special moment frames a- beams of special moment...
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163
Special Moment Frames
Based on ACI 2.3, special moment frames are beam-column frames assigned to
SDC D, E and F and complying with 18.6 through 18.8. ACI 18.6 deals with
requirements for beams, while ACI 18.7 deals with columns and ACI 18.8 deals
with joints of special moment frames.
A- Beams of Special Moment Frames
ACI 18.6 applies to beams of special moment frames that form part of the seismic-
force-resisting system and proportioned primarily to resist flexure and shear. ACI
318-14 is written with the assumption that special moment frames comprise beams
and columns interconnected by beam-column joints.
1- Dimensional Limits:
ACI 18.6.2 requires that the following conditions are to be satisfied:
Clear span,nl , shall be at least 4d, where d is effective depth of the beam.
Width, wb , shall be at least the lesser of 0.3 h and 25 cm, where wb is web
width and h is overall thickness of beam.
Projection of the beam width beyond the width of the supporting column
on each side shall not exceed the lesser of 2c and 175.0 c . Note that 1c is
the column dimension in the direction of analysis, and 2c is the column
dimension measured in the direction perpendicular to 1c , as shown in
Figure R18.6.2.
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2- Longitudinal Reinforcement:
ACI 18.6.3 specifies the following requirements for beam longitudinal
reinforcement:
At least two bars are to be provided continuously both top and bottom
faces.
At any section, for top as well as for bottom reinforcement, the amount of
reinforcement is not be less than the larger y
wc
f
dbf '80.0 and y
w
f
db14 .
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This requirement needs not to be satisfied if the tension reinforcement
provided at every section is 1/3 larger than required by analysis.
Maximum reinforcement ratio is not to exceed 0.025.
Positive moment strength at joint face is not to be less than ½ of the
negative moment strength provided at the face of the joint.
Both the negative and positive moment strength at any section along the
beam length is not to be less than ¼ the maximum moment strength
provided at face of either joint.
Lap splices of deformed longitudinal reinforcement are permitted only if
hoop or spiral reinforcement is provided over the lap length. Maximum
spacing of the transverse reinforcement enclosing the-lap-spliced bars is
not to exceed the lesser of d/4 or 10 cm.
Lap splices are not to be used; (a) within the joints, (b) within a distance
of twice the beam depth from the face of the joint, and (c) within a
distance of twice the beam depth from critical sections where flexural
yielding is likely to occur as a result of lateral displacements beyond the
elastic range of behavior.
Reinforcement Requirements for Beams of Special Moment Frames
3- Transverse Reinforcement:
ACI 18.6.4 specifies the following requirements for transverse
reinforcement:
Hoops are to be provided in the following regions of a beam:
(a) Over a length equal to twice the beam depth measured from the face of the
supporting column toward mid span, at both end of the beam.
166
(b) Over lengths equal to twice the beam depth on both sides of a section where
flexural yielding is likely to occur as a result of lateral displacements
beyond the elastic range of behavior.
The first hoop is to be located at a distance not more than 5 cm from the face
of a supporting column. Spacing of the hoops is not to exceed the smallest of:
(a) d/4, (b) b
d6 , where bd is the diameter of the smallest primary flexural
reinforcing bars, and (c) 15 cm.
Where hoops are required, they are designed to resist shear according to
18.6.5.
Where hoops are not required, stirrups with seismic hooks at both ends are to
be spaced at a distance not more than d/2 throughout the length of the beam.
Where hoops are required, primary longitudinal reinforcing bars closest to
the tension and compression faces shall have lateral support in accordance
with 25.7.2.3 and 25.7.2.4. The spacing of transversely supported flexural
reinforcing bars shall not exceed 35 cm.
Hoops in beams are permitted to be made up of two pieces of reinforcement:
a stirrup having seismic hooks at both ends and closed by a crosstie.
Consecutive crossties engaging the same longitudinal bar shall have their 90
deg hooks at opposite sides of a flexural member. If the longitudinal
reinforcing bars secured by the crossties are confined by a slab on only one
side of the beam, the 90-degree hooks of the crossties shall be placed on that
side.
