Structural Design Guidelines RC Buildings

Department: ED11 K&A–CEC Company Confidential Rev. Date: Aug 2007

Structural Design Guidelines for Reinforced Concrete Buildings

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Table of Contents Introduction Components of structural system Selection of floor system Selection of lateral load resisting system Selection of foundation system Design of ribs Design of concealed beams Design of drop beams Design of one-way slabs Design of two-way slabs Design of hollow core slab floors Design of prestressed concrete floor slabs Design of columns Design of shearwalls Design of cores Design of coupling beams Design of isolated centered footings Design of isolated eccentric footings Design of combined footings Design of tie-beams Design of rafts Design of pile foundations Design of pile caps Design of basement walls Design of water tanks Design against progressive collapse Calculation of superimposed dead loads Calculation of lateral wind loads Calculation of lateral seismic loads Calculation of vertical deflection in beams and ribs Calculation of vertical deflection in two-way slabs Calculation of drift due to lateral load


Introduction This document describes the procedure to be used in the design of the structural elements of reinforced concrete or prestressed concrete buildings. The purpose of the guidelines presented in this document is to speed up the design process, make it more uniform across different engineers and less prone to mistakes and omissions. It is not the purpose of this document to replace design codes, design courses or engineering judgement. The document briefly reviews the components of the structural system that have to be designed, the possible alternatives for each component, and then describes the design procedure for each component. For each component, the design guideline lists the elements to be designed, the checks to be performed, the typical extreme values of the design variables, detailing hints, the relevant code sections and the relevant references for more detailed information. The design code used in this document is the ACI318-05M and the UBC97. Components of structural system The major components of the structural system of a building are three:

-The floor system. -The lateral load resisting system -The foundations system

For each of these components several alternatives are available; the selection of the most appropriate choice is done based on several parameters listed below, with the ultimate goal of achieving maximum economy over the useful life of the building while meeting safety and serviceability requirements. The selection of the structural system is done during the conceptual phase of the project by a senior engineer, in coordination with the architect and the other disciplines (Electrical, Mechanical) senior engineers. Selection of floor system In selecting a floor system, the following parameters are used in order of decreasing importance: Local availability of materials and skilled labor: The local availability of materials (special forms) and skilled labor experienced in the construction of the system is major factor in obtaining a construction of good quality within a reasonable time and cost. Therefore, local availability of materials and skilled labor is a major comparison parameter. Cost: Since the floor system in a building constitutes the major part of the building structure, its cost contributes the most to the cost of the structure. Therefore, the unit cost per unit area of the floor system is a major comparison parameter. Weight: Since the floor system in a building constitutes the major part of the building structure, its weight contributes the most to the weight of the structure. Increased weight leads to more seismic loads, larger column sizes and larger foundations. Therefore the weight per unit area of the floor system is a major comparison parameter.

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Depth: In many cases where the allowable height of the building is limited, or the façade material is very expensive, limiting the floor depth to reduce the overall depth of the building is a desirable objective. Therefore, the floor depth is a significant comparison parameter, and may be a major one in high rise buildings where it may allow increasing the number of floors for the same overall building height. Speed of construction: The speed of construction is an important parameter that ultimately affects the cost of the building, particularly in high rise buildings or in buildings with large floor area. Therefore speed of construction is a significant comparison parameter. Shape of soffit: Some systems provide a flat soffit that can be exposed as is or with minor plastering, others present a soffit that has cavities or other irregularities that may have to be hidden by a false ceiling. If no false ceilings are planned and a flat soffit is desired, then the systems with irregular soffit have to be ruled out. Therefore, the shape of soffit is a significant comparison parameter. Acoustic insulation: The acoustic insulation properties of a floor system become important when the tiling to be used on top of it is inexistent or has poor acoustic insulation properties, and the sound level between floors needs to be controlled. Therefore, the acoustic insulation properties is a significant comparison parameter. Thermal insulation: In these days of increasing energy cost and interest in conserving energy (green initiatives), the thermal insulation of a floor system is in an important consideration. However, floor systems generally separate regions of equal temperature, and the concrete floor systems have comparable thermal insulation properties. Therefore, the thermal insulation properties is a minor comparison parameter. Except for ground floor slabs, which should be of solid slab construction (to resist a live load of 10Kpa and have a fire resistance of 4hr), the floor systems generally available for consideration are the following: Hourdi ribbed slabs: Hourdi blocks (hollow artificial bricks made of cement, sand and stone) are placed in rows on a flat formwork. The voids between rows of blocks will become the concrete ribs. Reinforcement cages are placed in the voids between rows. Shrinkage and temperature reinforcement is placed above the blocks. Concrete is poured to the required thickness. After the concrete has attained sufficient strength, the formwork and shoring is removed. Reshoring may be needed to support the next floor being constructed above. Hourdi ribbed slabs require minimal amounts of steel (~25kg/m2). They cost from 85 to 95 $/m21. They weigh from 0.96 to 1.22 t/m2. They can be economically used up to a span of 9m for a floor thickness of 400mm. Lightweight blocks and expanded polystyrene blocks are available to replace conventional Hourdi blocks, however they are more expensive and less fire resistant than the Hourdi blocks. T-form ribbed slabs: T-form ribbed slabs are similar in construction to Hourdi ribbed slabs, except that the Hourdi blocks are replaced by removable forms. T-form ribbed

1 Based on assumed material costs only.

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slabs are less tolerant of floor plan irregularities than Hourdi ribbed slabs; for maximum efficiency, the column lines should be orthogonal. For both Hourdi and ribbed slabs, column spacing normal to the rib direction should be significantly smaller than the rib span. T-ribbed slabs require minimal amounts of steel (~25kg/m2). They cost from 80 to 90 $/m2 (not including premium for reusable forms). They weigh from 0.79 to 0.96 t/m2. They can be economically used up to a span of 11m for a floor thickness of 470mm. They are inferior to Hourdi ribbed slabs in terms of sound insulation and fire resistance. A variant of T-ribbed slabs is the ribbed floor, where the ribs are spaced at 1m to 2m, and the slab in-between the ribs has a thickness of 110mm to 150mm. The ribs are generally 500mm to 700mm deep and have an optimal span from 9m to 13m. Solid slabs: Solid slabs may be supported by drop beams or drop panels around columns (two-way slab) or may be supported directly by columns, widened by capitals (flat plate). For maximum economy and speed drop beams and drop panels should be eliminated, column sizes should be unified, and column lines should be orthogonal and equally spaced in both directions. Solid slabs require substantial amounts of reinforcement (30-70kg/m2). They cost from 95 to 135 $/m2. They weigh from 0.88 to 1.25 t/m2. They can be economically used up to spans of 12m each way for a floor thickness of 300mm. Waffle slabs: Waffle slabs are similar to solid slabs in concept and construction, except that removable square pans are used to create cavities in the bottom of the slab. Waffle slabs are lighter than solid slabs but thicker; they are best used for long spans in both directions. Waffle slabs require moderate amounts of reinforcement (~30kg/m2). They cost from 90 to 95 $/m2 (not including premium for reusable pan forms). They weigh from 0.84 to 0.99 t/m2. They can be economically used up to spans of 14m each way, for a floor thickness of 500mm. Cast-in-place postensioned slabs: Cast-in-place postensioned slabs are similar to flat plate slabs except that they can be thinner and they use less conventional reinforcing steel thanks to the post-tensioning process. Post-tensioned slabs require special materials (high tensile strength steel cables, galvanized ducts, non-shrinking grout or grease, anchor blocs) specialized equipment (hydraulic jacks and gages) and specially trained labor. For best results, the floor plan should be regular and symmetric and the stiffest elements (shearwalls enclosing elevator and services core should be centrally located). Perimeter columns should be flexible to accommodate post-tensioning shrinkage and creep strains, or special construction precautions should be taken (slowing down construction). Precast pretensioned hollow core slabs: Precast hollow core slabs are prefabricated under controlled factory conditions and placed on site on steel beams or reinforced concrete beams. The structure is finally tied together by cast-in-place grout. This system achieves floor weights ranging between 0.77 and 0.97 t/m2 for spans ranging between 5.5 to 11.m for a slab thickness ranging between 20 and 40 0mm. However, the total floor depth is larger when the supporting beam is included.

