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The shear force v is the unit shear (force per unit length) in the sheathing of the s, however it may be factored differently for deflection calculations than for shear wall design.
The shear force used for deflection analysis is factored by 1.0, as O86 11.7.1.2 says to use specified loads for serviceability in the deflection equation. For wind, this is serviceability load combination 4 from O86-14 Table 5.2.4.2, so that the wind force is 1/1.4 times the design shear force. There is no serviceability load combination for earthquake loads, and the ultimate limit state factor from combination 5 from NBC Table 4.1.3.2-A. is 1.0, so seismic shear forces used for deflection are the same as those used for design of shear walls.
Distribution of v to Sides of Wall
The second and third terms of the 4-term equation and the second term of the 3-term equation apply to the sheathing, which can be different for each side of a composite wall. Therefore, the two sides of the wall can have a different shear value v (the third term includes v indirectly through en.) such that the sheathing deflection is the same on both sides. Refer to Deflection of Two-sided Shear Wall for an explanation of how shear is apportioned to each side of a composite wall.
Distribution of v Within Shear Lines
The distribution of v within a shear line depends on the Design setting which allows you to choose between capacity-based and deflection-based force distribution. For deflection-based design, an iterative procedure is required as distribution to shear wall segments within the line depends on the deflection calculated with the previous distribution.