ARCH28 – ARCHITECTURAL STRUCTURES
RESEARCH ACTIVITY
REINFORCED CONCRETE DESIGN OF SLABS AND COLUMNS
RONEL L. BACTOL
201810336
BSARCH 4-2
MA’AM KATHERINCE GRACE PEÑA LOPEZ
Introduction:
Reinforced concrete is a composite material. This means that it is made up of different materials
with very different properties that complement each other. In the case of reinforced concrete, the
component materials are almost always concrete and steel. Concrete is strong in compression.
Steel is strong in tension and compression, but in compression a steel bar that is thin enough to
be economic will buckle. A simple reinforced concrete structure therefore uses steel in tension,
and concrete in compression. Making the columns and slabs significantly enhance their strength,
ductility and energy absorption capability. So, proper design considerations for columns and slabs
are needed.
Structural behavior and loadings:
Within the context of the built environment, the term ‘structure’ refers to anything that is
constructed or built from different interrelated parts with a fixed location on the ground. The
structure is responsible for maintaining the shape and form under the influence of subjected
forces.
Forces. It is important that the strength and stability of a structure and its individual components
must be considered. Structural analysis is used to calculate the effects of the forces acting on any
component and, on the structure, overall. Three properties of forces that should be considered
are:
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Magnitude: The size of the force.
Direction: The direction in which the force is acting.
Position: The position on which the force acts.
Loads. Another principle is that the structure should be capable of withstanding the most severe
combination of forces that are likely to be applied. This is determined by the geolocation relevant
to the structure, such as in places where strong winds or heavy rain are common weather
conditions.
Dead loads. consist of all materials of construction incorporated into the building or other
structure, including walls, floors, roofs, ceilings, stairways, built-in partitions, finishes, cladding
and other similarly incorporated architectural and structural items.
Live loads shall be the maximum loads expected by the intended use or occupancy but in no
case shall be less than the loads required.
Wind load. is an important consideration when designing and building structure. This will depend
on the angle at which the wind strikes the structure and the shape of the structure (height, width,
etc.).
Seismic load. is one of the basic concepts of earthquake engineering which means application
of a seismic oscillation to a structure. It happens at contact surfaces of a structure either with the
ground or with adjacent structures.
Combination of loads. Buildings, towers and other vertical structures and all portions thereof
shall be designed to resist the load combinations. The most critical effect can occur when one or
more of the contributing loads are not acting. All applicable loads shall be considered, including
both earthquake and wind, in accordance with the specified load combinations.
Symbols and Notations. D = dead load E = earthquake load set forth, Em = estimated maximum
earthquake force that can be developed in the structure, F = load due to fluids with well-defined
pressures and maximum heights, H = load due to lateral pressure of soil and water in soil L = live
load, except roof live load, including any permitted live load reduction, Lr = roof live load, including
any permitted live load reduction, P = ponding load, R = rain load on the undeflected roof, T =
self-straining force and effects arising from contraction or expansion resulting from temperature
change, shrinkage, moisture change, creep in component materials, movement due to differential
settlement, or combinations thereof, W = load due to wind
Basic Load Combinations. Where strength design or load and resistance factor design is used,
structures and all portions thereof shall resist the most critical effects from the following
combinations of factored loads:
Where: f1 = 1.0 for floors in places of public assembly, for live loads in excess of 4.8 kPa, and for
garage live load, or 0.5 for other live loads
Basic Load Combinations. Where allowable stress or allowable strength design is structures
and all portions thereof shall resist the most critical effects resulting from the following
combinations of loads
Alternate Basic Load Combinations. In lieu of the basic load, structures and portions thereof
shall be permitted to be designed for the most critical effects resulting from the following load
combinations. When using these alternate basic load combinations, a one-third increase shall be
permitted in allowable stresses for all combinations, including W or E.
Special Seismic Load Combinations.
Where: f1 = 1.0 for floors in places of public assembly, for live loads in excess of 4.8 kPa, and for
garage live load, or = 0.5 for other live loads
Em = the maximum effect of horizontal and vertical forces
Materials. The effectiveness of a structure depends on the mechanical properties of the materials
from which it is constructed. These properties include:
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





Strength
Toughness
Elasticity
Plasticity
Ductility
Malleability
Brittleness
Hardness
Shear force. A shear force is a force that acts tangentially on the body. Shear force is caused by
a tangential component of a force applied on a body. Shearing stresses are also produced by the
shear force in the body.
Bending moment. Any load-bearing object will deflect within the structure. In other words,
bending indicates that the load applied perpendicular to a bar's axis causes the bar to deform.
The tendency of a force to cause a body to rotate around a particular point or axis is measured
by its moment.
Thus, bending moment refers to the moment produced by a force or bending in any structural
part. The algebraic sum of the applied load to the specified distance from the reference point is
the Bending Moment. This is directional since it is influenced by the direction of applied tension.
Axial forces. refers to a load whose line of action runs along the length of a structure or
perpendicular to the structure’s cross-section. Moreover, the line of force goes through the center
of gravity of the member’s cross-section. When this load tends to compress the member along its
line of action, it is an axial compression load and carries a negative sign by convention. While if
the load extends the member along its line of action, it is an axial tension load, carrying a positive
sign.
Design codes and standards:
The design of concrete structures is generally done within the framework of codes giving specific
requirements for materials, structural analysis, member proportioning, etc. The International
Building Code is an example of a consensus code governing structural design and is often
adopted by local municipalities. The responsibility of preparing material-specific portions of the
code rests with various professional groups, trade associations, and technical institutes. In
contrast with many other industrialized nations, the United States does not have an official,
government-sanctioned, national code.
American Concrete Institute (ACI). has long been a leader in such efforts. As one part of its
activity, the American Concrete Institute has published the widely recognized Building Code
Requirements for Structural Concrete and Commentary which serves as a guide in the design
and construction of reinforced concrete buildings. The ACI Code has no official status in itself.
However, it is generally regarded as an authoritative statement of current good practice in the
field of reinforced concrete. As a result, it has been incorporated into the International Building
Code and similar codes, which in turn are adopted by law into municipal and regional building
codes that do have legal status. Its provisions thereby attain, in effect, legal standing. Most
reinforced concrete buildings and related construction in the United States are designed in
accordance with the current ACI Code. It has also served as a model document for many other
countries. The commentary provides background material and rationale for the Code provisions.
The American Concrete Institute also publishes important journals and standards, as well as
recommendations for the analysis and design of special types of concrete structures.
AASHTO (American Association of State Highway and Transportation Officials). Most
highway bridges in the United States are designed according to the requirements of the AASHTO
bridge specifications, which not only contain the provisions relating to loads and load distributions
mentioned earlier but also include detailed provisions for the design and construction of concrete
bridges. Some of the provisions follow ACI Code provisions closely, although a number of
significant differences will be found.
National Structural Code of The Philippines. is designed to meet these needs through various
model codes/regulations, generally from the United States, to safeguard the public health and
safety nationwide. This Structural Code establishes minimum requirements for structural systems
using prescriptive and performance-based provisions. It is founded on broad based principles that
make possible the use of new materials and new building designs. Also, this code reflects the
latest seismic design practice for earthquake-resistant structures.
No code or design specification can be construed as a substitute for sound engineering judgment
in the design of concrete structures. In structural practice, special circumstances are frequently
encountered where code provisions can serve only as a guide, and the engineer must rely upon
a firm understanding of the basic principles of structural mechanics applied to reinforced or
prestressed concrete, and an intimate knowledge of the nature of the materials
Design of slabs:
ONE-WAY SLABS. This section shall apply to the design of non-prestressed and prestressed
slabs reinforced for flexure in one direction, including: solid slabs: slabs cast on stay-in-place,
non-composite steel deck; composite slabs of concrete elements constructed in separate
placements but connected so that all elements resist loads as a unit; precast, prestressed hollowcore slabs. The effects of concentrated loads and openings shall be considered in design.
