Prof. Dr. Zahid A. Siddiqi, UET, Lahore
SEISMIC DESIGN
Various building codes consider the following
categories for the analysis and design for
earthquake loading:
1. Seismic Performance Category (SPC), varies
from A to E, depending on how the structure is
expected to behave during the event of an
earthquake which in turn requires different levels of
detailing requirements.
2. Seismic Design Category (SDC), varies from A
to F, depending on how the design and detailing is
carried out.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
3.
Seismic Soil Type, varies from A to F,
depending on how the waves travel through
the soil.
4.
Seismic Zones, 0, 1, 2A, 2B, 3, and 4,
depending on the maximum design ground
acceleration of a particular area.
5.
Seismic Risk Categories, low, moderate,
high.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Low seismic risk corresponds to Seismic
Zones 1 and 2A of UBC-97, Seismic design
category (SDC) A and B of IBC, and Seismic
performance category (SPC) A and B of NBC.
Moderate / intermediate seismic risk
corresponds to Seismic Zones 2B of UBC-97,
Seismic design category (SDC) C of IBC, and
Seismic performance category (SPC) C of NBC.
High seismic risk corresponds to Seismic
Zones 3 and 4 of UBC-97, Seismic design
category (SDC) D, E and F of IBC, and Seismic
performance category (SPC) D and E of NBC.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
6. Lateral Load Resisting System,
a)
Intermediate moment frame — A cast-inplace frame complying with the requirements of
ACI 21.2.2.3 and 21.12 in addition to the
requirements for ordinary moment frames.
b)
Ordinary moment frame — A cast-in-place
or precast concrete frame complying with the
requirements of ACI Chapters 1 through 18.
c)
Special moment frame — A cast-in-place
frame complying with the requirements of ACI
21.2 through 21.5. In addition, the requirements
for ordinary moment frames should be satisfied.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
d)
Structural walls — Walls proportioned to
resist combinations of shears, moments, and
axial forces induced by earthquake motions. A
shear wall is a structural wall.
Structural walls shall be categorized as follows:
i)
Intermediate precast structural wall
— A wall complying with all applicable
requirements of ACI Chapters 1 through 18 in
addition to 21.13.
ii)
Ordinary reinforced concrete
structural wall — A wall complying with the
requirements of ACI Chapters 1 through 18.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
iii) Ordinary structural plain
concrete wall — A wall complying with
the requirements of ACI Chapter 22.
iv)
Special precast structural wall —
v)
Special reinforced concrete
structural wall — A cast-in-place wall
complying with the requirements of ACI
21.2 and 21.7 in addition to the
requirements for ordinary reinforced
concrete structural walls.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Interrelationship Of Design Categories
A. Low Seismic Risk corresponds to Seismic Zones
0 and 1 of UBC 97, seismic design category (SDC) of
A and B (IBC), and seismic performance category of
A and B (NBC).
B. Moderate / Intermediate Seismic Risk
corresponds to Seismic Zones 2A and 2B of UBC 97,
seismic design category (SDC) of C (IBC), and
seismic performance category of C (NBC).
C. High Seismic Risk corresponds to Seismic
Zones 3 and 4 of UBC 97, seismic design category
(SDC) of D, E, and F (IBC), and seismic performance
category of D and E (NBC).
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
According to ACI 21.2.1.3, regions of
moderate seismic risk or for structures
assigned to intermediate seismic performance
or intermediate design categories (Zones 2A,
2B), use one of the following systems or their
combination to resist the seismic forces:
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
1. Intermediate moment frame
2. special moment frame
3. ordinary structural walls
4. intermediate structural walls
5. special structural walls
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
According to ACI 21.2.1.4, regions of high
seismic risk or for structures assigned to high
seismic performance or high design category
(Zones 3, 4), use one of the following
systems or their combination to resist the
earthquake loads:
1. Special moment frames
2. Special structural walls
3. Diaphragms and trusses
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
GENERAL CONSIDERATIONS
FOR SEISMIC DESIGN
As already explained, buildings are designed to
withstand moderate earthquakes without damage
and severe earthquakes without collapse.
Earthquake movements impose deformations on
the structures.
We find inertial forces due to these earthquake
movements depending upon the structure.
Dynamic effects like resonance are also important
to be considered.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Due to availability of limited data, the design is
generally based on statistical studies of the
previous earthquakes.
As more and more earthquake data become
available and understanding of the structural
behavior is improved, Building Codes undergo
modifications to cover the weaknesses in design
criteria of the previous codes.
