Continuous Reinforced Concrete Structures - Design of Reinforced Concrete - page 448

with an “exact” analysis. A specific example is the analysis of a building frame for
wind loads where the walls, partitions, and floors contribute an indeterminate
amount to wind resistance. Wind forces calculated in the frame by either method
are not accurate.
3. To design the members of a statically indeterminate structure, it is sometimes nec-
essary to make an estimate of their sizes before structural analysis can begin by an
exact method. Approximate analysis of the structure will yield forces from which
reasonably good initial estimates can be made as to member sizes.
4. Approximate analyses are quite useful in rough-checking exact solutions.

From the discussion of influence lines in Section 14.3 you can see that unless a computer
is used (a very practical alternative today), an exact analysis involving several different place-
ments of the live loads would be a long and tedious affair. For this reason it is common when
a computer is not readily available to use some approximate methods of analysis, such as the
ACI moment and shear coefficients, the equivalent rigid-frame method, the assumed point-
of-inflection-location method, and others discussed in the pages to follow.

ACI Coefficients for Continuous Beams and Slabs
A very common method used for the design of continuous reinforced concrete structures
involves the use of the ACI coefficients given in Section 8.3.3 of the Code. These coeffi-
cients, which are reproduced in Table 14.1, provide estimated maximum shears and

Table 14.1 ACI Coefficients

Positive moment
End spans
If discontinuous end is unrestrained

1
11 w u

2
n

1
14 w u

2
n

If discontinuous end is integral with the support

1
16 w u

2
n

Interior spans
Negative moment at exterior face of first interior support
Two spans

1
9 w u

2
n

1
10 w u

2
n

More than two spans

1
11 w u

2
n

Negative moment at other faces of interior supports
Negative moment at face of all supports for (a) slabs with spans not exceeding
10 ft and (b) beams and girders where ratio of sum of column stiffnesses to
beam stiffness exceeds eight at each end of the span
Negative moment at interior faces of exterior supports for members built
integrally with their supports
Where the support is a spandrel beam or girder

1
12 w u

2
n

1
24 w u

2
n

1
16 w u

2
n

Where the support is a column
Shear in end members at face of first interior support

1.15( w u n /2)

w u n /2

Shear at face of all other supports