SECTION 412B – ANALYSIS AND DESIGN

412B.1  Analysis of Vertical Elements of the Lateral Force-Resisting System. General.  The following requirements are applicable to both the General Procedure and Special Procedure.

412B.2  Existing Unreinforced Masonry Walls.

412B.2.1  Flexural rigidity.  Flexural components of deflection may be neglected in determining the rigidity of an unreinforced masonry wall.

412B.2.2  Shear walls with openings.  Wall piers shall be analyzed according to the following procedure which is diagrammed in Figure 4B-2:

412B.2.2.1  For any pier:

   1.   The pier shear capacity shall be calculated as:

      Va = vaAx         (4B-19)

   2.   The pier rocking shear capacity shall be calculated as:

      Vr = 0.5PDD/H      (4B-20)

412B.2.2.2  Pier behavior.  The wall piers at any level are acceptable if they comply with one of the following modes of behavior:

   1.   Rocking controlled mode. When the pier rocking shear capacity is less than the pier shear capacity, i.e., Vr < Va for each pier in a level, forces in the wall at that level, Vwx, shall be distributed to each pier in proportion to PDD/H.

      For the wall at that level:

         Vwx < ΣåVr      (4B-21)

   2.   Shear controlled mode. Where the pier shear capacity is less than the pier rocking capacity, i.e., Vr < Va in at least one pier in a level, forces in the wall at the level, Vwx, shall be distributed to each pier in proportion to D/H.

      For each pier at that level:

         Vp < Va         (4B-22)

      and

         Vp < Vr          (4B-23)

      If Vp < Va for each pier and Vp > Vr for one or more piers, such piers shall be omitted from the analysis, and the procedure shall be repeated for the remaining piers, unless the wall is strengthened and reanalyzed.

412B.2.2.3  Masonry pier tension stress.  Unreinforced masonry wall piers need not be analyzed for tension stress.

412B.2.3  Shear walls without openings.  Shear walls without openings shall be analyzed as for walls with openings except that Vr shall be calculated as follows:

   Vr = (0.50PD + 0.25Pw) D/H      (4B-24)

412B.3  Plywood Sheathed Shear Walls.  Plywood sheathed shear walls may be used to resist lateral forces for buildings with wood diaphragms analyzed according to provisions of Section 410B. Plywood sheathed shear walls may not be used to share lateral forces with other materials along the same line of resistance.

412B.4  Combinations of Vertical Elements.

412B.4.1  Lateral force distribution.  Lateral forces shall be distributed among the designated vertical resisting elements in a line in proportion to their relative rigidities except that moment frames shall comply with Section 412B.4.2.

412B.4.2  Moment-resisting frames.  A moment frame shall not be used with an unreinforced masonry wall in a single line of resistance unless the wall has piers that are capable of sustaining rocking in accordance with Section 412B.2.2 and the frames are designed to carry 100 percent of the lateral forces, and the story drift ratio shall be limited to 0.0025.

412B.5  Shear Force.  The shear force used in the design of any party wall shall be the sum of the shear forces contributed by each building sharing that wall.