1.5 C OMMENTARY
1.5.5 Releases
Since STEEL uses fiber based elements the creation of pinned connections is not as straightforward as in ETABS. To simulate the release of moments at the end of elements special fiber properties need to be assigned. STEEL accomplishes this through the use of fiber area categories in which specific fibers in specific sections of an element can have their areas increased or decreased by a certain percentage. An image describing the number of fibers per element for beams, columns and braces can be seen in Figure 1-‐12, while an image describing the default segment breakdown for beams, columns and braces can be seen in Figure 1-‐13.
Figure 1-‐12: STEEL Element Fiber Description
Figure 1-‐13: STEEL Beam/Column Segment Description
Currently, when creating a fixed-‐fixed connection on a beam element the web of the first two and last two segments are reduced to 30% of their original area to better correspond with empirical data. More information on this can be found in [1].
Creating a pinned connection in STEEL is slightly more complicated. The fiber modifications need to minimize the inertia of the section as much as possible while still allowing the section to generate its full capacity. The inertia is reduced by eliminating the flanges and the top and bottom fibers of the web while the capacity of the section is preserved by increasing the area of the middle two fibers of the web. For example, if a beam had its left end pinned and its right end fixed segments 1 and 2 fibers 1, 2, 7 and 8 would have an area modifier
of 0 to eliminate the flanges, fibers 3 and 6 would have an area modifier of 0 to eliminate the top and bottom fibers of the web, and fibers 4 and 5 would have their area modifier set to a value such that the axial capacity of the section remains roughly constant.
While it would be possible to have exact modifiers for every possible section, the increase to the size of the input file was deemed to be not worthwhile as each section would require 3 premade fiber area modification categories; namely for pinned-‐pinned elements, pined-‐fixed elements, and fixed-‐pinned elements. Instead, only beam sections greater than 18”
but less than 36” in depth were chosen as the most common beam sections and an appropriate modifier was chosen which best represented all beams in this range.
To calculate the area modifier an equivalent area was calculated by first determining the height of the web via,
ℎ!"# =𝑑−2𝑡!
Where d is the depth of the beam and 𝑡! is the thickness of the flange. Since the new modified cross-‐section has its flanges eliminated with all web area condensed into two equal fibers, each fiber area can be calculated as,
𝐴!"#_!"#$% =1
2ℎ!"#𝑡!"# = 1
2 𝑑−2𝑡!"# 𝑡! Therefore, the multiplier to the original fiber area can be found to be,
𝐹𝐴𝐹𝑅𝐴𝐶 = 𝐴!"#$%&'
𝐴!"#_!"#$%
where FAFRAC is the multiplier for the middle two fibers and 𝐴!"#$%&' is the area of the original section.
Following this calculation for all reasonable beams in the desired range gave a maximum and minimum multiplier of 7.17 and 3.63, an average multiplier of 5.4 with a standard deviation of 0.9. In most sections where the actual multiplier was far from the given average the weight of the section was such that it would be more practical to increase the depth rather than use such a heavy section. Therefore, it was then chosen to assign a fiber area modifier of 6.0 to the middle two fibers of the two segments nearest a pinned connection. Since the multiplier chosen is greater than the minimum there will be a non-‐conservative area for some sections types, however as drag element failure is generally not a global failure mechanism of interest in lateral analysis the error should not be significant. However, if the user wishes additional area modification categories can be created to achieve a more accurate representation of pinned connections.
It was decided that beams which are fixed-‐pinned or pinned-‐fixed would be given no modifications on the fibers of the fixed end since, at this stage in the analysis, this element fixity type only occurs when the beam is meshed at the intersection point of a brace. Since there is continuity of the element over this connection reducing the area of the fibers at this location would be incorrect. However, this does mean that modeling a fixed-‐pinned or pinned-‐fixed beam that spanned between a moment frame and a brace frame would result in a non-‐
conservative response, therefore, as of the current version the user should take care to avoid these situations and simply span the space between these types of systems with a pinned-‐
pinned beam.
Element fiber categories for braces are done automatically and can be given a fiber modification category of 0. Similarly, all column elements are given a fiber modification category of 0.
A description of every release type available is shown in Table 1-‐1. Note that some of the release types are out of date and are unused, namely the column releases as it was determined that pinning columns can result in large computational errors. The user may either create their own release definitions using these as a guide by editing the for001 file or customize the current element definitions utilizing the existing element fiber area modification categories.
Table 1-‐1: STEEL Element Release Definitions
1.5.6 Damping / Special Columns