Elements of RCC Design
UNIT 1 Structure of this unit Concept of Reinforced Cement Concrete, Theory of R.C.C. Beams, Reinforcement Materials Objectives to be learned 1. Various types of reinforcing materials 2. Suitability of steel as a reinforcing materials 3. Properties of different types of steel (mild steel, medium tensile steel and deformed bars) 4. Assumption in the theory of simple bending for RCC beam 5. Flextural strength of a singly reinforced beam 6. Position of Neutral axis, resisting moment of the section, critical neutral axis, concept of balanced, under reinforced over reinforced sections. 7. Shear strength of singly reinforced RCC beam. 8. Assumptions made, permissible shear stresses as per IS code of practice, 9.
actual average shear stresses in singly reinforced concrete beam,
10. concept of diagonal stirrups and inclined bars, shear strength of a RCC beam section 1.1Concrete is a stone like substance obtained by permitting a carefully proportioned mixture of cement, sand and gravel or other aggregate and water to harden in forms of the shape and of dimensions of the desired structure. 1.1.2Reinforced cement concrete: Since concrete is a brittle material and is strong in compression. It is weak in tension, so steel is used inside concrete for strengthening and reinforcing the tensile strength of concrete. The steel must have appropriate deformations to provide strong bonds and interlocking of both materials. When completely surrounded by the hardened concrete mass it forms an integral part of the two materials, known as "Reinforced Concrete". 1.1.3 Advantages and disadvantages of reinforced concrete Reinforced Concrete is a structural material, is widely used in many types of structures. It is competitive with steel if economically designed and executed. Advantages of reinforced concrete
It has relatively high compressive strength
It has better resistance to fire than steel
It has long service life with low maintenance cost
In some types of structures, such as dams, piers and footings, it is most economical structural material
It can be cast to take the shape required , making it widely used in pre-cast structural components
It yields rigid members with minimum apparent deflection
Yield strength of steel is about 15 times the compressive strength of structural concrete and well over 100 times its tensile strength
By using steel, cross sectional dimesions of structural members can b ereducede.g in lower floor columns
Disadvantages of reinforced concrete
It needs mixing, casting and curing, all of which affect the final strength of concrete
The cost of the forms used to cast concrete is relatively high
It has low compressive strength as compared to steel (the ratio is about 1:10 depending on material) which leads to large sections in columns/beams of multistory buildings Cracks develop in concrete due to shrinkage and the application of live loads
1.1.4 Reinforced cement concrete Design philosophy and concepts The design of a structure may be regarded as the process of selecting proper materials and proportioned elements of the structure, according to the art, engineering science and technology. In order to fulfill its purpose, the structure must meet its conditions of safety, serviceability, economy and functionality. 1.1.4 Strength design method It is based on the ultimate strength of the structural members assuming a failure condition, whether due to the crushing of concrete or due to the yield of reinforced steel bars. Although there is additional strength in the bar after yielding (due to Strain Hardening), this additional strength in the bar is not considered in the analysis or design of the reinforced concrete members. In the strength design method, actual loads or working loads are multiplied by load factor to obtain the ultimate design loads. The load factor represents a high percentage of factor for safety required in the design. The ACI code emphasizes this method of design. 1.1.5 Working stress design This design concept is based on elastic theory, assuming a straight line stress distribution along the depth of the concrete. The actual loads or working loads acting on the structure are
estimated and members are proportioned on the basis of certain allowable stresses in concrete and steel. The allowable stresses are fractions of the crushing strength of concrete (fc') and the yield strength (fy). Because of the differences in realism and reliability over the past several decades, the strength design method has displaced the older stress design method. 1.1.5 Limit state design It is a further step in the strength design method. It indicates the state of the member in which it ceases to meet the service requirements, such as, loosing its ability to withstand external loads or local damage. According to limit state design, reinforced concrete members have to be analyzed with regard to three limit states: 1. Load carrying capacity (involves safety, stability and durability) 2. Deformation (deflection, vibrations, and impact) 3. The formation of cracks The aim of this analysis is to ensure that no limiting sate will appear in the structural member during its service life. 1.1.6 Fundamental assumptions for Reinforced Concrete's Behavior Reinforced concrete's sections are heterogeneous, because they are made up of two different materials - steel and concrete. Therefore, proportioning structural members by ultimate stress design is based on the following assumptions: 1. Strain in concrete is the same as in reinforcing bars at the same level, provided that the bond between the concrete and steel is adequate 2. Strain in concrete is linearly proportional to the distance from the neutral axis. 3. Modulus of elasticity for all grades of steel is taken as Es = 29 x 10 ^ 6 psi. The stress in the elastic range is equal to the strain multiplied by Es. 4. Plane cross sections continue to be plane after bending. 5. Tensile strength of concrete is neglected because:
Concrete's tensile strength is about 1/10 of its compressive strength.
6. Cracked concrete is assumed to be not effective Before cracking, the entire cross section is effective in resisting the external moments. 7. The method of elastic analysis, assuming an ideal behavior at all levels of stress is not valid. At high stresses, non-elastic behavior is assumed, which is in close agreement with the actual behavior of concrete and steel.
8. At ultimate strength, the maximum strain at the extreme compression fibers is assumed to be equal to 0.003 by the ACI code provisions. At the ultimate strength, the shape of the compressive stress distribution may be assumed to be rectangular, parabolic or trapezoidal. 1.2 Loads Structural members must be designed to support specific loads. Loads are those forces for which a structure should be proportioned. Loads that act on structure can be divided into three categories. 1. Dead loads 2. Live loads 3. Environmental loads 1.2.1 Dead Loads: Dead loads are those that are constant in magnitude and fixed in location throughout the lifetime of the structure. It includes the weight of the structure and any permanent material placed on the structure, such as roofing, tiles, walls etc. They can be determined with a high degree of accuracy from the dimensions of the elements and the unit weight of the material. 1.2.2 Live loads: Live loads are those that may vary in magnitude and may also change in location. Live loads consists chiefly occupancy loads in buildings and traffic loads in bridges. Live loads at any given time are uncertain, both in magnitude and distribution. 1.2.3 Environmental loads: Consists mainly of snow loads, wind pressure and suction, earthquake loads (i.e inertial forces) caused by earthquake motions. Soil pressure on subsurface portion of structures, loads from possible ponding of rainwater on flat surfaces and forces caused by temperature differences. Like live loads, environmental loads at any given time are uncertain both in magnitude and distribution. 1.3 ACI Code Safety Provisions Structural members must always be proportioned to resist loads greater than service or actual loads, in order to provide proper safety against failure. In the stenght design method, the member is designed to resist the factored loads which are obtained by multiplying the factored loads with live loads. Different factors are used for different loadings. As dead loads can be estimated quite accurately, their load factors are smaller than those of live loads, which have a high degree of uncertainity. Several load factor conditions must be considered in the design to compute the maximum and minimum design forces. Reduction factors are used for some combinations of
loads to reflect the low probability of their simultaneous occurrences. Now if the ultimate load is denoted by U, the according to the ACI code, the ultimate required strength U, shall be the most critical of the following 1.3.1 Basic Equation U = 1.2D + 1.6L In addition to the load factors, the ACI code specifies another factor to allow an additional reserve in the capacity of the structural member. The nominal strength is generally calculated using accepted, analytical procedures based on statistics and equilibrium. However, in order to account for the degree of accuracy within which the nominal strength can be calculated and for adverse variations in materials and dimensions, a strength reduction factor (Ø) should be used in the strength design method. Values of the strength reduction factor Ø (Phi) are: For flexure of tension controlled sections Ø = 0.9 For shear and torsion Ø = 0.75 For compression members with spiral reinforcement Ø = 0.70 For compression members with laterla ties Ø = 0.65 1.3.2Nominal strength Actual strength from the material properties is called the nominal strength. Nominal x Ø = Design strength As safe design is achieved when the structural strength obtained by multiplying the nominal strength by the reduction factor Ø, exceeds or equals the strength needed to withstand the factored loads. where Mu, Vu and Pu equals external factored moments, shear forces and axial forces. Mn, Vn and Pnequals the nominal moment, shear and axial capacity of the member respectively 1.4 Strucural Concrete elements 1.4.1 Slab: Slabs are horizontal slab elements in building floors and roof. They may carry gravity loads as well as lateral loads. The depth of the slab is usually very small relatively to its length and width. 1.4.2 Beams: Long horizontal or inclined members with limited width and height are called beams. Their main function is to transfer loads from the slab to the columns.
1.4.3 Column: Columns are vertical members that support loads from the beam or slabs. They may be subjected to axial loads or moments. 1.4.4 Frames: Frames are structural members that consists of combination of slab, beams and columns 1.4.5Footings: Footings are pads or strips that support columns and spread their load directly to the soil. 1.4.6 Walls: Walls are vertical plate elements resisting gravity as well as lateral loads e.g retaining walls, basement walls. etc 1.5 Basic Concepts of Plain concrete Plain concrete is formed from hardened mixture of cement, water, fine aggregate, coarse aggregate (crushed stone or gravel), air, and often other admixtures. The plastic mix is placed and consolidated in the formwork, then cured to accelerate of the chemical hydra-of the cement mix and results in a hardened concrete. It is generally known that concrete high compressive strength and low resistance to tension. Its tensile strength is approximately one-tenth of its compressive strength. Consequently, tensile reinforcement in the ten-zone has to be provided to supplement the tensile strength of the reinforced concrete section. For example, a plain concrete beam under a concentrated load p is shown in Fig.1.1(a),when the concentrated load increases and reaches a value p=14kN, the tensile region at the midspan will be cracked and the beam will fail suddenly. A reinforced concrete beam of the same size but has two steel reinforcing bars (2Φ20) embedded at the bottom under concentrated load q is shown in Fig.1. 1(b). The reinforcing bars take up tension there after the concrete is cracked. When the load p is increased, the width of the cracks, the deflection and the stress of steel bars will increase. When the steel approaches yielding stress , the deflection and the crack width are so large offering some warning the beam is going to fail. The failure of the beam is characterized by the crushing of the concrete in the compression zone. The failure load p= 69.4kN, is approximately 6.8 times that for the plain concrete beam.
1.5.1 Characteristics of Reinforced Concrete Concrete and reinforcement can work together because there is a sufficiently strong bond between the two materials： (1) There are no relative movements of the bars and the surrounding concrete before cracking. (2) The thermal expansion coefficients of the two materials are 1.2 10-5K-1 for steel and 1. 0×10-5～1. 5×10-5K-1 for concrete. 1.1.3 Generally speaking, reinforced concrete structure possess the following features (1)
Durability
With the reinforcing steel protected by the concrete, reinforced concrete is perhaps one of the most durable materials lot construction. It does not rot or rust, and is not vulnerable to efflorescence. (2) Fire resistance Both concrete and steel are not inflammable materials. They would not be affected by fire below the temperature of 2000C when there is a moderate amount of concrete cover giving sufficient thermal insulation to the embedded reinforcement bars. (3) High stiffness
Most reinforced concrete structures have comparatively large cross-sections. As concrete has high modulus of elasticity, reinforced concrete structures are usually stiffer than structures of other materials, thus they are less prone to large deformations. This property also makes the reinforced concrete less adaptable to situations requiring certain flexibility, such as high-rise buildings under seismic load, and particular provisions have to be made if reinforced concrete is used. (4)
Locally available resources
It is always possible to make use of the local resources of labour and materials such as fine and coarse aggregates. Only cement and reinforcement need to be brought in from outside provinces. (5)
Cost effective
Comparing with steel structures, reinforced concrete structures are cheaper. (6)
Large dead mass
The density of reinforced concrete may reach 2400～2500kg/m3. Compare with structures of other materials, reinforced concrete structures generally have a heavy dead mass. However, this may be not always disadvantageous, particularly for those structures which rely on heavy dead weight to maintain stability, such as gravity dam and other retaining structure. The development and use of light weight aggregate have to a certain extent make concrete structure lighter. (7) Long curing period It normally takes a curing period of 28 day under specified conditions for concrete to acquire its full nominal strength. This makes the progress of reinforced concrete structure construction subject to seasonal climate. The development of factory prefabricated members alleviates this disadvantage. The development of using prefabricated members and investment in metal formwork also reduce the consumption of timber formwork materials. (8) Easily cracked Concrete is weak in tension and is easily cracked in the tension zone. reinforcing bars are provided not to prevent the concrete from cracking but to take up the tensile force. So most of the reinforced concrete structure in service is behaving in a cracked state. This is an inherent weakness of reinforced concrete structure. The concrete in prestressed concrete structure is subjected to a compressive force before working load is applied. Thus the compressed concrete can take up some tension from the load. 1.6 REINFORCING MATERIALS Various materials are used to reinforce concrete. Roundsteel bars with deformations, also known as deformed bars,are the most common type of reinforcement. Others includesteel welded wire fabric, fibers, and FRP bars. It is importantto note that not all structural concrete
containing reinforcementmeets the ACI Building Code (ACI 318) definition ofreinforced concrete. 1.6.1—Steel reinforcement Steel reinforcement is available in the form of plain steelbars, deformed steel bars, colddrawn wire, welded wirefabric, and deformed welded wire fabric. Reinforcing steelmust conform to applicable ASTM standard specifications. 1.1 Deformed steel bars—Deformed bars are round steelbars with lugs, or deformations, rolled into the surface of thebar during manufacturing. These deformations create amechanical bond between the concrete and steel. Deformedsteel bars (Fig. 1.1) are the most common type of reinforcementused in structural concrete. 1.2 Threaded steel bars—Threaded steel bars are made byseveral manufacturers in Grade 420/Grade 60 conforming toASTM A 615M/A 615, but are not available in all sizes. Thesebars can be spliced with threaded couplers or anchoredthrough steel plates, while still providing continuous bondbetween the bar and concrete. They are used as an alternativeto lapping standard deformed bars when long bar lengths arerequired and lap splices are impractical, or where bars need tobe anchored close to the edge of a member. 1.3 Welded wire fabric—Welded wire fabric reinforcement(WWF), also known as welded wire reinforcement, is a square or rectangular mesh of wires, factoryweldedat all intersections. It is used for many applicationssuch as to resist temperature and shrinkage cracks in slabs, asweb stirrups in beams, and as tie reinforcement in columns. Itis manufactured with either plain or deformed wire accordingto ASTM standards A 184M/A 184 (deformed steel bar mats),A 185 (plain steel welded wire fabric), A 497 (deformed steelwelded wire fabric) or A 884M/A 884 (epoxy-coated steelwire and welded wire fabric). Welded wire fabric in whichonly the minimum amount of cross wire required for fabricationand handling is used is called “one-way” fabric. Where anappreciable amount of wire is provided crosswise (transversely)as well as lengthwise (longitudinally), it is called a“two-way” fabric. The lighter fabrics are shipped in rolls,while the heavier fabrics, generally 4.9 mm (No. 6 gage) wireand heavier, are shipped in flat sheets.Metric wire fabric is usually designated as follows: WWFfollowed by the spacing of longitudinal and transverse wiresin millimeters and then the areas of the individual longitudinaland transverse wires in square millimeters. Each wire area ispreceded by the letters “MW” for plain wire reinforcement(“W” only for U.S. customary units) or “MD” for deformedwire reinforcement (“D” only for U.S. customary units). 1.6.2—Fiber-reinforced polymer (FRP) bars FRP bars are sometimes used as an alternative to steeldeformed bars where corrosion of steel bars is likely or wheresensitive electrical or magnetic equipment might be affectedby a large amount of steel reinforcement. The development ofthe various fiber-reinforced polymer composites, or FRPs, hasoccurred over a number of decades and the materials continueto evolve. (Originally, the “p” in FRP stood for “plastic,” but“polymer” is now the preferred
term to avoid confusion.) FRPmaterials are available in many forms, including bars, tapes,cables, grids, sheets, and plates.FRP bars have several qualities that make them suitable asreinforcement for concrete: they thermally expand andcontract at a rate very close to that of concrete, they do not rust,and they have a very high strength-weight ratio. In addition,FRP is nonmagnetic. The main FRP benefit for the constructionindustry is durability, as FRP composites do not rust. Assuch, bridges and paper and chemical plants have been themost common applications for FRP bars used to date. Theelectrical insulating properties are important in certain highlyspecialized applications, the best known being magnetic resonanceimaging (MRI) equipment. Other benefits of FRPcomposites include light weight, high strength and highmodulus, electromagnetic permeability, and impact resistance.Disadvantages of FRP bars include their brittle nature(they do not stretch as far as steel bars before breaking), theirsusceptibility to damage from ultraviolet light, and the factthat they cannot be field-bent. 1.6.3 Fiber reinforcement Fiber-reinforced concrete (FRC) is concrete with the additionof discrete reinforcing fibers made of steel, glass, synthetic(nylon, polyester, and polypropylene), and natural fiber materials.At appropriate dosages, the addition of fibers mayprovide increased resistance to plastic and drying shrinkagecracking, reduced crack widths, and enhanced energy absorptionand impact resistance. The major benefit derived from theuse of FRC is improved concrete durability.Common lengths of discrete fibers range from 10 mm (3/8in.) to a maximum of 75 mm (3 in.). They are normally addedto the concrete during the batching operation but alternatelycan be added at the job site. It is important that sufficientmixing time be provided after fibers are added to a mixture. (Aminimum of 4 minutes may be required with a transit mixingdrum spinning at mixing speed. In precast and central mixingplants, mixing efficiency is much higher and mixing time isreduced to as little as 90 seconds.)Synthetic fibers can be delivered to the mixing system inpreweighed, degradable bags that break down during themixing cycle. Steel fibers are introduced to the rotating mixervia conveyor belt, either at the same time as the coarse aggregate,or on their own after all the conventional ingredientshave been added. Placement and finishing operations for FRC are comparableto those used for concrete without fibers. 1.6.4 Materials for repair and strengthening ofstructural concrete members Strengthening a structural concrete member after it is builtusually involves removing and replacing concrete, attachingadditional material to the member, or wrapping the member inanother material. Strengthening by adding reinforcing bar or prestressing reinforcement(external to the member) uses materials coveredelsewhere in this document. 4.1 External steel reinforcement—Structural steel platesor structural shapes can be used to externally reinforceconcrete members. Depending on the application, plates,structural shapes
or prestressed steel straps can be attached tothe member with bolts, epoxy, or both. Care must be exercisedwhen using epoxy to prevent damage by exposure to ultravioletlight. Bolts can either go through the member or be secured indrilled holes with epoxy. For beam repairs, plates or channelsare frequently attached to the bottom or both sides of thebeam, or where all sides of the beam are accessible, the beamcan be wrapped and prestressed with steel straps. Both thebending and shear strength of the beam can be increased bythese methods. For columns, plates are commonly placed onall sides to form a continuous shell or jacket, increasing theductility and/or shear strength of the column. This is particularlycommon when retrofitting columns to resist earthquakeforces. These jackets can be square, rectangular, round, or ovalshaped. When the shape of the jacket is not identical to theshape of the column, the annular space—the space betweenthe steel shell and the concrete column—is usually filled witha cementitious grout. Cracked walls can be repaired byattaching steel plates or a series of channels to the face of thewall, or by “stapling” the crack with a series of C-shaped reinforcingbars doweled into the face of the wall on either side ofthe crack. 4.2 FRP plates, sheets, and jackets—Several types ofglass, carbon, or aramid fiberreinforced polymer (FRP)composites are used to strengthen concrete members. FRPsheets come in two forms, precured laminates (that is, rigidplates) that can only be applied to flat surfaces, and thin sheetsthat can either be attached to flat surfaces or wrapped around columns or beams by in-place impregnation withresin (manual lay-up). In either case, they are typicallyattached to the concrete with epoxy. Rigid plates are mostcommonly attached to the bottom of beams to increase flexuralapacity, or to reduce deflections. Flexible sheets can be usedto strengthen flexural members. They are also used for shearstrengthening or confinement of round or rectangularmembers, particularly columns and beams. In confinementapplications, the sheets are usually continuously wrappedaround the member to form a jacket that increases the strength,ductility, and shear capacity. Sheets can also be applied towalls and floor slabs to increase bending strength and in-planeshear capacity, as well as to reduce deflections. 1.6.5 Type of Steel Bars Mild steel bars (as per IS: 432, part-I -1982) Mild steel bars are used for tensile stress of RCC (Reinforced cement concrete) slab beams etc. in reinforced cement concrete work. These steel bars are plain in surface and are round sections of diameter from 6 to 50 mm. These rods are manufactured in long lengths and can be cut quickly and be bent easily without damage. Deformed steel bars (as per IS: 1786-1985) As deformed bars are rods of steels provided with lugs, ribs or deformation on the surface of bar, these bars minimize slippage in concrete and increases the bond between the two materials. Deformed bars have more tensile stresses than that of mild steel plain bars. These bars can be used without end hooks. The deformation should be spaced along the bar at substantially uniform distances.