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Precast hollow core slabs have good sound insulation and fire resistance capacity. They are quick to erect; they do not need formwork or shoring. They are best used with regular floor plans, with few but large service shafts, parallel beam lines and orthogonal column lines. Local precast hollow core manufacturers are available and should be contacted to check for required order lead times. Selection of lateral load resisting system The lateral load resisting system is usually part of the vertical load carrying system and has to fulfil the dual function of resisting both vertical and lateral loads. In reinforced concrete buildings, the lateral load system consists of shear walls, moment resisting frames or a combination of both (dual systems). The selection of the lateral load resisting system in a building depends on several factors:

-magnitude of lateral loads -building height -building height to width ratio -floor height -bay width

Moment resisting frames: moment resisting frames may be used for low rise buildings in highly seismic areas or for medium rise buildings in intermediate to low seismic risk areas. (UBC97 Table 16.N). The use of moment resisting frames requires the use of squarish columns, drop beams and ductile detailing in the beams, columns and beam-column joint regions. They are most effective when the floor height and the bay width are limited. An extreme variant of this structural system is the “tube” and “tube in tube”, where moment resisting frames are used along the perimeter of the building (tube) and in the center around the services core (tube in tube) where each frame consists of closely spaced mullion columns connected by deep spandrel beams. These systems may be used in high rise buildings of 40 (tube) to 80 stories high (tube in tube). Shear wall buildings: are braced laterally by shear walls acting individually or two-by-two (connected by coupling beams) or grouped into cores. The use of shear wall bracing in buildings gives the designer freedom in arranging the columns of the vertical load carrying system. Sufficient shear walls should be placed along every principal direction. In plan, the center of stiffness of the shear walls should be as close as possible to the center of mass of the building to minimize torsional excitations. To maximize torsional resistance, shear walls parallel to the façade, should as close to the façade as possible (on the façade if possible). Shear wall cores should be placed as close as possible to the center of mass of the floor plan. In buildings with large plan dimensions, shear walls should be located near the middle of the plan dimension and not at the ends to minimize thermal restraint forces. In tall buildings with moderate to small plan dimensions, shear walls are best located near the corners to maximize the resistance to overturning moments. For best resistance against lateral loads, shear walls should carry a significant part of the vertical load (otherwise they might uplift at the foundation, or have a limited flexural capacity). Dual systems: combine both moment resisting frames and shear walls in the same structure. These are used when neither moment resisting frames or shear walls alone are possible or sufficient to resist the applied lateral loads and to provide the required lateral stiffness. Since the deformation characteristics of both systems are

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different (shearwalls have larger interstory deformations at the top of the structure rather at the base, while moment resisting frames have larger interstory deformations at the base of the structure rather than at the top), the combination of both systems in a single structure leads to structure stiffer than the sum of stiffnesses of both systems alone. Dual systems are recommended for mid to high rise buildings, particularly when outriggers are used to increase the coupling between both systems. Selection of foundation system: The selection of a foundation system depends mainly on the nature of the soil under the structure, and secondly on the type of structure, its height and its width. There are four main types of foundations: Shallow isolated footings: Each vertical load carrying element is connected to a shallow isolated footing. Footings are connected to one another by tie-beamsto restrain mainly differential horizontal movements, and to a certain extent differential vertical movements. This system is used when the loads applied to the foundation are light or the soil resistance at a shallow depth is high. Raft foundation: A raft foundation consists of a single slab supporting all vertical elements. A raft foundation is necessary when the lowest level of the structure is below the water table. When the vertical loads on each footing are high enough, or the soil resistance at shallow depth is weak enough, such that the sum of footings area is more than 60% of the overall area of the building footprint, then a raft foundation may be more economical to use than a set of shallow isolated footings. Pile foundation: Piles consist mainly of vertical concrete elements cast in holes drilled in the ground or of precast concrete elements driven into the soil, and connected to the vertical load carrying elements of the structure by means of pile caps. Piles are used when the soil resistance at a shallow depth is not sufficient to permit the use shallow isolated footings or rafts (either because the resistance to failure is low, or the expected settlements are high). Raft on pile foundation: As the name implies, a raft on pile foundation is a raft supported on piles. This type of foundation is used mainly for high rise buildings, where the required bearing capacity under the raft cannot not be achieved by the soil at shallow depth, or where the number of piles under each vertical element is so large that the pile caps would run into each other. Design of structural elements: In the following, the design of each of the main structural elements of a building is reviewed; listing the verifications to be done, the usual proportioning rules, the range of practical dimensions and the relevant code sections. Design of ribs: This item covers hourdi ribs (with in-fill blocks), T-form ribs and ribbed floors. The design items for ribs are:

Overall thickness: The overall thickness of the rib is decided when choosing the floor depth according to Table 9.5.6a of ACI318 based on the largest panel dimensions, or according to the largest cantilever length. Typically the floor depth is taken as the L/20 where is the longest rib span, or Lc/10 where Lc is the largest rib cantilever span.

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Thickness of the flange: The flange thickness is determined from minimum cover considerations (ACI318 Art. 7.7) and from fire resistance considerations (Table 7-7-C-C UBC, 2hr fire resistance) and is never less than 60mm for hourdi ribbed slabs and T-ribbed slabs and never less than 110mm for a ribbed slab. Width of the flange: The width of the flange is determined from the size of the hourdi block for the hourdi ribbed slab, the size of the mold for the T-rib slab, and from structural optimization for the ribbed slab. Width of the rib: The width of flange is determined from minimum cover considerations (ACI318-8.11.2) and is never less than 125mm for T-ribbed slab and never less than 150mm for hourdi ribbed slabs and ribbed slabs. Flexural reinforcement of the rib: Ribs may be designed as simply supported or as continuous over the supporting beam. In either case no more than 2 bars may be placed in one row at the top or bottom of the rib. No more than 2 rows of bars should be used at the top or bottom of the rib. The minimum bar size in a rib should be 10mm and the maximum bar size should be 16mm in hourdi ribbed slab and T-rib slabs. For ribbed slabs, 20mm or 25mm bars may be used when the rib width is 200mm to 250mm respectively. Moreover, for adequate development of the bottom flexural reinforcement, the bottom bar size should not be more than L/200 where L is the rib length between inflection points. The flexural reinforcement in the rib shall be such that flexural failure occurs before shear failure. Transverse reinforcement of the rib: Transverse reinforcement of the rib generally consists of single stirrup of 8mm size at a spacing of at least 120mm. The maximum spacing of stirrups should not exceed d/2 or 200mm, where d is the flexural depth of the rib. The 200mm spacing is applied whenever the ultimate shear Vu is less than fVc (ACI318-11.1). Flange reinforcement: Flange reinforcement is determined from shrinkage reinforcement considerations (ACI318-7.12). In hourdi ribbed slabs and T-ribbed slabs it generally consists of one 8mm bar in the longitudinal direction in each flange and one 8mm every 200mm in the transverse direction. In ribbed floor slabs, the transverse reinforcement may be determined from flexural considerations. Rib framing plan: Generally the rib is oriented along the longest direction of the floor panel in which it is located, unless cantilever balcony ribs require a different orientation of the ribs in the interior panel adjacent to the balcony. Double ribs, parallel to the ribs are placed along lines connecting columns, and cross-ribs are placed in the middle of floor panels over 6m long.