Materials. Design properties for concrete shall be selected to be in accordance with concrete
design and durability requirements. Design properties for steel reinforcement shall be selected to
be in accordance with Steel Reinforcement Properties, Durability and Embedment. Materials,
design and detailing requirements for embedment in concrete shall be in accordance with
Embedment section.
Connection to Other Members. For cast-in-place construction, slab-column joints shall satisfy
Beam-concrete and slab-column joint section. For precast construction, connections shall satisfy
the force transfer requirements of connections of precast member’s section.
Design Limits. Minimum Slab Thickness. For solid non-prestressed slabs not supporting or
attached to partitions or other construction likely to be damaged by large deflections, overall slab
thickness h shall not be less than the limits in Table below, unless the calculated deflection limits
are satisfied.
For fy other than 420 MPa, the expressions in Table above be multiplied by (0. 4 + fy/ 700).
For non-prestressed slabs made of lightweight concrete having wc in the range of 1440 to 1840
kg/m3, the expressions in Table above shall be multiplied by the greater of (a) and (b): a. 1.65 –
0.003Wc, b. 1.09
For non-prestressed composite slabs made of a combination of lightweight and normal weight
concrete that are shored during construction, where the lightweight concrete is in compression,
the modifier of Section above shall apply. The thickness of a concrete floor finish shall be
permitted to be included in ft if it is placed monolithically with the floor slab, or if the floor finish is
designed to be composite with the floor slab in accordance with Horizontal Shear Transfer in
Composite Concrete Flexural Members Section.
Calculated Deflection. For non-prestressed slabs not satisfying minimum slab thickness and for
prestressed slabs, immediate and time-dependent deflections shall be calculated in accordance
with shrinkage and temperature reinforcement section and shall not exceed the limits in deflection
due to service-level gravity loads Section. For non-prestressed composite concrete slabs
satisfying minimum slab thickness, deflections occurring after the member becomes composite
need not be calculated. Deflections occurring before the member becomes composite shall be
investigated, unless the pre- composite thickness also satisfies minimum slab thickness.
Reinforcement Strain Limit in Non-Prestressed Slabs. For non-prestressed slabs, et shall be
at least 0.004.
Stress Limits in Prestressed Slabs. Prestressed slabs shall be classified as Class U, T, or C,
stresses at service loads shall be permitted to be calculated using the uncracked. Stresses in
prestressed slabs immediately after transfer and at service loads shall not exceed the permissible
stresses in Permissible Concrete Stresses at Transfer of Prestress and Permissible Concrete
Compressive Stresses at Service Loads.
Required Strength. shall be calculated in accordance with the factored load combinations in
loads and shall be calculated in accordance with the analysis procedures in structural analysis.
For prestressed slabs, effects of reactions induced by prestressing shall be considered in
accordance for post-tensioned anchorage zone design, a load factor of 1.2 shall be applied to the
maximum prestressing reinforcement jacking force.
Factored Moment. For slabs built integrally with supports, Mu at the support shall be permitted
to be calculated at the face of support.
Factored Shear. For slabs built integrally with supports, Vu at the support shall be permitted to
be calculated at the face of support.
Sections between the face of support and a critical section located d from the face of support for
non-prestressed slabs or ft/2 from the face of support for prestressed slabs shall be permitted to
be designed for Vu at that critical section if (a) through (c) are satisfied: a. Support reaction, in
direction of applied shear, introduces compression into the end region of the slab; b. Loads are
applied at or near the top surface of the slab; c. No concentrated load occurs between the face of
support and critical section.
Design Strength. For each applicable factored load combination, design strength at all sections
shall satisfy Ø Sn > U including (a) and (b): a. Ø Mn > Mu, b. Ø Vn > Vu. Interaction between load
effects shall be considered. Ø shall be determined in accordance with Strength Reduction Factors
for Structural Concrete Members and Connect Section.
Moment. Mn shall be calculated in accordance with Flexural Strength. For prestressed slabs,
external tendons shall be considered as unbonded tendons in calculating flexural strength, unless
the external tendons are effectively bonded to the concrete section along its entire length. If
primary flexural reinforcement in a slab that is considered to be a T-beam flange is parallel to the
longitudinal axis of the beam, reinforcement perpendicular to the longitudinal axis of the beam
shall be provided in the top of the slab in accordance with (a) and (b). This provision does not
apply to joist construction: a. Slab reinforcement perpendicular to the beam shall be designed to
resist the factored load on the overhanging slab width assumed to act as a cantilever; b. Only the
effective overhanging slab width in accordance with Section 406.3.2 need be considered.
Shear. Fn shall be calculated in accordance with One-way Shear Strength. For composite
concrete slabs, horizontal shear strength, Vnh, shall be calculated in accordance with Horizontal
Shear Transfer in Composite Concrete Flexural Members.
Reinforcement Limits. Minimum Flexural Reinforcement in Non-Prestressed Slabs. A
minimum area of flexural reinforcement Asi min shall be provided in accordance with Table below
Minimum Flexural Reinforcement in Prestressed Slabs. For slabs with bonded prestressed
reinforcement, total quantity of As and Aps shall be adequate to develop a factored load at least
1.2 times the cracking load calculated on the basis of fr as given in Modulus of Rupture.
For slabs with both flexural and shear design strength at least twice the required strength, the
said above need not be satisfied. For slabs with unbonded tendons, the minimum area of bonded
deformed longitudinal reinforcement, As, min, shall be: As min — 0. 004 Act. where Act is the area
of that part of the cross section between the flexural tension face and the centroid of the gross
section.
Minimum Shear Reinforcement. A minimum area of shear reinforcement, Av, min shall be
provided in all regions where Vu > Ø Vc. For precast prestressed hollow-core slabs with untopped
h > 315mm, Av, min shall be provided in all regions where Vu > 0.5 Ø Vcw.
If shown by testing that the required Mn and Vn can be developed, the said above need not be
satisfied. Such tests shall simulate effects of differential settlement, creep, shrinkage, and
temperature change, based on a realistic assessment of these effects occurring in service. If
shear reinforcement is required, Av, min, shall be in accordance with table below
Reinforcement Detailing. Concrete cover for reinforcement shall be in accordance with
Specified Concrete. Development lengths of deformed and prestressed reinforcement shall be in
accordance with Development of Reinforcement. Splices of deformed reinforcement shall be in
accordance with Splices Section. Bundled bars shall be in accordance with Bundle
Reinforcement.
Reinforcement Spacing. Minimum spacing s shall be in accordance with Minimum Spacing of
Reinforcement Section. For non-prestressed and Class C prestressed slabs, spacing of bonded
longitudinal reinforcement closest to the tension face shall not exceed s calculated in accordance
with Distribution of Flexural Reinforcement in One-Way Slabs and Beams. Maximum spacing s of
deformed reinforcement shall be the lesser of 3h and 450 mm. Spacing of reinforcement required
shall not exceed the lesser of 5h and 450 mm.
Flexural Reinforcement in Non-Prestressed Slabs. Calculated tensile or compressive force in
reinforcement at each section of the slab shall be developed on each side of that section. Critical
locations for development of reinforcement are points of maximum stress and points along the
span where bent or terminated tension reinforcement is no longer required to resist flexure.
Reinforcement shall extend beyond the point at which it is no longer required to resist flexure for
a distance at least the greater of d and 12db, except at supports of simply-supported spans and
at free ends of cantilevers. Continuing flexural tension reinforcement shall have an embedment
length at least €d beyond the point where bent or terminated tension reinforcement is no longer
required to resist flexure.