To limit cracks that may develop in reinforced concrete around mild steel bars due to stretching of bars and some lose of bond under load it is common to use deformed bars that have projecting ribs or are twisted to improve the bond with concrete. These bars are produced in sections from 6 mm to 50 mm dia.In addition the strength of bonds of deformed bars calculated should be 40 to 80 % higher than that of plain round bars of same nominal size. And it has more tensile stress than that of plain round bars of same nominal size.Cold twisted deformed (Ribbed or Tor Steel Bars) bars are recommended as best quality steel bars for construction work by structural Engineer. 1.6.5.1 Various Grades of Mild Steel Bars Reinforcement bars in accordance with standard IS No. 432 part-I can be classified into following types. 1) Mild Steel Bars: Mild steel bars can be supplied in two grades a)Mild steel bars grade-I designated as Fe 410-S or Grade 60 b) Mild steel bars grade-II designated as Fe-410-o or Grade 40 2) Medium Tensile Steel Bars designated as Fe- 540-w-ht or Grade 75
1.6.5.1 Physical Requirement: Grade II Mild steel bar are not recommended for use in structures located in earth quake zones subject to severe damage and for structures subject to dynamic loading (other than wind loading) such as railways and highways bridges. Every lot or consignment of mild steel bars brought at the site of work should be tested in laboratory before use in the work. However for small work one can use mild steel bars on the basis of verifying tests results made by manufacturer in his own laboratory; which are available with supplier. Some of manufacturers stamped MS bars grade with their make /name and also give certification of test and grade. On the basis of the above information you can store mild steel bars grade-wise at the site of work. 1.6.5.2 Steel Bars for RCC Work All finished steel bars for reinforced work should be neatly rolled to the dimension and weights as specified. They should be sound, free from cracks, surface flaws, laminations, rough, jagged and imperfect edges and other defects. It should be finished in a work manlike manner.
Column made of steel bars 1.6.5.3 General precautions for steel bars in reinforcement •
Steel bars are clear, free from loose mil scales, dust and loose rust coats of paints, oil or other coatings which may destroy or reduce bond strength.
•
Steel bars should be stored in such a way as to avoid distortion and to prevent deterioration and corrosion.
•
Steel bars should not be clean by oily substance to remove the rust.
•
The bar is bent correctly and accurately to the size and shape as shown in drawings.
•
If possible, the bar of full length is used.
•
Overlapping bars do not touch each other and these should be kept apart with concrete.
•
The overlap if given should be staggered.
•
The cranks in the bar at the end should be kept in position by using spots.
•
The steel bars should not be disturbed while lying cements concrete.
•
Required cover under steel bars should be given before laying the cement concrete.
•
No over lap is given in the bar having a diameter more than 36 mm, if required, the bar should be welded.
1.6.5.4 Weight of Different Steel Bars When we want to purchase Mild steel members from the market, the shopkeeper quotes the price of steel members in weight. When any type of steel members for use in house construction is required, we calculate the length of steel member in feet or meter but we are ignorant about the weight of steel. Here are details of weight per meter for various types of steel members:This will help us for estimated weight and cost. It will also help at the time of purchase to avoid pilferage in weight. M S Steel round & square Bar Sr.No.
Dia of steel bar
Weight per meter Round Bar
Square Bar
a
6 mm
0.22 Kg.
0.28 Kg
b
8 mm
0.39 Kg
0.50 Kg
c
10 mm
0.62 Kg
0.78 Kg
d
12 mm
0.89 Kg
1.13 Kg
e
16 mm
1.58 Kg
2.01 Kg
f
20 mm
2.46 Kg
3.14 Kg
g
25 mm
3.85 Kg
4.91 Kg
h
28 mm
4.83 Kg
6.15 Kg
i
32 mm
6.31 Kg
8.04 Kg
j
36 mm
7.99 Kg
10.17 Kg
k
40 mm
9.86 Kg
12.56 Kg
l
45 mm
12.49 Kg
15.90 Kg
m
50 mm
15.41 Kg
19.62 Kg
1.6.6 Structural Steel: This specification covers steel sections, plates and bars of the following categories for use in structural work:-
1.6.7 Quality of Finished Structural steel All finished steel subject to tolerances should be fine and rolled cleanly to the dimension, sections and weights specified. The finished material should be free from cracks, surface flaw lamination rough, jagged and imperfect edges and all other defects. The material should comply in all respects with the test and requirements mentioned in INDIAN standard 226, applicable to the material (Members, sections, plates and bars.) specified or required.
Structure Steel
S.No
Steel Designation
Purpose for which intended
1.
A
In structures subject to dynamic loading and other special cases.
2.
B
In structures not subject to dynamic loading.
3.
C
In structures subject to dynamic loading and when special welding jobs are involved.
The following varieties of steel should be used for structural purposes. •
S.T 42-S: The standard quality steel designated as ST-42, confirming to IS: 226 should be used for all types of structures (riveted or bolted) including those subject to dynamic loading and where fatigue, wide fluctuation of stress and reversal of stress
are involved, as for example: - Girders, Crane Gantry, road and railway bridges etc. It is also suitable for welding up to 200 mm thick material. •
S.T 42-W: The fusion welding quality steel designated as ST 42 W confirming to IS: 2062 is used for the structures subject to dynamic loading.
•
S.T 42-O: The ordinary quality steel designated as ST 42-O confirming to IS: 1977 is used for the structures not subject to dynamic loading, other than wind load where welding is not used.
•
S.T 32-O: This ordinary quality of steel designated as ST 32-O confirming to IS: 1977 is used for door window frames, grills, steel gates, building hardware fencing etc.
Mild steel and medium tensile steel bars for concrete reinforcement The specification covers requirement and methods of the test for rolled mild steel and medium tensile steel bars in round and square sections.
1.6.7 TMT Steel bar Tolerance of medium tensile steel for Construction Work The bars should be rolled up to following tolerances. S. No.
Diameter of Bar(mm)
Total Tolerances(mm)
1.
19 and below
0.4
2.
20 and 21
0.45
3.
22,23 and 24
0.5
4.
25 and over
2% of dia.
Quality of Finished medium tensile steel: The following points ensure the quality of finished steel for construction work. •
All finished steel should be fine and rolled cleanly to the dimension and should have weight as specified by BIS subject to permissible tolerance.
•
The finished material should be free from cracks, surface flaws laminations, rough and imperfect edges and other harmful defects.
•
Steel section should be free from excessive rust, scaling and tilting and be well protected.
1.6.7.1Pipes made of mild steel Manufacturing of steel: All type of steel should be manufactured by open hearth, electric, duplex or by acid Bessemer process or by a combination of the processes. 1.7 Assumption in the theory of simple bending for RCC beam In engineering mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam. A closet rodsagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A large diameter, but thin-walled, short tube supported at its ends and loaded laterally is an example of a shell experiencing bending. In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. To make the usage of the term more precise, engineers refer to
the bendiing of rods, the bending of beams, thhe bending of o plates, thee bending off shells and sso on. Quasistattic bending of o beams A beam deforms d and d stresses develop insidee it when a transverse t looad is applied d on it. In thhe quasistatiic case, the amount of bendingdefle b ection and th he stresses that t develop p are assumeed not to change over tim me. In a horrizontal beam m supported at the ends and loaded downwards d i in the midddle, the mateerial at the ovver-side of tthe beam is compressedd while the material m at thhe undersidee is stretched d. There are two forms oof internal sttresses causeed by lateral loads:
Shear stress parallel p to thhe lateral loaading plus complementa c ary shear strress on planees perpendicularr to the load direction;
Direct comprressive stresss in the uppeer region off the beam, aand direct teensile stress in D i thhe lower region of the beeam.
These lasst two forces form a couuple or mom ment as they are equal inn magnitude and opposite in directiion. This bending momeent resists thhe sagging deformation d m characteristtic of a beam experienccing bendin ng. The stresss distributioon in a beam m can be ppredicted quiite accuratelly even wheen some sim mplifying assu umptions aree used. 1.7.1 Euller-Bernoullli bending theory t Element of a bent beeam: the fibbers form cooncentric arccs, the top fiibers are com mpressed annd bottom fiibers stretched.
Bending moments in n a beam In the Euuler-Bernoullli theory off slender beaams, a majo or assumptioon is that 'pplane sectionns remain plane'. p In other words, any deform mation due to shear across a the section is noot accounteed for (no shhear deformaation). Also, this linear distributionn is only appplicable if thhe maximum m stress is less l than thee yield stresss of the matterial. For sttresses that exceed yield,
refer to article plastic bending. At yield, the maximum stress experienced in the section (at the furthest points from the neutral axis of the beam) is defined as the flexural strength. The Euler-Bernoulli equation for the quasistatic bending of slender, isotropic, homogeneous beams of constant cross-section under an applied transverse load q(x) is
where E is the Young's modulus, I is the area moment of inertia of the cross-section, and w(x) is the deflection of the neutral axis of the beam. After a solution for the displacement of the beam has been obtained, the bending moment (M) and shear force (Q) in the beam can be calculated using the relations
Simple beam bending is often analyzed with the Euler-Bernoulli beam equation. The conditions for using simple bending theory are: 1. The beam is subject to pure bending. This means that the shear force is zero, and that no torsional or axial loads are present. 2. The material is isotropic and homogeneous. 3. The material obeys Hooke's law (it is linearly elastic and will not deform plastically). 4. The beam is initially straight with a cross section that is constant throughout the beam length. 5. The beam has an axis of symmetry in the plane of bending. 6. The proportions of the beam are such that it would fail by bending rather than by crushing, wrinkling or sideways buckling. 7. Cross-sections of the beam remain plane during bending. Deflection of a beam deflected symmetrically and principle of superposition Compressive and tensile forces develop in the direction of the beam axis under bending loads. These forces induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary linearly, there therefore exists a point on the linear path between them where there is no bending stress. The locus of these points is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse. Wide-flange beams (I-beams)
and truss girders effectively address this inefficiency as they minimize the amount of material in this under-stressed region. The classic formula for determining the bending stress in a beam under simple bending is:
where
σ is the bending stress
M - the moment about the neutral axis
y - the perpendicular distance to the neutral axis
Ix - the second moment of area about the neutral axis x
1.8 BASIC ASSUMPTIONS IN FLEXURE THEORY
Five basic assumptions are made: 1. Plane sections before bending remain plane after bending. 2. Strain in concrete is the same as in reinforcing bars at the same level, provided
that the bond between the steel and concrete is sufficient to keep them acting together under the different load stages i.e., no slip can occur between the two materials. 3. The stress-strain curves for the steel and concrete are known.
4. The tensile strength of concrete may be neglected. 5. At ultimate strength, the maximum strain at the extreme compression fiber is assumed equal to 0.003, by the Egyptian Code. The assumption of plane sections remaining plane (Bernoulli's principle) means that strains above and below the neutral axis NA are proportional to the distance from the neutral axis, Fig. 1.1. Tests on reinforced concrete members have indicated that this assumption is very nearly correct at all stages of loading up to flexural failure, provided good bond exists between the concrete and steel. This assumption, however, does not hold for deep beams or in regions of high shear.
FIGURE 1.1. Single reinforced beam section with strain distribution.
1.9 BEHAVIOR OF A REINFORCED CONCRETE BEAM SECTION LOADED TO FAILURE
To study the behavior of a reinforced concrete beam section under increasing moment, let us examine how strains and stresses progress at different stages of loading:
1.9.1 Noncracked, Linear Stage
As illustrated in Fig. 1.2, where moments are small, compressive stresses are very low and the maximum tensile stress of concrete is less than its rupture strength, fctr. In this stage the entire concrete section is effective, with the steel bars at the tension side sustaining a strain equal to that of the surrounding concrete (
) but the
stress in the steel bars is equal to that in the adjacent concrete multiplied by the modular ratio n. Utilizing the Transformed Area Concept, in which the steel is transformed into an equivalent concrete area , the conventional elastic theory may be used to analyze the "all concrete" area in Fig. 1.2.
FIGURE 1.2. Transformed section for flexure before cracking. This stage should be considered as the basis for calculating the cracking moment Mcr, which produces tensile stresses at the bottom fibers equal to the
modulus of rupture of concrete, Fig. 1.3. The Egyptian Code recommends the flexural formula M/Z to compute the flexural strength of the section:
(1.1a)
where
is the moment of inertia of gross concrete section about the centroidal
axis, neglecting the reinforcement, yt is the distance from the centroidal axis of cross section, neglecting steel, to extreme fiber tension andfctr is the modulus of rupture of concrete. The Egyptian code (ECCS) suggests an imperical formula relates the modulus of rupture of concrete to its compressive strength: N/mm2
(1.1b)
FIGURE 1.3. Transformed section for flexure just prior to cracking.
1.9.2 Cracked, Linear Stage
When the moment is increased beyond Mcr, the tensile stresses in concrete at the tension zone increased until they were greater than the modulus of rupture fctr, and cracks will develop. The neutral axis shifts upward, and cracks extend close to the level of the shifted neutral axis. Cracked concrete below the neutral axis is assumed to be not effective and the steel bars resist the entire tensile force. The stress-strain curve for concrete is approximately linear up to 0.40 fcu; hence if the concrete stress does not exceed this value, the elastic (straight line) theory formula M/Z may be used to analyze the "all concrete" area in Fig. 1.4.
FIGURE 1.4. Transformed section for flexure somewhat after cracking.
1.9.3 Cracked, Nonlinear Stage For moments greater than these producing stage 2, the maximum compressive stress in concrete exceeds 0.40 . However, concrete in compression has not crushed. Although strains are assumed to remain proportional to the distance from the neutral axis, stresses are not and, therefore, the flexural formula M/Z of the conventional elastic theory cannot be used to compute the flexural strength of the section. The Internal Couple Approach, instead, will be used to compute the section strength. This approach allows two equations for equilibrium, for the analysis and design of structural members, that are valid for any load and any section. As Fig. 1.5 indicates, the compressive force C should be equal to the tensile force T, otherwise the section will have a linear displacement plus rotation. Thus,
C=T
(1.2a)
The internal moment is equal to either the tensile force T multiplied by its arm yct or the compressive force C multiplied by the same lever arm. Thus, (1.2b)
FIGURE 1.5. Transformed section for flexure after cracking. The resultant internal tensile force T is given by
(1.3)
where is the area of steel and is the steel stress. The resultant internal compressive force is obtained by integrating the stress block over the area bc. Taking an infinitesimal strip dy of area dA equals b by dy, located at a distance y from the neutral axis and subject to an assumed uniform compressive stress f and strain X the compressive force C is given by (1.4)
This stage may be considered as the basis for calculating the flexural strength of the section at first yield of the tension steel (known as the yield moment When the tension steel first reaches the yield strain (
).
), the strain in the extreme
fiber of the concrete may be appreciably less than 0.003. If the steel reaches the yield strain and the concrete reaches the extreme fiber compression strain of 0.003, simultaneously, the yield moment occurs and equals the ultimate moment Mu. Otherwise, if the concrete crushed before the steel yields, the yield moment will never take place.
1.9.4 Ultimate Strength Stage
For the given section, when the moment is further increased, strains increased rapidly until the maximum carrying capacity of the beam was reached at ultimate moment Mu. The section will reach its ultimate flexural strength when the concrete reaches an extreme fiber compression strain Xcu of 0.003 and the tensile steel
strain Xs cloud have any value higher or lower than the yield strain . As Fig. 1.6 indicates, the compressive forces C1 and C2 are obtained by integrating the parabolic and rectangular stress blocks over the rectangular areas A1 and A2 of
and
, respectively.
FIGURE 1.6. Single reinforced beam section with flexure at
ultimate. The corresponding lever arms y1 and y2 are given by
The resultant force C is, then, computed from (1.5)
The position of C is at a distance y from the top fiber where y is computed from
The distance between the resultant internal forces, known as the internal lever arm, is
yct = d - 0.4 c
(1.6)
where d, the distance from the extreme compression fiber to the centroid of the steel area, is known as the effective depth. The ultimate strength Mu is therefore (1.7)
1.10 EQUIVALENT RECTANGULAR COMPRESSION STRESS BLOCK As a means of simplification, the Egyptian Code has suggested the replacement of the actual shape of the concrete compressive stress block (a second-degree parabola up to 0.002 and a horizontal branch up to 0.003) by an equivalent rectangular stress block, Fig. 1.7.
FIGURE 1.7. Actual and equivalent stress distribution at
failure.
A concrete stress of
is assumed uniformly distributed over an
equivalent compression zone bounded by the edges of the cross section and a line
parallel to the neutral axis at a distance from the fiber of maximum compressive strain, where c is the distance between the top of the compressive section and the neutral axis NA. For the resultant compressive forces of the actual and equivalent stress blocks of Fig. 1.7, to have the same magnitude and line of action, the average stress of the equivalent rectangular stress block and its depth are
and
where and . These values are as already derived when calculating the ultimate strength Mu in Section 1.4.4. The equivalent rectangular stress block applies, as the Egyptian Code permits, to rectangular, T and trapezoidal sections, Fig. 1.8.
FIGURE 1.8. Applicability of equivalent rectangular stress block to some
sections. For sections as shown in Fig. 1.9, stress distribution should be based on the actual stress-strain diagram. The above procedure, however, can be implemented to
obtain the parameters
and
that correspond to these sections.
FIGURE 1.9. Inapplicability of equivalent rectangular stress block to some sections. 1.11 TYPES OF FLEXURAL FAILURE
The types of flexural failure possible (tension, compression and balanced) and the nominal (ideal) strength Mu of the beam section (a singly reinforced rectangular section) are discussed next.
1.11.1 Tension Failure If the steel content of the section is small (an under-reinforced concrete section), the steel will reach its yield strength before the concrete reaches its maximum capacity. The flexural strength of the section is reached when the strain in the extreme
compression fiber of the concrete is approximately 0.003, Fig. 1.10. With further increase in strain, the moment of resistance reduces, and crushing commences in the compressed region of the concrete. This type of failure, because it is initiated by yielding of the tension steel, could be referred to as a "primary tension failure," or simply "tension failure." The section then fails in a "ductile" fashion with adequate visible warning before failure.
FIGURE 1.10. Single reinforced section when the tension failure is reached.
For a tension failure,
; for equilibrium, C = T. Hence from from
and
we have
which results in (1.8)
The nominal strength Mu (which obtained from theory predicting the failure of the section on assumed section geometry and specified materials strengths i.e., 1.0), is
=
=
(1.9)
1.11.2 Compression Failure If the steel content of the section is large (an over-reinforced concrete section), the concrete may reach its maximum capacity before the steel yields. Again the flexural strength of the section is reached when the strain in the extreme compression fiber of the concrete is approximately 0.003, Fig. 1.11. The section then fails suddenly in a "brittle" fashion if the concrete is not confined and there may be little visible warning of failure.
FIGURE 1.11. Single reinforced section when the compression
failure is reached.
For a compression failure, as the steel remains in the elastic range. The steel stress may be determined in terms of the neutral axis depth considering the similar triangles of the strain diagram of Fig. 1.11.
(1.10)
The steel stress is (1.11a)
or, since Es = 200 kN/mm2, (1.11b)
For equilibrium, , hence (1.12)
The above quadratic equation may be solved to find c and, on substituting a = 0.8c, the nominal strength is (1.13)
1.11.3 Balanced Failure At a particular steel content, the steel reaches the yield strength and the concrete reaches its extreme fiber compression strain of 0.003, simultaneously, Fig. 1.12. Then, can write
and from the similar triangles of the strain diagram of Fig. 1.12 we
(1.14)
where
= neutral axis depth for a balanced failure. Then (1.15)
or, on substituting
= 0.80
, Eq. 1.15 becomes (1.16)
FIGURE 1.12. Single reinforced section when the balanced failure is reached. For equilibrium, ; hence we have (1.17)
which results in
(1.18)
where
is the balanced steel ratio.
The type of failure that occurs will depend on whether the steel ratio (where
=
) is less than or greater than
. Figure 1.13 shows the strain
profiles at a section at the flexural strength for three different steel contents. As Fig. 1.13 indicates, if for the section
is less than
tension failure occurs. Similarly, if and a compression failure occurs.
, then c < cb and
is greater than
; hence a
, then c > cb and
,
FIGURE 1.13. Strain profiles at the flexural strength of a section.
1.12 RCC Singly Reinforced Beams-working stress method To do the design of the structures we have different methods but here I am going to discuss here with you the working stress method of design of the singly reinforced beams. Singly reinforced rectangular beams are the beams which are reinforced either at the top or at the bottom. Reinforcement is provided at top in case of the cantilever beams otherwise we provide the reinforcement generally at the bottom. There are few assumptions in this method and some of the most important are: All the tension is taken up by the reinforcement provided, so the tensile force of the concrete in the tensile section is ignored. 1.12.1Critical Neutral Axis(Xc): Location of the Critical neutral axis is found out using the geometrical relations between the stresses in the compression side and the tensile sides, which are assumed to vary linearly with the depth of the beam. Stresses are zero at the critical neutral axis and compressive on one side and tensile on the other varying linearly. So there are two similar triangles formed and one can find out the location of the neautral axis using the relations between the various sides of the similar triangles. Xc= mc/(t+mc) * d here, Xc= Critical Neutral axis m= modular ratio = 280/(3*compressive stress in concrete in bending) c= maximum compressive stress in concrete d= effective depth of the beam section 1.12.2 Actual Neutral axis(Xa): Actual neutral axis of the section may be found by equating the moment of the areas on the two sides of the neutral axis about the neutral axis. On the compressive side the area of the concrete is considered and on the tensile side the equivalent area of the steel reinforcement is taken and its moment is taken about the neutral axis. By equating the two we can get the actual neutral axis. Balanced Section: When Xa=Xc, it is a balanced section (c'=c, ta=t) Over-reinforced section: When Xa>Xc, it is a over- reinforced section (c'= c, ta< t)
Under-reinforced section: when Xa
(c'
where, (Xa= Actual neutral axis, Xc=Critical Neutral Axis c'- actual compressive stess in concrete, c- maximum compressive stress in concrete, ta= actual tensile stress in steel, t= maximum tensile stress in steel) Questions 1. Explain the various types of reinforcing materials? 2. Find the flextural strength of a singly reinforced beam? 3. What are under reinforced over reinforced sections? 4. Find the Shear strength of singly reinforced RCC beam? 5. Briefly describe Reinforced Cement Concrete? 6. Describe the properties of different types of steel?