The verifications to be done are:

Flexural strength: Ribs may be designed as simply supported or as continuous over the supporting beam. The effective span length is taken as either distance from centreline to centreline of the supporting concealed beams or the clear distance between supporting drop beams plus one floor depth on each end. In case of continuous ribs, moment redistributions up to

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10% may be used to optimize the reinforcement scheme, provided the maximum reinforcement ratio and the compression reinforcement ratio satisfy the requirements of ACI318-7.11. Shear strength: The effective span length is calculated as for flexural strength calculation. Whenever the rib depth is less than twice the stirrup spacing (d<240mm), the shear strength of the rib may be taken either equal to the concrete shear strength, or may be calculated by strut-and-tie (ACI318-8.3.4). In the latter case the bottom reinforcement needs to be fully developed at the support. Deflection under service load: The effective span length is calculated as for flexural strength calculation. If the span to depth ratio of the rib exceeds the limit in table 9.5a of ACI318, the deflection under service load needs to be calculated according to sections 9.5.2.2 to 9.5.2.6 of ACI318. A camber to the formwork needs to be provided to compensate for the permanent load immediate and long term deflections. Crack width under service load: The allowable crack width under service load is obtained from ACI318-Appendix A-9 or BS8110 section 21.904 depending on the type of exposure. To minimize the crack width, the smallest possible bar size must be used.

Design of concealed beams: The design items for concealed beams are:

Beam depth: The overall thickness of the concealed beam is decided when choosing the floor depth according to Table 9.5a of ACI318 based on the largest panel dimensions, or according to the largest cantilever length. Typically the floor depth is taken as the L/20 where is the longest concealed beam span, or Lc/8 where Lc is the largest concealed beam cantilever span.

Beam width: The beam width should not exceed 4 times the beam depth, and should be such that the center-to-center spacing of longitudinal bars is not less than 120mm. Flexural reinforcement: The minimum bar size in a concealed beam should be 12mm and the maximum bar size should be 25mm. Moreover, for adequate development of the bottom flexural reinforcement, the bottom bar size should not be more than L/200 where L is the concealed beam length between inflection points.

Shear reinforcement: Transverse reinforcement of the concealed beam generally consists of multiple stirrups of 8mm to 10mm bar diameter at a spacing of at least 120mm. The stirrups should generally engage all the longitudinal bars in the beam. The maximum spacing of stirrups should not exceed d/2 or 200mm, where d is the flexural depth of the concealed beam. The 200mm spacing is applied whenever the ultimate shear Vu is less than fVc (ACI318-11.5.5).


Flexural strength: The effective span length is taken as either distance from centreline to centreline of the supporting concealed beams or the clear

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distance between supporting drop beams plus one floor depth on each end. The amount of tensile flexural reinforcement or of compression reinforcement may be increased in order to limit deflections under service load. The flexural reinforcement in the concealed beam shall be such that flexural failure occurs before shear failure. The fraction of bottom reinforcement developed at the support should satisfy the requirements of table 12.11 of ACI318, and strut and tie requirements for shear resistance at the support. The fraction of top reinforcement extending at midspan should satisfy the requirements of table 12.12 of ACI 318. Moment redistributions up to 10% may be used to optimize the reinforcement scheme, provided the maximum reinforcement ratio and the compression reinforcement ratio satisfy the requirements of ACI318-7.12.

Shear strength: The effective span length is calculated as for flexural strength calculation. Whenever the concealed beam depth is less than twice the stirrup spacing (d<240mm), the shear strength of the beam may be taken either equal to the concrete shear strength, or may be calculated by strut-and-tie (ACI318-8.3.4). In the latter case the bottom reinforcement needs to be fully developed at the support.

Deflection under service load: The effective span length is calculated as for flexural strength calculation. If the span to depth ratio of the concealed beam exceeds the limit in table 9.5a of ACI318, the deflection under service load needs to be calculated according to sections 9.5.2.2 to 9.5.2.6 of ACI318. A camber to the formwork needs to be provided to compensate for the permanent load immediate and long term deflections.

Crack width under service load: The allowable crack width under service load is obtained from ACI318-Appendix A-9 or BS8110-21.9.04 depending on the type of exposure. To minimize the crack width, the smallest possible bar size must be used.

Design of drop beams: Drop beams are used in four cases:

• When the applied gravity loads are too large to be resisted by a concealed beam.

• When supporting a two-way solid slab. • When supporting a precast hollow core slab, T or double T slab elements. • Within the context of a moment resisting frame.

The design items for a drop beam are as listed below, and the requirements differ significantly depending on the function of the drop beam:

Beam depth: The beam depth may be determined from the requirements of table 9.5a of ACI318 to satisfy deflection requirements, or it may determined from shear requirements (shear stress tu ~3 f vc such that stirrup spacing s<d/4) in conjunction with a determination of the beam width. Moreover, the flexural capacity of the beam at the beam-column connection in a moment resisting frame should be such that flexural yielding occurs in the beam rather than in the column. For beams supporting two-way slabs, the beam moment of inertia should be larger than the supported slab moment of inertia (ACI318-13.6).

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Beam width: The beam width B must satisfy the following requirements: B<L/50 where L is the beam span between inflection points. B > 250mm for beams in ductile moment resisting frames (ACI318-21.5.1.3). B > 200mm for proper support of precast elements. B > H/8 where H is the beam depth. B< Bc+D in moment resisting frames where Bc is the width of the column supporting the beam and D is the floor slab depth, when B>Bc. B<Bc-10 when B<Bc and Bc is the width of the supporting column. Moreover, B should be such that the minimum center-to-center spacing between top bar is 120mm and between bottom bars is 70mm.

Flexural reinforcement: The minimum bar size in a drop beam should be 12mm and the maximum bar size should be B/10 where B is the beam width. Moreover, for adequate development of the bottom flexural reinforcement, the bottom bar size should not be more than L/200 where L is the concealed beam length between inflection points. For beams in moment resisting frames, the longitudinal bar size at the support should be such that the bar may be developed within the length of the beam-column joint (ACI318-21.5.4). Skin reinforcement: Longitudinal skin reinforcement is needed in beams more than 600mm deep and in beams resisting torsional moments. The maximum spacing of longitudinal skin reinforcement should be 300mm.