Further, the safety of a structure subjected to
earthquake loading also depends on the
designer’s understanding of the response of the
structure to ground motion.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
It is prohibitively expensive to design the
structure in the elastic range.
Overall structural ductility is very important in
such designs.
Following are the general considerations for the
seismic design of structures:
1. Design for earthquakes differ from the
design for gravity and wind loads particular
with respect to greater sensitivity of
earthquake-induced forces to the geometry
of the structure.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Most structures, which are not extremely tall, are
designed by the equivalent static loading (up to
about 20 stories).
This is applicable for regular buildings with center
of mass and center of resistance very near to
each other.
Center of Resistance Against
Earthquake and Center of Mass of
a Regular Structure.
8
Center of Resistance
And Center of Mass
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
The configuration of a structure has a major effect
on its response to an earthquake.
Structures with a discontinuity in stiffness or
geometry can be subjected to very high
displacements and forces.
For example, the absence of shear walls, infill
walls or even cladding at a particular story level,
as compared to other stories, causes
concentration of displacements at this story.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
The ground floor of a shopping center generally
has this weakness.
This weak story compared with rest of the
structure is termed as open or soft story.
The larger displacements require a considerably
larger ductility at the level of soft story.
If this amount of ductility is not available, the
structure fails locally at this level.
Such a design is not recommended and the
stiffening members must be continued to the
foundations.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Flexible Story
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
2. Steps to strengthen a member for one type of
loading may actually increase the forces in the
member and change the mode of failure from
ductile to brittle.
3. As the frequency of the ground motion
becomes closer to one of the natural frequencies
of a structure, the chances of the structure to
experience resonance increases.
4. The first mode of vibration usually provides
the greatest contribution to lateral displacement.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
5. The taller structures are more affected by
the higher modes of vibration and their effect
actually adds to the effects of lower modes.
The upper stories attract more forces due to
the higher modes of vibration.
6. The longer duration of earthquake always
has a greater potential for damage to the
structure.
7. Vertical geometric and plan irregularities
may result in torsion induced by ground
motion.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Opening
a) Vertical Geometric Irregularities
b) Plan Irregularities
Geometrical Irregularities in Structures.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
8. The addition of stiff members, such as shear
wall, can on one side reduce the displacements
of the structure and hence the damage.
On the other side, stiff members pick up a
greater portion of the load.
When this effect is ignored in design,
unexpected and often undesirable results can
occur.
9. An adequate separation must be left between
structures.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Large lateral displacements can cause the
structures to come in contact with each other
during an earthquake.
This results in major damage due to hammering
effect.
10. Members designed for seismic loading must
behave in a ductile manner and should dissipate
energy without compromising the strength.
Confinement of concrete is to be provided to
ensure ductility in members subjected to shear
and bending.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Due to this confinement, the beams and columns
can undergo nonlinear cyclic bending.
11. It must be tried that the plastic hinges are
developed in the beams rather than columns.
The weak beam – strong column approach is
always preferred for the design of reinforced
concrete frames subjected to seismic loading.
The advantage of this approach is that the overall
vertical load carrying capacity is maintained near
collapse and smaller portion of the structure is
affected by the nonlinear behavior.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
12. Transverse reinforcement for the columns is
to be carefully designed for the shear force due to
lateral loads in addition to shear force resulting
from the dead and live loads.
A smaller length column closer to high stiffness
members or shear walls may attract large shear
forces and may fail in shear.
This type of column, called captive column, is
more critical for design in shear than in flexure.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
General Requirements For Moderate
Risk / Intermediate Moment Frames
ACI 21.12 deals with this type of frame.
Reinforcement details in a frame member should
satisfy ACI 21.12.4 if the factored axial
compressive load, Pu, for the member is less than
equal to Agfc′/10.
If Pu is larger, frame reinforcement details should
satisfy ACI 21.12.5 unless the member has spiral
reinforcement.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
ACI 21.12.4 deals with beams of such frames.
The positive moment strength at the face of the
joint should be not less than one-third 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
member should be less than one-fifth the
maximum moment strength provided at the face
of either joint.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
At both ends of the member, hoops should be
provided over lengths equal 2h measured from the
face of the supporting member toward midspan.
The first hoop should be located at not more than 50
mm from the face of the supporting member.
Spacing of hoops should not exceed the smallest of
the following:
(a) d/4;
(b) 8 times the diameter of the smallest longitudinal
bar enclosed;
(c) 24 times the diameter of the hoop bar;
(d) 300 mm.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Stirrups should be placed at not more than d/2
throughout the length of the member.
Columns
ACI 21.12.5 deals with columns of such frames.