UNIT 2 Structure of this unit Bond in RCC beams, Doubly Reinforced Concrete Beams, RCC Slabs Objectives to be learned 1. Concept of bond local and average bond 2. Permissible bond stresses for plain and deformed bars as per IS code of practice 3. Minimum length of embedment of bars 4. Actual bond stress in RCC Beams 5. Bond length (standard hook, slice length as per IS code of practice) 6. Loads and loading standards for beams as per IS_875 7. Design of singly reinforced concrete beam as per IS code of practice from the given data such as span, load and properties of materials used. 8. Design of lintel 9. Design of main/secondary beam for a RCC flat roof and floor 10. Design of a cantilever beam/slab 11. Doubly reinforced concrete beam and its necessity 12. Strength of a doubly reinforced concrete beam section
13. Design of a doubly reinforced concrete beam 14. Structural behaviour of slabs under UDL 15. Type of end supports 16. Design of one way slab 17. Design of two slab with the help of tables of IS:456
2.1 Bond in RCC beams Reinforcement for concrete to develop the strength of a section in tension depends on the compatibility of the two materials to act together in resisting the external load. The reinforcing element, such as a reinforcing bar, has to undergo the same strain or deformation as the surrounding concrete in order to prevent the discontinuity or separation of the two materials under load. The modulus of elasticity, the ductility, and the yield or rupture strength of the reinforcement must also be considerably higher than those of the concrete to raise the capacity of the reinforced concrete section to a meaningful level. Consequently, materials such as brass, aluminum, rubber, or bamboo are not suitable for developing the bond or adhesion necessary between the reinforcement and the concrete. Steel and fiber glass do possess the principal factors necessary: yield strength, ductility, and bond value. Bond strength results from a combination of several parameters, such as the mutual adhesion between the concrete and steel interfaces and the pressure of the hardened concrete against the steel bar or wire due to the drying shrinkage of the concrete. Additionally, friction interlock between the bar surface deformations or projections and the concrete caused by the micro movements of the tensioned bar results in increased resistance to slippage. The total effect of this is known as bond. In summary, bond strength is controlled by the following major factors: 1. Adhesion between the concrete and the reinforcing elements 2. Gripping effect resulting from the drying shrinkage of the surrounding concrete and the shear interlock between the bar deformations and the surrounding concrete 3. Frictional resistance to sliding and interlock as the reinforcing element is subjected to tensile stress 4. Effect of concrete quality and strength in tension and compression 5. Mechanical anchorage effect of the ends of bars through development length, splicing, hooks, and crossbars 6. Diameter, shape, and spacing of reinforcement as they affect crack development The individual contributions of these factors are difficult to separate or quantify. Shear interlock, shrinking confining effect, and the quality of the concrete can be considered as major factors.
2.1.1 Bond Stress Development Bond stress is primarily the result of the shear interlock between the reinforcing element and the enveloping concrete caused by the various factors previously enumerated. It can be described as a local shearing stress per unit area of the bar surface. This direct stress is transferred from the concrete to the bar interface so as to change the tensile stress in the reinforcing bar along its length.
2.1.2 Local Bond Effects near Cracks
Main Reinforcing Bars:
Deformed Bars
(assume no bond) -- Beam acts as a tied arch, will not collapse
-- Stress in stell is maximum only over a short section – less elsewhere
Tension in bars is uniform and equal
much smaller total deflection
T =Mmax/Z
Cracks are distributed, narrow
Linear total deformation results in large beam deflection, large cracks
2.2 Bond Failure Bond failure is likely to occur near ends of beams, where high flexural bond stresses can combine with high local bond stresses.
Bond failure may take two forms, both of which result from wedging action as the bar is pulled relative to the concrete and often acts in concrete with shear crack and often acts in concrete with shear crack.
Tests at N.B.S. (National Bureau of Standards) and University of Texas indicate that bond failure will occurwhen bond forceUreaches a critical value. It is interesting to note that at failure, the force U is independent of bar size. Consistent with concept of “wedge action”, when splitting force depends on driving force, not wedge width.
wedge action is when the ribs of deformed bars, bears against the concrete. Tests have shown that for single bars causing vertical splits or for bars spaced further than 6 inches apart. For bars spaced less than 6 inches apart, (causing horizontal splitting)
Horizontal crack Un= 0.80×35 fc′ = 28 fc′ Ultimate average bond force per inch of length of Bar In terms of stresses rather than forces
2.2.1 Development Length Consider a beam similar to that used to obtain the results above:
Ts= Abfs= Ul(Average bond force per inch ) * length or U =Ts/l =Abfs/l Average bond force per unit length We may also solve for l to obtain the critical development length. ld=Abfs/Un Un is the ultimate bond force per unit length Two criteria control development length calculation: 1) Bond must be counted on to develop bar yield force (fs = fy) 2) Average ultimate bond force is limited to 35sqrt(f’c) or 28sqrt(f’c) for spacing of greater than 6 inches
If these lengths are provided, bond failure will not occur, obviously, small bars have less bond problem than large bars. Smaller bars require less development length because Ab= π d2b/4 therefore, the development length, ld, is proportional to squared of bar diameter. the smaller the bar diameter the smaller will be the required development length. According to ACI, the development length for design is obtained by a basic development length as given above and then it is modified by a series of modification factors. 2.3 Determining Proper Anchor Length The length and load capacity of rock and soil anchor systems is dependent on many variables. Some of these variables are rock or soil properties, installation methods, underground or
overhead obstructions, existing structures, right of way and easement limitations, anchor material strength and anchor type. Topics such as these should be evaluated during an anchor feasibility study prior to final anchor design. Final embedment depths should be determined on a project to project basis after reviewing rock or soil samples, previous experience and geological data. On-site anchor tests are generally the best way to accurately determine anchor lengths and capacities for the given geological conditions. 2.3.1 Free-Stress Length Pre-stressed or post-tensioned earth anchors must be designed with a free-stress length. This is the portion of the anchor length that does not provide anchorage to the soil or rock during the stressing procedure. The purpose of the free-stress length is to allow the installer to transfer an immediate anchor load directly to a specific location in the soil or rock. For instance, when designing tie back anchors, the free-stress length should be long enough to transfer the pre-stress load behind the predicted failure plane of the soil or rock mass. The free-stress length also helps to minimize load loss due to movement at the anchor head during load transfer from the stressing jack. The Post Tensioning Institute recommends that for prestressed rock or soil anchors utilizing steel bars, the free-stress length shall be a minimum of 10 feet, and for steel strand a minimum of 15 feet due to greater seating losses. PTI recommendations on free-stress length are based on anchors utilizing high strength posttension steel and often have relatively high design loads. Lighter load pre-stressed mechanical rock anchors have been successfully designed and installed with overall lengths shorter than 10 feet in high quality rock. 2.3.2 Mechanical Rock Anchor Lengths One method that is used to estimate the embedment depth for mechanical rock anchors such as Williams Spin-Lock system is based on rock mass pullout capacity. The mass of rock mobilized in uplift is approximately conical in shape and often is angled outward from the longitudinal axis of the rock anchor between 15 and 60 degrees depending on the site's structural geology. The pullout capacity of the cone is a function of the weight of the cone and the shear resistance of the rock along the surface of the cone. Rock anchors are typically designed with embedments deep enough to ensure ductile failure of the steel bar. Mathematically, by setting the anchors ultimate steel capacity equal to the pull out capacity of the rock failure cone and applying necessary safety factors, a designer can estimate anchor embedment depth. Some designers neglect shear resistance and only use the weight of the cone for rock mass pullout resistance. This will typically provide a conservative anchor design.
The length of a mechanical rock anchor can be shorter than a cement grout or resin bond system since the load is being transferred by a mechanical head assembly rather than a grout or resin bond length. Therefore, the free-stress length plus the length of the mechanical head assembly makes up the embedment depth of the mechanical rock anchor. When anchors require couplers for longer lengths, Williams recommends the use of a hollow bar Spin-Lock
for ease of grouting. Williams lists useful design charts which tabulate anchor steel capacity based on corresponding anchor diameters and recommended safety factors. This section also reviews installation procedure and provides detailed information on Spin-Lock accessories and components. R= Radius of cone base H= Height of cone L= Incline length of cone V=
Volume of cone (right angle cone) = (1/3)( )(R²)(h)
S=
Rock shear resistance multiplied by the rock cone interface surface area
FS= Factor of Safety (.5 for a 2:1 Safety Factor) Y= Unit Weight of rock (approx. 150 pcf dry) Mechanical Assembly
Head U= Ultimate tensile strength of anchor rod O= Cone Angle P= Applied Design Load = 3.14 [(V)(Y) + S] > P < [ U / FS ]
Mechanical Soil Anchor Lengths Williams Form Engineering offers the Manta Ray and Stingray mechanical soil anchors. Manta Ray anchors can hold a maximum of 20,000 lbs, depending on soil properties and size of the Manta Ray head assembly. Their advantage is ease of installation, as no drilling or grouting is typically required. The anchor is simply driven into the soil with a driving hammer. 2.3.3 Bonded Rock Anchor Lengths Embedment depths for pre-stressed resin or cement grout bonded rock anchors are often determined by using the rock cone method as described under Mechanical Rock Anchor Lengths. However, unlike the mechanical anchor, the bonded anchor must also include a bond length in the embedment depth. The bond length allows the applied tensile load to be
transferred to the surrounding rock. Therefore the embedment depth of a prestressed bonded rock anchor is made up of the free-stress length and the bond length. When using the rock cone method, a conservative approach would be to assume the pullout cone starts at the top of the bond zone. The bond length can be estimated by using the following equation, however test anchors are generally the best way to determine anchor embedments and capacities. Typical values shown below are from the Post-Tensioning Institute. They are not meant to be used for final design. Final bond stresses should be determined after the review of sample cores, previous experience and geological data. Ultimate Grount/Bond Stress Estimates for Various Rock (from PTI) Granite and Basalt
250-450 psi
Dolomitic Limestone
200-300 psi
Soft Limestone
150-200 psi
Slates and Hard Shales
120-200 psi
Soft Shales
30-120 psi
Sandstones
120-250 psi
Concrete
200-400 psi
Average Ultimate Bond Stress Estimates for Various Rock P= =
Design Load for the anchor 3.14
D=
Diameter of the drill hole
Lb=
Bond Length
Tw= Working bond stress along the interface between the rock and grout (The working bond stress is normally 50 percent or less of the ultimate bond stress.) Note= The ultimate bond stress between the rock and the anchor grout is estimated by a value of 10% of the unconfined compressive strength of the rock, but not more than 450 psi (3.1 MPa). 2.3.4 Bonded Soil Anchor Lengths
Embedments for pre-stressed soil anchors consist of a 10 foot minimum free-stress length (for bar anchorages) and typically 20-40 feet of bonded length. Anchor drilling and grouting methods can have significant impact on soil bond stress values therefore final bond lengths are often determined by specialty anchor contractors. Shown below is a chart that can be used to estimate anchor bond length. This chart is for straight shaft anchors installed in small diameter holes using low grout pressure. However, final anchor capacity should be determined from field testing the anchors. For further guidance and recommendation on the design of pre-stressed bonded soil and rock anchors, refer to the Post-Tensioning Institutes manual on rock and soil anchors. Also refer to AASHTO for applicable publications.
Estimated Average Ultimate Bond Stress for Determining Soil/Grout Bond Lengths (taken from PTI) Cohesive Soil
Anchor Type
Cohesionless Soil Average Ultimate Bond Stress at Anchor Type Soil/Grout Interface (PSI)
Gravity Grouted Anchors 5 - 10 (straight shaft)
Gravity Grouted Anchors (straight shaft)
Pressure Grouted Anchors (straight shaft) - Soft silty Clay - Silty Clay - Stiff Clay, medium to high Plasticity - Very stiff Clay, medium to high Plasticity - Stiff Clay, medium Plasticity - Very stiff Clay, medium
Pressure Grouted Anchors (straight shaft) - Fine-medium Sand, medium dense - dense - Medium coarse Sand (w/Gravel), medium dense - Medium coarse Sand (w/Gravel), dense - very dense - Silty Sands - Dense glacial Till - Sandy Gravel, medium dense -
5 - 10 5 - 10 5 - 10 10-25 15 - 35 20 - 50 40 - 55
Average Ultimate Bond Stress at Soil/Grout Interface (PSI) 10-20
Plasticity - Very stiff sandy Silt, medium Plasticity
dense - Sandy Gravel, dense - very dense
2.4 Singly reinforced beam(Limit state method of design)
Different methods of design of RCC 1.Working Stress Method 2.Limit State Method 3.Ultimate Load Method 4.Probabilistic Method of Design 2.4.1 Limit state method of design •
The object of the design based on the limit state concept is to achieve an acceptable probability, that a structure will not become unsuitable in it’s lifetime for the use for which it is intended,i.e. It will not reach a limit state
•
A structure with appropriate degree of reliability should be able to withstand safely.
•
All loads, that are reliable to act on it throughout it’s life and it should also satisfy the subs ability requirements, such as limitations on deflection and cracking.
•
It should also be able to maintain the required structural integrity, during and after accident, such as fires, explosion & local failure.i.e. limit sate must be consider in design to ensure an adequate degree of safety and serviceability
•
The most important of these limit states, which must be examine in design are as follows Limit state of collapse - Flexur
- Compression - Shear - Torsion This state corresponds to the maximum load carrying capacity. 2.5 Types of reinforced concrete beams a)Singly reinforced beam b)Doubly reinforced beam c)Singly or Doubly reinforced flanged beams
2.5.1 Sin ngly reinforcced beam In singly reinforced simply s suppo orted beams or slabs reinnforcing steeel bars are placed near the bottom of the beaam or slabs where w they are a most effeective in resiisting the tennsile stressess.
x = Depthh of Neutrall axis b = breaddth of section n d = effective depth of section The depth of neutral axis can be obtained by consideringg the equilibrrium of the normal n forcees , that is, Resultantt force of coompression = average strress X area = 0.36 fcckbx Resultantt force of tennsion = 0.877 fy At Force of compression n should be equal to forcce of tensionn, 0.36 fckb bx = 0.87 fy At The distaance between n the lines of action of tw wo forces C & T is calleed the lever arm a and is denoted by b z. Lever arm m z = d – 0.4 42 x z = d – 0.42 z = d –(fy fy At/fck b) Moment of resistancee with respect to concrette = compresssive force x lever arm = 0.36 fcck b x z Moment of resistancee with respect to steel = tensile forcee x lever arm m = 0.87 fyy At z Maximu um depth off neutral axiis •
A compressioon failure is brittle b failurre.
•
The maximum T m depth of neutral n axis iis limited to ensure that tensile steel will reach its i yiield stress beefore concreete fails in coompression, thus a brittlee failure is avoided. a
•
The limiting values of thhe depth of nneutral axis xm for diffeerent grades of steel from T m sttrain diagram m.
g value of teension steel and momen nt of resistan nce Limiting •
Since the max ximum depthh of neutral axis is limiteed, the maxiimum value of moment of o reesistance is also a limited.
•
M Mlim with respect to concrete = 0.36 fck b x z
•
= 0.36 fck b xm x (d – 0.422 xm)
•
M Mlim with respect to steeel = 0.87 fck At (d – 0.422 xm)
Limiting g moment off resistance values, N m mm
Design of o a section Design of o rectangullar beam too resist a ben nding momeent equal too 45 kNm ussing (i) M155 mix and mild steel. The beam m will be dessigned so thaat under the applied mom ment both m materials reacch their maximum m stresses. Assume ratio of oveerall depth to t breadth oof the beam equal to 2. Breadth of o the beam = b Overall depth d of beam m=D thereforee , D/b = 2 For a baalanced desiign, Factored BM = mom ment of resisttance with reespect to conncrete = momen nt of resistan nce with resppect to steel = load faactor X B.M = 1.5 X 45 4 = 67.5 kN Nm For bala anced section, Moment of resistancee Mu = 0.366 fck b xm(d - 0.42 xm)
Grade for mild steel is Fe250
For Fe2550 steel, xm = 0.53d Mu = 0.336 fck b (0.553 d) (1 – 0.4 42 X 0.53) d = 2.22bdd Since D/b b =2 or, d/b = 2 or, b=d//2 Mu = 1.111 d Mu = 67..5 X 10 Nmm m d=394 mm m and b= 2000mm Adopt D = 450 mm , b = 250 mm m ,d = 415mm m
=(0.85xx250x415)/2550 = 353 m mm 353 mm
<
962 m mm
In beamss the diametter of main reinforced bbars is usually selected between 122 mm and 25 mm. Provide 2-20mm 2 andd 1-22mm baars giving total area =
6.28 + 3.80
=
10.008 cm > 9.62 cm
2.6 LINTELS 2.6.1 DEFINITION A lintel is a horizontal member which is placed across an opening to support the portion of the structure above it. The function of a lintel is just the same as that of an arch or a beam. However the lintels are easy and simple in construction. For an arch, or a beam. However the lintels are easy and simple in construction. For an arch. Special centering or form work is required. However the arches are suitable under the following circumstances: 1.
Loads are heavy,
2.
Span is more,
3.
Strong abutments or supports are available.
The ends of Lintels are built into the masonry and thus the load carried by lintels is transferred of the masonry in jambs. At present, the lintels of R.C.C are widely used to span the openings for doors, windows, etc in a structure. In generals, it should be seen that the bearing of lintel i.e. the distance up to which it is inserted in the supporting wall, should be the minimum of the following three considerations. Wall should be the minimum of the following three considerations. 1.
100 mm or
2.
Height of lintel; or
3.
One-tenth to one-twelfth of the span of lintel.
In this chapter, the topic of lintels will be discussed in detail.
2.6.2 MATERIALS FOR LINTELS The common materials used in the construction of lintels are as follows: 1.
Wood or timber lintels
2.
Stone lintels
3.
Brick lintels
4.
Steel lintels
5.
Reinforced cement concrete lintels.
1) Wood or timber lintels: These lintels consist of pieces of timber which are placed across the opening. The timber lintels are the oldest types of lintels and they have become obsolete except in hilly areas or places where timber is easily available. A single piece of timber can be used as a lintel or built-up sections may be formed as shown in fig. 18-1 and fig. 18-1, three timber pieces are bolted to serve as a lintel. Bolted to serve as a lintel. Fig. 18-2 shows a wood lintel composed of two timber pieces and two distances of packing pieces. The bolts are provided through the packing pieces as shown if the timber lintels are strengthened by the provision of mild steel plates at their top and bottom, they are known as the Fetched lintels. ) The important features of wood lintels are as follows:
1) A bearing of about 150 mm to 200 mm should be provided on the wall and the ends of lintel should be placed on mortar so as to create a level and firm bearing. 2) The width of lintel should be equal to the thickness of the opening and the depth of lintel should be about 1/12 to 1/8 of the span with a minimum value of 80 mm. 3) The wood lintels are liable to be destroyed by fire and also are liable to decay, if not properly ventilated. Hence sound and hard timber like teak should be used in the construction of wood lintels and a coat of suitable preservative should be applied. 4) The wood lintels are comparatively weak and relieving arches of brick or stone should therefore be provided as shown in fig 17-5 and fig. 17-14. 5)
The wood lintels help in securing the beads of frames of timber doors and windows.
6) If wood lintel is to be sued for larger spans, it is necessary to design it as a timber beam simply supported at its ends. 2) Stone Lintels: These lintels consist of slabs of stones which are placed across the openings. The stone lintels may be formed of a single piece or more than one piece. The stone lintels are not generally favoured mainly due to the following reasons: I. The stone possesses low tensile resistance. Hence the relieving arches are to be provided when the span exceeds I m. Otherwise the depth of stone lintel becomes considerable. The depth of stone lintel should be at least one mm per ten mm length of the opening. II. The stone cracks when subjected to the vibratory loads. Hence the stone lintels should be used with caution where shock waves are likely to occur frequently. III. It is difficult sot obtain a good stone of required depth. Hence the stone is not available. Moreover the stone which are to be used for lintels.Are to be properly dressed on site of work. This will increase the cost of work 2) Brick Lintels : These lintels consist of bricks which are generally placed on end or edge as shown in fig. A better way of providing and of a brick lintel is shown in fig. 18-4 The important features of brink lintels are as follows : I. The bricks should be well –burnt, copper-coloured, free from cracks and with sharp and square edges. II. construct a brink lintel.
A temporary wood support, known as a turning piece, is used to
III. In order to maintain the appearance of brickwork, a brink lintel should have a depth equal to some multiple of brick courses. IV. It is found that the bricks having frogs are more suitable for the brink lintels. It is due to the fact that the forge, filled with mortar, form keys between
different layers and thus the shear resistance of brink lintels. Results in overall increases of the strength of brink, lintel. V. A brick lintel is a weak form of construction and hence it is suitable up to a span of I mm with light loading for greater. Spans and slightly heavy a)
A brick lintel with reinforcement, as shown in fig. 11-41, may be provided.
b) A steel angle or steel flat bar of length equal to brick lintel, may be provided at the bottom of lintel. The exposed surfaces of steel angle or steel.Angle or steel flat bar may be suitably painted so as to make them inconspicuous. ) 4) Steel Lintels: These lintels consist of steel angles or rolled steel joists. The formed is used for small spans and light loading and the latter is used for large spans and heavy loading. A steel lintel becomes useful when there is no space available to and heavy loading. A steel lintel becomes useful when there is no space available to accommodate the rise of an arch. The steel joists may be used singly or in combination of two or three units. When used singly, the steel joist is either embedded in concrete or gladded with stone facing to match with the width of opening. When more than one unit are placed side by side, the tube stone facing to match with the width of opening. When more than one units are placed side by side, the tube separators are provided to keep the still joists in position. Side by see, the tube separators are provided to keep the steel joists in position. The joists are usually embedded in concrete to protect the steel corrosion and fire. The steel collapses quickly due to fire and hence the casing of concrete make the steel more fireresistant. 5) Reinforced cement concrete Lintels : These lintels consist of the reinforced cement concrete and they have replaced practically all other materials for the lintels The R.C.C Lintels are fire proof, durable , strong, economical and easy to construct No relieving arches are necessary when the R. C.C Lintels are adopted.