Shear reinforcement: Transverse reinforcement of the drop beam generally consists of stirrups of 8mm to 16mm bar diameter at a spacing of at least 120mm. The stirrups should generally engage all the longitudinal bars in the beam. The maximum spacing of stirrups should not exceed d/2 or 600mm, where d is the flexural depth of the concealed beam. The minimum stirrup bar diameter increases with beam depth to avoid buckling of the stirrup during construction under construction loads (see table 1 below). For beams in seismic moment resisting frames or beams resisting torsional moments, the stirrup should be terminated by a 135 or 180 degree hook. Table 1 maximum section depth for vertical bar diameter (construction considerations) Bar size (mm) Maximum section depth (mm) 8 540 10 700 12 1000 14 1400 16 1800 20 2800 Beam-column joint size: in moment resisting frames needs to satisfy the requirements of ACI318-21.7 for ductile moment resisting frames.


Flexural strength: The effective span length is taken as either distance from centreline to centreline of the supporting columns or the clear distance between supporting columns plus one beam depth on each end. The amount

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of tensile flexural reinforcement or of compression reinforcement may be increased in order to limit deflections under service load. The flexural reinforcement in the drop beam shall be such that flexural failure occurs before shear failure (ACI318-21.3.2). The fraction of bottom reinforcement developed at the support should satisfy the requirements of table 12.11 of ACI318, and strut and tie requirements for shear resistance at the support. The fraction of top reinforcement extending at midspan should satisfy the requirements of table 12.12 of ACI 318. The amount of compression reinforcement at the beam-column joint should be such that the required flexural ductility is realized (ACI318-7.12).

Shear strength: The effective span length is calculated as for flexural strength calculation. There is a minimum amount of shear reinforcement to be provided (ACI318-11.5.5,11.8.4-5), and for seismic applications, the shear failure load should be larger than the flexural failure load (ACI318-21.3.4). For ductile moment resisting frames where severe load reversal may occur at the beam-column joint, it is recommended to provide horizontal bars at beam mid-height to resist the shear load by shear-friction.

Torsional strength: Torsional resistance of drop-beam subjected to torsional moments is calculated according to ACI318-11.6.3.6-7 and involves transverse closed stirrups and longitudinal bars distributed at the corners of the section and along its sides.

Deflection under service load: The effective span length is calculated as for flexural strength calculation. If the span to depth ratio of the drop-beam exceeds the limit in table 9.5a of ACI318, the deflection under service load needs to be calculated according to sections 9.5.2.2 to 9.5.2.6 of ACI318. A camber to the formwork needs to be provided to compensate for the permanent load immediate and long term deflections.

Crack width under service load: The allowable crack width under service load is obtained from ACI318 Appendix A-9 or BS8110 Section 21.9.04 depending on the type of exposure. To minimize the crack width, the smallest possible bar size must be used.

Design of one-way slabs: One-way solid slabs are used mainly in attics and in ribbed slabs (between widely spaced ribs). The design items for a one-way solid slab are:

Slab thickness: The slab thickness is determined from shear strength requirements (provided solely by the concrete), punching shear strength (in case of concentrated loads) and deflection requirements, which may be satisfied either by conforming to the requirements of table 9.5a of ACI318, or by conducting a deflection analysis. Slab longitudinal reinforcement: Shallow one-way slabs are generally designed as simply supported. The bottom flexural reinforcement needs to be fully developed at the supports by 180 degree hooks either in the vertical plane (if the depth of the slab allows it) or in the horizontal plane (the bar spacing then cannot be less than the width of the hook). The amount of flexural reinforcement at the support should be sufficient to develop the

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strut-and-tie shear resistance mechanism, and the amount of flexural reinforcement should be limited such that flexural failure occurs before shear failure. The minimum bar size should be 10mm and the largest bar size should not exceed T/10 or L/200 where T is the slab thickness and L is the slab span length between inflection points. The minimum bar spacing compatible with the hook width, mentioned above, should be used in order to minimize crack width at service.


Flexural strength: One way slabs may be designed as simply supported or as continuous over the supporting element. The effective span length is taken as either distance from centreline to centreline of the supporting element or the clear distance between supporting elements plus one floor depth on each end.

Shear strength: The shear strength in the one-way slab is provided solely by the concrete (ACI318-11.3.1,11.5.5), and is a way of determining the required slab thickness. For additional safety, the bottom reinforcement at the support should be sufficient to develop the required shear strength by strut-and-tie action. Punching shear strength: is checked according to ACI 318-11.12.12.1 and may control the slab thickness in presence of heavy concentrated loads. Deflection under service load: The effective span length is calculated as for flexural strength calculation. If the span to depth ratio of the one way slab exceeds the limit in table 9.5a of ACI318, the deflection under service load needs to be calculated according to sections 9.5.2.2 to 9.5.2.6 of ACI318. A camber to the formwork needs to be provided to compensate for the permanent load immediate and long term deflections.

Crack width under service load: The allowable crack width under service load is obtained from ACI318-Appendix A-9 or BS8110 Section 21.9.04 depending on the type of exposure. To minimize the crack width, the smallest possible bar size must be used.

Design of two-way slabs Two-way slabs include flat plates, flat slabs with drop panels and two-way slabs on drop beams. The design elements of two-way slabs include the following:

Slab thickness: The minimum slab thickness to satisfy deflection requirements may be determined from ACI318-9.5.3. Punching shear considerations in presence of concentrated heavy loads may also determine the slab thickness. Drop panel thickness and extent: When heavy distributed loads or long spans are involved, it may be more economical to provide drop panels. The minimum depth and extent of drop panel are set in ACI318-13.3.7. Additional considerations may be the punching shear or flexural moment at the support column. The minimum drop panel depth is T/4 (ACI318-13.3.7.2) and the maximum drop panel depth is 0.7T (flexural strength considerations), where T is the slab thickness away from the drop panel. The extent of the drop

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panel should not be less than L/3, where L is the span length between column centrelines (ACI318-13.3.7.3). Slab punching shear reinforcement: When punching shear requirements at the slab-column connection are not met, punching shear reinforcement in the form of stud rails or transverse reinforcement elements (ACI318-11.5.6.2) may be used. Column capital extent: Alternatively, when punching shear requirements at the slab-column connection are not met, a local enlargement of the interface by means of a column capital (ACI318-10.11.3.2,13.7.4) may be used. Drop-beam dimensions: The drop beam dimensions in a two way slab system need to satisfy the proportioning rules of ACI318-13.2.4 and torsion stress requirements for edge beams. Slab flexural reinforcement: The minimum bar size should be 10mm and the maximum bar size should be T/10, where T is the slab thickness. The bar spacing needs to satisfy the requirements of ACI318-13.3.2, but should not be less than 120mm on-centers to allow proper placement and vibration of concrete. A maximum bar spacing of 300mm would allow the addition of intermediate bars for extra reinforcement while maintaining the minimum bar spacing requirement in the additional bars region. Only one layer of reinforcement in each direction should be used along each face of the slab.