In beams having factored axial compressive force exceeding 10/cg fA , hoops
satisfying 18.7.5.2 through 18.7.5.4 shall be provided along lengths given in
18.6.4.1. Along the remaining length, hoops satisfying 18.7.5.2 shall have
spacing, s not exceeding the lesser of six times the diameter of the smallest
longitudinal beam bars and 15 cm. Where concrete cover over transverse
reinforcement exceeds 10 cm, additional transverse reinforcement having
cover not exceeding 10 cm and spacing not exceeding 35 cm shall be
provided.
167
Transverse Reinforcement for Beams of Special Moment Frames
Splices and Hoop Reinforcement for Beams of Special Moment Frames
168
4- Shear Strength Reinforcement:
ACI R18.6.5 states that "Unless a beam possesses a moment strength that is
on the order of 3 or 4 times the design moment, it should be assumed that it
will yield in flexure in the event of a major earthquake. The design shear
force should be selected so as to be a good approximation of the maximum
shear that may develop in a member. Therefore, required shear strength for
frame members is related to flexural strengths of the designed member rather
than to factored shear forces indicated by lateral load analysis. The
conditions described by 18.6.5.1 are illustrated in Fig. R18.6.5."
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The design shear force, eV , is to be determined from consideration of the
forces on the portion of the beam between faces of the joints. It is assumed
that moments of opposite sign corresponding to probable flexural moment
strength, prM , act at the joint faces and that the beam is loaded with the
factored tributary gravity load along its span. For calculation of prM it is
assumed that tensile strength in the longitudinal bars is 1.25 yf and the
strength reduction factor is equal to 1.0.
2/25.1 adfAM yspr
where
bf
fAa
c
ys
'85.0
25.1
Transverse reinforcement over the lengths identified in 3(a) and 3(b) shall be
proportioned to resist shear assuming 0cV when both of the following
conditions occur:
(a) The earthquake induced shear force, eV , represents ½ or more of the
maximum required shear strength within those lengths;
(b) The factored axial compressive force, uP , including earthquake effects is
less than cg fA '05.0 .
Design Shear Forces for Beams of Special Moment Frames
170
Example (8):
Design the transverse reinforcement for the potential hinge regions of the
earthquake resisting beam in a monolithic reinforced concrete frame shown in the
figure. The beam which is part of a special moment resisting frame is subjected to a
service dead load of 3.0 t/m and a service live load of 2.0 t/m ( 2/480 mKgLL ).
Note that 2c cm/Kg300'f and 2
y cm/Kg4200f .
Solution: In this example, requirements of sections 18.6 through 18.8 of ACI 318-14 are to be
satisfied.
A- ACI 18.6.2 "Dimensional Limits":
Clear span of beam is not to be less than four times its effective depth.
cmd 75.5325.11460
0.43.1775.53
930 (O.K)
The width is not to be less than the smaller of 0.3h and 25 cm.
Beam width is 45 cm, which is larger than the greater of 0.3(60) and 25cm.
(O.K)
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Projection of the beam width beyond the width of the supporting columns is
not to exceed the smaller of c2 and 0.75 c1.
Width of beam = width of column. (O.K)
B- ACI 18.6.3 "Longitudinal Reinforcement":
Minimum ratio of top as well as bottom reinforcement is not to be less than
the larger of:
0033.04200
14 and 0033.0
4200
30080.0
0033.000406.075.5345
817.9providedmin (O.K)
Maximum reinforcement ratio is not to exceed 0.025.
025.001217.075.5345
452.29providedmax (O.K)
At least two bars are to be provided continuously top and bottom.
mm252 bars are provided throughout the length of the beam on the top side,
while mm254 bars are provided continuously on the bottom side. (O.K)
Positive moment strength at joint face is not to be less than 1/2 of the
negative moment strength provided at the face of the joint.