The usual concrete mix for R.C.C lintel is 1:2:4 i.e. I part of cement, 2 parts of sand and 4 parts of aggregates by volume. The plain concrete lintels can be used puts a span of about 800 mm. But some form of reinforcement is necessary in the R.C.C lintels as plain concrete is weak in tension. The amount of reinforcement depends on lintels as plain concrete is weak in tension. The amount of reinforcement depends on the span of lintel, width of opening and the total load to be supported by the lintel. The span of lintel, width of opening and the total load to be supported by the lintel. R.C.C. Lintel for an opening of span 1 meter and of width 1/1/2 bricks. The projection, in the form of weather shed, can be easily taken out from lintels weather shed throws the rain water away from the wall.
The R.C.C. Lintels may be pre-cast of cast-in-situ. The pre-cast R.C.C lintels are convenient for small span up to 2 meters or so and they are economical as the same mould can be used of prepare a number of lintels. The pre=cast R.C.C lintels increase the speed of construction and allow sufficient time for the curing before fixing. One precaution of be taken in case of pre-cast. R.C.C. lintels is that the top of lintel should be properly marked with tar of paint this will help I placing the lintel correctly. Fore cast-in-situ R.C.C lintels, the centering is prepared. Reinforcement is placed and concreting is done as usual. When finishing is to be done or where appearance is not of importance, the surface of R.C.C. lintel can be kept exposed. Otherwise a rebate may be provided in the lintel and the surface can be suitably finished. Surface can be suitably finished. Rebated boot lintel over an opening in a cavity wall. This arrangement helps in improving the quantity of concrete. A flexible D.P.C. should quantity of concrete. A flexible D.P.C should be provided. And the toe of boot lintel should be strong enough to bear the load of wall above it. 2.6.3 Design of Doubly Reinforced Sections When a beam of shallow depth is used, the flexural design strength obtained that is allowed for the section as singly reinforced Mumax ( if and 0) may be insufficient. The design moment capacity may be increased by placing compression steel and additional tension steel. In addition, to increasing the section strength when its depth is limited, compression steel may be required in design for the following reasons: 1. Compression steel may be used in design to increase the ductility of the section at the flexural strength. 2. Compression steel may be used to reduce deflection of beams at the service load. Compression steel also reduces the long-term deflections of beams due to creep. Curvatures due to shrinkage of concrete are also reduced by compression steel. 3. For the beams of continuous frames under gravity and lateral loading, consideration of possible combinations of external loading reveal that the bending moment can change sign. Such members require reinforcement near both faces to carry the possible tensile forces and therefore act as doubly reinforced members. 4. Compression steel provides hangers for stirrups. When designing double reinforced concrete sections, the Egyptian Code specifies that the maximum spacing s between stirrups should not be greater than 15 times the diameter of the compression steel. This helps to prevent buckling. 2.6.4 Design Equations: First calculate
from
(1.43)
If d is less than
, therefore, compression steel is required. As Fig. 1.17 indicates, (1.44)
and (1.45)
FIGURE 1.17. Double reinforced section when the flexural strength is reached. The difference in moment Mu2 is given by (1.46) which results in
and
. Of course, (1.47)
If
, we can write and
(1.48)
Otherwise; if the compression steel is not yielding, the stress in it may be found in terms of cmax, using the strain diagram of Fig. 1.18:
(1.49)
and thus, (1.50)
FIGURE 1.18. Double reinforced section when the flexural strength is reached. 2.6.5 Design Aids: With reference to Fig. 1.18, taking the moments of forces about T, Cc and Cs each a time: (1.51a)
(1.51b)
(1.51c) First, calculate K1 from Eq. 1.52. Then, with the known value of , determine the design table that corresponds (Tables C.1 through C.3). Traverse vertically to the and fcu values, then horizontally to theK1 value, and finally obtain the values of K2 and a to be used. In so doing, calculate As from Eq. 1.53 and that
if:
from Eq. 1.54. Inaddition, the Egyptian Code states
Table Steel 240/350
0.20
360/520
0.15
450/520
0.10
2.7 T Beam Design for Flexure as per IS 456 The design of reinforcement for Limit State of Collapse in Flexure and Shear for T Beam Section is carried out as per IS-456. Check for Minimum and Maximum Reinforcement criteria is considered for Flexure as per the Code. Check for minimum shear reinforcement, maximum spacing of shear reinforcement is done as per the Code. The Input data for the Beam design for Flexure
Factored BM (Mu), Beam Dimensions and Effective Cover for Tension and Compression Steel, Grade of Concrete fck
Clear cover for the beam would be as per Table16 for Durability criteria and as per Table 16A for Fire resistance criteria. In mild exposure condition for a fire resistance of 0.5 hour, 20mm cover is provided for stirrups. Based on this eff. cover would be calculated by designer based on no. of layers in which steel would be provided. To start with 40 to 50mm cover may adopted and corrected on finding the actual disposition of bars in next iteration by the designer.
For given BM, Mu
Mu,lim both tension and comp. steel are calculated. The Maximimum Tension Steel is 4 % of the gross area of section. If Ast,calculated >Ast,max, A message to “REV DEPTH” appers in the cell.
Based on the area of steel required ‘Ast’, use Rebar calculator to to determine size and number of bars required. Recalculate the effective cover based on the rebar arrangement, with input of revised cover recalculate design steel required. The spacing < 180mm as per Cl.26.3.3. for zero % redistribution of moment with Fe 415 steel.
2.8 Design of RCC Rectangular Slabs as per IS 456-2000
The design of Two way rectangular slabs supported on all four sides without provision for Torsion at corners is carried out as per Table 27, Indian Standard (IS) 456 App. D. Check for deflection is as per the provsions in Cl. 23.2 of the code. 2.8.1 Simply Supported Two Way Slab Design as per IS 456 The Input data for the slab design is :
Effective Short Span Lex, Effective Long Span Ley, Grade of Concrete fck, Floor Finish Loads and Imposed Loads.
Clear cover for the slab would be as per Table16 for Durability criteria and as per Table 16A for Fire resistance criteria. For a fire resistance of 0.5 hour 20mm cover is provided, based on the same eff. cover for short span would be d’x = ( D – short span bar dia. / 2) and for long span it would be d’y = ( D – shortspan bar dia. – long span bar dia /2). Generally speaking to start with d’x = 25mm and d’y = 35mm would be assumed considering 10mm bar dia.
Main variable in Slab Design is assumption of slab thickness. It should provide eff. depth more than required as per Cl. 23.2. d,reqd = Lex / (20 * MF). But MF = Modification Factor depends on Area of Steel provided. So the problem is iterative, assume a suitable slab thickness D as Lex/25 to Lex/30 depending on edge conditions and magnitude of loads.
Calculate total load incl. self weight of slab. Determine BM coefficient from Table 27 for given edge conditions and Ley/Lex ratio of spans by interpolation. Then after finding BM at critical sections ‘Ast’ at each critical location is calculated. Minimum area of steel Ast,min (mm2/m) = 1.2 * D(mm)i.e. 0.12%. For Modification Factor, ‘Ast’ for Short Span positive BM (span moment) is considered. If the check for deflection is not satisfied by a narrow margin, MF can be increased max. up to 2 by providing Ast more than the designed value for positive short span steel. This will reduce actual stress in steel and increase MF. But even after that If d,provided 2.9 Two Way Slab Design Spreadsheets
The formulation adopted is for Limit State of Collapse as per IS 456. The BM Coefficients are from Table 27, Based on Ley / Lex ratio and the design Case adopted. The interpolation for BM Coefficient is automated.
Concrete Grade M20 to M40, Steel Grade Fe 415 is considered.
The Spreadsheet calculates area of steel for Limit State of Collapse in Flexure at all relevant sections. If the Check for Deflection is not satisfied it will automatically calculate increased area of steel for positive short span BM to satisfy deflection
criteria. In case this can not be achieved, recommends the user to increase Slab Thickness.
The spacing calculation is provided for a no. of bar dia. the designer would select the most appropriate one.
Only singly reinforced section is considered in design. In case it becomes doubly reinforced, a message to revise thickness appears.
2.10 Design of RCC Rectangular Beams as per IS 456-2000 The design of reinforcement for Limit State of Collapse in Flexure and Shear for Rectangular Beam Section is carried out as per IS-456. Check for Minimum and Maximum Reinforcement criteria is considered for Flexure as per the Code. Check for minimum shear reinforcement, maximum spacing of shear reinforcement is done as per the Code. 2.10.1 Rectangular Beam Design for Flexure as per IS 456
The Input data for the Beam design for Flexure :
Factored BM (Mu), Beam Dimensions and Effective Cover for Tension and Compression Steel, Grade of Concrete fck
Clear cover for the beam would be as per Table16 for Durability criteria and as per Table 16A for Fire resistance criteria. In mild exposure condition for a fire resistance of 0.5 hour, 20mm cover is provided for stirrups. Based on this eff. cover would be calculated by designer based on no. of layers in which steel would be provided. To start with 40 to 50mm cover may adopted and corrected on finding the actual disposition of bars in next iteration by the designer.
For given BM, Mu Mu,lim both tension and comp. steel are calculated. The Maximimum Tension Steel is 4 % of the gross area of section. If Ast,calculated >Ast,max, A message to “REV DEPTH” appers in the cell.
Based on the area of steel required ‘Ast’, use Rebar calculator to to determine size and number of bars required. Recalculate the effective cover based on the rebar arrangement, with input of revised cover recalculate design steel required. The spacing < 180mm as per Cl.26.3.3. for zero % redistribution of moment with Fe 415 steel.
2.10.2 Rectangular Beam Design for Shear as per IS 456 The Input data for the Beam design for Shear :
Factored Shear Force at Critical Section (Vu), Effective Cover for Tension Steel, Grade of Steel for Strrups, No. of Legs and dia. Of Strrups
The spacing of stirrups would be calculated using Cl. 40.4, along with minimum shear reinforcement and max. spacing criteria as per Cl. 26.5.1.6. The designer should see thatclosest spacing should be approximately 100mm for ease of concreting, as far as possible.
2.11 Design Shear Force for Minimum Shear Reinforcement
It will calculate the magnitude of factored shear force which will be safely carried by minimum shear reinforcement. Hence the segment of beam can be identified by the designer from the Shear Force envelope obtained from the analysis results, for which minimum shear reinforcement would suffice.
The Input data for the Beam design for Shear :
The Input data : Area of Tension Steel at Critical Section, Effective Cover for Tension Steel, Grade of Steel for Strrups, No. of Legs and dia. Of Strrups
2.11.1 Design of RCC Rect. Columns for Biaxial Bending The design of rectangular RCC column for axial load and uniaxial bending is carried out using Pu-Mu Interaction Diagrams using SP 16. For axial compression and biaxial bending the procedure is to use the above mentioned Interaction diagrams to calculate limiting uniaxial bending moment( Muxl and Muyl) about each axes separately for given Pu and to satisfy inequality equation of IS-456 i.e. (Mux / Muxl) a + (Muy / Muyl) a < 1.
2.11.2 Column Design Spreadsheet The formulation adopted is for Limit State of Collapse as per IS 456. The Pu-Mu has been calculated considering concrete as well as each individual reinforcement bar separately. Concrete Grade M20, Steel Grade Fe 415 is considered. The column cross section accommodates up to maximum three internal equally spaced reinforcement bars on each face apart from the four corner bars. No. of bars on opposite faces are same, i.e. on any face no. of bars would be 2 to 5. At a time six load combinations are included but process can be repeated for any numbers in the same sheet. Pu, Mux and Muy input values are Positive only.
2.12 Types of Solid RCC Slab RCC solid slabs are three types depending on design criteria. •
One-way slab
•
Two-way slab
•
Cantilever slab
O slab b – When caan we calledd a solid slaab one-way slab? s If a soolid RCC slaab 2.12.1 One-way meets thee following criteria thenn we can calll that one-waay slab - Thee slab rests on o two beam ms only, Th he slab can be b rested onn four beamss but the lon ng-span of slab should bee greater thaan two times of short-sp pan. In one way w slab, thee main reinfoorcement shoould be alon ng slab’s shoort n. direction
2.12.2 Tw wo-way slab b – When a Solid RCC slab rests on n four beam ms but long-sspan of slab is less than or equal to two times of short-spann then we can n call that sllab a “two-w way slab”. Seee Image beelow “Two-W Way Slab”. In two-wayy slab, main reinforcemeent runs both h in short annd long direection and staay perpendiccularly with one anotherr.
2.12.3 Cantilever C sllab – Cantillever Slab hhas only onee support at one end an nd other threee ends are open. See thhe image beelow “Cantilever slab”. The T main reeinforcementt of cantileveer
slab
should
be
extended
one
and
half
times
beyond
its
support.
A slab is a flat two dimensional planar structural element having thickness small compared to its other two dimensions. It provides a working flat surface or a covering shelter in buildings. It primarily transfer the load by bending in one or two directions. Reinforced concrete slabs are used in floors, roofs and walls of buildings and as the decks of bridges. The floor system of a structure can take many forms such as in situ solid slab, ribbed slab or pre-cast units. Slabs may be supported on monolithic concrete beam, steel beams, walls or directly over the columns. Concrete slab behave primarily as flexural members and the design is similar to that of beams. 2.13 CLASSIFICATION OF SLABS Slabs are classified based on many aspects 1) Based of shape: Square, rectangular, circular and polygonal in shape. 2) Based on type of support: Slab supported on walls, Slab supported on beams, Slab supported on columns (Flat slabs). 3) Based on support or boundary condition: Simply supported, Cantilever slab, Overhanging slab, Fixed or Continues slab. 4) Based on use: Roof slab, Floor slab, Foundation slab, Water tank slab. 5) Basis of cross section or sectional configuration: Ribbed slab /Grid slab, Solid slab, Filler slab, Folded plate 6) Basis of spanning directions :
One way slab – Spanning in one direction Two way slab _ Spanning in two direction In general, rectangular one way and two way slabs are very common and are discussed in detail. 2.13.1 METHODS OF ANALYSIS The analysis of slabs is extremely complicated because of the influence of number of factors stated above. Thus the exact (close form) solutions are not easily available. The various methods are: a) Classical methods – Levy and Navierssolutions(Plate analysis) b) Yield line analysis – Used for ultimate /limit analysis c) Numerical techniques – Finite element and Finite difference method. d) Semi empirical – Prescribed by codes for practical design which uses coefficients. 2.13.2 GENERAL GUIDELINES a. Effective span of slab : Effective span of slab shall be lesser of the two 1. l = clear span + d (effective depth ) 2. l = Center to center distance between the support b. Depth of slab: The depth of slab depends on bending moment and deflection criterion. the trail depth can be obtained using: • Effective depth d= Span /((l/d)Basic x modification factor) • For obtaining modification factor, the percentage of steel for slab can be assumed from 0.2 to 0.5% • The effective depth d of two way slabs can also be assumed using cl.24.1,IS 456 provided short span is _ 3.5m and loading class is < 3.5KN/m2 Type of support
Fe-250
Fe-415
Simply supported
l/35
l/28
Continuous
l/40
l/32
OR The following thumb rules can be used • One way slab d=(l/22) to (l/28). • Two way simply supported slab d=(l/20) to (l/30) • Two way restrained slab d=(l/30) to (l/32) c. Load on slab: The load on slab comprises of Dead load, floor finish and live load. The loads are calculated per unit area (load/m2). Dead load = D x 25 kN/m2 ( Where D is thickness of slab in m) Floor finish (Assumed as)= 1 to 2 kN/m2 Live load (Assumed as) = 3 to 5 kN/m2 (depending on the occupancy of the building) 2.13.3 DETAILING REQUIREMENTS AS PER IS 456 : 2000 a. Nominal Cover : For Mild exposure – 20 mm For Moderate exposure – 30 mm However, if the diameter of bar do not exceed 12 mm, or cover may be reduced by 5 mm. Thus for main reinforcement up to 12 mm diameter bar and for mild exposure, the nominal cover is 15 mm b. Minimum reinforcement :The reinforcement in either direction in slab shall not be less than • 0.15% of the total cross sectional area for Fe-250 steel • 0.12% of the total cross sectional area for Fe-415 & Fe-500 steel. c. Spacing of bars :The maximum spacing of bars shall not exceed • Main Steel – 3d or 300 mm whichever is smaller Distribution steel –5d or 450 mm whichever is smaller Where, ‘d’ is the effective depth of slab. Note: The minimum clear spacing of bars is not kept less than 75 mm (Preferably 100 mm) though code do not recommend any value.
d. Maximum diameter of bar: The maximum diameter of bar in slab, shall not exceed D/8, where D is the total thickness of slab. 2.13.4 BEHAVIOR OF ONE WAY SLAB When a slab is supported only on two parallel apposite edges, it spans only in the direction perpendicular to two supporting edges. Such a slab is called one way slab. Also, if the slab is supported on all four edges and the ratio of longer span(ly) to shorter span (lx) i.ely/lx > 2, practically the slab spans across the shorter span. Such a slabs are also designed as one way slabs. In this case, the main reinforcement is provided along the spanning direction to resist one way bending.
Fig.1: Behavior of one way slab 2.13.5 BEHAVIOR OF TWO WAY SLABS A rectangular slab supported on four edge supports, which bends in two orthogonal directions and deflects in the form of dish or a saucer is called two way slabs. For a two way slab the ratio of ly/lx shall be _ 2.0 .
Fig. 2: Behavior of Two way slab
Since, the slab rest freely on all sides, due to transverse load the corners tend to curl up and lift up. The slab looses the contact over some region. This is known as lifting of corner. These slabs are called two way simply supported slabs. If the slabs are cast monolithic with the beams, the corners of the slab are restrained from lifting. These slabs are called restrained slabs. At corner, the rotation occurs in both the direction and causes the corners to lift. If the corners of slab are restrained from lifting, downward reaction results at corner & the end strips gets restrained against rotation. However, when the ends are restrained and the rotation of central strip still occurs and causing rotation at corner (slab is acting as unit) the end strip is subjected to torsion. 2.13.5.1 Types of Two Way Slab Two way slabs are classified into two types based on the support conditions: a) Simply supported slab b) Restrained slabs Two way simply supported slabs The bending moments Mx and My for a rectangular slabs simply supported on all four edges with corners free to lift or the slabs do not having adequate provisions to prevent lifting of corners are obtained using Mx =αx W lx2 My = αy W lx2 Where, αx and αy are coefficients given in Table 1 (Table 27,IS 456-2000) W- Total load /unit area lx&ly – lengths of shorter and longer span. Table 1 Bending Moment Coefficients for Slabs Spanning in Two Directions at Right Angles, Simply Supported on Four Sides (Table 27:IS 456-2000) ly/lx 1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0 2.5 3.0 αx 0.062 0.074 0.084 0.093 0.099 0.104 0.113 0.118 0.122 0.124 αy 0.062 0.061 0.059 0.055 0.05 1 0.046 0.037 0.029 0.020 0.014 Note: 50% of the tension steel provided at mid span can be curtailed at 0.1lx or 0.1ly from support. Two way Restrained slabs When the two way slabs are supported on beam or when the corners of the slabs are prevented from lifting the bending moment coefficients are obtained from Table 2 (Table 26,
IS456-2000) depending on the type of panel shown in Fig. 3. These coefficients are obtained using yield line theory. Common practice of design and construction is to support the slabs by beams and support the beams by columns. This may be called as beam-slab construction. The beams reduce the available net clear ceiling height. Hence in warehouses, offices and public halls sometimes beams are avoided and slabs are directly supported by columns. This types of construction is aesthetically appealing also. These slabs which are directly supported by columns are called Flat Slabs. Fig. 2.1 shows a typical flat slab.
The column head is some times widened so as to reduce the punching shear in the slab. The widened portions are called column heads. The column heads may be provided with any angle from the consideration of architecture but for the design, concrete in the portion at 45º on either side of vertical only is considered as effective for the design [Ref. Fig. 2.2].
Fig. 2.2 Slab without drop and column with column with column head
Moments in the slabs are more near the column. Hence the slab is thickened near the columns by providing the drops as shown in Fig. 2.3. Sometimes the drops are called as capital of the column. Thus we have the following types of flat slabs:
Fig. 2.3 Slab with drop and column with column with column head (i) Slabs without drop and column head (Fig. 2.1). (ii) Slabs without drop and column with column head (Fig. 2.2). (iii) Slabs with drop and column without column head (Fig. 2.3). (iv) Slabs with drop and column head as shown in Fig. 2.4.
Fig.2.4 Slabs with drop and column head as shown in Fig. 2.4. The portion of flat slab that is bound on each of its four sides by centre lines of adjacent columns is called a panel. The panel shown in Fig. 2.5 has size L1 * L2. A panel may be divided into column strips and middle strips. Column Strip means a design strip having a width of 0.25L1 or 0.25L2, whichever is less. The remaining middle portion which is bound
by the column strips is called middle strip. Fig. 2.5 shows the division of flat slab panel into column and middle strips in the direction y.
