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CEE 415
1
Example 4.4 – Design a doubly reinforced section for negative bending moment
in the indicated girder at the face of the first interior column of the floor plan
shown on the last page. We cannot use the ACI moment coefficients for this
case because of the concentrated loads applied to this girder from the floor
beams. For an initial calculation of the weight of the girder (web), assume it has
a depth of 26 in. and a width of 14 in. Calculations indicate that the reduced live
load for this design section is 30 psf.
Assume f
´
c
= 4000 psi and f
y
= 60 ksi.
From RISA analysis, M
u
=
610 kft = 7320 kin.
Start design process with
1
3
0.0189
0.019
cy
ff
ρβ
′
≅=
≅
Then,
ω
=
ρ
(f
y
/f
´
c
)
=
0.285
and,
R
=
ω
f
c
’ (1  0.59
ω
)
=
0.948 ksi
≅
0.95 ksi
Now, assuming
φ
= 0.9, the required value of b d
2
= (M
u
/
φ
)/R = 8560 in.
3
Select b
≅
0.6 d,
so
d
≅
[8560/0.60]
0.33
=
24.3 in.
(round to 23.5 in.)
( h
=
26 in.)
Then, with d = 23.5 in, b
≅
8560/(23.5)
2
=
15.4 in.
(round to 16 in.)
No need to adjust M
u
.
Selection of A
s
=
ρ
b d
=
(0.019)(15.4")(23.5")
=
6.92 in.
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This note was uploaded on 03/29/2011 for the course CEE 415 taught by Professor Wight during the Spring '11 term at University of Michigan.
 Spring '11
 Wight

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