Type drop-down list. Enter a value for the length of the section, and specify the length of the  nonprismatic segment as variable or absolute using the Length Type drop-down list. When a nonprismatic frame section is assigned to a line object, the actual lengths of each segment for that object are determined as follows:

• • The clear length of the object, Lc, is first calculated as the total length minus the end offsets: Lc = L - (ioff + joff). In that equation, L is the full length of the frame section and ioff and joff are the lengths of the end offsets along the length of the frame section at the i and j ends of the object, respectively.

  • If the sum of the absolute lengths of the segments exceeds the clear length, the absolute lengths are scaled down proportionately so that the sum equals the clear length. Otherwise the absolute lengths are used as specified.

  • The remaining length (the clear length minus the sum of the absolute lengths) is divided among the segments having variable lengths in the same proportion as the specified lengths. For example, for two segments with variable lengths, vl, specified as vl = 1 and vl =2, one third of the remaining length would go to the first segment, and two thirds to the second segment.

• El22 and EI33 Variation drop-down lists. Nonprismatic column/beam/brace section properties are interpolated along the length of each segment from the values at the two ends. Select linear, parabolic, or cubic from the EI22 and EI33 Variations drop-down lists to specify the variation of bending stiffnesses for the section.

SAP2000 calculates the linear, parabolic or cubic variation for EI33 as follows:

1. • Linear: The value EI33 varies linearly along the length of the segment.

   • Parabolic: The value varies linearly along the length of the segment.

   • Cubic: The value varies linearly along the length of the segment.

This usually corresponds to a linear variation in one of the section dimensions. For example, a linear variation in the width of a rectangular shape yields a linear variation for EI33. A linear variation in the depth of a rectangular shape yields a cubic variation for EI33. Finally, a linear variation in the depth of an I-shape yields a parabolic variation for EI33.

The interpolation of the bending stiffness in the 1-2 plane, EI22, is defined in the same manner to that for the 1-3 plane.

The remaining stiffness properties, other than EI33 and EI22, are always assumed to vary linearly between the ends of each segment. Similarly, the mass and weight densities are always assumed to vary linearly between the ends of each segment.

If a shear area is zero at either end, it is taken to be zero along the full segment, thus eliminating all shear deformation in the corresponding bending plane for that segment.

Effect on End Offsets Along the Length of Frame Sections

Frame section properties vary only along the clear length of the line object. Section properties within the longitudinal end offset at the i-end of the object are constant using the starting section of the first segment. Section properties within the end offset at the j-end of the object are constant using the ending section of the last segment. Note that if a longitudinal end offset rigidity factor is specified, the specified part of the end offset is rigid and the rest has the section property described herein.

• Add button. After parameters have been selected from the various drop-down lists and a value has been entered for the Length, click the Add button to add the definition to the section identified in the Nonprismatic Section Name edit box.

• Insert button. The Insert button is available only after at least one property has been defined. Highlight a previously specified definition and click the Insert button to insert another definition that is a duplicate of the highlighted definition. The option can be used to quickly add definitions when, for example, the length is the only item that requires changing.

• Modify button.

• 1. Highlight the definition to be changed.

  2. Select from the drop-down boxes or enter the revised values in the edit box.

  3. Click the Modify button to complete the change.

• Delete button. Highlight the definition to be deleted and click the Delete button.

Note: More than one pair of frame sections can be added to build the Nonprismatic section. Enter Absolute lengths (defined in the current units) to define sections that are of fixed length. Then the sections defined as Variable Length Type will be extended between the fixed sections. The Variable Length value is the ratio of the length of the section relative to all the variable length sections defining the Nonprismatic member. For example, if there are two Variable Length sections with lengths of 1 and 2, the section with length 1 will be 1/3 of the total variable length, and the section with a length of 2 will be 2/3 of the total variable length.

This method of defining Nonprismatic sections can be used to define sections that have top and bottom fixed length Nonprismatic sections with a prismatic section defined between them, like a bridge pier, where the prismatic part of the section can “telescope” to fit the space between the fixed ends.