The W21x57 steel beam has its compression flange laterally braced at the 1/3 points over its full length. Determine the maximum factored lead w, (kips/ft) that the beam can carry. Assume Fy=50ksi and C,=1.0 for the critical segment.

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Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.