Flexural tension reinforcement shall not be terminated in a tension zone unless (a), (b), or (c) is
satisfied: a. Vu ≤ (2/3) Ø Vn at the cutoff point; b. For 36 mm Ø bars and smaller, continuing
reinforcement provides double the area required for flexure at the cutoff point and Vu ≤ (2/3) Ø
Vn; c. Stirrup area in excess of that required for shear is provided along each terminated bar or
wire over a distance 3/4d from the termination point. Excess stirrup area shall be not less than
0.41 bw s/fyt. Spacing s shall not exceed d/(8βb).
Adequate anchorage shall be provided for tension reinforcement where reinforcement stress is
not directly proportional to moment, such as in sloped, stepped, or tapered slabs, or where tension
reinforcement is not parallel to the compression face. In slabs with spans not exceeding 3 m,
welded wire reinforcement, with wire size not exceeding MW30 or MD30, shall be permitted to be
curved from a point near the top of slab over the support to a point near the bottom of slab at midspan, provided such reinforcement is continuous over, or developed at, the support.
Flexural Reinforcement in Prestressed Slabs. External tendons shall be attached to the
member in a manner that maintains the specified eccentricity between the tendons and the
concrete centroid through the full range of anticipated member deflections. If non-prestressed
reinforcement is required to satisfy flexural strength, the detailing requirements of Flexural
Reinforcement in Non-Prestressed Slabs shall be satisfied.
Shear Reinforcement. If shear reinforcement is required, transverse reinforcement shall be
detailed according to Shear Section.
TWO-WAY SLABS. This section shall apply to the design of non-prestressed and prestressed
slabs reinforced for flexure in two directions, with or without beams between supports, including
(a) through (d): a. Solid slabs; b. Slabs cast on stay-in-place, non-composite steel deck; c.
Composite slabs of concrete elements constructed in separate placements but connected so that
all elements resist loads as a unit; d. Two-way joist systems.
A slab system shall be permitted to be designed by any procedure satisfying equilibrium and
geometric compatibility, provided that design strength at every section is at least equal to required
strength, and all serviceability requirements are satisfied. The direct design method of Direct
Design Method or the equivalent frame method of Equivalent Frame Method is permitted for
design where applicable. The effects of concentrated loads and openings shall be considered in
design. Slabs prestressed with an average effective compressive stress less than 0.9 MPa shall
be designed as non-prestressed slabs.
A drop panel in a non-prestressed slab, where used to reduce the minimum required thickness in
accordance with Minimum Slab Thickness or the quantity of deformed negative moment
reinforcement at a support in accordance with Moment, shall satisfy (a) and (b): a. The drop panel
shall project below the slab at least 1/4 of the adjacent slab thickness; b. The drop panel shall
extend in each direction from the centerline of support a distance not less than 1/6 the span length
measured from center-to-center of supports in that direction.
A shear cap, where used to increase the critical section for shear at a slab-column joint, shall
project below the slab soffit and extend horizontally from the face of the column a distance at least
equal to the thickness of the projection below the slab soffit.
Materials. Design properties for concrete shall be selected to be in accordance with Design and
Durability Requirements while design properties for steel reinforcement shall be selected to be in
accordance with Steel Reinforcement Properties, Durability, and Embedment. Materials, design
and detailing requirements for embedment in concrete shall be in accordance with Embedment
Section.
Connections to Other Members. Connections of two-way slabs to supporting members shall be
in accordance with Beam-Concrete and Slab-Column Joint.
Design Limits. Minimum Slab Thickness. For non-prestressed slabs without interior beams
spanning between supports on all sides, having a maximum ratio of long-to-short span of 2, overall
slab thickness h shall not be less than the limits in Table below, and shall be at least the value in
(a) or (b): a. Slabs without drop panels as given in drop panel section=125 mm; b. Slabs drop
panels as given in drop panel section=100 mm.
1. ℓn is the clear span in the long direction, measured face-to-face of supports (mm).
2. For fy between the values given in the table, minimum thickness shall be calculated by
linear interpolation.
3. Drop panels as given in drop panel Section.
4. Slabs with beams between columns along exterior edges. The value of af for the edge
beam shall be calculated in accordance with Connections to Other Members. Exterior
panels shall be considered to be without edge beams if af is less than 0.8.
For non-prestressed slabs with beams spanning between supports on all sides, overall slab
thickness h shall satisfy the limits in Table below, unless the calculated deflection limits are
satisfied.
1. afm is the average value of af for all beams on edges of a panel and af shall be calculated.
2. ℓn is the clear span in the long direction, measured face-to-face of beams (mm.).
3. β is the ratio of clear spans in long to short directions of slab.
At discontinuous edges of slabs conforming to table above, an edge beam with af > 0. 80 shall
be provided, or the minimum thickness required by (b) or (d) shall be increased by at least 10
percent in the panel with a discontinuous edge. The thickness of a concrete floor finish shall be
permitted to be included in h if it is monolithically with the floor slab, or if the floor finish is designed
to be composite with the floor slab. f single- or multiple-leg stirrups are used as shear
reinforcement, the slab thickness shall be sufficient to satisfy the requirements for d.
Calculated Deflection Limits. Immediate and time-dependent deflections shall be calculated
and shall not exceed the limits for two-way slabs given in (a) through (c): a. non-prestressed slabs
not satisfying minimum slab thickness; b. non-prestressed slabs without interior beams spanning
between the supports on all sides and having a ratio of long-to-short span exceeding 2.0; c.
Prestressed slab.
For non-prestressed composite concrete slabs minimum satisfying slab thickness or, deflections
occurring after the member becomes composite need not be calculated. Deflections occurring
before the member becomes composite shall be investigated, unless the pre- composite
thickness also satisfies minimum slab thickness.
Required Strength. shall be calculated in accordance with the factored load combinations and
shall be calculated in accordance with the analysis procedures. The provisions of for the direct
design method shall be permitted for the analysis of non-prestressed slabs and the provisions for
the equivalent frame method shall be permitted for the analysis of non-prestressed and
prestressed slabs. For prestressed slabs, effects of reactions induced by prestressing shall be
considered.
For a slab system supported by columns or walls, dimensions c1, c2, and ℓ3 shall be based on
an effective support area. The effective support area is the intersection of the bottom surface of
the slab, or drop panel or shear cap if present, with the largest right circular cone, right pyramid,
or tapered wedge whose surfaces are located within the column and the capital or bracket and
are oriented no greater than 45 degrees to the axis of the column. A column strip is a design strip
with a width on each side of a column centerline equal to the lesser of 0.25ℓ2 and 0.25ℓ1. A column
strip shall include beams within the strip, if present. A middle strip is a design strip bounded by
two column strips. A panel is bounded by column, beam, or wall centerlines on all sides.
For monolithic or fully composite construction supporting two-way slabs, a beam includes that
portion of slab, on each side of the beam extending a distance equal to the projection of the beam
above or below the slab, whichever is greater, but not greater than four times the slab thickness.
Combining the results of a gravity load analysis with the results of a lateral load analysis shall be
permitted.
Factored Moment. For slabs built integrally with supports, Mu at the support shall be permitted
to be calculated at the face of support, except if analyzed. For slabs analyzed using the direct
design method or the equivalent frame method, Mu at the support shall be located.