Columns should be spirally reinforced in
accordance with ACI 7.10.4 or should conform
with ACI 21.12.5.2 through 21.12.5.4. Section
21.12.5.5 should apply to all columns.
At both ends of the member, hoops should be
provided at spacing so over a length lo measured
from the joint face. Spacing so shall not exceed
the smallest of (a), (b), (c), and (d):
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(a)
Eight times the diameter of the smallest
longitudinal bar enclosed;
(b)
24 times the diameter of the hoop bar;
(c)
One-half of the smallest cross-sectional
dimension of the frame member;
(d)
300 mm.
Length lo shall not be less than the largest of (e),
(f), and (g):
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(e)
One-sixth of the clear span of the member;
(f)
Maximum cross-sectional dimension of the
member;
(g)
450 mm.
The first hoop shall be located at not more than
so /2 from the joint face.
Outside the length lo, spacing of transverse
reinforcement should satisfy the normal spacing
requirements.
Joint transverse reinforcement should be
provided as per ACI 11.11.2.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
GENERAL REQUIREMENTS
FOR HIGH RISK
In regions of high seismic risk or for structures
assigned to high seismic performance or design
categories, special moment frames, special
structural walls, and diaphragms and trusses
complying with ACI 21.2.2 through 21.2.8 and
21.3 through 21.10 should be used to resist forces
induced by earthquake motions.
Members not proportioned to resist earthquake
forces should comply with ACI 21.11.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Analysis And Proportioning
Of Structural Members
Rigid members assumed not to be a part of the
lateral-force resisting system are permitted
provided their effect on the response of the
system is considered and accommodated in the
structural design.
Consequences of failure of structural and
nonstructural members, which are not a part of
the lateral force resisting system, should also be
considered.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
All structural members assumed not to be part of
the lateral-force resisting system should satisfy
ACI 21.11.
Specified compressive strength of concrete, fc ′,
should be not less than 21 MPa.
Reinforcement In Members Resisting
Earthquake-Induced Forces
Reinforcement resisting earthquake-induced
flexural and axial forces in frame members should
comply with ASTM A 706M. ASTM A 615M
Grades 280 and 420 reinforcement should be
permitted in these members if:
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(a) The actual yield strength based on mill tests
does not exceed fy by more than 125 MPa
(retests should not exceed this value by more
than an additional 21 MPa); and
(b) The ratio of the actual tensile strength to the
actual yield strength is not less than 1.25. The
value of fyt for transverse reinforcement including
spiral reinforcement should not exceed 420 MPa.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Flexural Members Of Special
Moment Frames
Factored axial compressive force on the member,
Pu, should not exceed Agfc′/10.
Clear span for member, ln, shall not be less than
four times its effective depth.
Width of member, bw, should not be less than the
smaller of 0.3h and 250 mm.
Width of member, bw, should not exceed width of
supporting member plus distances on each side
of supporting member not exceeding three-fourths
of the depth of flexural member.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
At any section of a flexural member, except as
provided in ACI 10.5.3, for top as well as for
bottom reinforcement, the amount of
reinforcement should not be less than that given
by ACI Eq. (10-3) but not less than 1.4bwd /fy,
and the reinforcement ratio, ρ, should not exceed
0.025.
At least two bars should be provided
continuously both top and bottom.
Positive moment strength at joint face should be
not less than one-half of the negative moment
strength provided at that face of the joint.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Neither the negative nor the positive moment
strength at any section along member length
should be less than one-fourth the maximum
moment strength provided at face of either joint.
Spacing of the transverse reinforcement
enclosing the lapped bars should not exceed
the smaller of d/4 and 100 mm. Lap splices
shall not be used in the following situations:
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(a) within the joints;
(b) within a distance of twice the member depth
from the face of the joint; and
(c) where analysis indicates flexural yielding is
caused by inelastic lateral displacements of the
frame.
Hoops should be provided in the following regions
of frame members:
(a) Over a length equal to twice the member
depth measured from the face of the supporting
member toward midspan, at both ends of the
flexural member;
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(b) Over lengths equal to twice the member 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 shall be located not more than 50
mm from the face of a supporting member.
Spacing of the hoops shall not exceed the
smallest of (a), (b), (c) and (d):
(a)
(b)
(c)
(d)
d/4;
eight times the diameter of the smallest
longitudinal bars;
24 times the diameter of the hoop bars; and
300 mm.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Where hoops are
not required,
stirrups with
seismic hooks at
both ends should
be spaced at a
distance not more
than d/2
throughout the
length of the
member.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Special Moment Frame Members
Subjected To Bending And Axial Load
Discussed in ACI 21.4.