Positive moment strength at face of joint is evaluated as follows:
2/adfAveM yve,sn
From equilibrium of forces, veTveC nn and
420063.1945a30085.0 and cm18.7a
m.t35.412/18.775.5310
420063.19veM
5n
Negative moment strength at face of joint is evaluated as follows:
2/adfAveM yve,sn
From equilibrium of forces, veTveC nn and
420045.2945a30085.0 and cm78.10a
mtveM n .82.592/78.1075.5310
420045.295
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Thus, 2
veMveM n
n
at face of joint. (O.K)
The negative or positive moment at any section along the beam is not to be
less than 1/4 the maximum moment strength provided at face of either joint.
At section of least reinforcement moment strength is evaluated as follows:
From equilibrium of forces, nn TC and
4200817.945a30085.0 and cm59.3a
m.t
4
82.59m.t42.212/59.375.53
10
4200817.9M
5n (O.K)
Lap splices of flexural reinforcement are permitted only if hoop or spiral
reinforcement is provided over the lap length. Maximum spacing of the
transverse reinforcement in the lap region is not to exceed the smaller of d/4
or 10 cm. Thus, maximum spacing is not to exceed 10 cm within the lap
length.
Lap splices are not to be used (a) within the joints; (b) within a distance of
twice the beam depth from the face of the joint and (c) at locations where
analysis indicates flexural yielding caused by inelastic lateral displacements
of the frame.
Development length of top bars (in tension):
bd
cf
bd
trK
bc
setyf
dl
'5.3
3.1t , 1e , 1s , and 1
bc = 4.0 + 1.0 + 1.25 = 6.25 cm
or
bc = [(45 – 4 (2) – 2 (1) – 2.5]/ (2) = 16.25 cm
i.e., bc is taken as 6.25 cm
cm
ns
AK tr
tr 14.32)10(
)785.0)(2(4040
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5.2756.35.2
14.325.6
b
trb
d
Kc, taken as 2.5.
07.905.2
3005.25.3
3.14200
dl
Required development length cm90ld
Development length of bottom bars (in tension):
b
c
b
trb
sety
d d
fd
Kc
fl
'5.3
1t , 1e , 1s , and 1
bc = 4.0 + 1.0 + 1.25 = 6.25 cm
or
bc = [(45 – 4 (2) – 2 (1) – 2.5]/ (6) = 5.42cm
i.e., bc is taken as 5.42 cm
cm
ns
AK tr
tr 57.14)10(
)785.0)(2(4040
5.279.25.2
57.142.5
b
trb
d
Kc, taken as 2.5.
28.695.2
3005.25.3
4200
dl
Required development length cm70ld
C- ACI 18.6.4 "Transverse Reinforcement":
Hoops are to be provided in the following regions of beams:
(a) Over a length equal to twice the beam depth measured from the face of the
supporting member (column) toward mid span, at both end of the beam;
(b) Over lengths equal to twice the beam depth on both sides of a section
where flexural yielding is likely to occur in connection with inelastic lateral
displacements of the frame.
The first hoop is to be located at a distance not more than 5 cm from the face
of the supporting member. Maximum spacing of such reinforcement is not to
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exceed the smallest of: d/4, b
d6 where b
d is the diameter of the smallest
longitudinal bars and 15 cm.
Hoops are to be provided over a distance of 2h = 120 cm from faces of joints.
Maximum hoop spacing
cm
cmd
cmd
b
15
155.266
44.134/75.534/
, taken as 12.5 cm.
Where hoops are required they are arranged in away similar to that of column
ties.
Where hoops are not required, stirrups with seismic hooks at both ends are to
spaced at a distance not more than d/2 throughout the length of the beam.
Maximum spacing = d/2 = 53.75/2 = 26.875 cm, taken as 25 cm.
D- ACI 18.6.5 "Shear Strength Requirements":
The design shear force eV is to be determined from consideration of the static
forces on the portion of the member between faces of the joint. It is assumed
that moments of opposite sign corresponding to probable flexural moment
strength prM act at the joint faces and that the beam is loaded with the
factored tributary gravity load along its span. For calculation of prM it is
assumed that tensile strength in the longitudinal bars is 1.25 yf and a strength
reduction factor of 1.0.
m/t6.425.032.1wu
t39.212/3.96.42
wclu
2/adfveA25.1veM yspr
420063.1925.145a30085.0 or cm98.8a
175
m.t77.502/98.875.5310
420063.1925.1veM
5pr
2/adfveA25.1veM yspr
420045.2925.145a30085.0 or cm47.13a
m.t69.722/47.1375.5310
420045.2925.1veM
5pr
t27.13
3.9
69.7277.50
l
M
c
veMvepr pr
t66.3439.2127.13V max,e
For sway to the right max,eV occurs at the right side, while it occurs at the left
side for sway to the left.
