Simplified Frame Analysis - Simplified Design of Reinforced Concrete Buildings - page 40

where:

q Du = uniformly distributed factored dead load, psf

q Lu = uniformly distributed factored live load (including any live load reduction; see

Section 2.2.2), psf

˜ n = clear span length of longer adjacent span, ft

= clear span length of shorter adjacent span, ft

n ʹ

˜ 2 = length of span transverse to ˜ n and , measured center-to-center of supports, ft n ʹ

For equal adjacent spans, this equation further reduces to:

( ) 2 = 0.035q Lu

M u = 0.07 0.5q Lu

2
n

2
n

2

The factored moment M u can then be distributed to the columns above and below the floor in proportion to their
stiffnesses. Since the columns will usually have the same cross-sectional area above and below the floor under
consideration, the moment will be distributed according to the inverse of the column lengths.

2.6 LATERAL LOAD ANALYSIS

For frames without shear walls, the lateral load effects must be resisted by the “sway” frame. For low-to-
moderate height buildings, lateral load analysis of a sway frame can be performed by either of two simplified
methods: the Portal Method or the Joint Coefficient Method. Both methods can be considered to satisfy the
elastic frame analysis requirements of the code (ACI 8.3). The two methods differ in overall approach.
The Portal Method considers a vertical slice through the entire building along each row of column lines.
The method is well suited to the range of building size and height considered in this topic, particularly to build-
ings with a regular rectangular floor plan. The Joint Coefficient Method considers a horizontal slice through
the entire building, one floor at a time. The method can accommodate irregular floor plans, and provision is
made to adjust for a lateral loading that is eccentric to the centroid of all joint coefficients (centroid of
resistance). The Joint Coefficient Method considers member stiffnesses, whereas the Portal Method does not.

The Portal Method is presented in this topic because of its simplicity and its intended application to buildings
of regular shape. If a building of irregular floor plan is encountered, the designer is directed to Reference 2.2
for details of the Joint Coefficient Method.

2.6.1 Portal Method

The Portal Method considers a two-dimensional frame consisting of a line of columns and their connecting
horizontal members (slab-beams), with each frame extending the full height of the building. The frame is
considered to be a series of portal units. Each portal unit consists of two story-high columns with connecting
slab-beams. Points of contraflexure are assumed at mid-length of beams and mid-height of columns. Figure 2-11
illustrates the portal unit concept applied to the top story of a building frame, with each portal unit shown
separated (but acting together).

The lateral load W is divided equally between the three portal units. The shear in the interior columns is twice that
in the end columns. In general, the magnitude of shear in the end column is W/2n, and in an interior column it is
W/n, where n is the number of bays. For the case shown with equal spans, axial load occurs only in the end columns
since the combined tension and compression due to the portal effect results in zero axial loads in the interior