Civil Engineering Reference
In-Depth Information
Figure 6.6
Deflections for a continuous T beam.
the moment will be so low that the beam will probably be uncracked, and thus the whole
cross section is effective, as shown for section 3-3 in the figure. (For this case
I
is usually cal-
culated only for the web, and the effect of the flanges is neglected as shown in Figure 6.10.)
From the preceding discussion it is obvious that to calculate the deflection in a con-
tinuous beam, theoretically it is necessary to use a deflection procedure that takes into ac-
count the varying moment of inertia along the span. Such a procedure would be very
lengthy, and it is doubtful that the results so obtained would be within
20% of the actual
values. For this reason the ACI Code (9.5.2.4) permits the use of a constant moment of in-
ertia throughout the member equal to the average of the
I
e
values computed at the critical
positive- and negative-moment sections.
The I
e
values at the critical negative-moment
sections are averaged with each other, and then that average is averaged with I
e
at the
critical positive-moment section.
It should also be noted that the multipliers for long-term
deflection at these sections should be averaged, as were the
I
e
values.
Example 6.2 illustrates the calculation of deflections for a continuous member. Al-
though much of the repetitious math is omitted from the solution given herein, you can
see that the calculations are still very lengthy and you will understand why approximate
deflection calculations are commonly used for continuous spans.
