Problem Description

Cb calculation for back-span of a beam with a cantilever can be unconservative due to skip load patterns. 

Reason

For beams with a cantilever on one or both ends, the program automatically skip loads (i.e., pattern loads) the Live Load to determine the maximum negative (hogging) moment at the support and the maximum positive (sagging) moment in the back span. The skip load cases identified as Case 1, Case 2, and Case 3 are shown graphically in the images below.

Where beams are braced at intermediate points, the maximum positive and negative moments are determined for each unbraced segment. In the calculation of the member capacity for the limit state of lateral-torsional buckling, there is a modification factor (called Cb in AISC, mLT in BS 5950, and am in AS 4100) to account for non-uniform moment that is calculated using moments at the quarter points within the unbraced segment. These moments are determined from the same skip load condition that produced the maximum moment within the segment (either Case 1 or Case 2).  A potential problem can occur when calculating the modification factor for unbraced within the back span directly adjacent to the support near the cantilever end. For that unbraced segment, the maximum negative moment is the same as the maximum negative moment in the unbraced segment in the cantilever (see the moment diagram for Case 1). When calculating the modification factor for lateral-torsional buckling (Cb, mLT, or am), the program uses moments from Case 1 only. However, it is possible that a smaller modification factor may result from Case 3, which has the same negative moment. The smaller modification factor could result in a smaller moment capacity. This could result in a design failure that is not detected by the program.

Note that this is a rare condition. The most susceptible configuration is a beam that does not support other framing members, that is unbraced over the entire span, and that has a short cantilever with a heavy load. It is not likely to occur for beams that support other framing members or have brace points modeled in the backspan and carry large loads in the span. The error will also will not occur when:

1. The beam does not have a cantilever.

2. The beam design is not governed by lateral-torsional buckling.

3. The beam design is governed by lateral-torsional buckling but the capacity is limited to the plastic capacity (Mp). When this occurs, the modification factor does not affect the capacity or only marginally affects the capacity by pushing it to the plastic capacity limit.

Also, note that when the option to "Consider Point of Inflection" is unchecked in RAM Steel Beam - Criteria - Design Defaults, the unbraced length for negative moment in the back span is taken as length between brace points on the bottom flange. In Case 3, positive moment occurs for a significant portion of the back span and the top flange bracing is not considered in the design. When a beam supports a deck that braces the top flange, this design methodology will mitigate the impact of the defect to some degree.

This defect affects the following design codes:

• AISC 360
• AISC LRFD 3rd
• BS 5950 (m_LT   p54)
• AS 4100  (am  Clause 5.6.1.1)

Solution

None.