Fig. 2.5 panels, column strips and middle strips in y- direction Proportioning of flat slabs Drops The drops when provided shall be rectangular in plan, and have a length in each direction not less than one third of the panel in that direction. For exterior panels, the width of drops at right angles to the noncontinuous edge and measured from the centre-line of the columns shall be equal to one half of the width of drop for interior panels. Column heads Where column heads are provided, that portion of the column head which lies within the largest right circular cone or pyramid entirely within the outlines of the column and the column head, shall be considered for design purpose as shown in Figs. 2.2 and 2.4. Thickness of slab The maximum value of ratio of larger span to thickness shall be
= 40, if mild steel is used = 32, if Fe 415 or Fe 500 steel is used the ratio shall not exceed 0.9 times the value specified above i.e., = 40 * 0.9 = 36, if mild steel is used. = 32 * 0.9 = 28.8, if HYSD bars are used It is also specified that in no case, the thickness of flat slab shall be less than 125 mm. 2.14 Advantages of flat slab construction Faster construction The benefits of using flat slab construction are becoming increasingly recognised. Flat slabs without drops (thickened areas of slab around the columns to resist punching shear) can be built faster because formwork is simplified and minimised, and rapid turn-around can be achieved using a combination of early striking2 and flying systems. The overall speed of construction will then be limited by the rate at which vertical elements can be cast. Reduced services and cladding costs Flat slab construction places no restrictions on the positioning of horizontal services and partitions and can minimize floor-to-floor heights when there is no requirement for a deep false ceiling. This can have knock-on benefits in terms of lower building height, reduced cladding costs and prefabricated services. Flexibility for the occupier Flat slab construction offers considerable flexibility to the occupier who can easily alter internal layouts to accommodate changes in the use of the structure. This flexibility results from the use of a square or near-square grid and the absence of beams, down stands or drops that complicate the routing of services and location of partitions. Slab thickness Having chosen a flat slab solution, the next key issue is to determine an appropriate slab thickness. In general, thinner slabs not only save on direct material costs for the frame and the supporting foundationsbut also provide knock-on benefits in terms of reduced height of the structure and lower cladding costs. Further guidance is given in Reference 1. There is, of course, a lower limit to the slab thickness. As this is approached, the savings identified above become outweighed by the extra reinforcement required to deal with serviceability issues and the increased difficulty in designing and fixing it. There is also a case for providing some margin, particularly at outline scheme stage, to accommodate late changes in architectural requirements. Flexibility in room layout:
Allows Architect to introduce partition walls any anywhere required, allows owner to change the size of room layout, allows choice of omitting false ceiling and finish soffit of slab with skim coating. Saving in building height: Lower storey height will reduce building weight due to lower partitions and cladding to façade, approx. saves 10% in vertical members, reduce foundation load.
Shorter construction time:
Flat plate design will facilitate the use of big table formwork to increase productivity
Single soffit level
Simplified the table formwork needed Ease of installation of m&e services: all M & E services can be mounted directly on the underside of the slab instead of bending them to avoid the beams, avoids hacking through beams.
Questions 1. Explain bond local and average bond? 2. What is the permissible bond stresses for plain and deformed bars? 3. What is the actual bond stress in RCC Beams? 4. Describe Design of lintel? 5. Explain the Design of cantilever beam? 6. Briefly explain Doubly reinforced concrete beam? 7. What are the type of end supports?
UNIT 3 Structure of this unit Reinforced Brick Work, TBeams Objectives to be learned 1. Reinforced brick work and its use in slab and lintels 2. Limitations of the use of RB work 3. General principles of design of reinforced brick lintels and slabs 4. Design of RB lintels and slabs 5. Specifications for RB work construction 6. Structural behaviour of beam and slab floor laid monolithically 7. Rules for the design of Rbeams 8. Economical depth of Tbeams, strength of Tbeams 9. Design of simply supported Tbeams using IS code of practice
3.1 Reinforced brickwork Entire panels of brickwork can be reinforced to increase their strength to resist wind loads, or to enable a panel of prefabricated brickwork to be handled and transported. Reinforcement can also be used locally to resist potential cracking at the corners of openings, or to restrain freestanding parapets, particularly in seismic areas, where unreinforced brickwork would be too unstable. Reinforcement can also be used over openings, to form a lintel in the brickwork itself. This has the advantage of showing a clean brick profile without a separate steel lintel, and also has better fire resistance. Special provisions have to be made to support the lowest course of bricks, which are hung below the reinforcement, usually with wire loops in the perpends. The simplest form of reinforcement for brick walls is to incorporate wire reinforcement into the bed joints. This is commonly done above and below openings, since the corners of openings create a stress concentration and they are common sites for the commencement of a crack. There are practical difficulties in placing reinforcement in the wet mortar of a bed joint. The common form of reinforcement is a ladder of wires (from 3mm to 6mm diameter
longitudinally, with thinner wires welded across them), supplied flat. The reinforcement must be totally enclosed by the mortar. Galvanised steel is likely to be satisfactory in locations of low corrosion hazard, while stainless steel is preferred in maritime or polluted environments. Horizontal joint reinforcement will provide a slight improvement in resistance to wind loads, if the panel is supported at both ends. It is of little assistance if the panel is supported top and bottom. It does not contribute to vertical loadbearing capacity. Vertical reinforcement cannot be incorporated into the joints of a single-leaf stretcher bond panel, because there are no continuous vertical joints. In a one-brick (230mm) wall, it would be possible to place small-diameter bars in the 10mm central joint, but they would have to be located very accurately, and placed as the wall is laid. The practical ways of incorporating vertical reinforcement involve creating continuous voids in the bond pattern, or using purpose-made bricks with holes in the right place. A one-and-a-half brick wall (340mm thick) laid in Flemish bond has small continuous vertical spaces in the central thickness, normally filled with cut bricks. These can be used as cores into which vertical bars can be inserted, and grouted in after several courses have been laid. This detail has been used for heavy work such as air-raid shelters and blast walls, but walls of this thickness are seldom used in normal construction. Bricks with purpose-made core holes are the most practical solution for accommodating vertical reinforcement. The core holes must be located in the bricks so that they will align in normal stretcher bond. They have to be large enough to allow some tolerance in laying, and also large enough to allow bars of the required diameter to be inserted, lapped where necessary, and grouted with mortar or fineaggregate concrete.
It is unreliable to insert a storey-height reinforcing bar down the holes after the wall is laid, because any mortar droppings in the holes will be impossible to remove. It is also impossible to put storey-height bars in place first and thread the bricks over them. Therefore the use of this system for laid-in-place walls requires some pre-planning and discussion with the bricklayers involved. It is more easily adapted to prefabricated wall panels in which the bricks are laid out dry on a horizontal table and the joints are then filled with grout. On the other hand, if the weather resistance provided by a cavity wall is not an issue, the cavity itself could be reinforced and filled with a fine concrete grout. It is still necessary to use cavity ties to hold the leaves together, and to fill the cavity in reasonably small lifts to avoid excessive hydrostatic pressure from the wet concrete.
3.2 Lintels Since people first began putting windows in their shelters, they have needed a way to support the weight of the wall above the window. The solution was the lintel, a beam that spans from one side of the window to the other. Wood, stone, steel, concrete, brick, and block all have been used as lintels in masonry walls. Of these, though, the only material that matches the appearance of masonry is masonry itself. Masonry lintels must be reinforced. They can be constructed of standard clay masonry units (solid or hollow), glazed brick and tile, specially formed concrete masonry lintel units, bond beam concrete masonry units, or standard concrete masonry units with grooved, depressed, or cutout webs. These units are laid in a masonry wall in a way that creates a channel in which steel reinforcing and grout are placed. Masonry lintels are not difficult to construct, whether built in place or prefabricated onsite or at a plant and then delivered. Shoring is used if the lintel is built in place. Prefabricated masonry lintels eliminate shoring and can be loaded immediately after they’re placed in the wall. Though steel angles are the simplest way to make lintels in masonry walls, reinforced brick and block lintels have several advantages. Though they must be reinforced, masonry lintels require much less steel (and thus material cost) to carry loads. They cost less to maintain because they don’t need periodic painting as exposed steel does. Their built-in fireproofing provides additional safety. If built in place, they require no special lifting equipment, as precast concrete lintels do. And they eliminate cracking that can be caused by differential movement between steel lintels and masonry. 3.2.1 Determining the loads To design a masonry lintel, you must first determine the load to be supported.. In this method, the lintel is designed to support a triangular section of masonry above it. The height of this triangle (triangle ABC in the drawing) is one-half the clear span of the opening (L/2); its sides are at 45° to the lintel. Outside this triangle, arching action of the masonry is assumed to support the weight of the wall and any uniform loads, such as roof trusses or floor joists. But for this arching to occur, sufficient masonry must be above the apex of the triangle. For normal wall thicknesses and loads, a height of 8 to 16 inches of masonry above the apex allows arching. This arching action produces a horizontal thrust at each end of the lintel. If a lintel over a long span supports heavy loads and one end is near a wall corner, another opening, or an expansion joint, arching action may have to be ignored. The lintel must then be designed to support all the loads above it. Concentrated loads from roof trusses or floor joists, whether above or below the apex, are transferred down as a uniform How to design reinforced masonry lintels
Lintels are designed to support a triangular section of wall above the opening that is half as high as the opening is wide. Outside this triangle, arching action of the masonry is assumed to support the wall. load along the base of a triangle with sides at 60° to the horizontal. Schneider and Dickey calculate the length of influence of the concentrated load (distance AE in drawing). No arch action should be assumed for walls laid in stack bond. All loads above the lintel are considered to act directly down on the lintel unless distributed by bond beams or other structural members.
A lintel is a horizontal beam over a door or window opening usually carrying the load of the wall above. Lintels can often be partially or completely hidden from view. There are many different shapes of lintels, determined by the properties of the material and the purpose for which the lintel is required. Concrete lintels are generally rectangular, although variations of the rectangular configuration are available for use in cavity walls. The development of concrete and steel lintels for larger span opening in the 1950's and 1960’s, were required to carry the increased loads. Windows up to 2.4m wide are not uncommon and these larger spans require more attention to be paid to the bearings at the ends of these lintels resulting from the increased loads from them onto the masonry below. Lintels specifically designed for cavity wall construction are also available Concrete lintels are generally provided precast or preformed from manufacturers and links are provided to typical manufacturers literature for detail design review Reference standard BS 5977-1:1981 Lintels. Method for assessment of load
The method of assessing loads on lintels in masonry structures for openings up to 4,5m in single storey structures and up to 3,6m in normal 2 and 3 storey domestic structures is described in BS 5977. Typically there should not be less than 0,6m opr 0,2L of masonry to each side of the opening (L is the clear span). and not less than 0,6m masonry above the lintel at mid span and not less then 0,6m of masonry over the lintel supports. The loading on the lintel is based on the following assumptions 1) The weight of the masonry in the loaded triangle as shown above is carried by the lintel. 2) Any point load or distributed load applied within the load triangle is dispersed at 45o and carried by the linter 3) Half of any point or distributed load applied to the masonry within the zone of interaction is carried by the lintel Loads above the lintel which are outsize the zone of interaction need not be considered.
3.2.2 Concrete lintels Concrete lintels can be basic precast reinforced or prestressed. The latter having the highest load bearing capacity. Concrete lintels can be composite or non composite Composite lintels utilise the composite action of the concrete and brick/block work together to provide the load-bearing capacity. This option generally requires A strong mortar mix and brick reinforcing fully interleaving each course. Non-composite concrete lintels are based on the load bearing capacity of the lintel itself with it internal reinforcement. This option provides higher load bearing capacity and does not require propping during construction. Simple sketch showing conditions for a concrete lintel
Table showing a typical non- composite precast reinforced concrete beam (150mm x 100mm) load bearing capacity. Sectio Maximum UDL kg/m for Clear Span (m) n (w x 1,3 1,6 1,9 2,2 2,5 2,8 3,1 h) 0,75 0,9 1,05 1,2 1,5 1,8 2,1 2,4 2,7 3,0 3,3 5 5 6 5 5 5 5 mm 150 x 238 173 128 100 66 46 34 25 19 15 12 808 551 395 295 226 176 140 100 1 9 2 6 2 4 0 7 9 7 5
3.2.3 Profiled steel lintels Profiled galvanised steel or stainless steel are very useful for cavity wall construction because they can be formed to support both leaves and also incorporate insulation in the section. Detailed information on steel lintels is found in the links at the foot of this page. There are numerous steel lintel profiles for solid and cavity walls..A typical cavity wall lintel with provision for insulation is shown below
Table showing a set of load bearing properties for a typical standard lintel of the above shape suitable for a 95mm external leaf, 85mm gap and a 100mm internal leaf and a lintel height of 100mm). The relevant section has properties Ixx 374.64 cm4 Zxx 37.76 cm3 Weight 13.46 kg/m Area 17.14 cm2
Opening Lintel Span (mm) Length(mm)
Safe Load (kN)
600
900
30
750
1050
30
900
1200
30
1050
1350
30
1200
1500
30
1350
1650
30
1500
1800
28
1650
1950
25
1800
2100
23
1950
2250
22
2100
2400
20
2250
2550
19
2400
2700
18
2550
2850
17
2700
3000
16
For this table the safe load in the total load which is uniformly distributed over the length of the opening span. 3.3 THE BENEFITS OF CONCRETE SLABS
Thermal Mass describes the potential of a material to store and re-release thermal energy. Materials with high thermal mass, such as concrete slabs or heavyweight walls, can help regulate indoor comfort by radiating or absorbing heat, creating a heating or cooling effect. Thermal mass is useful in most climates, and works particularly well in cool climates and climates with a high day/night temperature range. To be effective, thermal mass must be used in conjunction with good passive design. Design slabs to absorb heat from the sun or other sources during winter. Heat can be stored in the slab and re-radiated for many hours afterwards. In summer, allow slabs to be exposed to cooling night breezes so that heat collected during the day can dissipate. Earth coupling is achieved when the thermal mass of the slab is in direct contact with the additional thermal mass of the earth below. This greatly enhances thermal performance. Earth coupling is most simply achieved using slab-on-ground construction.
Earth coupling allows the floor slab of a well insulated house to achieve the same temperature as the earth a few metres below the ground surface, where temperatures are more stable (cooler in summer, warmer in winter). In winter, added solar gain boosts the surface temperature of the slab to a very comfortable level. Durability is one of the other main advantages of concrete slabs. Concrete’s high embodied energy can be offset by its permanence. If reinforcement is correctly designed and placed, and if the concrete is placed and compacted well so there are no voids or porous areas, concrete slabs have a long lifespan. Control of cracking is important. A number of factors affect this and should be considered, including: •
Size of slab – if it is large or has two distinct separate parts, control and/or movement joints may be needed;
•
Proper preparation of foundations – this will prevent settlement cracking;
•
Curing – curing will help reduce surface cracking. Concrete typically takes 28 days to reach its design strength, and the first three to seven days are critical, beginning as soon as finishing of the slab is complete. An applied liquid curing membrane is usually the most practical method. Covering with a plastic sheet will also work but is harder to maintain. Keeping the concrete continuously wet, while the best method of curing, is not advised due to the large amounts of water that may be required;
•
Addition of water – excess water added to the concrete mix prior to placing will increase the risk of cracking and may result in dusting of the surface and a decrease in the strength of the concrete;
•
Placing and Compaction – inadequate placing and compaction will result in a lower strength and/or honeycombed (porous) concrete and lead to increased cracking.
Termite resistance is achieved with concrete slabs by designing and constructing them in accordance with the Australian Standards to minimise shrinkage cracking, and by treating any joints, penetrations and the edge of the slab. •
Slab edge treatment can be achieved simply by exposing the concrete edge for a minimum height or width of 75mm above the ground, forming an inspection zone at ground level.
•
Cavity physical barriers are used where a brick cavity extends to below ground, and can be formed by using sheet materials, a fine stainless steel mesh, or finely graded stone.
•
Pipe penetrations through concrete slabs should have some form of physical barrier. Options include sheet materials, stainless steel mesh or graded stone.
•
Although physical barriers are environmentally preferable, chemical deterrents are also available. These must be re-applied at regular intervals to maintain efficacy.
3.4 STRUCTURAL ISSUES Reactive soil sites can be difficult to build on, but ‘floating’ stiffened concrete raft slabs cope well with these conditions. Some stiffened raft slabs known as waffle raft slabs use void formers at regular intervals, forming closely spaced deep reinforced beams criss-crossing the slab underside. These void formers are mostly expanded foam boxes, which interfere with earth coupling, but more thermally connective alternatives are available. These include proprietary systems that use recycled tyres, or re-used detergent bottles filled with water and grouped together as void formers.
Steep sites may have geotechnical requirements which make slab-on-ground construction impracticable. Although slab-onground construction is more thermally efficient, a suspended slab can be a suitable way to gain the advantage of thermal mass on a steep site. Typical pole frame construction can be adapted easily to incorporate a slab. The slab underside should be insulated in some climates. Permanent structural formwork or one of the many precast flooring alternatives are usually the most cost effective way of constructing high set suspended slabs. These are normally designed by an engineer and installed by builders. These systems can provide useful thermal mass in situations where long spans are needed, such as pole homes or upper floors of two storey homes. These systems are often designed and installed as part of one supply contract by the manufacturer. Suspended autoclaved aerated concrete (AAC) panels can provide clear spans with acoustic and thermal benefits, and allow speedy installation on site. AAC floor panels have
approximately 25 per cent of the mass of normal concrete but still provide thermal comfort due to their insulation properties. Level sites are well suited to slab-on-ground construction. Use of slab-on-ground allows earth coupling and, because floor levels are close to ground level, facilitates free flow from interior to exterior spaces. Renovations can often incorporate concrete slabs even when the original building does not. Added rooms can use slab-on-ground or suspended slabs. Renovated rooms with timber floors are often capable of having the timber replaced with a concrete slab, for added thermal mass and quietness underfoot. These slabs can be either suspended on the original subfloor walls and footings, or if the old floor is close to ground they can be an infill slab on fill. Most advantage is gained if passive design principles are followed. Curing of all cement-based building materials is critical to achieving the design strength and other desired properties, especially with structural concrete slabs. Concrete takes 28 days to reach the design strength, although a sufficient minimum design strength may be achieved in less time if the concrete is specified accordingly. It is essential that the curing regime specified by the design engineer is followed exactly. Compaction is usually achieved by vibrating the concrete. This reduces the air entrapped in the concrete giving a denser, stronger and more durable concrete better able to resist shrinkage cracking. While deeper beams should be compacted, thin slabs (100mm-thick typically) receive adequate compaction through the placing, screeding and finishing operations. 3.5 DESIGN ISSUES Passive solar design principles and high mass construction work well together, and concrete slabs are generally the easiest way to add thermal mass to a house. Living rooms should face north in all but warm and high humidity climates to enable winter sun to invest warmth into the slab. Concrete slabs perform better as the diurnal temperature range increases. Natural ventilation must be provided for in the design. On summer evenings, heat stored in the slab must be allowed to dissipate. This is particularly important for slabs on upper storeys, where warm air accumulates. Zone off the upper space from lower living areas where possible and ensure the space can be naturally ventilated. This is particularly important if bedrooms are located upstairs, to maintain night time sleeping comfort. Insulation of the slab edge is important in cooler climates, to prevent warmth escaping through the edges of the slab. This insulation needs to be designed to complement the footing design, and should be undertaken in consultation with a structural engineer. It is possible to retro-fit slab edge insulation to existing slabs on ground. Renovations are an ideal time to do this, but it can be done at any time. Advice from an engineer should first be
sought regarding disturbance to foundations and reinstatement of material, and termite barriers must not be breached.
Balconies extended from the main slab of a house may act as cooling or heating fins, carrying precious warmth away to the cold exterior during winter, or transferring heat from summer sun inside. Consider building such slabs independently of the main slab and incorporating a thermal break at the interface. Acoustics need to be considered. Generally concrete slabs are a great way to reduce music or conversation noise being transferred from one level of a home to another, and between rooms on the same level. These noises will not be transmitted through a slab. Impact noise needs to be considered. For instance, the sound of high heels on a tiled floor will be transmitted directly to the room below. While seldom a problem in detached houses, an acoustic barrier can be included in the ceiling below. Open plan houses may transmit more noise than is convenient from one living area to another. Thermally efficient hard flooring will exacerbate this, so other elements within the room need to be designed to limit noise: •
Design the floor plan to be able to close spaces off from each other when needed.
•
Large flat ceilings can transmit too much noise. Dropped bulkheads or suspended cupboards around kitchens will help to absorb and dissipate sound.
•
Use absorbent materials on wall panels, or add large fabric wall hangings. Heavy drapes and curtains can also assist to absorb sound, as well as keeping warmth in during winter.
3.6 FINISHES For the thermal mass of a concrete slab to work effectively, it must be able to interact with the house interior. Covering the slab with finishes that insulate, such as carpet, will reduce the effectiveness of the thermal mass. However, a wide variety of finishes are available that allow thermal mass to be utilised: 3.6.1 Tiles
Tiles fixed by cement or cement-based adhesives are commonly available in many colours, sizes and patterns. (If thermal mass is to be utilised, avoid rubber-based adhesives due to their insulating effect). Darker colours with a matt surface work better than light shiny finishes. Choices include ceramic tiles, slate tiles, terracotta tiles, pavers and bricks. 3.6.2 Polished concrete Polished concrete is a term which covers two distinct types of finishes: •
Trowel finished floors, with or without post-applied finishes.
