A single-story frame like the one shown consists of two exterior vertical members that serve as columns to resist the gravity loads, and a vertical member with RBS at its ends inserted at midbay of the frames to resist the lateral loads.

(1)    Design the lightest W12 shape that can be used as the mid-bay vertical member, having a 50% reduction in flange width at the RBS locations, to resist the applied loads and to meet the AISC 358 specified limitations for the pre-qualified connection details. Clearly show the geometry/dimensions of the selected RBS.

(a) Design the vertical member assuming that the shear force in that member does not affect its flexural plastic strength.

(b) For the resulting vertical member designed in(a), calculate the flexural plastic strength of the member taking into account the presence of shear in that member. Indicate by how much (in %) the calculated strength of the structure is reduced as a result of this more refined calculation.

(c) Compare the results in (a) and (b) and comment on why the difference is significant or insignificant. If significant, explain what could be done to compensate for this. (2) Draw the moment and axial force diagrams for the top horizontal beam of that system, indicating the magnitude of the moments and forces that would have to be considered for the design of that beam. Additional notes:

• The beams have simple connections at their ends.

• Organize design iterations in a tabular format. There is no gravity load applied to this frame. Optional design aspects that could be considered in this problem include:

(a) design the shear connection of the vertical member to the beams;

(b) design the beams, including checking the panel zone strength; and

(c) check if continuity plates in the beams are needed.