Question 9.73: Show that the shear center for the zee-shaped section shown ...

If the shear center O was located at some distance e away from the centroid of the zee shape, the shear flows through the zee shape would be directed as sketched to the right. The shape would not satisfy equilibrium in the horizontal direction because the sum of F_{1} \text { and } F_{3} would not equal zero. Therefore, to satisfy equilibrium, forces F_{1} \text { and } F_{3} must each equal zero. Hence, the sum of moments about the centroid gives:
V e=0         \quad \therefore e=0