The verifications specific to the two-way slabs are as follows (drop-beams and columns are treated elsewhere):

Flexural strength: The calculation of moments and the required flexural strength may be done using the direct design method, the equivalent frame method or the finite elements method. In the first two methods middle strips and column strips are defined (ACI318-13.6.1,13.7.2) and assigned design moments. Additional reinforcement needs to be placed at the slab-column connection to transmit the vertical load from the slab to the column (ACI318-13.5.3). Shear strength: Normally, two-way slabs satisfying the requirements of ACI318 table 9.5.c should have sufficient shear strength. Concrete beam shear can be checked for the longest column strip and middle strip; no shear reinforcement is used in two-way slabs. Punching shear strength: Punching shear strength needs to be checked under concentrated loads and at the slab-column connection (ACI318-11.12.12.2). Deflection under service load: Two way slabs satisfying the requirements of ACI318 table 9.5.c should have satisfactory deflection under service loads. Otherwise, the effective long term deflection shall be calculated using the appropriate spreadsheet.

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Crack width under service load: The allowable crack width under service load is obtained from ACI318-Appendix A-9 or BS8110 Section 21.9.04 depending on the type of exposure. To minimize the crack width, the smallest possible bar size must be used.

Design of hollow core slab floors: The design elements of a hollow core slab floor include the following items:

Selection of framing plan: Hollow core slab floors are best used with rectangular regular floor bays without cantilevers. Since the slab support beam is a drop beam, it may not be necessarily more advantageous to have the beam spanning in the short direction, and the slab spanning in the long direction. Hollow core slabs should meet the support at an angle as close to right angle as possible (skew support lines need to be avoided because they may lead to splitting of the slab). Shafts in hollow core floor slabs can occur only between slab elements or within concrete cores (service, elevator, stairs)

Selection of slab depth: is done from manufacturer’s catalogues given the superimposed service load (additional dead load and service live load), the span length, the required fire resistance (normally 2hr), the screed thickness (and whether it is structural or not). The catalogue gives the required depth and number of pretensioned prestressed 7 wire strands.

Design of supporting drop beam: The supporting drop beam may be entirely located under the hollow core slab, or it may have its top at the same level as the slab top and extend partially below the slab soffit. In that case, the slab is supported on a ledge projecting from the drop beam. The design of the support ledge is done according to the procedure described in PCI Design Handbook 6.14.

The specific verifications to be performed are (in addition to those for drop beams):

Slab support ledge: The design of the slab support ledge is done according to the procedure described in PCI Design Handbook 6.14 and involves determining the following parameters:

• Ledge width: based on minimum bearing stress and slab length tolerance.

• Ledge depth: based on shear, flexure and reinforcement arrangement; it is never less than 200mm.

• Ledge reinforcement: based on flexure, shear and shear-friction. • Cumulation of ledge reinforcement with that of beam shear and

torsion reinforcement (consideration of partial load to maximize torsion on beam).

Diaphragm action: Is the transfer of in-plane seismic or wind forces from the floor slab (seismic) or the loaded façade (wind) to the lateral load resisting (shearwall or moment resisting frame). The beams supporting the hollow core slab act as tension or compression struts. The hollow core slabs and the screed on top of them transfer shear by in-plane shear stresses. Refer to UBC97-1630.1 to 1630.6 to calculate the seismic in-plane forces, and to UBC97-1633.2.9 for flexible diaphragm force calculations.

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Design of prestressed concrete floor slabs: The design elements of a cast-in-situ prestressed concrete floor slab include the following items:

Selection of framing plan: Cast-in-situ prestressed concrete floor slabs include several variants: flat-plate, ribbed slab, waffle slab, slab with band-beams (listed in order of increasing span length and floor depth). Based on the governing bay dimension, the most appropriate variant is selected, the direction of the distributed tendons and the direction of the banded tendons, and hence the framing plan is set.

Selection of slab thickness: Once the appropriate variant is selected, the slab thickness is selected based on ACI318 table 9.5.4, the concept of load balancing, and an average final prestress ranging from 0.9 Mpa (ACI318-18.12.4) to 3.5 Mpa (ACI318-21.5.2.5).

Selection of prestressing system: meaning the choice of the strands diameter, and whether bonded or unbonded strands will be used. Compared to unbonded tendons, bonded tendons require more workmanship due to subsequent grouting, but they have superior ultimate flexurals strength, and are more accommodating for future remodelling (they can be cut to open new shafts). Unbonded tendons are easier and faster to use than bonded tendons and are therefore often preferred by contractors. Strand diameter and number of strands per tendon is decided based on the maximum prestress force needed, the minimum and maximum tendon spacing, and the available anchorage types (monostrand for unbonded tendons, 4 or 5 strands for bonded tendons).

Design of prestressing cables profile and spacing: The minimum concrete cover is set based on ACI318-7.7.2 for the required fire resistance (usually 2hr). Then, the tendon profile and spacing are calculated to achieve the required load balancing ratio and average prestress force.

The specific verifications to be performed are:

Checking of stresses during the various phases: The main phases for which the top and bottom slab flexural stresses must be checked are: initial prestressing under self-weight only (may be partial prestress), final prestressing under self-weight and some or all superimposed dead load, prestress after occurrence of all time-dependant losses and in presence of all permanent loads (self weight and superimposed dead loads), and finally prestress after occurrence of all time-dependant losses and in presence of all loads (permanent and live). The flexural stresses must be within the allowable limits for tension and compression stress (ACI318-18.3.3 and 18.4.1 to 18.4.4).

Calculation of passive reinforcement: passive reinforcement is calculated based on two criteria; ultimate flexural strength (ACI318-18.8.2) and total tensile service force (ACI318-18.9.3.2). Moreover, in the case of unbonded tendons, there is a minimum amount of passive reinforcement to be provided (ACI318-18.9).

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Calculation of punching shear reinforcement: prestressed concrete slabs are often quite thin and punching shear becomes a critical item. At least two tendons need to cross over each column in each direction, to prevent catastrophic failure (ACI318-18.12.6). Punching shear check and punching shear reinforcement are calculated as per ACI318-11.12.2.2.

Calculation of anchor zone reinforcement: the reinforcement of the anchor zone consists of surface reinforcement, bursting reinforcement and diffusion reinforcement (ACI318-18.13, AASHTO-LFD-9.21.7).

Design of columns: The design elements of a cast-in-situ reinforced concrete column include the following items:

Section shape: The column section shape is generally rectangular or circular (but other shapes may occur) and is generally agreed upon with the architect. No drainage pipes should be allowed inside columns. Section dimensions: are determined based on the column length, required fire resistance and column design loads. The transition in dimensions from one floor to the next should be such that the maximum deviation in longitudinal bars does not exeed 1/6 (this is equivalent to 1/3 of the floor thickness as maximum dimension change). Longitudinal reinforcement: is determined based on the column design loads. The reinforcement ratio should range between 0.8% and 4%. Moreover, the minimum bar size should be 12mm. The center-to-center bar spacing should range between 120mm and 150mm. Transverse reinforcement: is determined based on the column design loads. The minimum tie diameter is 10mm. The maximum spacing of ties is the minimum of half the column dimension (for shear resistance), eight times the smallest longitudinal bar diameter (to avoid longitudinal bar buckling) or 300mm (ACI318-21). The tie spacing is reduced in the potential plastic hinge region, which extends at least one sixth the column height, largest column dimension, or 450mm (ACI318-21.12.5.2). Outside the plastic hinge region, spacing of transverse reinforcement should conform to ACI318-7.10 and 11.5.4.1. The spacing of tie legs should not exceed 350mm (ACI318-21.6.4.2), and should not be much smaller than this value to allow easy access for the concreting tremie. The transverse ties should be continued through the beam-column joint (ACI318-21.12.5.5 and 11.11.2).