Factored Slab Moment Resisted by the Colum. If gravity load, wind, earthquake, or other
effects cause a transfer of moment between the slab and column, a fraction of Msc., the factored
slab moment resisted by the column at a joint, shall be transferred by flexure. The fraction of
factored slab moment resisted by the column, yfMsc , shall be assumed to be transferred by
flexure, where yf shall be calculated by:
The effective slab width bstab for resisting yfMsc shall be the width of column or capital plus 1.5
h of slab or drop panel on either side of column or capital. For non-prestressed slabs, where the
limitations on vug and εt in Table below are satisfied, Yf shall be permitted to be increased to the
maximum modified values provided in Table, where vc is calculated and vug is the factored shear
stress on the slab critical section for two-way action due to gravity loads without moment transfer.
Concentration of reinforcement over the column by closer spacing or additional reinforcement
shall be used to resist moment on the effective slab width.
The fraction of Msc not calculated to be resisted by flexure shall be assumed to be resisted by
eccentricity of shear.
Factored Two-Way Shear. Critical Section. Slabs shall be evaluated for two-way shear in the
vicinity of columns, concentrated loads, and reaction areas at critical sections. Slabs reinforced
with stirrups or headed shear stud reinforcement shall be evaluated for two-way shear at critical
sections. Slabs reinforced with shear heads shall be evaluated for two-way shear at critical
sections.
Factored Two-Way Shear Stress Due to Shear and Factored Slab Moment Resisted by the
Column. For two-way shear with factored slab moment resisted by the column, factored shear
stress vu shall be calculated at critical sections. Factored shear stress vu corresponds to a
combination of vug and the shear stress produced by Yv Msc, where Yv is given and Mscis given.
The fraction of Msc transferred by eccentricity of shear, yvMSC, shall be applied at the centroid
of the critical section where:
The factored shear stress resulting from YvM sc shall be assumed to vary linearly about the
centroid of the critical section.
Design Strength. For each applicable factored load combination, design strength shall satisfy
∅Sn ≥ U, including (a) through (d). Interaction between load effects shall be considered. a. ∅Mn
≥ Mu at all sections along the span in each direction; b. ∅Mn ≥ YfMsc within b slab; c. ∅ Vn≥Vu at
all sections along the span in each direction for one-way shear; d. ∅ vn≥vu at the critical sections
defined in Section for two-way shear. If shear heads are provided, (a) shall be satisfied in the
vicinity of the column. Beyond each arm of the shear head (a) through (d) shall apply.
Moment. Mn shall be calculated, for non-prestressed slabs with a drop panel, the thickness of
the drop panel below the slab shall not be assumed to be greater than 1/4 the distance from the
edge of drop panel to the face of column or column capital. For prestressed slabs, external
tendons shall be considered as unbonded unless the external tendons are effectively bonded to
the slab along its entire length.
Shear. Design shear strength of slabs in the vicinity of columns, concentrated loads, or reaction
areas shall be the more severe. For one-way shear, where each critical section to be investigated
extends in a plane across the entire slab width, Vn shall be calculated. For two-way shear, vn
shall be calculated. For composite concrete slabs, horizontal shear strength, Vnh, shall be
calculated.
Openings in Slab Systems. any size shall be permitted in slab systems if shown by analysis that
all strength and serviceability requirements, including the limits on deflections, are satisfied. As
an alternative, openings shall be permitted in slab systems without beams in accordance with (a)
through (d): a. Openings of any size shall be permitted in the area common to intersecting middle
strips, but the total quantity of reinforcement in the panel shall be at least that required- for the
panel without the opening; b. At two intersecting column strips, not more than 1/8 the width of
column strip in either span shall be interrupted by openings. A quantity of reinforcement at least
equal to that interrupted by an opening shall be added on the sides of the opening; c. At the
intersection of one column strip and one middle strip, not more than 1/4 of the reinforcement in
either strip shall be interrupted by openings. A quantity of reinforcement at least equal to that
interrupted by an opening shall be added on the sides of the opening; d. If an opening is located
within a column strip or closer than 10h from a concentrated load or reaction area.
Reinforcement Limits. Minimum Flexural Reinforcement in Non-Prestressed Slabs. A
minimum area of flexural reinforcement, As min shall be provided near the tension face in the
direction of the span under consideration in accordance with table below.
Minimum Flexural Reinforcement in Prestressed Slabs. For prestressed slabs, the effective
prestress force Apsfse shall provide a minimum average compressive stress of 0.9 MPa on the
slab section tributary to the tendon or tendon group. For slabs with varying cross section along
the slab span* cither parallel or perpendicular to the tendon or tendon group, the minimum
average effective prestress of 0.9 MPa is required at every cross-section tributary to the tendon
or tendon group along the span. For slabs with bonded prestressed reinforcement, total quantity
of As and Aps shall be adequate to develop a factored load at least 1.2 times the cracking load
calculated on the basis of fr. For slabs with both flexural and shear design strength at least twice
the required strength.
For prestressed slabs, a minimum area of bonded deformed longitudinal reinforcement, Asmin,
shall be provided in the pre-corn pressed tensile zone in the direction of the span under
consideration in accordance with Table below.
1. The value of fy shall not exceed 420 MPa.
2. Nc = the resultant tensile force acting on the portion of the concrete cross section that is
subjected to tensile stresses due to the combined effects of service loads and effective
prestress.
3. Acf = greater gross cross-sectional area of the slab beam strips of the two orthogonal
equivalent frames intersecting at a column of a two-way slab.
4. For slabs with bonded tendons, it shall be permitted to reduce As min by the area of the
bonded prestressed reinforcement located within the area used to determine Nc for
positive moment, or within the width of slab for negative moment.
Reinforcement Detailing. Concrete cover for reinforcement shall be in accordance with
Specified Concrete Cover. Development lengths of deformed and prestressed reinforcement shall
be in accordance with Development of Reinforcement. Splice lengths of deformed reinforcement
shall be in accordance with Splices Section. Bundled bars shall be detailed in accordance with
Bundled Reinforcement.
Flexural Reinforcement Spacing. Minimum spacing s shall be in accordance with Minimum
Spacing of Reinforcement. For non-prestressed solid slabs, maximum spacing s of deformed
longitudinal reinforcement shall be the lesser of 2h and 450 mm at critical sections, and the lesser
of 3h and 450 mm at other sections. For prestressed slabs with uniformly distributed loads,
maximum spacing s of tendons or groups of tendons in at least one direction shall be the lesser
of 8h and 1.5m. Concentrated loads and openings shall be considered in determining tendon
spacing.
Flexural Reinforcement in Non-Prestressed Slabs. Termination of Reinforcement. Where a
slab is supported on spandrel beams, columns, or walls, anchorage of reinforcement
perpendicular to a discontinuous edge shall satisfy (a) and (b): a. Positive moment reinforcement
shall extend to the edge of slab and have embedment, straight or hooked, at least 150 mm. into
spandrel beams, columns, or walls; Negative moment reinforcement shall be bent, hooked, or
otherwise anchored into spandrel beams, columns, or walls, and shall be developed at the face
of support.
For slabs without beams, reinforcement extensions shall be in accordance with (a) through (c): a.
Reinforcement lengths shall be at least, and if slabs act as primary members resisting lateral
loads, reinforcement lengths shall be at least those required by analysis; If adjacent spans are
unequal, extensions of negative moment reinforcement beyond the face of support shall be based
on the longer span; c. Bent bars shall be permitted only where the depth-to span ratio permits use
of bends of 45 degrees or less.
Structural Integrity. All bottom deformed bars or deformed wires within the column strip, in each
direction, shall be continuous or spliced with full mechanical, full welded, or Class B tension
splices.
