Civil Engineering Reference
In-Depth Information
able to make some preliminary estimates as to sizes. If an approximate analysis of the
structure has been made, it will be possible to make very reasonable member size esti-
mates. The result will be appreciable saving of both computer time and money.
An experienced designer can usually make very satisfactory preliminary size esti-
mates based upon his or her previous experience. In the absence of such experience, how-
ever, the designer can still make quite reasonable size estimates based on his or her
knowledge of structural analysis. For instance, to approximately size columns, a designer
can neglect moments and assume an average axial stress or
P
u
/
A
g
value of about 0.4 to
This rough value can be divided into the estimated column load to obtain its esti-
mated area. If moments are large, lower values of average stress (0.4 to
c
.
0.6
f
c
0.5
f
) may be
c
used; if moments are small, higher values (0.55 to ) may be used.
Preliminary beam sizes can be obtained by considering their approximate moments.
A uniformly loaded simple beam will have a maximum bending moment equal to
w
u
0.60
f
2
/8,
2
/12.
For a continuous uniformly loaded beam, the designer might very well estimate a maxi-
mum moment somewhere between the values given, perhaps
w
u
whereas a uniformly loaded fixed-end beam will have a maximum moment of
w
u
2
/10, and use that value
to estimate the beam size.
For many structures it is necessary to conduct at least two different analyses. One
analysis is made to consider the effect of gravity loads as described in Section 14.7 of this
chapter, while another might be made to consider the effect of lateral loads as discussed in
Section 14.8. For the gravity loads only,
U
usually equals 1.2
D
1.6
L
.
Because the gravity loads affect only the floor to which they are applied, each floor can
probably be analyzed independently of the others. Such is not the case for lateral loads be-
cause lateral loads applied anywhere on the frame affect the lateral displacements through-
out the frame and thus affect the forces in the frame below. For this situation the load factor
equations involving lateral forces (ACI Equations 9-3, 9-4, etc.) must be applied.
Sometimes a third analysis should be made—one that involves the possibility of
force reversals on the windward side or even overturning of the structure. If overturning is
being considered, the dead and live gravity loads should be reduced to their smallest pos-
sible values (that is, zero live load and 0.9
D
, in case the dead loads have been overesti-
mated a little) while the lateral loads are acting. For this case ACI load factor equations
9-6 and 9-7 must be considered.
14.7
APPROXIMATE ANALYSIS OF CONTINUOUS FRAMES
FOR VERTICAL LOADS
Statically indeterminate structures may be analyzed “exactly” or “approximately.” Some
approximate methods involving the use of simplifying assumptions are presented in this
section. Despite the increased use of computers for making “exact” analyses, approximate
methods are used about as much or more than ever, for several reasons. These include the
following:
1.
The structure may be so complicated that no one who has the knowledge to make
an “exact” analysis is available or no suitable computer software is available.
2.
For some structures, either method may be subject to so many errors and imper-
fections that approximate methods may yield values as accurate as those obtained