The requirements of this section apply to special
moment frame members
(a) resisting earthquake induced forces and
(b) having a factored axial compressive force Pu
exceeding Ag fc′/10.
These frame members should also satisfy the
following conditions:
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
The shortest cross-sectional dimension,
measured on a straight line passing through the
geometric centroid, should not be less than 300
mm.
The ratio of the shortest cross-sectional
dimension to the perpendicular dimension
should not be less than 0.4.
Flexural strength of any column proportioned to
resist Pu exceeding Agfc′ /10 should satisfy ACI
21.4.2.2 or 21.4.2.3.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Lateral strength and stiffness of columns not
satisfying ACI 21.4.2.2 should be ignored when
determining the calculated strength and stiffness
of the structure, but such columns should
conform to ACI 21.11.
The flexural strengths of the columns should
satisfy the following:
Σ Mnc
≥
(1.2) Σ Mnb
ΣMnc = sum of nominal flexural strengths of
columns framing into the joint, evaluated at the
faces of the joint.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Column flexural strength is to be calculated for the
factored axial force, consistent with the direction of
the lateral forces considered, resulting in the
lowest flexural strength.
ΣMnb = sum of nominal flexural strengths of the
beams framing into the joint, evaluated at the
faces of the joint.
Flexural strengths should be summed such that
the column moments oppose the beam moments.
The above equation is to be satisfied for beam
moments acting in both directions in the vertical
plane of the frame considered.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Longitudinal Reinforcement
Area of longitudinal reinforcement, Ast , should
not be less than 0.01Ag or more than 0.06Ag.
Lap splices should be permitted only within the
center half of the member length, should be
designed as tension lap splices, and shall be
enclosed within transverse reinforcement.
Transverse reinforcement required in (a)
through (e) should be provided unless a larger
amount is required by ACI 21.4.3.2 or 21.4.5.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(a) The volumetric ratio of spiral or circular hoop
reinforcement, ρs, should not be less than
required by the following:
ρs = 0.12 fc ′/fyt
and should not be less than required normally.
(b) The total cross-sectional area of rectangular
hoop reinforcement, Ash, should not be less than
required by the following:
Ash = 0.3(sbc fc′/fyt )[(Ag /Ach) –1]
Ash = 0.09sbcfc ′/fyt
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(c) Transverse reinforcement should be provided
by either single or overlapping hoops. Crossties of
the same bar size and spacing as the hoops shall
be permitted. Each end of the crosstie should
engage a peripheral longitudinal reinforcing bar.
Consecutive crossties shall be alternated end for
end along the longitudinal reinforcement.
(d) If the design strength of member core satisfies
the requirement of the design loading
combinations including E, the above need not be
satisfied.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
(e) If the thickness of the concrete outside the
confining transverse reinforcement exceeds 100
mm, additional transverse reinforcement shall be
provided at a spacing not exceeding 300 mm.
Concrete cover on the additional reinforcement
shall not exceed 100 mm.
Spacing of transverse reinforcement shall not
exceed the smallest of (a), (b), and (c):
(a) one-quarter of the minimum member
dimension;
(b) six times the diameter of the longitudinal
reinforcement; and
(c) so,
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
The value of so shall not exceed 150 mm and
need not be taken less than 100 mm.
Horizontal spacing of crossties or legs of
overlapping hoops, hx, shall not exceed 350 mm
on center.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Transverse reinforcement should be provided
over a length lo from each joint face and on both
sides of any section where flexural yielding is
likely to occur as a result of inelastic lateral
displacements of the frame. Length lo should not
be less than the largest of (a), (b), and (c):
(a) the depth of the member at the joint face or at
the section where flexural yielding is likely to
occur;
(b) one-sixth of the clear span of the member; and
(c) 450 mm.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Transverse reinforcement should extend at least
the development length in tension, ld, into
discontinued member.
If the lower end of the column terminates on a
wall, transverse reinforcement should extend into
wall at least ld of the largest longitudinal column
bar at the point of termination.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Where transverse reinforcement is not provided
throughout the full length of the column, the
remainder of the column length should contain
spiral or hoop reinforcement with center-to-center
spacing, s, not exceeding the smaller of six times
the diameter of the longitudinal column bars and
150 mm.
The design shear force, Ve, is to be determined
from consideration of the maximum forces that
can be generated at the faces of the joints at each
end of the member.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
These joint forces shall be determined using the
maximum probable moment strengths, Mpr, at
each end of the member associated with the
range of factored axial loads, Pu, acting on the
member.
