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Section 1.4
Computational Considerations
Last Revised:
05/01/2016
When computing the forces on and the strength of structures there is,
inherently, a degree of uncertainty and variability. Some sources of uncertainty
and variability include:
- Variation in actual material properties. For example, you will recall from
your laboratory experiences in material properties and knowledge of statistics,
there is variation between samples when determining material properties.
Reinforcing steel tends to be more homogeneous than other materials so the
variably may be less, however, there is still some! Concrete, on the other hand,
has a high variability of material strength--even within the same
batch.
- Construction Tolerances. Most structural
calculations use very precise dimensions, however, the exact
placement of reinforcing and precise form dimensions are difficult
to achieve in the field. The Code specifies (Chapter 26) allowable
tolerances for many critical dimensions, thus allowing actual
dimensions to be slightly different to those shown on the design
documents and in the design calculations.
- Estimated loads. When determining what loads are to be applied to a structure,
estimates are made of the weight of the structure, the magnitude of the live
loads that the building is likely to see base on the assumed occupancy of the
structure (which may change over time), and the magnitude of environmental loads
such as ponding, snow, wind, and seismic. The magnitude estimates of these loads
are generally based on probabilistic methods and have been generally accepted by
committees of experts as likely to be sufficient in most cases. In many complex
loading cases, engineers, will make conservative simplifying approximations of
how loads are actually applied to structures and/or their components. See A
Beginner's Guide to ASCE 7-05 for more specific information on load
calculations.
- Approximate analysis methods. All structural analysis techniques are based on
theoretical approximations of very complex natural phenomena. This is not to be
confused with "approximate methods" taught in most structural analysis courses.
Some techniques and methods are more approximate than others.
- Simplifying assumptions regarding the strength contribution of "non structural"
building elements. This can be considered to be part of the issue under
approximate analysis methods. Engineers typically ignore the strength
contributions of partitions or other non-structural elements that may indeed add
to the strength of a structure. Ignoring the contributions of these elements is
generally conservative, except where they actually transmit load to elements
that don't have the strength to carry them.
As a result of the uncertainty inherent in structural calculations, it does not
make sense to provide extraordinary precision in computations. In all likelihood
your engineering calculations may be off by as much 6% from what the actual
conditions will finally be. In almost every case, three significant figures
(this does NOT mean three decimal places!) will give you accuracy to 1%. This is
greater than the accuracy that the computations warrant.
When using electronic computation tools (calculators and computers), it does
not make sense to truncated the imprecise digits carried along in the
calculations. However, when reporting the results of you calculations, be sure
to include only 3-5 significant figures.
Also, you should note that one or two significant figures is not sufficient.
For example, the number 0.001 is reported to only one significant figure. This
is not enough to know the precision to three significant figures. The reporting
should be 0.00100. This is because 0.001 can be interpreted as anything between
0.00050 and 0.001499. This gives a variation of about 50% of the reported value.
This level of imprecision is not acceptable.
Always remember, in any engineering computation, that units matter! If ever
in doubt about what units to use for a particular variable in any ACI 318 equation
or specification, refer to ACI 318-14 Chapter 2 where all the variables and
their units are listed. A common error among new users of this Code is to
use f'c in ksi units where the square root of f'c is
called for. You can try this out, but the square root of f'c in
psi units is significantly different than the square root of f'c in
ksi units--you will get the wrong answer if you use f'c in ksi units
whenever a square root is called for.
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