At least two of the column strip bottom bars or wires in each direction shall pass within the region
bounded by the longitudinal reinforcement of the column and shall be anchored at exterior
supports. In slabs with shear heads where it is not practical to pass the bottom bars through the
column, at least two bottom bars or wires in each direction shall pass through the shear head as
close to the column as practicable and be continuous or spliced with full mechanical, full welded,
or Class B tension splices. At exterior columns, the bars or wires shall be anchored at the shear
head.
Flexural Reinforcement in Prestressed Slabs. External tendons shall be attached to the slab
in a manner that maintains the specified eccentricity between the tendons and the concrete
centroid through the full range of anticipated member deflections. If bonded deformed longitudinal
reinforcement is required to satisfy flexural strength or for tensile stress conditions. Bonded
longitudinal reinforcement required shall be placed in the top of the slab, and shall be in
accordance with (a) through (c): a. Reinforcement shall be distributed between lines that are 1.5h
outside opposite faces of the column support; b. At least four deformed bars, deformed wires, or
bonded strands shall be provided in each direction; c. Maximum spacing s between bonded
longitudinal reinforcement shall not exceed 300 mm.
Structural Integrity. Except as permitted, at least two tendons with 12 mm. diameter or larger
strand shall be placed in each direction at columns in accordance with (a) or (b): a. Tendons shall
pass through the region bounded by the longitudinal reinforcement of the column; b. Tendons
shall be anchored within the region bounded by the longitudinal reinforcement of the column, and
the anchorage shall be located beyond the column centroid and away from the anchored span.
Outside of the column and shear cap faces, the two structural integrity tendons required shall
pass under any orthogonal tendons in adjacent spans. Slabs with tendons not shall be permitted
if bonded bottom deformed reinforcement is provided in each direction.
Minimum bottom deformed reinforcement As in each direction shall be the greater of (a) and (b):
where bw is the width of the column face through which the reinforcement passes.
Bottom deformed reinforcement calculated shall pass within the region bounded by the
longitudinal reinforcement of the column and shall be anchored at exterior supports. Bottom
deformed reinforcement shall be anchored to develop fy beyond the column or shear cap face.
Shear Reinforcement – Stirrups. Single-leg, simple-U, multiple-U, and closed stirrups shall be
permitted as shear reinforcement. If stirrups are provided, location and spacing shall be in
accordance with Table below.
Shear Reinforcement - Headed Studs. shall be permitted if placed perpendicular to the plane
of the slab. The overall height of the shear stud assembly shall be at least the thickness of the
slab minus the sum of (a) through (c): a. Concrete cover on the top flexural reinforcement; b.
Concrete cover on the base rail; c. 1/2 the bar diameter of the flexural tension reinforcement.
Headed shear stud reinforcement location and spacing shall be in accordance with Table below.
Direct Design Method. Two-way slabs satisfying the limits shall be permitted to be designed in
accordance with this section. Variations from the limitations in Section 408.10.2 shall be permitted
if demonstrated by analysis that equilibrium and geometric compatibility are satisfied, the design
strength at every section is at least equal to the required strength, and serviceability conditions,
including limits on deflection, are met. Circular or regular polygon-shaped supports shall be
treated as square supports with the same area.
Limitations for Use of Direct Design Method. There shall be at least three continuous spans in
each direction. Successive span lengths measured center-to center of supports in each direction
shall not differ by more than one-third the longer span. Panels shall be rectangular, with the ratio
of longer to shorter panel dimensions, measured center to center of supports, not to exceed 2.
Column offset shall not exceed 10 percent of the span in direction of offset from either axis
between centerlines of successive columns. All loads shall be due to gravity only and uniformly
distributed over an entire panel. Unfactored live load shall not exceed two times the unfactored
dead load. For a panel with beams between supports on all sides, Eq. shall be satisfied for beams
in the two perpendicular directions.
Factored Shear in Slab Systems with Beams. Beams between supports shall resist the portion
of shear caused by factored loads on tributary areas.
In addition to shears calculated, beams shall resist shears caused by factored loads applied
directly to the beams, including the weight of the beam stem above and below the slab.
Calculation of required slab shear strength based on the assumption that loads is distributed to
supporting beams shall be permitted. Shear resistance to total Vu occurring on a panel shall be
provided.
FLAT SLAB. consists of a reinforced concrete slab that is directly supported by concrete columns.
Flat slabs are basically used for introducing more head rooms to the floors and to give better
appearances for interiors. Major components of flat slab are capital/head, drop panel, columns
strip and middle strips.
Classification of Flat Slab. Based on structural design. Conventional reinforced flat slabs
and post tensioned flat slabs
Based on the components of slab. Slabs without drop and column head. Slabs without drop
and column with column head. Slabs with drop and column head.
Recommendations for Proportioning Flat Slab. The thickness of flat slab shall be generally
controlled by considerations of span to effective depth ratio. The drops when provided shall be
rectangular in plan, and have a length in each direction not less than one third of the panel
length in each direction. For exterior panels, with drops at right angles to the non-continuous
edge and measured from center line of the columns shall be equal to one half the width of drop
for interior panels.
General Considerations for use of Flat slab Floor System. Spacing of columns. Long term
deflection of the flat plate. Punching shear checks at column areas
Steps involved in the design of flat slab structures. Framing system. provides a detailed
geometric description of the column spacing and overhang. Architect provides this part of the
design; the engineer should emphasis on the following: Three continuous spans in each direction
or have an overhang least one-fourth times adjacent span length in case of only two continuous
spans and typical panel must be rectangular and the spans must be similar in length i.e., adjacent
span in each direction must not differ in length by one-third
Engineering Analysis. Flat plate/slab may be analyzed and designed by any method as long as
they satisfy the strength, stiffness and stability requirements. A typical flat plate/slab can be
analyzed by direct design method or equivalent frame method. However, if the flat plate/slab is a
typical one with unusual geometry, with irregular column spacing, or with big opening then the
designer can use finite element method model analysis using various software. The design of flat
slabs irrespective of the methodology used must first assume a minimum slab and drop thickness
and a minimum column dimension to ensure adequate stiffness of the system to control deflection.
Critical reactions for the load combinations are used for the design of the supporting columns and
foundations.
Reinforcement Design and Detailing. one of the critical parts of flat slab design; maximum
forces from the analysis shall be used in the design of the reinforcement. Reinforcement required
for flexure by using minimum slab thickness typically will not require compression reinforcement.
However, design for punching shear force (including additional shear due to unbalanced moment)
per is 32%. Design of Flat slab by Direct Design Method has some restrictions that it should have
minimum three spans in each direction. It must not have staggered column orientation.
WAFFLE SLAB. is an economical floor system when the spans are long and/or loads are high.
Waffle slab analysis and design is similar to the procedure used with flat plates except that special
considerations need to be taken into account to reduce the complexity of calculations needed
when using exact geometry of the two-way joists. The following summarizes all the relevant
analysis and design provisions in accordance with the Equivalent Frame Method (EFM). Also,
included are detailed illustration of the reference provisions in applicable standards.
Rib dimensions. The ACI code requires that joist dimensions should be limited to the following:
a. Width of ribs shall be at least 4 in. at any location along the depth; b. Overall depth of ribs shall
not exceed 3.5 times the minimum width; c. Clear spacing between ribs shall not exceed 30 in; d.
Slab thickness (with removable forms) shall be at least the greater of:
a. 1/12 clear distance between ribs
b. 2 in
Minimum Thickness. The minimum slab thickness allowed for joist slabs is one-twelfth the
clear rib spacing or 1.5 in.
Drop Panels (Drop Heads). n waffle slabs a drop panel is automatically invoked to guarantee
adequate two-way (punching) shear resistance at column supports. The drop panel dimensions
are limited by the ACI code as follows: a. The drop panel shall project below the slab at least onefourth of the adjacent slab thickness. Drop panel depth is also controlled by the rib depth (the
soffit of both at the same plane). The total thickness includes the actual slab plus the drop panel
thickness; b. The drop panel shall extend in each direction from the centerline of support a
distance not less than one-sixth the span length measured from center-to-center of supports in
that direction.
