Civil Engineering Reference
In-Depth Information
T
u
˜
+
t
u
+
T
u
Figure 3-15 Torsional Loading on a Spandrel Beam
At the critical section, at distance d away from the support, the critical torsional moment is:
⎛
2
−
⎞
0.3M
o
⎛
2
−
⎞
⎛
2d
⎞
T
u
=
t
u
⎜
d
⎟ =
⎜
d
⎟ =
0.15M
o
1
⎜
−
⎟
h
For preliminary sizing of spandrel to neglect torsion, assume d = 0.9h and = 20 per Table 3-1
Therefore
d
=
0.9h
20h
=
0.05
T
u
=
0.15M
o
(1
−
2
×
0.05)
=
0.135M
o
For preliminary sizing of spandrel beam to neglect torsion:
A
cp
p
cp
T
u
≤φ
ʹ
f
c
b
f
h
f
)
2
0.75 4000
(bh
+
0.135M
o
≤
2(h
+
b
+
b
f
)
b
f
h
f
)
2
(bh
+
0.135(M
o
×
12,000)
×
2
b
f
)
>
>
68.2M
o
2(h
+
b
+
0.75 4000
for simplicity:
(bh
+
b
f
h
f
)
2
b
f
)
>
70M
o
2(h
+
b
+
For one-way slab or one-way joists with spandrel beams, the exterior negative slab moment is equal to w
u
˜
n
2
/24
(ACI 8.3.3). This negative moment can also be expressed as 0.33M
o
where M
o
= total static span moment for
one-way slab = w
u
˜
2
˜
n
2
/8. Thus for one-way system with spandrel beam, sizing to neglect torsion for the selected
concrete (compressive strength = 4000 psi) reduces to:
(bh
+
b
f
h
f
)
2
b
f
)
>
76M
o
(h
+
b
+
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