fundamentals of engineering supplied-reference handbook - Ventech!

BEAMS − FLEXURE: φMn ≥ Mu (CONTINUED)
Doubly-reinforced beams (continued)
Compression steel does not yield (continued)
⎛ c − d'
⎞
2. fs'=87,000 ⎜ ⎟
⎝ c ⎠
0. 85 fc
'β1
b ⎛ 3d
⎞ ⎛ ⎞
t
3. As,max= ⎜ ⎟ − As' ⎜
fs '
⎟
f y ⎝ 7 ⎠ ⎜ ⎟
⎝
f y ⎠
4. a =
( As
f y − As
' fs
')
0.
85 f ' b
Mn = fs'
c
⎡⎛
As
f
⎢⎜
⎜
⎢⎣
⎝ fs
'
y
⎞⎛
a ⎞
⎤
− As
'⎟
⎟ ⎜ d − ⎟ + As
' ( d − d')
⎥
⎠⎝
2 ⎠
⎥⎦
T-beams − tension reinforcement in stem
Effective flange width:
smallest beam centerline spacing
Design moment strength:
As
f y
a =
0.
85 f c 'be
If a ≤ hf :
0.85 fc'β1be ⎛ 3dt
⎞
As,max =
f
⎜
⎝ 7
⎟
⎠
a
Mn = 0.85 fc' a be (d- )
2
y
If a > hf :
0. 85 fc
'β1
be
⎛ 3d
⎞ 0. 85 f
t
c '(
be
−bw
) h
As,max = ⎜ ⎟ +
f ⎝ 7 ⎠ f
y
1/4 • span length
be = bw + 16 • hf
h f
Mn = 0.85 fc' [hf (be − bw) (d −
2
)
y
a
+ a bw (d − )]
2
f
117
Beam width used in shear equations:
b (rectangular beams )
bw =
bw (T−beams)
Nominal shear strength:
Vn = Vc + Vs
Vc = 2 bw d f c '
Vs =
Av f y d
s
CIVIL ENGINEERING (continued)
[may not exceed 8 bw d fc ' ]
Required and maximum-permitted stirrup spacing, s
V
V
u
u
Required
spacing
Maximum
permitted
spacing
BEAMS − SHEAR: φVn ≥ Vu
φVc
≤ : No stirrups required
2
φVc
> : Use the following table ( Av given ):
2
φV
2
c < Vu
≤ φVc
Smaller of:
Av
f y
s =
50bw
Av
f y
s =
0. 75bw
f c '
Smaller of:
d
s =
2
OR
s =24"
Vu > φVc
V
V = −V
φ
Av fyd s =
V
u
s c
Vs ≤ 4 bw d f c '
Smaller of:
d
s = OR
2
s =24"
Vs > 4 bw d f c '
Smaller of:
d
s =
4
s =12"
s