•
Ground and polished or abrasive blasted floors.
Some of the finishes below can be used in combination with other finishes to achieve a wider range of results, to suit any style or taste. Trowel finishes include: •
Steel trowel finish, where a normal hand or machine trowelled finish is used for the surface of the slab, usually with a clear sealer applied.
•
Burnished concrete, where the surface is finely steel trowelled, bringing the surface up to a glossy finish free of any trowelling marks.
Coloured concrete can be used in either steel trowel or burnished finishes, to achieve various results. It may be advisable to use experienced specialist contractors to carry out this work. These can be applied as oxides in the mix, or as ‘dry shake’ pigments applied to freshly screeded concrete and then trowelled in, or by chemically staining the concrete. Chemical stains are used with either steel trowel or burnished finishes. Metallic salts are carried into the surface of the concrete by mild acids, making the stains deep and permanent. Saw cuts can be added to enhance or separate panels of colour. Ground and polished finishes include: •
Exposed aggregate, where the normal grey concrete is ground back by several millimetres to expose whatever aggregate exists in the slab. This is often used in renovations of older buildings to reveal some of their history.
•
Exposed selected aggregates, where the cement colour and aggregate in a new slab are carefully selected, so when the surface is< ground back they produce desired effects.
Abrasive blasting of the concrete surface will also provide varied effects. Toppings can also be used on their own or together with some of the effects listed above to provide interesting visual finishes that do not interfere with thermal performance. Terrazzo is one of many toppings which is also ground and polished. Other toppings may be left in the ‘as placed’ or ‘as trowelled’ state.
Note that some of these options require careful protection of the slab during subsequent construction works. Also note that many sealer finishes have toxicity impacts but environmentally preferred alternatives are available such as bees wax or other natural wax polishes. These will need regular buffing to maintain sheen. 3.7 HEATING Because concrete slabs offer so much thermal mass, they lend themselves well to long cycle in-slab heating systems. Slab heating is usually used in colder climates where limited solar access is available to the slab. Insulation is required to minimise heat loss to the ground. Despite the fact that latest systems provide flexible thermostat settings for different house zones, slab heating is in operation for the whole of winter and is therefore best suited to houses with permanent or high occupancy. Electric resistance heating coils are the most common type of slab heating, and are attached to the reinforcement. These are usually controlled by timed switching so a relatively even temperature is maintained over a daily cycle with top up periods of just a few hours per day. They have a greenhouse gas penalty when fed with coal-fired electricity. Hydronic heating coils in the slab are very energy efficient, giving lower running costs and heating bills. Hydronic heating slabs can be powered by a range of energy sources, including solar, groundsource heat pumps, gas furnaces and heat recovery units. Unlike electric coil heating, hydronic heating can be reverse cycled in summer, dumping excess heat into the night sky. Recycling concrete is cost effective, minimises waste, and reduces the need to use more of the earth’s resources. 3.7 RECYCLED CONTENT IN SLABS There are two ways to contribute to the recycling of concrete: •
During demolition, by recycling waste concrete.
•
During construction, by using recycled materials as a component of new concrete.
Demolition waste makes up 40 per cent of all landfill. Taking demolition waste to landfill is expensive as well as damaging to the environment. Crushable concrete can instead be recycled to make economic and ecological savings. If demolition concrete is kept separate without mixing with other demolition materials, a more usable product can be achieved from the crushing for recycling into new concrete. Concrete is composed of three main components, coarse aggregate (stone), fine aggregate (sand) and cement. Recycled concrete and masonry can be utilised, as well as other industrial wastes, within these components.
Concrete’s main environmental impacts are greenhouse gas emissions from cement production and the mining of raw materials. Replacing a proportion of the cement with waste products such as fly ash, slag and silica fume can significantly reduce embodied energy and greenhouse gas emissions. Use of crushed concrete from demolition as aggregate, as well as the use of slag aggregates and manufactured sands to replace nature stone and sand within concrete, decreases landfill, reduces embodied energy and can be low cost. 3.7.1 Using substitutes for natural stone – Coarse aggregate can be replaced with recycled crushed concrete. The simplest approach is to use up to 30 per cent recycled aggregate for structural concrete. There is no noticeable difference in workability and strength between concrete with natural stone aggregate and concrete with up to 30 per cent recycled aggregate. It is possible to use up to 100 per cent recycled coarse aggregate in concrete under controlled conditions. However concrete with more than 30 per cent recycled concrete aggregate can have a greater water demand, can be less workable and result in lower strengths. 3.7.2 Using substitutes for natural sand – Fines from concrete crushing can be used to reduce natural sand content, as can other industrial by-products such as ground glass, fly-ash, bottom-ash and slag sands. However, the properties of these products can affect workability, strength and shrinkage cracking. 3.7.3 Using substitutes for portland cement – Cement substitutes (called ‘supplementary cementitious materials’ or ‘extender’) for Portland cement include fly ash, ground blast furnace slag and silica fume. These are all waste materials from other manufacturing processes. Various blended cements are available, some with high substitution of portland cement with SCM’s (up to 85 per cent). The reduced amount of portland cement results in a significant reduction in greenhouse gas emissions. New technologies currently being researched have the potential to reduce greenhouse gas emissions even further. 3.7.4 Obtaining these substitutes – Recycled aggregate (stone and sand) is readily available in many locations, with the only barrier being whether batching plants have the capacity to stockpile additional types of aggregate. Most batch plants have the ability to provide blended cements. In some smaller plants it may not be feasible to have two cement silos, or an additional silo for fly ash or slag, but hand loading may be an option. While slag aggregates are readily available in areas close to steelworks, cartage costs may prohibit their use in more remote areas. For similar reasons, manufactured sands and crushed concrete may not be readily available in all areas. 3.8 Specifications for RB work construction Reinforced brick masonry (RBM) is different from more conventional brick veneer in many ways. Key to those differences is the concept of grouting the brick masonry. Ground brick
masonry is defined as construction made with clay or shale units in which cavities or pockets in elements of solid units, or cells of hollow units are filled with grout. Common examples of RBM elements are beams, columns, pilasters, multi-wythe brick walls with grouted collar joints and hollow brick walls. This Technical Notes reviews the materials and construction practices used to build RBM elements. The different techniques are discussed with particular emphasis on the concepts of grouting and the placement of reinforcement. Quality assurance and minimum standards of workmanship to ensure a high level of consistency and adequate masonry performance are addressed. The information in this Technical Notes should be carefully reviewed by the mason contractor prior to constructing reinforced brick masonry. It should also be studied by the masonry inspector. Other Technical Notes in this series provide design theories and design aids for RBM elements such as beams, walls, columns and pilasters. 3.9 RBM MATERIALS The materials used to construct RBM elements should comply with applicable ASTM standards. Brick should meet the requirements of ASTM C 62 Specification for Building Brick, C 216 Specification for Facing Brick, or C 652 Specification for Hollow Brick. Mortar should comply with the requirements of ASTM C 270 Specification for Mortar for Unit Masonry. Grout should comply with ASTM C 476 Specification for Grout for Masonry. Metal wall ties, bar positioners, and reinforcing bars and wires should comply with the applicable ASTM standards as required by the Specification for Masonry Structures (ACI 530.1/ASCE 6/TMS 602)[2], also known as the MSJC Specification. All metal wall ties, positioners and joint reinforcement should be corrosion resistant or protected from corrosion by appropriate coatings. The materials in both fine and coarse grout should comply with the requirements of ASTM C 476 Specification for Grout for Masonry. Both fine grout and coarse grout should comply with the volume proportions given in ASTM C 476. Specifying grout by proportions is preferred over specifying a minimum grout strength. Typically, the maximum aggregate size should be 3/8 in. (9.5 mm) for coarse grout. While larger size aggregate can be used when filling large grout spaces, it must be noted that such grout likely cannot be pumped and will require placement by pouring from a hopper. It must be remembered that grout is different from concrete. Concrete is placed with a minimum of water into nonporous forms. Grout is poured with considerably more water, as the brick masonry creates absorptive forms. Grout should be sufficiently fluid to flow into the space to be filled, and surround the steel reinforcement, leaving no voids. It should be wet enough to flow without separation of the constituents. Whereas good mortar should stick to atrowel, it should be impossible for grout to do so. The water cement ratio as mixed, highly important in concrete work, is less important for grout in brick masonry. Although excessive water is detrimental to the strength and durability of the grout, when introduced into the brick masonry the water cement ratio rapidly changes from a high to a low value.
Grout is often mixed too dry and stiff for proper placement. One concern with the use of a very fluid grout mixture is excessive shrinkage. Shrinkage can create voids in the grout space, which are to be avoided. For this reason, plasticizers and shrinkage-compensating admixtures are recommended for grout in brick masonry. Such admixtures will provide the necessary fluidity while also providing a hardened grout mixture with minimal voids. There is a temptation to fill the grout space with the mortar that is used to lay up the brickwork, especially when simultaneously laying brick and grouting. This is not recommended, but may be permitted by local building codes. It is common to find excessive voids in the grout space with this practice. Proper placement and consolidation of grout or grout mixture with a shrinkage-compensating admixture and poured in a continuous process is much more likely to form a solid grout fill. 3.10 RBM CONSTRUCTION The construction of RBM elements can be separated into three parts: brick masonry construction, placement of the steel reinforcement and grouting. Each of these steps is critical to the end result. Following is a review of the three construction procedures in the order of their execution. There are two key points to remember when laying the brick. First, the brick masonry is the permanent formwork for the grout. This masonry formwork must be built in a manner that facilitates placement and positioning of the steel reinforcement and installation of grout. Second, the quality of workmanship will have a significant impact on the strength of the RBM. Unfilled mortar joints and elements that are out-of-plumb will not provide the performance assumed by the designer. All RBM elements constructed of solid brick should be laid with full head and bed joints. The ends of brick should be buttered with sufficient mortar to fill the head joints. Furrowing of bed joints should not be deep enough to result in voids. Years ago, it was believed by some that the head joints in solid brick masonry could be made only half full and that the grout would flow into the remainder of the head joint and fill the voids. It was felt that the grout would form a shear key and make the brick masonry bond more strongly to the grout core. This is not the case. In fact, creation of voids is more likely with this practice, which reduces the masonry's strength and can promote efflorescence due to entrapped water. Hollow brick are normally laid with face shell bedding. That is, the unit's face shells are filled solidly with mortar and head joints are filled with mortar to a depth equal to the face shell thickness. In some instances, bed joints of cross webs are covered with mortar to confine grout or to increase net area. Head joints may be filled solid for similar reasons. 3.10.1 Cleanouts and Maintaining a Clear Grout Space Cleanouts are used to remove all mortar droppings and debris from the bottom of a grout space and also to ensure proper placement of reinforcement prior to grouting. Cleanouts should be provided in the bottom course of all spaces to be grouted when the grout pour exceeds 5 ft (1.5 m) in height. In partially grouted masonry, a cleanout is recommended at
each vertical bar. In fully grouted masonry, the spacing of cleanouts should not exceed 32 in. (813 mm) on center according to the MSJC Specification. For reinforced brick masonry elements constructed with solid brick, cleanouts should be formed by omitting brick in the bottom course periodically along the base of the element. For hollow brick masonry, cleanouts should be provided in the bottom course of masonry by removing the face shell of the cells to be grouted. Examples of cleanouts in brick masonry walls are shown in Figure 1. 3.10.2 Example of Grout Space Cleanouts
FIG. 1 The minimum cleanout opening dimension should be 3 in. (76 mm). However, smaller spaces can be used if it is shown with a demonstration panel that the spaces can be cleaned. The grout spaces should be cleaned prior to grouting. It is good practice to clean out grout spaces at the end of each work day so that mortar droppings can be easily removed. A high pressure water spray, compressed air or industrial vacuum cleaner should be used for this purpose. Many contractors have found that cleaning of the grout space isfacilitated by placing a layer of sand or sheets of plastic film at the bottom of the cleanout to catch mortar droppings. After cleaning and prior to grouting, cleanouts should be closed with masonry units or sealed with a blocker to resist grout pressure. A minimum curing time of two days is recommended for the cleanout plugs or they should be adequately braced against the grout pressure. Bracing is discussed further in the section on Shoring and Bracing. For solid brick masonry, the top of the mortar bed joint should be beveled outward from the center of the grout space to minimize the amount of mortar extruded into the grout space when the brick are laid, as illustrated in Fig. 2. 3.10.3 Beveling Mortar Bed Joints
FIG. 2 Mortar protruding from bed or head joints into the grout space should be struck flush with the surface or removed prior to grouting. The maximum protrusion of a mortar fin should be 1/2 in. (13 mm). The spaces to be grouted should also be kept free of mortar droppings. One method of keeping collar joints clear consists of laying wood strips on the metal ties as the two wythes of brick masonry are built. The strips catch mortar droppings during construction and are removed by means of attached heavy strings or wires as the wall is built. To keep the cells of hollow brick clear for grouting, sponges are typically used, as shown in Fig. 3. 3.10.4 Sponges to Keep Cell Clear of Mortar Droppings FIG. 3
3.10.5 Erection Tolerances All RBM elements should be laid within the permitted dimensional tolerances found in the MSJC Specifications. Masonry elements that are not constructed within these limits are not as strong in compression as those that are. The thickness of mortar joints will also influence the masonry's strength. Excessively thin or thick mortar joints will reduce brick masonry's tensile and compressive strength. The erection tolerances stated in the MSJC Specification are given in Table 1.
This specification and its accompanying Building Code Requirements for Masonry Structures (ACI 530/ASCE 5/TMS 402) [1] [also known as the MSJC Code] stipulate minimum size of grout spaces that are dependent on the height of grout pour and the grout type. The limits given in Table 2 are to ensure adequate access of grout to the space.
3.10.6 Shoring and Bracing RBM elements typically require temporary support during construction provided by shoring and bracing. These supporting members are typically of wood or steel construction. Temporary support is required for two reasons. First, grout is very fluid when placed and exerts considerable pressure on the surrounding brick masonry. Second, RBM elements gain strength over time as the mortar and grout cure and harden. RBM walls, columns and pilasters are often braced along their height. RBM beams and arches may require both shoring for vertical support and bracing for lateral load resistance and grout pressure resistance. Shoring and bracing should be left in place until it is certain that the masonry has gained sufficient strength to carry its own weight and all other imposed loads including temporary loads that occur during construction. The most common problem related to temporary
supports for masonry elements is inadequate lateral bracing to resist wind pressures during construction until the masonry has gained sufficient strength to resist these loads. This is especially true when the roof and floor diaphragms have not been installed and anchored to the top of the masonry wall. Without proper bracing, the wall is a free-standing cantilever element and is more vulnerable to collapse. Appropriate time for removal of shoring and bracing depends on many factors. For example, proper curing of the mortar and grout may take considerably longer under cold weather conditions. The results of suitable compression tests of prisms or grout may be necessary as evidence that the masonry has attained sufficient strength to permit removal of shoring or bracing. Rules-of-thumb for the minimum time which should elapse before removal of shoring or bracing that have been recommended for many years include the following: 1. For RBM beams, 10 days after completion of the element 2. For RBM arches, 7 days after completion 3. Lateral bracing for walls, columns and pilasters, 7 days after placement of the grout. Longer time periods will be necessary with inadequate curing conditions. It is always a good idea to consult the project engineer for a recommended bracing scheme and the length of time required for bracing to remain in place. 3.10.6 Curing Time Prior to Grouting. If grouting is performed too rapidly after construction the hydrostatic pressure of the grout can cause "blowout" of mortar joints or even entire sections of brickwork. This is especially true when the grout pour is high. Blowout of the grout can be avoided by a combination of proper curing time, adequate wall ties or joint reinforcement across the grout space and bracing. Recommended duration of curing prior to grouting depends upon the method of grouting and the extent of bracing to resist the grout pressure. If no bracing against grout pressure is provided, the masonry should be permitted to cure for at least 3 days to gain strength before placement of grout in lifts greater than 5 ft (1.5 m) in height. For shorter grout liftheights, grout may be poured relatively soon after the brick are laid. Since grout lift heights are very short, the mason contractor should adjust the speed of construction as needed to avoid blowout of the wall. 3.10.7 Wall Ties Across Grout Spaces. Freshly placed grout exerts a hydrostatic pressure on the surrounding masonry formwork. This pressure increases with increasing pour height. To resist the grout pressure, wall ties are used across the grout space to tie the brick wythes together. For multi-wythe masonry walls, a minimum number of wall ties will already be provided to tie the wythes together in accordance with the building code. The wall ties resist the grout pressure by their tensile capacity. The ties provide the additional benefit of a positive mechanical anchorage between the grout core and the surrounding masonry. Ties may not be required across small grout spaces such as in columns or pilasters.
Wall ties across grout spaces should be at least W 1.7 (9 gage) wire. For masonry elements laid in running bond, ties should be spaced not more than 24 in (610 mm) o.c. horizontally and not more than 16 in. (406 mm) o.c. vertically. If stack bond is used, the vertical spacing should be reduced to 12 in. (305 mm) o.c. All ties should be placed in the same line vertically to facilitate the grout consolidation process. Ties should be embedded at least one-half the thickness of the masonry wythe. 3.10.8 Bracing Against Grout Pressure. For grout pour heights less than approximately 5 ft (1.5 m), bracing of the brick masonry may not be necessary. If the grout pour height is greater, consideration should be given to bracing the masonry. This is especially true when a longer curing time for the brick masonry prior to grouting is not feasible. Bracing members are typically externally applied wood construction. The bracing members should be designed by an engineer, based on the grout pour height.
3.11 PLACEMENT OF STEEL REINFORCEMENT Steel reinforcement should be placed in accordance with the size, type and location indicated on the project drawings, and as specified. Dissimilar metals should not be placed in contact with each other because this can promote corrosion of the reinforcement. Nonmetallic flashing should be used when the flashing will come in contact with the reinforcement. If it is possible, all vertical steel reinforcement should be placed after completion of the masonry surrounding the grout space. This keeps the reinforcement out of the mason's way during construction and makes cleaning of the grout space easier. It also prevents contamination of the reinforcement by mortar droppings or protrusions that can adversely affect grout bond to the reinforcement. Applicable building codes should be consulted regarding placement requirements for reinforcement in masonry elements. A summary of the placement requirements for reinforcement in masonry stated in the MSJC Code is given in Table 3. 1 In Flexual members, the "d" dimension is the distance from the extreme compression face to the centroid of the tensile reinforcement.