Equivalent Solid Slab Thicknesses. For the purposes of analysis and design, the ribbed slab can
be replaced with a solid slab of equivalent moment of inertia, weight, punching shear capacity,
and one-way shear capacity. The equivalent thickness based on moment of inertia is used to find
slab stiffness considering the ribs in the direction of the analysis only. The ribs spanning in the
transverse direction are not considered in the stiffness computations. This thickness is given by:
where: Irib = Moment of inertia of one joist section between centerlines of ribs; brib = The centerto-center distance of two ribs (clear rib spacing plus rib width).
Find system self-weight using the equivalent thickness based on the weight of individual
components. This thickness is given by:
where: Vmod = The volume of one joist module; Vmod = V longitudinal joist +V transverse joists
In - V intersection between joists; Amod = The plan area of one joist module.
One-Way (Beam Action) and Two-Way (Punching) Shear Considerations. For two-way joist
slab, it is necessary to check shear at multiple sections. The critical sections shall be located with
respect to: 1. Edges or corners of columns; 2. Changes in slab thickness, such as edges of drop
panels.
One-way shear check at distance d from the supporting column. One way shear capacity is
calculated assuming the shear cross section area consisting of ribs and the portion of slab above,
decreased by the concrete cover. And the equivalent shear width of single rib is calculated as
follows:
Where: b = rib width; d = distance from extreme compression fiber to tension reinforcement
centroid.
The one-way shear capacity for the ribbed slab portions shown is permitted to be increased by
10%.
Two-way shear check around drop panels. Two-way shear is critical on a rectangular section
located at d/2 away from the face of the drop panel. The equivalent thickness based on shear
area is used to compute the area of concrete section resisting punching shear transfer (Ac) around
drop panels in two-way joist (waffle) systems. The equivalent slab thickness used to compute Ac
is calculated as follows:
Where: b = rib width; d = distance from extreme compression fiber to tension reinforcement
centroid.
The two-way shear capacity for the ribbed slab is permitted to be increased by 10%
Immediate Deflection Considerations.
For positive moment (midspan) section: Ig = Moment of inertia of the gross uncracked concrete
section; Ig = I g/rib x # of ribs; yt = Distance from centroidal axis of gross section, neglecting
reinforcement, to tension face, in.; Yt = hrib – Ybar
For averaged effective moment of inertia:
Since midspan stiffness (including the effect of cracking) has a dominant effect on deflections,
midspan section is heavily represented in calculation of Ie and this is considered satisfactory in
approximate deflection calculations. Both the midspan stiffness (Ie+) and averaged span stiffness
(Ie,avg) can be used in the calculation of immediate (instantaneous) deflection.
The averaged effective moment of inertia (Ie,avg) is given by:
However, the waffle slab is considered as non-prismatic members and the following expressions
are recommended:
Design of columns:
COLUMNS. This section shall apply to the design of non-prestressed, prestressed, and
composite columns, including reinforced concrete pedestals. Design of plain concrete pedestals
shall be in accordance with plain concrete section.
Materials. Design properties for concrete shall be selected to be in accordance with Concrete:
Design and Durability Requirements. Design properties for steel reinforcement and structural
steel used in composite columns shall be selected to be in accordance with Steel Reinforcement
Properties, Durability, and Embedment. Materials, design, and detailing requirements for
embedment in concrete shall be in accordance with embedment section.
Composite Columns. If a structural steel shape, pipe, or tubing is used as longitudinal
reinforcement, the column shall be designed as a composite column.
Connection to Other Members. For cast-in-place construction, beam-column and slab-column
joints shall satisfy Beam-Concrete and Slab-Column Joints. For precast construction, connections
shall satisfy the force transfer requirements of Connections of Precast Members. Connections of
columns to foundations shall satisfy Connections to Foundations.
Design Limits. Dimensional Limits. For columns with a square, octagonal, or other shaped
cross section, it shall be permitted to base gross area considered, required reinforcement, and
design strength on a circular section with a diameter equal to the least lateral dimension of the
actual shape. For columns with cross sections larger than required by considerations of loading,
it shall be permitted to base gross area considered, required reinforcement, and design strength
on a reduced effective area, not less than one-half the total area. This provision shall not apply to
columns in special moment frames designed.
For columns built monolithically with a concrete wall, the outer limits of the effective cross section
of the column shall not be taken greater than 40mm. outside the transverse reinforcement. For
columns with two or more interlocking spirals, outer limits of the effective cross section shall be
taken at a distance outside the spirals equal to the minimum required concrete cover. If a reduced
effective area is considered, structural analysis and design of other parts of the structure that
interact with the column shall be based on the actual cross section.
For composite columns with a concrete core encased by structural steel, the thickness of the steel
encasement shall be at least (a) or (b):
Required Strength. shall be calculated in accordance with the factored load combinations in
Loads section. Required strength shall be calculated in accordance with the analysis procedures
in Structural Analysis Section.
Factored Axial Force and Moment. Pu and Mu occurring simultaneously for each applicable
factored load combination shall be considered.
Design Strength. For each applicable factored load combination, design strength at all sections
shall satisfy ∅Sn ≥ U, including (a) through (d). Interaction between load effects shall be
considered: a. ∅Pn ≥ Pu; b. ∅Mn ≥ Mu; c. ∅Vn ≥ Vu; d. ∅Tn ≥ Tu
Axial Force and Moment. Pn and Mn shall be calculated in accordance with Axial Strength or
Combined Flexural and Axial Strength. For composite columns, forces shall be transferred
between the steel section and concrete by direct bearing, shear connectors, or bond in
accordance to the axial strength assigned to each component.
Shear. Vn shall be calculated in accordance with One-way Shear Strength.
Torsion. If Tu ≥ ∅Tth, where Tth is given in Section Torsional Strength, torsion shall be considered
in accordance with Beams section.
Reinforcement Limits. Minimum and Maximum Longitudinal Reinforcement. For nonprestressed columns and for prestressed columns with average fpe < 1.6 MPa, area of
longitudinal reinforcement shall be at least 0.01 Ag but shall not exceed 0.08 Ag. For composite
columns with a structural steel core, area of longitudinal bars located within the transverse
reinforcement shall be at least 0.01(Ag-Asx), but shall not exceed 0.08(Ag — Asx).
Minimum Shear Reinforcement. A minimum area of shear reinforcement, Av,min, shall be
provided in all regions where Vu > 0.5 ∅Vc. If shear reinforcement is required, Av,mln shall be
the greater of (a) and (b):
Reinforcement Detailing. Concrete cover for reinforcement shall be in accordance with
Specified Concrete Cover. Development lengths of deformed and prestressed reinforcement shall
be in accordance with Development of Reinforcement. Bundled bars shall be in accordance with
Bundled Reinforcement.
Reinforcement Spacing. Minimum spacing s shall be in accordance with Minimum Spacing of
Reinforcement.
Longitudinal Reinforcement. For non-prestressed columns and for prestressed columns with
average fpe < 1.60 MPa, the minimum number of longitudinal bars shall be (a), (b), or (c): a.
Three within triangular ties; b. Four within rectangular or circular ties; c. Six enclosed by spirals
or for columns of special moment frames enclosed by circular hoops.
For composite columns with structural steel cores, a longitudinal bar shall be located at every
comer of a rectangular cross section, with other longitudinal bars spaced not farther apart than
one-half the least side dimension of the composite column.
