Civil Engineering Reference
In-Depth Information
(b) Instantaneous or short-term deflection for dead
full live load (
D
L
)
M
a
(1.7)(20)
2
8
85 ft- k
Noting that the value of
I
e
changes when the moments change
3
(8000)
3
27.4
85
27.4
85
(4067)
4199 in.
4
I
e
1
1700
12
(12
20)
4
(5)
D
L
10
6
)(4199)
0.467 in.*
(384)(3.122
(c)
Initial deflection for full live load (
L
)
L
D
L
D
0.467
0.245
0.222 in.*
(d) Initial deflection due to dead load
30% live load (
D
SL
)
M
a
(1.0
0.30
0.7)(20)
2
60.5 ft- k
8
3
3
27.4
60.5
27.4
60.5
I
e
(8000)
1
(4067)
4432 in.
4
(5)
(1000
0.30
700)
12
(12
20)
4
D
SL
0.315 in.*
(384)(3.122
10
6
)(4432)
(e)
Initial deflection due to 30% live load (
SL
)
SL
(
D
SL
)
D
0.315
0.245
0.070 in.*
(f)
Long-term deflection for dead load plus three years of 30% sustained live load (
LT
)
2.0
1
50
2.0
0
2.0
1
1.80
1
0
3
yrs
1.80
LT
L
D
3
yrs
SL
0.222
(2.0)(0.245)
(1.80)(0.070)
0.838 in.*
6.8
CONTINUOUS-BEAM DEFLECTIONS
The following discussion considers a continuous T beam subjected to both positive and nega-
tive moments. As shown in Figure 6.6, the effective moment of inertia used for calculating
deflections varies a great deal throughout the member. For instance, at the center of the span
at section 1-1 where the positive moment is largest, the web is cracked and the effective sec-
tion consists of the hatched section plus the tensile reinforcing in the bottom of the web. At
section 2-2 in the figure, where the largest negative moment occurs, the flange is cracked and
the effective section consists of the hatched part of the web (including any compression steel
in the bottom of the web) plus the tensile bars in the top. Finally, near the points of inflection,