These requirements are to ensure proper bond to the grout, corrosion protection and fire resistance of the reinforcement. Table 3 also identifies the tolerance limits on positioning reinforcement in masonry elements. Reinforcement should only be spliced where indicated on the project drawings. Reinforcement should not be bent or disturbed after placement of the grout. Vertical reinforcement should be accurately placed and secured prior to the grouting process. Reinforcement can be secured by wire ties or other spacing devices. Some examples of common bar spacing devices are shown in Fig. 4. 3.11.1Bar Spacing Devices
FIG. 4 Vertical reinforcement should be braced at the top and bottom of the element. Additional positioners may be necessary to facilitate proper placement of the bars. When reinforcement is spliced in a grout space between wythes or within an individual cell of hollow brick masonry, the two bars should be placed in contact and wired together. Vertical reinforcement in hollow brick masonry may be spliced by placing the bars in adjacent cells, provided the distance between the bars does not exceed 8 in. (204 mm). Horizontal reinforcement is usually placed in the mortar joints as the work progresses or in bond beams at the completion of the bond beam course. In partially grouted walls, the bond beam should be grouted prior to further construction of brick masonry on top of the bond beam. For two-wythe, solid brick masonry walls, the horizontal reinforcement may be placed in the grouted collar joint. All horizontal bars should be on the same side of the verticalreinforcement to facilitate consolidation of the grout. 3.12 GROUTING The most crucial aspect of constructing RBM elements is the grouting process. While grouting may seem a simple matter of filling cavities or cells of masonry, it is the one aspect of RBM construction that can cause the most problems. The most common problem is the creation of voids in the grout space due to stiff grout, excessive pour height, grout shrinkage, or blocked grout spaces. To ensure proper grouting, four sequential steps should be properly executed: preparation of the grout space, grout batching, grout placement and consolidation, and curing and protection. 3.12.1 Preparation of the Grout Space The configuration and condition of the grout space can vary considerably. Common grout spaces for RBM elements are the cells of hollow brick, the collar joint between multi-wythe brick walls, the core of columns or pilasters and the depth of a beam. For a multi-wythe brick wall with a grouted collar joint, vertical grout barriers, or dams, should be built across the grout space for the entire height of the wall at intervals of not more than 25 ft (7.6 m). Grout barriers control the horizontal flow of grout and reduce segregation. With hollow brick, mortar is placed on the cross webs to confine grout to certain vertical cells. Wire mesh is installed beneath a bond beam to prevent the flow of grout into the masonry below the bond beam. Examples of common grout barrier techniques are shown in Fig. 5. 3.12.2 Vertical Grout Barriers
FIG. 5 Grout spaces should be checked to see that all foreign materials and debris have been removed prior to grouting. The reinforcement should be clean and properly positioned in the grout space. If cleanouts are used, they should be sealed and braced if needed. All grout barriers should be secured and braced, if necessary. The absorption rate of brick masonry will vary considerably with different units and weather conditions. To make the absorption more consistent, the grout space may be wetted prior to grouting. No free water should be on the units when the grout is placed. 3.12.3Grout Batching The quantities of solid materials in the grout mix should be determined by accurate volume measurement at the time of placing in the mixer. All materials for grout should be mixed in a mechanical mixer. Grout is most often supplied in bulk by ready-mix trucks and pumped into place because of the volume and speed of placement required. Batching onsite is more common for smaller projects. When prepared on site, the grout mix should be batched in multiples of a bag of portland cement as a quality control measure. If less than a single bag of portland cement is used, extreme care should be used to accurately measure all parts. Water, sand, aggregate and portland cement should be mixed for a minimum of 2 minutes, then the hydrated lime (if any) and additional water should be added and mixed for an additional 5 to 10 minutes. Make and maintain as high a flow as possible, consistent with good workability. This means that the grout should be wet enough to pour without segregation of the constituent materials or excessive bleeding. Grout should be a plastic mix that is suitable forpumping. The grout slump should be tested in accordance with ASTM C 143 Test Method for Slump of Hydraulic Cement Concrete and should be between 8 and 11 in. (203 and 279 mm). 3.12.4 Grout Placement and Consolidation
Grout should be placed within 1 1/2 hours after the water is first added to the mix and prior to the initial set. Grout slump should be maintained during placement. The grout pour should be done in one or more lifts and the total height of each pour should be from the center of one course to the center of another course of brick masonry. When groutingis stopped for 1 hour or longer, the grout pour should be stopped approximately 1 1/2 in. (38 mm) below the top of the masonry to create a shear key.Whenever possible, grouting should be done from the unexposed face of the masonry element. Extreme care should be expanded to avoid grout staining on the exposed face or faces of the masonry. If grout does contact the face, it should be cleaned off immediately with water and a bristle brush. Waiting until after curing has occurred will make removal difficult. Grout in contact with brick solidifies more rapidly than that in the center of the grout space. It is, therefore, important toconsolidate the grout immediately after pouring to completely fill all voids. The best procedure is to have two people performing the operation jointly; one to pour the grout and the other to consolidate it. A mechanical vibrator or pudding stick is used for this purpose, depending on the construction method used. There are two methods of RBM construction: simultaneous brick construction and grouting, and grouting after brick construction. These are sometimes referred to as "low lift" and "high lift" grouted masonry. In the first method, grout is placed in the masonry as the courses are laid. The grout is consolidated with a pudding stick or a mechanical vibrator. This method is typically used with narrow grout spaces. In the second method, the masonry is built to the story height or its full height, after which grout is poured from a hopper or pumped by mechanical means. The grout is consolidated with a low velocity vibrator with a 3/4 in. (19 mm) head. When grouting between wythes, the vibrator should be placedin the grout at points spaced 12 to 16 in. (305 to 406 mm) apart. The grout pour height restrictions given in Table 2 will limit the method of grout placement permitted in some instances. The mason contractor should give consideration tothe advantages and disadvantages of each method. 3.12.5 Simultaneous Brick Construction and Grouting. The main benefits of simultaneous construction and grouting are elimination of cleanouts, reduction of grout pressures, and simplicity of construction. With this method of grouting, the entire grout space can be kept entirely clear of blockage and can be easily inspected prior to grouting. Consolidation of the entire grout pour is also easier and bracing may be lessened or eliminated. For a multi-wythe brick wall with grouted collar joint, one wythe should be built up not more than 16 in. (406 mm) ahead of the other wythe. Typically, the grout pour height will not exceed 12 in. (305 mm) for such walls and a pudding stick may be used for consolidation purposes. If the grout is carried up too rapidly, there is a chance blowout will occur. If a wythe does move, even as little as 1/8 in. (3 mm) out-of-plumb, the work should be torn down rebuilt. This is because the bed joint bond has been broken and cannot be repaired merely by shoving the wall back into plumb. The grout should be placed to a uniform height between grout barriers and should be consolidated with a mechanical vibrator or pudding stick immediately after placement.
Extreme care should be exercised during grout placement and consolidation to avoid displacement of the brick masonry. 3.12.6 Grouting After Brick Construction. Grouting after construction of the masonry has become the industry standard due to its speed and the fact that grout is often supplied by ready-mix trucks. These trucks deliver large quantities of grout, but cannot remain on site indefinitely during construction. Grout delivery must be coordinated with brick constructionand preparation of grout spaces. The grout spaces in RBM elements can be very small and become crowded with reinforcing bars and wall ties. In addition, some contractors have commented that the highly absorptive nature of somebrick masonry causes the grout to dry out and not flow properly to the bottom of grout spaces if the lift height is too great. The first lift of grout should be placed to a uniform height between the grout barriers or the surrounding brick masonry,and should be mechanically vibrated to fill all voids. This first vibration should be done within 10 minutes after pouring the grout, while the grout is still plastic and before it has set. Grout pours in excess of 12 in. (305 mm) should be reconsolidated by mechanical vibration after initial water loss and settlement has occurred. The succeeding lift shouldbe poured, vibrated and reconsolidated in a similar manner. In the first vibraton, the vibrator should extend 6 to 12 in. (152 to 305 mm) into the preceding lift. This further reconsolidates the first lift and closes any shrinkage cracks orseparations that may have formed. The work should be planned for a single, continuous grout pour to the top of thewall in 5 ft (1.5 m) lifts. Under normal weather conditions, in the range of 40 to 90 degrees F of (4 to 32 degrees C), the waiting period between lifts should be between 30 and 60 minutes. 3.12.7 Curing and Protection The masonry work, particularly the top of the grout pour, should be kept covered and damp to prevent excessive drying. The newly grouted masonry should be fog sprayed three times each day for a period of three days followingconstruction when the ambient temperature exceeds 100 degrees F (38 degrees C) or 90 degrees F (32 degrees C) with a wind speed in excess of 8 mph (13 km/hr). The exposed faces of brickwork should be cleaned prior to the fog spraying. Cleaning will be much more difficult if it is postponed until after this curing. The water from cleaning will also aid in the curing process. For walls, columns and pilasters, at least 12 hours should elapse after construction before application of floor or roof members, except that 72 hours should elapse prior to application of heavy, concentrated loads such as truss, girder or beam members. 3.13 Tbeam In the construction of reinforced concrete structural element, fresh concrete is normally poured into the slab and the beam’s form work simultaneously. When concrete hardens, a homogeneous concrete is formed. This will enable part of the slab to act as part of the beam. In practice, the flange is often the floor slab and this is shown in Figure 5.1 below: Actual width
Slab
13.1
Effective width, b
The question arises of what width of the slab is to be taken as the effective width? The answer is, the width b in Figure 5.2
b
bw Figure 5.2: T‐Beam
Clause 3.4.1.5 BS 8110 gives the following recommendation for a T-beam, the effective width b should be taken as: bw + 0.2 l z or The actual flange width or whichever is lesser.
l z is the distance between points of zero moment along the span of the beam. For a continuous beam (we shall discuss this type of beam in Unit 6), l z may be determined from the bending moment diagram, but BS 8110 states that l z be taken as 0.7 times the effective span.
Ex: Given the floor plan showing the arrangement of T-beams, calculate the effective width of the beam.
T‐Beam
T‐Beam
T‐Beam 9.0 m
bw = 250mm
2.0 m
2.0 m Plan
Section Figure 5.3: Arrangement of T‐Beam
bw + 0.2lx = 250 + 0.2(9000) = 2050 mm
Actual flange width = 2000mm The effective width, b is the lesser of these values i.e. b = 2000 mm 13.2
Analysis of T-section
There are three cases to be considered. They are as follows: 13.2.1 Neutral axis in the flange 13.2.2 Neutral axis under the flange 13.2.3 Neutral axis outside the flange 13.3
Neutral axis in the flanged.
This happens when the depth of the stress block is less than the flange thickness(hf). This is shown in Figure 4 below:
b
Fcc=0.405fcubx
0.9x
d Z=d – 0.45x As Fst=0.87fyAs
bw section is given by, Moment of resistance the
M = Fcc . Z
Figure 5.4: Stress Block
= 0.405 fcub (0.9x) (d-0.45x) In this case the maximum depth of the stress block which is equal to 0.9x is equivalent to hf. Therefore,
M = Mf =
0.45 f cu bh f (d −
hf 2
)
(Where Mf is known as the ultimate moment of resistance of the flange) It can be shown that when the applied moment, M is lesser or equal to Mf, the neutral axis is located in the flange. In this case the design of the section is similar to that of the rectangular section which has been discussed in Unit 4.
13.3.1 Design Example (N.A in the flange)
A T-Beam is to carry a design moment (M = 165 kNm). The beam section is shown in Figure 5.5. If concrete of grade 30 and steel of grade 460 are used, calculate the area and the total number of bars required.
b hf=100 mm d =320
Solution: Resistance moment of flange: M f = 0.45 f cubh f (d −
hf 2
)
100 = 0.45 x 30 x 1450 x 100 (320 – 2 )
=528.5 kNm Since M< Mf, the neutral axis is located in the flange. K=
=
M bd 2 f cu
165 × 106 1450 × 3202 × 30 = 0.036 < K’ (=0.156)
Z = d{0.5 + (0.25 −
= d{0.5 + (0.25 −
K )} 0.9
0.036 )} 0.9
= 0.957d > 0.95d
As =
M 0.87 f y Z
165 × 106 = 0.87 × 460 × 0.95 × 320
= 1356 mm2
Provided 3T25 (As=1470 mm2) Ex: For the T-Beam shown in Figure 5.6, calculate the area and number of bars required to carry a design moment of 450 kNm. Use fcu = 30N/mm2and fy=460 N / mm2
800 mm hf=150 d=420mm
150 Mf = 0.45 x 30 x 800 x 150 x (420 - 2 )
= 558.9 kNm M < Mf bw=200 Figure 5.6: T‐Beam Therefore, this shows that neutral axis is located in the flange.
K=
450 × 106 800 × (420) 2 × 30 = 0.106 < K’
∴
Only tension reinforcement is needed.
Z = d {0.5 + 0.25 −
0.106 } 0.9
= 0.86d < 0.95d As =
450 × 106 0.87 × 460 × 0.86 × 420 = 3113 mm2
4T32 (As = 3218 mm2)
Provided:
N.A Located Under the Flange.
13.4
When the applied moment, M is greater than the moment of resistance, Mf, the neutral axis will be located under the flange as shown in Figure 5.7.
Fcc2 2
1
2
Fcc1
Z 1 AS Fst Figure 5.7: N.A Located Under the Flange.
Referring to Figure 5.7,
The Internal forces are: Fcc1 = (0.45fcu)(bw . 0.9x) = 0.405fcubwx Fcc2 = (0.405fcu)( b- bw )hf Fst = 0.87fyAs
Lever Arm: Z1 = d -0.45x Z2 = d – 0.5hf
Moment of resistance is given as follows: M = Fcc1 . Z1 + Fcc2 . Z2
Z 2
= (0.405fcubwx)(d - 0.45x) + (0.45fcu)(b - bw)hf(d - 0.5hf)
The ultimate moment of resistance of the section (when x = 0.5d) is given by,
Muf = 0.405fcubw0.5d [d - 0.45(0.5d)] + (0.45fcu)(b - bw)hf(d - 0.5hf) = 0.156fcubwd2 + (0.45fcu)(b-bw) hf (d-0.5hf)
When the applied moment, M
M = Fst .Z2 - Fcc1. (Z2 - Z1) = 0.87fyAs(d - 0.5hf) - 0.405fcubw x [(d - 0.5hf)-(d - 0.45x)]
M + 0.405 f cubw x(0.45 x − 0.5h f ) ∴
As =
0.87 f y (d − 0.5h f )
Equating x = 0.5d (at ultimate limit) Therefore,
As =
M + 0.1 f cubwd (0.45d − h f ) 0.87 f y (d − 0.5h f )
This is equation 1, BS 8110 and should be used when hf< 0.45d.
13.4.1 Design example (N.A under the flange) (Use concrete grade 30 and steel grade 460). T-Beam as shown in Figure 5.6 above is subjected to a design moment of 550kNm. Calculate the area of reinforcement required.
Solution:
Mf = 528.5 kNm. (Calculated before in 5.5) Mf< M (=550 kNm) Muf = 0.156fcubwd2 + (0.45fcu)(b - bw)hf(d-0.5hf) =0.156(30)(250)(320)2 + (0.45)(30)(1450 – 250)(100)(320 – 50) =552.3 kNm> M This shows that, only tension reinforcement is required and is calculated as follows:-
As =
=
M + 0.1 f cubwd [0.45d − h f ] 0.87 f y (d − 0.5h f )
550 × 106 + 0.1(30)(250)(320)(0.45 × 320 − 100) 0.87(460)(320 − 50) = 5188 mm2 3T40 + 3T25 (5240 mm2)
Use:
The approximate arrangement of these bars is shown below: -`
Figure T‐Beam
3T25 3T40
Ex: Calculate the area of reinforcement required for the beam section given below if the bending moment is 2750 kNm. Use fcu = 30 N/mm2 and fy = 460 N/mm2. b = 1600 mm
hf = 250 mm d = 700 h
M f = 0.45 f cu bh f (d −
f
2
)
= 0.45(30)(300)( 250)(700 −
250 ) 2 Figure 5.10: T‐Beam
= 582.2 kNm. bw = 300
M > Mf. (N.A. under the flange)
M uf = 0.156 f cubwd 2 + (0.45) f cu (b − bw )h f (d − 0.5h f ) = 0.156(30)(300)(700) 2 + (0.45)(30)(1600 − 300)( 250)(700 −
250 ) 2
= 687.96 + 2522.8 = 3210.8 kNm
Muf> M (=2750 kNm). This indicates that only tension reinforcement is required Check that hf< 0.45d 0.45d = 0.45(700) =315 mm ∴ hf< 0.45d and we are going to use equation 1, BS 8110 shown below:
To calculate the area of reinforcement required.
As =
M + 0.1 f cubwd [0.45d − h f ) 0.87 f y (d − 0.5h f )
=
2750 × 106 + 0.1(30)(300)(700)(0.45(700) − 250) 0.87(460)(700 − 0.5 × 250)
=
2790.95 × 106 230115 = 12128.5 mm2
Use: 13.5
7T40 + 7T32 (As = 12238 mm2) Neutral Axis Outside The Flange
When the applied moment M >Muf, the compression reinforcement should be provided so that the depth of neutral axis, x does not exceed 0.5d. The stress distribution for a flanged beam provided with compression reinforcement is shown in Figure 5.11 below:-
Fsc Fcc2 Fcc1
Fst
Figure 5.11: The stress distribution for a flanged beam
Referring to Figure 5.11, the forces in the stress block are as follows: Fcc1 = 0.405fcubwx Fcc2 = 0.45fcu(b - bw)hf Fst= 0.87fyAs Fsc= 0.87fyAs’
The lever arm is: Z1 = d - 0.45x Z2 = d - 0.5hf Z3 = d – d’
Taking moments about the tension reinforcement, we have: M = Fsc . Z3 + Fcc1 . Z1 + Fcc2 . Z2 = 0.87fyAs’(d -d’)+(0.405fcubwx)(d - 0.45x) + (0.45fcu)(b - bw)hf(d - 0.5hf)
At ultimate limit state, x = 0.5d, M = 0.87fyAs’(d - d’) + Muf
M − M uf Therefore, As’ =
0.87 f y (d − d ' )
For Equilibrium of the forces: -
Fst = Fcc1 + Fcc2 + Fsc d 0.87fyAs =0.405fcubw( 2 )+ 0.45fcu(b -bw)hf + 0.87fyAs’
Therefore, As = [0.2fcubwd + 0.45fcuhf (b - bw)+ 0.87
As =
[0.2 f cubw d + 0.45 f cu h f (d − d ' ) + 0.87 f y As 0.87 f y
Design Example (N.A outside the Flange)
Given the beam section and data, calculate the area of reinforcement required so that beam can carry a design moment of 650 kNm. Assume that d’ = 50 mm
b = 1450 hf = 100
fcu=30 N/mm2 fy = 460 N/mm2
d = 320
Figure 5.12
bw = 250
Solution: Mf = 528.5 kNm< M (=650 kNm) ¾ Neutral axis located outside the flange.
Muf = 552.3 kNm< M (=650kNm) ¾ Compression reinforcement is required.
As =
=
M − M uf 0.87 f y (d − d ' )
(650 − 552.3) × 106 0.87 × 460 × (320 − 50) = 904 mm2
As = [
=[
0.2 f cubw d + 0.45 f cu h f (b − bw ) 0.87 f y
] + As '
0.2(30)(250)(320) + (0.45)(30)(100)(1450 − 250) ] + 904 0.87(460)
= 5247 + 904 = 6151 mm2
Use: 3T20 (As = 943 mm2) for compression reinforcement 5T40 (As = 6286 mm2) for tension reinforcement. Calculate the reinforcement required for a flanged beam with the following information: M = 1700 kNm
d = 618 mm
fcu = 30 N/mm2
d’ = 60 mm (embedment of compression reinforcement)
M f =fy = 460 30 N/mm 0.45 f cu bh f (d − 0 .5h f ) 2
b = 1200 mm
= 0.45(30)(1200 )(150)(618 − 0.5 × 150)
=1319.5 kNm
Mf< M (=1700)
M uf = 0.156 f cubw d 2 + (0.45 f cu )(b − bw )h f (d − 0.5h f ) = 0.156(30)(300)(618) 2 + (0.45 × 30)(900)(150)(543)
=1525.8 kNm Muf< M (=1700 kNm) ∴ Compression reinforcement is required.
As ' =
M − M uf 0.87 f y (d − d ' )
(1700 − 1525.8) × 106 = 0.87(460)(618 − 60) =780 mm2
As = [
=
0.2 f cu bw d + 0.45 f cu (b − bw ) ] + As ' 0.87 f y
0.2(30)(300)(618) + (0.45)(30)(1200 − 300) + 780 0.87(460)
= 3590 mm2 Use: 7T12 (As = 792 mm2) as compression reinforcement 5T25 + 4T20 (As = 3712 mm2) as the tension reinforcement To design flanged beam, the following procedure can be used: ¾ Calculate Mf = 0.45fcubhf(d - 0.5hf) ¾ Compare Mf with M (applied moment) ¾ If M
Z = d [0.5 + (0.25 − As =
M bd 2 f cu
M 0.87 f y Z
K )], butZ < 0.95d 0.9
¾ If M > Mf, neutral axis is located at outside of flange. Calculate: βf from Table 3.7 or equation 2 BS8110 Mu f = βffcubd2 Compare M with Muf Check that hf< 0.45d ¾ If M
As =
M + 0.1 f cubwd (0.45d − h f ) 0.87 f y (d − 0.5h f )
If M >Muf, compression reinforcement is required. Calculate:
As ' =
As =
( M − M uf ) 0.87 f y (d − d ' )
0.2 f cubwd + 0.45 f cu h f (b − bw ) 0.87 f y
+ As '
Questions
1. What is Reinforced brick work? 2. Explain general principles of design of reinforced brick lintels and slabs? 3. What are the specifications for RB work construction? 4. What is the structural behaviour of T beam? 5. Describe the rules for the design of R beams? 6. Design simply supported T beams?
UNIT 4 Structure of this unit
Columns, Basic Concept of Prestressed Concrete Objectives to be learned
1. Concept of long and short columns 2. IS specifications for main and lateral reinforcement 3. Behavior of RCC columns under axial load 4. Design of Axially loaded short and long columns with hinged ends 5. Design of Isolated footings 6. Introduction of prestressed concrete, general theory, Linear post tensioning general, post tensioning advantages to the design engineer and the contractor 7. Linear post tensioning system, high strength post tensioned stands, parallel lay wire, high strength alloy steel bars 8. Techniques of post tensioning general, special requirements for forming and false work, ducts and closures, 9. placing of ducts or tendons, concreting, stressing procedure, grouting, protecting anchorage from corrosion 10. Pretionsioning general, pretensioning yards set up, forms for partitioning structural elements. Special techniques of pretension 11. Materials of prestressing cement,aggregates, concrete, admixtures, vibrations, curing light weight aggregates, 12. high strength steel bars, high strength stand, stress relaxation, 13. galvanization Codes specifications and inspection, 14. manufacturers of prestressing equiment, specifications, sizes and costs
4.1 Columns Columns may be divided into three general types: Short Columns, Intermediate Columns, and Long Columns. The distinction between types of columns is not well defined, but a generally accepted measure is based on the Slenderness Ratio. The Slenderness Ratio is the (effective) length of the column divided by its radius of gyration.
The radius of gyration is the distance from an axis which, if the entire cross sectional area of the object (beam) were located at that distance, it would result in the same moment of inertia
that the object (beam) possesses. Or, it may be expressed as: Radius of Gyration: rxx = (Ixx/A)1/2 (radius of gyration about xx-axis) So, Slenderness Ratio = Le / r. Notice that we have put a subscript "e" by the length of the column. This is to indicate that, depending on how the column is supported, we do not use the actual length but an ‘effective length’. The effective length is given by: Le = K L, where K could be called an effective length constant. The values for K depend on how the column is supported.
A generally accepted relationship between the slenderness ratio and the type of Column is as follows: Short Column: 0< Le / r < 60 Intermediate Column: 60< Le / r <120 Long Column: 120< Le / r < 300 4.1.I. Short Columns: When slenderness ratio < 60, a column will not fail due to buckling, as the ratio of the column length to the effective cross sectional area is too small. Rather a short, 'thick' column, axially loaded, will fail in simple compressive failure: that is when the load/area of the column exceeds the allowable stress, P/A > s allow. Eccentrically loaded short columns have a slightly more complicated result for compression failure, which we will look at later in this section. We also will put off discussion of intermediate length columns until we have discussed long columns. Idealized buckling in long columns was first treated by the famous mathematician Leonard Euler.