The specific verifications to perform are:

Minimum dimensions: to satisfy fire resistance (UBC-Tables 7) and seismic resistance (UBC-1921). Column slenderness: and the attendant moment magnification. Flexural strength: is calculated using PCACOL or similar programs.

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Shear strength: is calculated for the applied loads and may take advantage of the shear strength enhancement due to compression caused by axial loads (gravity load cases). Alternatively, a capacity approach may be taken such that the shear strength is larger than the maximum shear that can be caused by the flexural moment strength (fVn > (Mntop+Mnbot)/H, ACI318-21.6.5.1). Curvature ductility: In ductile moment resisting frames, the strength reduction factor R implies a displacement ductility factor md = R or (R-1)^2/(2R). A curvature ductility mm = ecu/x is necessary to achieve the displacement ductility md.

Design of shearwalls The design elements of a shearwall include the following items:

Wall length: wall length is mainly determined from architectural considerations in coordination with structural requirements. Wall thickness: wall thickness is mainly determined from structural requirements based on required fire resistance, minimum slenderness, required structural strength (compression, flexure, shear) and stiffness. Boundary elements: that consist of specially reinforced or thickened regions at the ends of the wall section may be required in walls subjected to severe seismic loading. Longitudinal reinforcement: needs to be calculated based on axial load and flexural load requirements. Transverse reinforcement: needs to be calculated based on shear loads.

The specific verifications to perform are: Minimum dimensions: to satisfy fire resistance (UBC-Tables 7) and seismic resistance (UBC-1921). Wall slenderness: and the attendant moment magnification. Flexural strength: is calculated using PCACOL or similar programs. Shear strength: is calculated for the applied loads and may take advantage of the shear strength enhancement due to compression caused by axial loads (gravity load cases). Curvature ductility: In ductile shearwall buildings, the strength reduction factor R implies a displacement ductility factor md = R or (R-1)^2/(2R). A curvature ductility mm = ecu/x is necessary to achieve the displacement ductility md.

Design of cores: The design elements of cores are identical to those of shearwalls. The specific verifications to perform are (in addition to those done for shearwalls):

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Calculation of section flexural inertia: is necessary for calculation of drift under lateral loads and fundamental period of the building. Shear stiffness should be taken into account, as well as the effective flange width. Calculation of additional reinforcement around openings: The longitudinal reinforcement interrupted by an opening should be replaced by three times the amount, distributed evenly on each side of the opening. The transverse reinforcement interrupted by an opening should be replaced by an equal amount distributed evenly on each side of the opening.

Design of coupling beams: The design of coupling beams includes the following elements:

Section depth: Section depth is often limited by the required false ceiling clearance and mechanical ducting requirements. In case diagonal main reinforcement is adapted, some sleeves may be allowed in the coupling beam and the depth may be increased slightly. The overall shear stress in the coupling beam should not exceed 5fvc, especially when conventional reinforcement arrangement is used. Section width: Section width is constrained by the thickness of the shearwalls connected by the coupling beam, especially when a diagonal main reinforcement arrangement is adopted. In case a traditional reinforcement arrangement is adopted, the coupling beam width may be larger than that of the connected walls provided the following precautions are taken:

-The extension of the widened section is sufficient to develop the flexural reinforcement of the coupling beam. -The bearing area of the coupling beam on the wall is sufficient to transfer the coupling beam shear force. -The wall vertical reinforcement in the bearing area is sufficient to transfer the coupling beam shear force by tension.

Longitudinal reinforcement arrangement: The longitudinal reinforcement arrangement in a coupling beam can be either:

-conventional as in a regular beam. In the conventional arrangement, the amount of longitudinal reinforcement is calculated based on the end moments applied to the coupling beam by lateral loads (wind, seismic). -or diagonal in an X arrangement. The X arrangement can be used only when the length to depth ratio of the coupling beam L/d is less than 2 (ACI318-21.9.7.2). The X arrangement is preferred in highly seismic zones when a large ductility needs to be achieved. In the X arrangement, the longitudinal reinforcement of the struts is calculated based on the end shears applied to the coupling beam by lateral loads (wind, seismic) resolved into axial forces along the struts. Since the compression strut is stiffer than the tension strut, the compression strut will have a larger axial force magnitude than the tension tie. Additional horizontal top and bottom reinforcement must be provided to resist the horizontal component of the difference of force between the compression strut and the tension strut.

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Transverse reinforcement arrangement: The transverse reinforcement arrangement in a coupling beam depends on the arrangement of the longitudinal reinforcement: -For a conventional reinforcement arrangement, the transverse shear reinforcement must be calculated from capacity principles, such that flexural yielding occurs before shear failure. -For an X arrangement, the main transverse shear reinforcement is around the longitudinal reinforcement of the struts, and its function is to provide confinement to the concrete inside the struts to increase its compressive strength and ultimate failure strain. The overall stirrups may be a nominal amount.


Shear strength: As indicated above, shear strength verification depends on the configuration of the longitudinal reinforcement in the coupling beam. Flexural strength: As indicated above, flexural strength verification depends on the configuration of the longitudinal reinforcement in the coupling beam. Flexural stiffness: For the conventional reinforcement arrangement, the effective section moment of inertia may be calculated assuming a cracked section. For the X reinforcement arrangement, an effective section moment of inertia may be estimated from the following equivalence K=V/D=12E.Ieff/L3, where: V = maximum shear capacity of the coupling beam. D = vertical relative displacement between ends of the beam corresponding to V. E = concrete modulus of elasticity. L = span length of coupling beam. Ieff = effective section moment of inertia. Loading/unloading effect on connected shearwalls: The accumulation of shear forces from the coupling beams increases the vertical force on one of the shearwalls and decreases the vertical force on the opposite shearwall. Both shearwalls must be checked for the applied moment with the increased or reduced axial force. In a 2D or 3D FEM model this loading/unloading effect is automatically accounted for.

Design of isolated centered footings: The design elements of an isolated centered footing include the following items:

Plan dimensions: The plan dimensions of a footing are determined from bearing stress considerations. For footings with mainly vertical loads (low eccentricity), the plan dimensions are selected such that a constant width overhang is provided outside the column limit. For footings with relatively large moments (high eccentricity) the plan dimensions are determined from bearing stress considerations, using Meyerhoff’s approach (for a reduced uniformly loaded bearing area). Thickness: The thickness of the footing is determined from four considerations: punching shear strength, beam shear strength, flexural

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reinforcement economy and development length for the column’s longitudinal bars. A minimum thickness of 350mm is recommended. Reinforcement: The footing main reinforcement is flexural reinforcement at the bottom face of the footing. The minimum reinforcement ratio (after applying the 4/3r provision of ACI318-10.5.3) should be rmin > 0.25ft/fy, where:

-ft = tensile strength of concrete. -fy = yield strength of reinforcement.

The reinforcement on the top face of the footing is calculated for the moment caused by the weight of the overburden soil, but not less than temperature and shrinkage requirements (r > 0.0009). For footing thickness greater than 600mm a side reinforcement of 500mm2/m should be provided along the edges of the footing.