The member shears need not exceed those
determined from joint strengths based on Mpr of
the transverse members framing into the joint.
In no case shall Ve be less than the factored
shear determined by analysis of the structure.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Transverse reinforcement over the lengths lo
should be proportioned to resist shear assuming Vc
= 0 when both (a) and (b) occur:
(a) The earthquake-induced shear force represents
one-half or more of the maximum required shear
strength within lo;
(b) The factored axial compressive force, Pu,
including earthquake effects is less than Ag fc′/ 20.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
If columns are not stronger than beams framing
into a joint, there is likelihood of inelastic action.
In the worst case of weak columns, flexural
yielding can occur at both ends of all columns in a
given story, resulting in a column failure
mechanism that can lead to collapse.
When determining the nominal flexural strength of
a girder section in negative bending (top in
tension), longitudinal reinforcement contained
within an effective flange width of a top slab that
acts monolithically with the girder increases the
girder strength.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Joints Of Special Moment Frames
Discussed in ACI 21.5.
Forces in longitudinal beam reinforcement at the
joint face should be determined by assuming that
the stress in the flexural tensile reinforcement is
1.25fy.
Strength of joint should be governed by the
appropriate φ factors.
Beam longitudinal reinforcement terminated in a
column should be extended to the far face of the
confined column core and anchored in tension
and in compression according to ACI Chapter 12.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
Where longitudinal beam reinforcement extends
through a beam-column joint, the column
dimension parallel to the beam reinforcement
should not be less than 20 times the diameter of
the largest longitudinal beam bar for normal
weight concrete.
Within h of the shallowest framing member,
transverse reinforcement equal to at least onehalf the amount required by ACI 21.4.4.1 should
be provided where members frame into all four
sides of the joint and where each member width is
at least three-fourths the column width.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
At these locations, the spacing required in ACI
21.4.4.2 is to be increased to 150 mm.
Transverse reinforcement as required by ACI
21.4.4 should be provided through the joint to
provide confinement for longitudinal beam
reinforcement outside the column core if such
confinement is not provided by a beam framing
into the joint.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
GENERAL PROVISIONS FOR
MEMBERS NOT RESISTING
EARTHQUAKES IN HIGH RISK
Frame members assumed not to contribute to
lateral resistance, except two-way slabs without
beams, should be detailed according to ACI
21.11.2 or 21.11.3 depending on the magnitude
of moments induced in those members when
subjected to the design displacement δu.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
If effects of δu are not explicitly checked, it shall
be permitted to apply the requirements of ACI
21.11.3.
Where the induced moments and shears under
design displacements, δu, combined with the
factored gravity moments and shears do not
exceed the design moment and shear strength
of the frame member, the conditions of ACI
21.11.2.1, 21.11.2.2, and 21.11.2.3 should be
satisfied.
The gravity load combinations of (1.2D + 1.0L +
0.2S) or 0.9D, whichever is critical, should be
used.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
The load factor on the live load, L, is permitted
to be reduced to 0.5 except for garages, areas
occupied as places of public assembly, and all
areas where L is greater than 490 kg/m2.
Members with factored gravity axial forces not
exceeding Agfc′/10 should satisfy ACI 21.3.2.1.
Stirrups should be spaced not more than d/2
throughout the length of the member.
Members with factored gravity axial forces
exceeding Agfc ′/10 should satisfy ACI 21.4.3,
21.4.4.1(c), 21.4.4.3, and 21.4.5.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
The maximum longitudinal spacing of ties should
be so for the full column height.
Spacing so should not exceed smaller of six
diameters of the smallest longitudinal bar
enclosed and 150 mm.
Members with factored gravity axial forces
exceeding 0.35Po should satisfy ACI 21.11.2.2
and the amount of transverse reinforcement
provided should be one-half of that required by
ACI 21.4.4.1 but should not be spaced greater
than so for the full height of the column.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore
If the induced moment or shear under design
displacements, δu, exceeds φMn or φVn of the
frame member, or if induced moments are not
calculated, the conditions of ACI 21.11.3.1,
21.11.3.2, and 21.11.3.3 should be satisfied.
Members with factored gravity axial forces not
exceeding Agfc′/10 should satisfy ACI 21.3.2.1
and 21.3.4. Stirrups should be spaced at not
more than d/2 throughout the length of the
member.
Members with factored gravity axial forces
exceeding Agfc′/10 should satisfy ACI 21.4.3.1,
21.4.4, 21.4.5, and 21.5.2.1.
Prof. Dr. Zahid A. Siddiqi, UET, Lahore