Structural Concrete - Hassoun

17.10 Transfer of Unbalanced Moments to Columns 659
Figure 17.24
Interior column loading.
where
q Du , q Lu = factored dead and live loads on longer span
q ′ = factored dead load on shorter span
Du
l n , l n ′ = length of longer and shorter spans, respectively
α ec =
K ec
∑ (Ks + K b )
(Eq. 17.21)
The moment in Eq. 17.22 should be distributed between the columns above and below the slab at
the joint in proportion to their flexural stiffnesses (Fig. 17.24). For equal spans l 2 = l ′ 2 and l n = l n,
′
⎧0.07 ( )
0.5q Lu l 2 ln
2 (17.23a)
⎪
M u = ⎨0.08(0.5q ⎪
Lu l 2 ln)
2 (17.23b)
⎩ (1 + 1∕α ec )
The development of these equations is based on the assumption that half the live load acts on the
longer span, whereas the dead load acts on both spans. Equation 17.22 can also be applied to an
exterior column by assuming the shorter span length is 0 (Fig. 17.25).
17.10 TRANSFER OF UNBALANCED MOMENTS TO COLUMNS
17.10.1 Transfer of Moments
In the analysis of an equivalent frame in a building, moments develop at the slab–column joints due
to lateral loads, such as wind, earthquakes, or unbalanced gravity loads, causing unequal moments
in the slab on opposite sides of columns. A fraction of the unbalanced moment in the slabs must be
transferred to the columns by flexure, and the balance must be transferred by vertical shear acting
on the critical sections for punching shear. Approximately 60% of the moment transferred to both
ends of the column at a joint is transferred by flexure, and the remaining 40% is transferred by