Offset Bent Longitudinal Reinforcement. The slope of the inclined portion of an offset bent
longitudinal bar relative to the longitudinal axis of the column shall not exceed 1 in 6. Portions of
bar above and below an offset shall be parallel to axis of column. If the column face is offset 75
mm or more, longitudinal bars shall not be offset bent and separate dowels, lap spliced with the
longitudinal bars adjacent to the offset column faces, shall be provided.
Splices of Longitudinal Reinforcement. Lap splices, mechanical splices, butt-welded splices,
and end-bearing splices shall be permitted. Splices shall satisfy requirements for all factored load
combinations. Splices of deformed reinforcement shall be in accordance with Splices Section and
shall satisfy the requirements of Lap Splices Section or End-bearing Splices Section.
Lap Splices. If the bar force due to factored loads is compressive, compression lap splices shall
be permitted. It shall be permitted to decrease the compression lap splice length in accordance
with (a) or (b), but the lap splice length shall be at least 300 mm: a. For tied columns, where ties
throughout the lap splice length have an effective area not less than 0.0015lhs in both directions,
lap splice length shall be permitted to be multiplied by 0.83. Tie legs perpendicular to dimension
h shall be considered in calculating effective area; b. For spiral columns, where spirals throughout
the lap splice length, lap splice length shall be permitted to be multiplied by 0.75.
If the bar force due to factored loads is tensile, tension lap splices shall be in accordance with
Table below.
End-bearing Splices. If the bar force due to factored loads is compressive, end-bearing splices
shall be permitted provided the splices are staggered or additional bars are provided at splice
locations. The continuing bars in each face of the column shall have a tensile strength at least
0.25fy times the area of the vertical reinforcement along that face.
For composite columns, ends of structural steel cores shall be accurately finished to bear at
end- bearing splices, with positive provision for alignment of one core above the other in
concentric contact. Bearing shall be considered effective to transfer not greater than 50 percent
of the total compressive force in the steel core.
Transverse Reinforcement. shall satisfy the most restrictive requirements for reinforcement
spacing. Details of transverse reinforcement shall be in accordance with Lap Splices, End-bearing
Splices for spirals, or Offset Bent Longitudinal Reinforcement for hoops. For prestressed columns
with average fpe ≥ 1.6 MPa, transverse ties or hoops need not satisfy the 16db spacing
requirement. For composite columns with a structural steel core, transverse ties or hoops shall
have a minimum db of 0.02 times the greater side dimension of the composite column, but shall
be at least 10 mm ∅ and need not be larger than 16 mm ∅. Spacing shall satisfy, but not exceed
0.5 times the least dimension of the composite column. Deformed wire or welded wire
reinforcement of equivalent area shall be permitted.
Longitudinal reinforcement shall be laterally supported using ties or hoops in or spirals, unless
tests and structural analyses demonstrate adequate strength and feasibility of construction. If
anchor bolts are placed in the top of a column or pedestal, the bolts shall be enclosed by
transverse reinforcement that also surrounds at least four longitudinal bars within the column or
pedestal. The transverse reinforcement shall be distributed within 125 mm. of the top of the
column or pedestal and shall consist of at least two 12 mm ∅ or three 10 mm ∅ bars.
Lateral Support of Longitudinal Bars Using Ties or Hoops. In any storey, the bottom tie or
hoop shall be located not more than one-half the tie or hoop spacing above the top of footing or
slab. In any storey, the top tie or hoop shall be located not more than one-half the tie or hoop
spacing below the lowest horizontal reinforcement in the slab* drop panel, or shear cap. If beams
or brackets frame into all sides of the column, the top tie or hoop shall be located not more than
75 mm below the lowest horizontal reinforcement in the shallowest beam or bracket.
Lateral Support of Longitudinal Bars Using Spirals. In any storey, the bottom of the spiral shall
be located at the top of footing or slab. In any storey, the top of the spiral shall be located in
accordance with Table below.
Lateral Support of Offset Bent Longitudinal Bars. Where longitudinal bars are offset,
horizontal support shall be provided by ties, hoops' spirals, or parts of the floor construction and
shall be designed to resist 1.5 times the horizontal component of the calculated force in the
inclined portion of the offset bar. If transverse reinforcement is provided to resist forces that result
from offset bends, ties, hoops, or spirals shall be placed not more than 150 mm. from points of
bend.
Shear. If required, shear reinforcement shall be provided using ties, hoops, or spirals. Maximum
spacing of shear reinforcement shall be in accordance with Table below.
Case studies and practical applications:
Case Study of the Structural Performance of Composite Slabs with Low Strength CRC
Delivered by Concrete Truck
Presents case study of crumb rubber concrete (CRC) composite slabs. The concrete of CRC
slabs was designed to have similar compressive strength to conventional concrete (CC) control
slabs; however, the delivered CRC that was mixed in the concrete plant for first time had a lower
strength than designed (with 30–66 % strength reduction). The flexural behavior of profiled steel
reinforced CRC/CC composite slabs was measured by implementing 4-point bending loading. All
specimens showed characteristics of a ductile failure mode. Although, CRC composite slabs
poured on site resulted in unsatisfactory compressive strength that was significantly lower than
that of CC slab, they were still able to achieve acceptable performance under flexural loading.
This indicates that CRC in residential composite slabs is a viable option.
Conclusions:
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All CC and CRC composite slabs failed due to longitudinal shear failure at the interface
between steel deck and concrete soffit prior to the development full concrete compressive
-
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-
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strain capacity. This failure mode made the lower compressive strength in the concrete
topping not so significant in terms of impacting on the flexural capacity.
Although the CRC composite slabs had 30 % reduction in compressive strength compared
to CC, this had not affected the chemical adhesion and load carrying capacity of the lowstrength CRC slabs under bending. The CRC slabs experienced significant strength
reduction (66 %) compared to CC; however, they achieved acceptable performance (75
% load carrying capacity) under flexural loading.
CRC appeared to exhibit stronger chemical adhesion with profiled steel than that of CC,
and utilizing of CRC in composite slabs has allowed better partial interaction between the
steel decks and concrete, hence the slabs could withstand higher deformation.
CRC appeared to exhibit stronger chemical adhesion with profiled steel than that of CC,
and utilizing of CRC in composite slabs has allowed better partial interaction between the
steel decks and concrete, hence the slabs could withstand higher deformation.
CRC performed better in terms of alleviating the impact of load drops, which might be the
credit of rubber particles.
The addition of crack inducers influenced the initiation of major cracking, and the load
drops were smaller; hence the commencement of the partial interaction stage was delayed
until after the two major load drops.
The asymmetrical shape of embossment caused the initiation of the end slippage towards
the weak side of the embossment, and hence symmetrical shape of embossment is
recommended for future product.
A Study into the Behavior of Reinforced-Concrete Columns Under Fire Exposures using
a Spreadsheet-Based Numerical Model
The primary goal is to study the behavior of reinforced-concrete columns under fire conditions
and to analyze the various characteristics of a reinforced-concrete column that affect its overall
fire performance. A secondary goal is to provide a tool to help further the education of engineers
in the analysis of reinforced-concrete columns under fire exposures. To accomplish these goals,
a numerical calculation model was constructed in Microsoft Excel. The heat transfer and the
structural analysis portions of the model were benchmarked using ANSYS and published results
of experimental reinforced-concrete column furnace tests, respectively. After the model was
shown to be working correctly and providing acceptable results, it was used to perform a study
on the behavior of a reinforced-concrete column under various fire exposures and variations of
column characteristics.