Bearing stress: The net bearing stress due to vertical loads and moments may be checked using Meyeroff’s approach where:

s = Pnet/(Lx’.Ly’) Bearing stress Lx’=Lx-2*ex Effective uniform contact area x length Ly’=Ly-2*ey Effective uniform contact area y length ex = |My|/Pnet Load eccentricity in x direction ey=|Mx|/Pnet Load eccentricity in y direction Pnet Net vertical load (external load + footing weight - overburden weight) Mx Moment about x axis on footing centroid My Moment about y axis on footing centroid

This verification is done using service load combinations. Stability against overturning: The ratio of overturning moment to restoring moment for x and y directions should be larger than 2. The overturning moment consists of the applied external moment. The restoring moment is the total vertical load (external load+footing weight+overburden weight) multiplied by half the footing length in the concerned direction. This verification is done using service load combinations. Stability against sliding: The ratio of resisting force to sliding force for x and y directions should be larger than 2. The sliding force is the external horizontal force. The resisting force is Fres = m.Ptot+c.Afoot where:

m = coefficient of friction between footing and soil tan(2/3f) Ptot = total vertical force (external load+footing weight+overburden weight) f = internal angle of friction of foundation soil c = foundation soil cohesion

Afoot = footing area This verification is done using service load combinations. Punching shear: The punching shear in the footing due to externally applied ultimate vertical load and moments is calculated at a perimeter at d/2 away from the column limit as per ACI318-11.11.1.2. The thickness of the

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footing should be such that punching shear check is satisfied without having to use punching shear reinforcement. Beam shear: Beam shear in the footing due to externally applied ultimate vertical load and moments is calculated at two orthogonal sections d away from the column limit as per ACI318-11.1.3.1. The thickness of the footing should be such that punching shear check is satisfied without having to use punching shear reinforcement. Flexural strength: Flexural strength in the footing due to externally applied ultimate vertical load and moments is calculated at two orthogonal sections at the face of the column limits as per ACI318-15.4.1. The thickness of the footing should be such that the reinforcement ratio is within allowable limits, the number and spacing of reinforcement bars within acceptable limits, and the overall design is optimized costwise. Calculation of equivalent spring stiffness: In some cases where the distribution of the loads to the foundations is affected by the relative stiffness of the foundations, the stiffness of the foundations in the vertical direction and in rotation about the principal axes needs to be accounted for in the analytical model (instead of the usual fixed base assumption). In those cases, the design shall proceed by iteration, starting with a fixed base calculation, estimating the required footing dimensions, calculating and inserting the corresponding foundation stiffness in the model and redesigning the footings for the new force distribution. The process is repeated until the assumed and the required footing dimensions are within an allowable tolerance (5% or 100mm). The foundation spring stiffness is calculated as follows:

Kz = Af.Ks Kxx = Lx/12.Ly3.Ks Kyy = Lx3.Ly/12.Ks Ks = Modulus of subgrade reaction (~120qa) qa = Allowable net bearing capacity.

Design of isolated eccentric footings (with strap beam): Isolated eccentric footings are used when the supported column or wall is immediately at the lot boundary such that a concentric footing cannot be used. The design of an isolated eccentric footing is similar to that of a concentric isolated footing except for the following additional items (suppose in the following that the strap beam is along the X axis):

Load eccentricity: The sign of the moment about the Y axis (normal to the strap beam direction) is significant and may increase the load eccentricity. The load eccentricity is calculated with respect to the centroid of the footing and may be balanced completely or partially by the shear and moment applied by the strap beam at the edge of the footing opposite to the edge where the column is situated. Strap beam section: The strap beam section needs to be determined from 3 considerations: shear strength, flexural strength and flexural stiffness. The distribution of loads between the footing and the strap beam should take into account their rotational and vertical translation stiffness.

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Punching shear area: In case the strap beam connects to the footing along its side face, then punching shear stress under the eccentric column needs to be checked (reduced punching shear perimeter). In case the strap beam connects to the footing along its top face and extends to the eccentric column, then no punching shear needs to be checked.

The specific verifications to be done are identical to those done for a concentric footing. Design of combined footings: Combined footings are used when adjacent isolated footings are likely to overlap. The design elements of a combined footing are:

Plan dimensions: The plan dimensions of a footing are determined from bearing stress considerations. Generally, a trapezoidal plan form is selected, such that the centroid of the trapezoid coincides with the resultant of the vertical permanent loads, in order to obtain a uniform permanent soil stress and uniform settlement.

Footing thickness: The thickness of the footing is determined from four considerations: punching shear strength, beam shear strength, flexural reinforcement economy and development length for the column’s longitudinal bars. A minimum thickness of 350mm is recommended.

Footing reinforcement: The footing main reinforcement is flexural reinforcement at the bottom face of the footing outside the columns, in the transverse direction, and on the top face of the footing between the columns. The minimum reinforcement ratio (after applying the 4/3r provision of ACI318-10.5.3) should be rmin > 0.25ft/fy, where:

-ft = tensile strength of concrete. -fy = yield strength of reinforcement.

The top transverse reinforcement is calculated for the moment caused by the weight of the overburden soil, but not less than temperature and shrinkage requirements (r > 0.0009). For footing thickness greater than 600mm a side reinforcement of 500mm2/m should be provided along the edges of the footing.

The specific verifications to be done are:

Bearing stress: The net bearing stress due to vertical loads and moments may be checked using strength of materials approach:

s = P/A+/-Mx/Sx+/-My/Sy : Bearing stress s = 0.75 smax+0.25 smin : Effective bearing stress P Net vertical load (external load + footing weight - overburden weight) Mx Moment about x axis on footing centroid My Moment about y axis on footing centroid Sx Section modulus for bending about x axis Sy Section modulus for bending about y axis

If a negative stress (tension) is obtained at one or more corners of the footing, then the line of zero stress must be obtained by trial and error. The

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effective bearing stress is compared to the allowable bearing stress. This verification is done using service load combinations. Stability against overturning: The ratio of overturning moment to restoring moment for x and y directions should be larger than 2. The overturning moment consists of the applied external moment. The restoring moment is the total vertical load (external load+footing weight+overburden weight) multiplied by half the footing length in the concerned direction. This verification is done using service load combinations. Stability against sliding: The ratio of resisting force to sliding force for x and y directions should be larger than 2. The sliding force is the external horizontal force. The resisting force is Fres = m.Ptot+c.Afoot where:

m = coefficient of friction between footing and soil tan(2/3f) Ptot = total vertical force (external load+footing weight+overburden weight) f = internal angle of friction of foundation soil c = foundation soil cohesion

Afoot = footing area This verification is done using service load combinations. Punching shear: The punching shear in the footing due to externally applied ultimate vertical load and moments is calculated at a perimeter at d/2 away from the column limit as per ACI318-11.11.1.2. The thickness of the footing should be such that punching shear check is satisfied without having to use punching shear reinforcement. Beam shear: Beam shear in the footing due to externally applied ultimate vertical load and moments is calculated at orthogonal sections d away from the column limits as per ACI318-11.1.3.1. The thickness of the footing should be such that punching shear check is satisfied without having to use shear reinforcement. Flexural strength: Flexural strength in the footing due to externally applied ultimate vertical load and moments is calculated at orthogonal sections at the face of the column limits as per ACI318-15.4.2 and at the maximum moment in the span between the two columns. The thickness of the footing should be such that the reinforcement ratio is within allowable limits, the number and spacing of reinforcement bars within acceptable limits, and the overall design is optimized costwise. Calculation of equivalent spring stiffness: In some cases where the distribution of the loads to the foundations is affected by the relative stiffness of the foundations, the stiffness of the foundations in the vertical direction and in rotation about the principal axes needs to be accounted for in the analytical model (instead of the usual fixed base assumption). In those cases, the design shall proceed by iteration, starting with a fixed base calculation, estimating the required footing dimensions, calculating and inserting the corresponding foundation stiffness in the model and redesigning the footings for the new force distribution. The process is repeated until the assumed and the required footing dimensions are within an allowable tolerance (5% or 100mm). The foundation spring stiffness is calculated as follows:

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Kz = Af.Ks Kxx = ∫∫Ks.y2dxdy Kyy = ∫∫Ks.x2dxdy Ks = Modulus of subgrade reaction (~120qa) qa = Allowable net bearing capacity.