Transverse reinforcement over the lengths identified in C(a) and C(b) shall
be proportioned to resist shear assuming 0Vc when both of the following
conditions occur:
(a) The design shear force represents ½ or more of the maximum required
shear strength within these lengths;
(b) The factored axial compressive force including earthquake effects is less
than cg 'fA05.0 .
Seismic induced shear tons2/66.34tons27.13 and the above-mentioned
requirement is not applicable.
tons20.221000/75.534530053.0db'f53.0V cc
cns VVV and cu
s VV
V
tons01.2420.2275.0
66.34Vs
For two-legged 10 mm transverse reinforcement,
)1000(01.24
S
75.534200785.02
S
dfAV
yvs and cmS 76.14
Use two-legged 10 mm stirrups @ 12.5 cm.
Stirrups at other locations:
At the end of the hoop region, 3.9
1.8
12.866.34
12.8Vu
and tons14.29Vu
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cns VVV and cu
s VV
V
tons65.1620.2275.0
14.29Vs
For two-legged 10 mm transverse reinforcement,
)1000(65.16
S
75.534200785.02
S
dfAV
yvs and cms28.21S < 53.75/2 cm
Use 10 mm stirrups @ 20 cm.
177
178
Requirements for Intermediate Moment Resisting Frames
A- Beams
1- Scope:
Requirements of ACI 18.4.2 are applicable for beams of intermediate moment
frames forming part of the seismic-force-resisting system and assigned to SDC C.
2- Longitudinal Reinforcement:
Beams shall have at least two continuous bars at both top and bottom
faces.
Continuous bottom bars shall have area not less than one-fourth the
maximum area of bottom bars along the span. These bars shall be
anchored to develop yf in tension at the face of support.
The positive moment strength at the face of the joint is not to be less than
1/3 of the negative moment strength provided at that face of the joint.
Neither the negative nor the positive moment strength at any section along
the length of the beam shall be less than 1/5 the maximum moment
strength provided at the face of either joint.
3- Transverse Reinforcement:
At both ends of the beam, hoops shall be provided over a length equal of
at least h2 measured from the face of the supporting member toward
midspan.
The first hoop is to be located at a distance not more than 5 cm from the
face of the supporting member. Maximum hoop spacing is not to exceed
the smallest of: d/4, bd8 where
bd is the diameter of the smallest
longitudinal bars, 24 times the diameter of the hoop bar, and 30 cm.
Transverse reinforcement spacing shall not exceed d/2 throughout the
length of the beam.
In beams having factored axial compressive force exceeding cg fA '10.0 ,
transverse reinforcement shall conform to 25.7.2.2 and either 25.7.2.3 or
25.7.2.4 (column tie requirements).
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4- Shear Strength Reinforcement:
Design shear strength, nV shall be at least the lesser of (a) and (b):
(a) The sum of the shear associated with development of nominal moment
strengths of the beam at each restrained end of the clear span due to reverse
curvature bending and the shear calculated for factored gravity loads.
(b) The maximum shear obtained from design load combinations that include
earthquake effect E, with E taken as twice that prescribed by the general
building code.
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Requirements for Ordinary Moment Resisting Frames
A- Beams
1- Scope:
Requirements of ACI 18.3 are applicable for beams of ordinary moment frames
forming part of the seismic-force-resisting system and assigned to SDC B.
2- Longitudinal Reinforcement:
Beams shall have at least two continuous bars at both top and bottom
faces.
Continuous bottom bars shall have area not less than one-fourth the
maximum area of bottom bars along the span. These bars shall be
anchored to develop yf in tension at the face of support.