Column Behavior. From the column studies completed, it was shown that increasing the initial
load eccentricity on a column reduces the column’s fire performance for both carbonate and
siliceous aggregate. The time to failure for both the crushing and flexural buckling modes was
decreased significantly as the eccentricity was increased by several millimeters above the ACI
specified minimum value. Increasing the column length also decreases the performance of a
reinforced-concrete column. However, unlike increasing the load eccentricity, increasing the
length of the column does not decrease the crushing failure time. Only the flexural buckling failure
time is decreased with increasing column length. The same is also true for increasing the
slenderness ratio of the column. As the slenderness ratio increases, the flexural buckling failure
time decreases as the crushing failure time remains the same.
The results also show that increasing fixity of the end connections dramatically increases the
failure time. For two identical columns in which one has pinned connections and the other has
fixed connections, the failure time is approximately two hours more for the fixed column than the
pinned column. This result is also demonstrated in the slenderness ratio results. Increasing the
amount of cover on a reinforced-concrete cover will also increase the failure time. The increase
in time is several minutes.
The use of carbonate aggregate over siliceous aggregate yields longer failure times. This is due
in part to the deterioration in the compressive strength of the concrete as well as due to the
thermal properties of both types of aggregate. Because siliceous aggregate allows the crosssection to increase in temperature faster than carbonate aggregate, a siliceous aggregate column
will lose cross-section faster and thus lose strength leading to failure faster.
According to ACI 318, if a column’s slenderness ratio is below a certain criteria slenderness effect
can be ignored. However, the results show that when dealing with fire conditions, slenderness
effects cannot be neglected. A column’s load eccentricity depending on the fire exposure will
increase along with the slenderness ratio. The difference in failure time between a column for
which slenderness effects were ignored and the same column with those effects accounted for is
approximately four hours. These findings indicate that the location of the plastic centroid and its
effects on the overall capacity of the column need to be analyzed.
Finally, the phenomenon of latent heating can lead to collapse of a reinforced-concrete column
during the cooling phase of a fire curve. This is a dangerous threat due to the timing of such a
collapse. Firefighters and first-responders could be in the building continuing to rescue occupants.
The results showed that failure could occur one half-hour after the fire starts to decay. This is
consistent with published data on the subject of latent heating.
Numerical Calculation Model. The numerical calculation model for determining the fire
performance of a reinforced-concrete column yielded good approximations to the failure times
obtained from the published test data. The model does not take into account water effects, spalling
of the concrete, spiral reinforcement, and it uses the 500°C isotherm method for calculating the
column’s strength capacity. All these factors could result in the observed differences between the
actual failure time and the model’s predicted failure time. Several factors possibly lead to the
differences in the heat transfer portion of the model and the results from ANSYS. The first
difference is that the equations for temperature-dependent thermal properties used in the model
could not be input in ANSYS. The thermal properties remained constant in ANSYS. Also, the
radiation model in ANSYS was not taken into account due to its complexity. The model used a
combined convective and radiation model based solely on the hot gases surrounding the column.
ANSYS required a point source of radiation and a distance to the point source to calculate
radiation. Therefore, radiation was neglected in ANSYS. All these dissimilarities could result in the
differences between nodal temperatures of ANSYS and model. However, even with these
assumptions, the model yielded fairly accurate results against the benchmarking test performed
both for the heat transfer and structural analysis portions. The model is considered an acceptable
level 2 evaluation tool for calculating the fire performance of a reinforced-concrete column.
Conclusion:
After researching on the reinforced design of slabs and columns, the key findings and insights
that the researcher obtained is that reinforced concrete has high compressive strength which is
durable can withstand good amount of tensile stress, fire and weather resistance. Has low-cost
maintenance and an economical construction material which is very good material for slabs and
columns since the strength, ductility and energy absorption capability can enhance significantly.
This will achieve if proper design principles and considerations are well met.
When it comes to behavior and loadings, the researcher understood the fundamental principles
such as forces and its properties magnitude, direction and position. The different type of loads
such as dead loads, live loads, wind loads, seismic loads and the symbol and notations for the
computation of basic, alternate basic and special seismic loads as per the design codes and
standard. The material properties which is strength, toughness, elasticity, plastically, ductility,
malleability, brittleness and hardness. And lastly, the concepts of shear force, bending moment
and axial force.
In design codes and standards, the researcher learned more about the prominent design codes
and standards used for the design of reinforced slabs and columns. The first one is the National
Structural Code of the Philippines used for the firm understanding of the basic principles of
structural mechanics applied to reinforced concrete. Other related codes such as American
Concrete Institute (ACI) who publishes important journals and standards, as well as
recommendations for the analysis and design of special types of concrete structures. The
AASHTO (American Association of State Highway and Transportation Officials) for detailed
provisions of the design and concrete constructions. They all have key provisions, requirements
and design philosophies outlined to their codes and standards specifically for the design of slabs
and columns.
For the design of slabs and columns, aside from one-way and two-way slab, the researcher
learned more about flat and waffle slabs. For the columns, the researcher has learned more about
sections like rectangular, circular, and composite. Also, their various design methods employed in
the calculation for the slab thickness, reinforcement detailing, flexural and shear design which
insights of these is that the methods are similar but different application due to different types of
slabs. Same as the Design of columns, their calculation of column dimensions, reinforcement
detailing, and design for axial load, flexure and shear.
And after researching for the two case studies, one for showcasing the design of reinforced
concrete slabs and one for columns. The researcher obtained lesson and conclusions of the case
study, the design challenges that the authors of the case study faced, the innovative solutions
implemented such as performance of reinforced concrete slab with low strength crumb rubber
concrete and the behavior of reinforced concrete columns under fire exposures using a
spreadsheet based numerical model. And having these studies reinforce the advantages of
reinforced design of slabs and columns to the structures.
References:
National structural code of the Philippines. (2010). Association of Structural Engineers of the
Philippines, Inc.
Reinforced concrete. Reinforced Concrete - an overview | ScienceDirect Topics. (n.d.).
https://www.sciencedirect.com/topics/materials-science/reinforcedconcrete#:~:text=Reinforced%20concrete%20is%20a%20composite,The%20steel%20is
%20the%20reinforcement.
Structural
principles.
Structural
principles
Designing
https://www.designingbuildings.co.uk/wiki/Structural_principles
Buildings.
(n.d.).
The ultimate guide to shear and moment diagrams. DegreeTutors.com. (2021, October 8).
https://www.degreetutors.com/shear-and-moment
diagrams/#10_What_is_a_Bending_Moment
Etukudo, D. (2023, April 10). Axial Force - calculation and formula, diagram, vs other forces.
Punchlist Zero. https://punchlistzero.com/axial-force/
Two-way joist (waffle) slab design approach and methodology. (n.d.). Structure Point Concrete
Software
Solution
https://structurepoint.org/publication/pdf/TwoWay_Joist_Waffle_Slab_Design_Approach_
and_Methodology.pdf
Design considerations for reinforced concrete flat slab floor (n.d.a). International Journal of
Scientific & Engineering Research, https://www.ijser.org/researchpaper/DesignConsiderations-for-Reinforced-Concrete-Flat-Slab-Floor-System.pdf
Ou Yi a, a, b, c, &amp; Abstract Concrete mixing in laboratory conditions has a high level of quality
control enabling it to achieve the designed workability and strength by accurately
controlling the material quantity. (2020, November 2). Case study of the structural
performance of composite slabs with low strength CRC delivered by Concrete Truck. Case
Studies
in
Construction
Materials.
https://www.sciencedirect.com/science/article/pii/S221450952030125X
Richard Lawrence Emberley; A Study into the Behavior of Reinforced-Concrete Columns under
Fire Exposures using a Spreadsheet-Based Numerical Model (2013, May). WORCESTER
POLYTECHNIC INSTITUTE.