Design of tie-beams: Tie-beams connect isolated footings and may support slabs on grade. The design elements of tie-beams are:

Location with respect to top of footing: Generally, the tie beams frame into the columns immediately above the top face of the footing and may support the slab on grade. In some cases Section dimensions: Tie beam sections are such that the vertical dimension is larger than the horizontal dimension. The horizontal dimension should not be less than 250mm and should be either smaller or larger (by at least 50mm) than the column dimension into which it is framing (to avoid interference between the tie-beam longitudinal reinforcement and the column longitudinal reinforcement). The vertical dimension is determined from analysis, based on the required compression capacity, buckling resistance and flexural stiffness. Section reinforcement: The longitudinal reinforcement is determined on the basis of the required axial tension and compression capacity and the required flexural capacity. The transverse reinforcement is determined on the basis of the required shear capacity, and the minimum transverse reinforcement requirements. The longitudinal top and bottom reinforcement are equal, and the vertical faces receive skin reinforcement. The shear reinforcement is often a single tie.

The verifications to perform on tie-beams are as follows:

Axial capacity in tension and compression: the tie-beam section and reinforcement should be able to resist 10% of the maximum ultimate column load at each end of the tie-beam, as either a tension force or as a compression force. Resistance to buckling: when subjected to its design compression force, the tie-beam should not buckle. The effective length may be taken as half the clear length (fixed ends). The effective moment of inertia shall be taken as 0.35Ig, according to ACI-318-10.10.4.1. Flexural and shear resistance: the tie-beam shear and flexural strength shall be sufficient to resist imposed deformations corresponding to the expected differential settlement under vertical load, the imposed rotations due to lateral loads and the vertical loads directly applied to the tie-beam (from slabs-on-grade monolithically connected to the tie-beam).

Design of rafts:

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Rafts are used when the bearing capacity is so low, or the column loads so high, that individual footings would overlap over one another. The design elements of a raft are: The extent in plan: The extent in plan of a raft is usually the footprint of the building (particularly when it is a high-rise or has basements below the water table), in which case it also supports the perimeter basement walls. Otherwise, the extent in plan outside the high-rise core is determined from soil bearing capacity considerations. The thickness: The thickness of a raft is determined from punching shear and beam shear considerations, since it is not practical to provide punching shear reinforcement in the raft. In some cases, where uplift due to shallow water table is encountered, the raft thickness may be increased to provide ballast weight against uplift, and to have the reinforcement work at a reduced stress to limit the flexural crack widths. The flexural reinforcement: The flexural reinforcement is calculated for the moments induced in the raft. Two approaches are possible for the detailing of the reinforcement; either a constant bar spacing is used with changes in the bar diameters where needed, or a basic reinforcement mesh at twice the minimum bar spacing (250mm to 300mm) is laid and additional reinforcing bars are inserted between the mesh bars, where needed. The minimum bar spacing should not be less than 120mm or 150mm preferably, to allow proper placement of reinforcement. The punching shear reinforcement: Punching shear reinforcement may be used around a few heavily loaded columns to keep the raft thickness to a reasonable value. When the raft thickness necessary for these column to satisfy punching shear stress is much larger than the thickness necessary to satisfy beam shear or punching shear at the other columns, then it is more economical to use punching shear reinforcement at these columns. The construction sequence and heat of hydration control: For large or thick rafts that cannot be poured in one phase, it is necessary to preview a construction sequence with either construction joints either along vertical planes or along horizontal planes. In either case, the reinforcement has to be detailed to provide sufficient development length across the construction joints, and the construction joint faces must be keyed or roughened to provide sufficient shear resistance across the planes. Moreover, in case of thick rafts, some measures need to be taken to avoid excessive rise of temperature inside the raft and thermal gradients leading to cracking of the raft. The verifications to perform are: Analytical model: Flexural strength: Punching shear strength: Beam shear strength: Design of slab-on-grade: Design of pile foundations: Design of pile caps:

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Design of basement walls: Design of water tanks: Design against progressive collapse: Calculation of superimposed dead loads The main vertical loads on a structure consist of self weight dead load, superimposed dead load and live load. Self weight dead load is easily computed from the structural elements sections and material density. The superimposed dead load consists of floor covering (tiling, screed), partition walls and ceiling fixtures (false ceiling, lighting fixtures, cable trays, water supply piping, drainage piping, fire-fighting piping, HVAC ducting) Floor covering: Three typical scenarios may be encountered:

Floor tiling: would typically involve about 60mm of sand for levelling (g=18KN/m3), 20mm of screed (g=22KN/m3) and 20mm for tiles (g=24KN/m3) for a total thickness of 100mm and a weight of 18x0.06+22x0.02+24x0.02=2 KN/m2. A 0.5KN/m2 is added for ceiling fixtures on the ceiling below for a total of 2.5KN/m2.

Floor screed: When screed is used to cover a floor, a minimum screed thickness of 50mm is usually required. The screed is sloped to falls at a rate of 2%. The screed thickness is variable, and the average thickness is 0.5(tmax+50mm). A 0.5KN/m2 is added for ceiling fixtures on the ceiling below. Roof covering: Roof covering typically involves levelling screed (~50mm), waterproofing, protection screed (50mm<t<tmax) or protection gravel (~150mm). A 0.5KN/m2 is added for ceiling fixtures on the ceiling below. The total weight is 0.5+22x0.05+0.1+22x0.15=5KN/m2.

Partition loads: can be analyzed either as line loads or as equivalent uniformly distributed loads. The first option is recommended for perimeter cladding and façade loads, whose location is fixed and whose value could be large. The second option is generally used for interior partition walls for its simplicity.

Partitions equivalent distributed loads: There are three ways to compute partition equivalent distributed loads. In the following, let:

Wp be the weight of a partition section 1m long in the horizontal direction. Hp be the thickness of the partition wall

Then: Case of partition normal to a beam of length L:

We=2xWp/L for simply supported beams. We=1.5xWp/L for continuous beams.

Case of partition parallel to a beam of length L: We=Wp/e, where: E=max(1,Hp+0.6L) for an interior partition E=max(1,Hp+0.3L+h) for an exterior partition, where h is the distance from the edge.

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Unspecified case: We=Wp/3 > 1KN/m2.

Generally partition loads would not be less than 4.5KN/m2. Calculation of lateral wind loads Calculation of lateral seismic loads Calculation of vertical deflection in beams and ribs Calculation of vertical deflection in two-way slabs Calculation of drift due to lateral load

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