4.1.II. Long L Colum mns & Euleer's Equatioon: In 17577, Leonard E Euler (pronoounced Oileer) developeed a relationsship for the critical coluumn load whhich would pproduce bucckling. A verry brief deriivation of Euuler's equatioon goes as foollows:
A loadedd pinned-pin nned columnn is shown iin the diagrram. A top section s of thhe diagram is shown with w the bend ding momennt indicated,, and in term ms of the looad P, and the t deflectioon distance y, we can write: 1. M = - P y. We also can write that for beeams/columnns the bendding momennt is proporrtional to thhe curvaturee of the beam, which, w for small deeflection ccan be ex xpressed as: a 2 2 2. (M /EII) = (d y /dx x) (See Streength of Material M text chapters onn beams annd beam deformations.)) Where E = Young's modulus, annd I = mom ment of Inerttial. Then suubstituting from f EQ. 1 to EQ. 2, we w obtain: dx2) = -(P/EII)y or (d2y /d dx2) + (P/EII)y = 0 3.(d2y /d This is a second order differrential equaation, whichh has a geeneral soluttion form of o 4. : dary conditioons: y = 0 att x = 0, and y = 0 at x = L. That is, the deflectioon We next apply bound of the coolumn mustt be zero att each end since it is pinned p at eaach end. Appplying thesse conditionns (putting thhese values into the equuation) givess us the folloowing resultts: For y to be b zero at x =0, the valuue of B must be zero (siince cos (0) = 1). While for y to be zero at x = L, L then eitheer A must bee zero (whicch leaves us with no equation at all, if i A and B are a both zeroo),
or .
Which
resuults
in
thee
facct
that
w solve for P and find: Andd we can now
5. initiated.
, wheere Pcr standds for the crittical load wh hich can be aapplied befoore buckling is
placing L wiith the effecctive length, Le, which was w defined above, we can c generalizze 6. By rep foormula the too: , whicch then appllies to Pinned-Pinned, Fiixed-Pinned, Fixed-Fixeed, and FixeddFree coluumns. This equaation is a forrm of Euler's Equation. Another form m may be obbtained by solving for thhe
critical sttress: and then rememberinng that the Radius R of Gyyration: rxxx = (Ixx/A)1/2 , and substiituting we caan obtain:
which giives the critiical stress inn terms of Young's Y Mod dulus of the column maaterial and thhe slenderneess ratio. Let us at this time also point outt that Euler'ss formula appplies only while w the matterial is in thhe r Thatt is, the critical stress must m not exceeed the propportional lim mit elastic/prroportional region. stress. If we now subbstitute the proportional p limit stress for f the criticcal stress, wee can arrive at an equatiion for the minimum m slen nderness rattio such that Euler's equaation will be valid.
As an exxample: Forr structural steel with a proportion nal limit streess of 35,00 00 psi., and a Young's Modulus off E = 30 x 10 1 6 psi., we can obtain (Le/r) =sqrrt( 3.142 x 30 3 x 106 psii / 35,000 psi) p = 92 Thhis is the minimum m sleenderness raatio for whiich we coulld use Eulerr's buckling equation wiith this colum mn material..
Euler's Equation for columns while useful, is only reasonably accurate for long columns, or slenderness ratio's of general range: 120< Le / r < 300, and in addition will work for axially loaded members with stress in the elastic region, but not with eccentrically loaded columns. Some additional points need to be mentioned.
The slenderness ratio (Le/r) depends on the radius of gyration, (rxx = (Ixx/A)1/2&ryy = (Iyy/A)1/2 ), which in turns depends on the moment of inertia of the column cross section. The value of the moment of inertia depends on the axis about which it is calculated. That is, for a rectangular 2" x 4" cross section, the column will buckle in the 2" direction rather than the 4" direction, as the moment of inertia for the 2" direction is considerable smaller than the moment of inertia in the 4" direction. (I = (1/12) b d3 = (1/12) (4")(2")3 = 2.67 in4, as compared to I = (1/12) b d3 = (1/12) (2")(4")3 = 10.67 in4 ) It is important to point this out, so that when given a column cross section, the student must be sure to determine the minimum moment of inertia, as buckling will occur in the direction. It should also be pointed out that while these formulas give reasonable values for critical loads causing buckling, it should not be assumed the values are completely accurate. Buckling is a complicated phenomena, and the buckling in any individual column may be influenced by misalignment in loading, variations in straightness of the member, presence of initial unknown stresses in the column, and defects in the material. Several examples of buckling calculations follow. Example 1
An 16 ft. long ASTM-A36 steel, W10x29 I-Beam is to be used as a column with pinned ends. For this column, determine the slenderness ratio, the load that will result in Euler buckling, and the associated Euler buckling stress. The beam characteristics may be found in the IBeam Table, and are also listed below. -
-
-
Flange Flange Web Cross Section Info. Cross Section Info.
Designation Area Depth Width thick
x-x thick axis
-
Ain2
W 10x29
8.54 10.22 5.799 0.500 0.289 158.0 30.8
d - in wf - in tf - in
tw in
–
x-x axis
I - in4 S -in3
x-x axis
y-y axis
y-y axis
y-y axis
r - in I - in4 S -in3
r - in
4.30
1.38
16.30 5.61
The slenderness ratio = Le / r = 16 ft. * 12 in./ft./ 1.38 in = 139
Notice that we must use the smallest radius of gyration, with respect to the y-y axis, as that is the axis about which buckling will occur. We also notice that the slenderness ratio is large enough to apply Euler’s buckling formula to this beam. To verify this we use the relationship for the minimum slenderness ratio for Euler’s equation to be valid.
Or, after finding for ASTM-A36 Steel, E = 29 x 106lb/in2, and yield stress = 36,000 lb/in2, we can solve and determine that Le/r = 89. The Euler Buckling Load is then give by: , and after substituting values, we obtain: Pcr = [(3.14)2*29x106lb/in2 * 16.30 in4/(16’x12"/ft)2] = 126,428 lb
c) The Euler Stress is then easily found by Stress = Force/Area = 126,428 lb/8.54 in2 = 14,800 lb/in2. Notice that this stress which will produce buckling is much less than the yield stress of the material. This means that the column will fail in buckling before axial compressive failure. Example 2
A 8 ft. long southern pine 2" x 4" is to be used as a column. The yield stress for the wood is 6,500 lb/in2, and Young’s modulus is 1.9 x 106lb/in2. For this column, determine the slenderness ratio, the load that will produce Euler buckling, and the associated Euler buckling stress. The slenderness ratio = Le / r . To determine the slenderness ratio in this problem, we first have to find the radius of gryration (smallest), which we may do from the relationship: Radius of Gyration: rxx = (Ixx/A)1/2 , where this is the radius of gyration about an x-x axis, and where I = (1/12)bd3 for a rectangular cross section. Or rxx = [(1/12)bd3/bd]1/2 , where we have substituted A = bd. We now simplify and obtain: rxx = [(1/12)d2]1/2 = .5774(d/2) We want the smallest radius of gyration, so we use d =2". That is, buckling will first occur about the x-x axis shown is the diagram, and r = .5774 in.
Then Slenderness ratio is given by: Le / r = ( 8ft x 12"/ft)/.5774" = 166 which puts the beam in the long slender category.
The Euler Buckling Load is then give by: obtain:
, and after substituting values, we
Pcr = [(3.14)2*1.9x106 lb/in2 * (4*23/12) in4/(8’x12"/ft)2] = 5,420 lb. c) The Euler Stress is then easily found by Stress = Force/Area = 5,420 lb/(2"*4") in2 = 678 lb/in2. Notice that this stress which will produce buckling is much less than the yield stress of the material. 4.1.III. Intermediate Columns
There are a number of semi-empirical formulas for buckling in columns in the intermediate length range. One of these is the J.B. Johnson Formula. We will not derive this formula, but make several comments. The J.B. Johnson formula is the equation of a parabola with the following characteristics. For a graph of stress versus slenderness ratio, the parabola has its vertex at the value of the yield stress on the y-axis. Additionally, the parabola is tangent to the Euler curve at a value of the slenderness ratio, such that the corresponding stress is onehalf of the yield stress. In the diagram below, we have a steel member with a yield stress of 40,000 psi. Notice the parabolic curve beginning at the yield stress and arriving tangent to the Euler curve at 1/2 the yield stress.
We first note that at the point where the Johnson formula and Euler's formula are tangent, we can relate the stress to Euler's formula as follows (where C represents the slenderness ratio when the stress is 1/2 the yield stress):
From this we find an expression for C (critical slenderness ratio) of: For our particular case, where we have a steel member with a yield stress of 40,000 psi, and a Young's modulus of 30 x 106 psi., we find C = sqrt(2 * 3.142 * 30 x 106 / 40,000 psi) = 122. If our actual beam has a slenderness ratio greater than the critical slenderness ratio we may use Euler’s formula. If on the other hand our actual slenderness ratio is small than the critical slenderness ratio, we may use the J.B. Johnson Formula. Example: As an example let us now take a 20 foot long W12 x 58 steel column (made of same steel as above), and calculate the critical stress using the J.B. Johnson formula. (Beam information and Johnson formula shown below.)
-
-
-
Flange Flange Web Cross Section Info. Cross Section Info.
Designation Area Depth Width thick
x-x thick axis tw in
-
x-x axis
-
A-in2 d - in wf - in tf - in
I - in4 S -in3
W 12x58
17.10 12.19 10.014 0.641 0.359 476.0 78.1
x-x axis
y-y axis
y-y axis
y-y axis
r - in I - in4 S -in3
r - in
5.28 107.00 21.40
2.51
J.B. Johnson's formula:
For our beam the slenderness ratio = (20 ft * 12 in/ft)/2.51in = 95.6 (where 2.51 in. is the smallest radius of gyration, about y-y axis). Inserting values we find: Critical Stress = [ 1 - (95.62/2* 1222)]*40,000 psi. = 27,720 psi. This is the critical stress that would produce buckling. Note we did not have a safety factor in this problem. As a result we really would not want to load the column to near the critical stress, but at a lower 'allowable' stress.
The Critical Load will equal the product of the critical stress and the area, or Pcr = 27,720 psi. * 17.10 in2 = 474,012 lb. 4.1.VI. The Secant Formula:
Another useful formula is known as the Secant formula. We will not go through the derivation of this relationship, but focus on its application. The Secant formula may be used for both axially loaded and eccentrically loaded columns. It may be used with pinned-pinned (Le = L), and with fixed-free (Le = 2L) end columns, but not with other end conditions.
The Secant formula gives the maximum compressive stress in the column as a function of the average axial stress (P/A), the slenderness ratio (L/r), the eccentricity ratio (ec/r2), and Young’s Modulus for the material. If, for a given column, the load, P, and eccentricity of the load, e, are known, then the maximum compressive stress can be calculated. Once we have the maximum compressive stress due to the load, we can compare this stress with the allowable stress for the material and decide if the column will be able to carry the load. On the other hand, if we know the allowable compressive stress for the column, we may use the Secant formula to determine the maximum load we can safely apply to the column. In this case we will be solving for P, and we take note that the equation is a transcendental equation when solved for P. Thus, the easiest method of solution is to simply try different values of P, until we find a satisfactory fit. See following example.
The eccentricity ratio has a normal range from 0 to 3, with most values being less than 1. When the eccentricity value is zero (corresponding to an axial loading) we have the special case that the maximum load is the critical load:
and th he correspo onding stress is the criitical stress
o or
This is one o way to look l at axiaal loads. On the other hand h a comm mon practicee with axiallly loaded sttructural steeel columns is i to use an eeccentricity ratio of .25 to account for f the effeccts of imperfections, ectt. Then the allowable sttress does no ot have to bbe reduced to t account foor column imperfectionns, ect, as this is taken intto account in n eccentricitty ratio.
4.1.5. Em mpirical Dessign Formu ulas for Colu umns: A numbeer of empiriccal design fo ormulas have been developed for m materials suchh as structurral steel, aluuminum andd wood, and may be fouund in such publicationns as the Ma anual of Steel Construcction, Mecha anic, Speciffications forr Aluminum Structures, Aluminum Constructioon Manuel, Timber Coonstruction Manual, aand Nationaal Design SSpecificationns for Woood Constucttion. 4.1.5.1. Structural S S Steel:
4.1.5.2. Aluminum A
4.1.5.3. Wood Columns
4.1.VI Short Eccentrically Loaded Columns
An eccentrically loaded short column is shown in the diagram, with the force, P, acting a distance, e, from the centroid of the column cross sectional area. We may replace the eccentrically acting force, P , with an axial force, P, plus a moment whose value will be M = P x e. Next we calculate the compressive stress due to the axial force, P, which will simply be P/A. Then we calculate the bending stress due to the moment P x e, which gives (Pe)c/I where the bending stress will be a compressive maximum on the right side of the column and a tensile maximum on the left side of the column (and zero at the centroid). Finally, we add the two stress and obtain Total Maximum Compressive Stress = (P/A)(1 + A e c1/I) (right side of column), and the Total Minimum Compressive Stress = (P/A)(1 - A e c1/I) (left side of column). And in fact, if the bending stress is large enough, the left side on the column may be in tension.
Topic 1a - Example 1 - Combined Stress
A loaded beam (shown in Diagram 1) is pinned to the wall at point A, and is supported by a rod DB, attached to the wall at point D and to the beam at point B. The beam has a load of 6,000 lb. acting downward at point C. The supporting rod makes an angle of 25o with respect to the beam. The beam cross section is a W8 x 24 I-Beam, with the characteristics shown in Diagram 1. We would like to determine the maximum axial stress acting in the beam cross section.
Solution:
We first apply static equilibrium to the beam and determine the external support reactions acting on the beam at point A. Sum of Forcex = Ax - T cos 25o = 0 Sum of Forcey = Ay + T sin 25o - 6,000 lb. = 0 Sum of TorqueA = -6,000 lb (10ft) + T cos 25o (2.8 ft.) = 0 (where 2.8 ft. = distance from A to D) Solving: T = 23,640 lb.; Ax = 21,430 lb., and Ay = -3990 lb. (Ay acts downward) We next draw the Shear Force and Bending Moment Diagrams, and use the Bending Moment Diagram to determine the Maximum Bending Stress in the beam. (See Diagram2.)
We next will consider the axial stress due to the horizontal force acting on the beam. In section AB the beam is in compression with horizontal axial force of 21,430 lb. (Due to the force Ax and the horizontal component of the force in rod DB.) For beam section BC, there is no horizontal axial force due to an external horizontal force. That is, section AB is in compression, but section BC is not experiencing normal horizontal stress, since it is to the right of where the support rod is attached. (However, there is a horizontal bending stress due to the bending moment, which is in turn due to the vertical loads being applied. This will be considered in a moment.) The compressive horizontal axial stress in section AB is given simply by: F/A = 21,430 lb. / 7.08 in2 = 3,030 lb/in2. (We have considered the force to act along the centroid of the beam.) There is a bending stress also acting in the beam. The maximum bending stress occurs at the outer edge of the beam, and at the point in the beam where the bending moment is a maximum. From our bending moment diagram, we see that the maximum bending moment occurs at 6 feet from the left end, and has a value of -24,000 ftlb. = -288,000 in-lb. ( The negative sign indicating that the top of the beam is in tension and the bottom of the beam is in compression.) We can then calculate the maximum bending moment by: Maximum Bending Stress = M / S Where S is the section modulus for the beam. In this example S = 20.9 in3. Then:Maximum Bending Stress = (288,000 in-lb.)/20.9 in3 = 13,780 lb/in2.Since the bending moment was negative, the top of the I-Beam will be in tension, and the bottom of the beam will be in compression.The total axial stress at a point in the beam will be the sum of the normal axial stress and the axial bending stress. (See Diagram 3)
We can now combine (sum) the axial stresses at the very top and bottom of the beam to determine the maximum axial stress. We see in the beam section (at 6 ft from left end) in Diagram 3, that the stresses at the bottom of the beam are both compressive, and so add to a total compressive stress of 13,780 lb./in2 + 3,030 lb./in2 = 16, 810 lb./in2. At the top of the beam, the bending stress is tensile and the normal axial stress in compressive so the resultant bottom stress is: +13,780 lb./in2 - 3,030 lb./in2 = 10,750 lb./in2 (tension).
4.2 Specifications as per IS: 456-2000
Longitudinal reinforcement
1. The cross-sectional area of longitudinal reinforcement, shall be not less than 0.8 percent nor more than 6 percent of the gross cross sectional area of the column. 2. NOTE - The use of 6 percent reinforcement may involve practical difficulties in placing and compacting of concrete; hence lower percentage is recommended. Where bars from the columns below have to be lapped with those in the column under consideration, the percentage of steel shall usually not exceed 4 percent. 3. In any column that has a larger cross-sectional area than that required to support the load, the minimum percentage of steel shall be based upon the area of concrete required to resist the direct stress and not upon the actual area. 4. The minimum number of longitudinal bars provided in a column shall be four in rectangular columns and six in circular columns. 5. The bars shall not be less than 12 mm in diameter 6. A reinforced concrete column having helical reinforcement shall have at least six bars of longitudinal reinforcement within the helical reinforcement. 7. In a helically reinforced column, the longitudinal bars shall be in contact with the helical reinforcement and equidistant around its inner circumference. 8. Spacing of longitudinal bars measured along the periphery of the column shall not exceed 300 mm. 9. In case of pedestals in which the longitudinal reinforcement is not taken in account in strength calculations, nominal longitudinal reinforcement not less than 0.15 percent of the cross-sectional area shall be provided.
4.3 Transverse reinforcement
A reinforced concrete compression member shall have transverse or helical reinforcement so disposed that every longitudinal bar nearest to the compression face has effective lateral support against buckling. The effective lateral support is given by transverse reinforcement either in the form of circular rings capable of taking up circumferential tension or by polygonal links (lateral ties) with internal angles not exceeding 135°. The ends of the transverse reinforcement shall be properly anchored. Arrangement of transverse reinforcement
If the longitudinal bars are not spaced more than 75 mm on either side, transverse reinforcement need only to go round corner and alternate bars for the purpose of providing effective lateral supports (Ref. IS:456). If the longitudinal bars spaced at a distance of not exceeding 48 times the diameter of the tie are effectively tied in two directions, additional longitudinal bars in between these bars need to be tied in one direction by open ties (Ref. IS:456).
4.3.1 Pitch and diameter of lateral ties
1) Pitch-The pitch of transverse reinforcement shall be not more than the least of the following distances: i) The least lateral dimension of the compression members; ii) Sixteen times the smallest diameter of the longitudinal reinforcement bar to be tied; and iii) 300 mm. 2) Diameter-The diameter of the polygonal links or lateral ties shall be not less than onefourth of the diameter of the largest longitudinal bar, and in no case less than 6 mm. Helical reinforcement 1) Pitch-Helical reinforcement shall be of regular formation with the turns of the helix spaced evenly and its ends shall be anchored properly by providing one and a half extra turns of the spiral bar. Where an increased load on the column on the strength of the helical reinforcement is allowed for, the pitch of helical turns shall be not more than 7.5 mm, nor more than one
sixth of the core diameter of the column, nor less than 25 mm, nor less than three times the diameter of the steel bar forming the helix. 4.4 Behavior of RCC columns under axial load
Short reinforced concrete columns under axial load with uniaxial bending behave in a different manner than when it is subjected to axial load, though columns subjected to axial load can also carry some moment that may appear during construction or otherwise. The behaviour of such columns and the three modes of failure. It is explained that the moment M, equivalent to the load P with eccentricity e (= M/P), will act in an interactive manner. A particular column with specific amount of longitudinal steel, therefore, can carry either a purely axial load Po (when M = 0), a purely moment Mo (when P = 0) or several pairs of P and M in an interactive manner. Hence, the needed interaction diagram of columns, which is a plot of P versus M, is explained discussing different positions of neutral axis, either outside or within the cross-section of the column. Depending on the position of the neutral axis, the column may or may not have tensile stress to be taken by longitudinal steel. In the compression region however, longitudinal steel will carry the compression load along with the concrete as in the case of axially loaded column. 4.4.1 Behaviour of Short Columns under Axial Load and Uniaxial Moment Normally, the side columns of a grid of beams and columns are subjected to axial load P and uniaxial moment Mxcausing bending about the major axis xx, hereafter will be written as M. The moment M can be made equivalent to the axial load P acting at an eccentricity of e (= M/P). Let us consider a symmetrically reinforced short rectangular column subjected to axial load Puat an eccentricity of e to have Mu causing failure of the column. For the strain profile IN, the depth of the neutral axis kDis less than D, i.e., neutral axis is within the section resulting the maximum compressive strain of 0.0035 on the right edge and tensile strains on the left of the neutral axis forming cracks. This column is in a state of collapse for the axial force Puand moment Mu for which IN is the strain profile. Reducing the eccentricity of the load Puto zero, we get the other strain profile EF resulting in the constant compressive strain of 0.002, which also is another collapse load. This axial load Puis different from the other one, i.e., a pair of Puand Mu, for which IN is the profile. For the strain profile EF, the neutral axis is at infinity (k = α). Figure presents the strain profile EF with two more strain profiles IH and JK intersecting at the fulcrum point V. The strain profile IH has the neutral axis depth kD = D, while other strain profile JK has kD> D. The load and its eccentricity for the strain profile IH are such that the maximum compressive strain reaches 0.0035 at the right edge causing collapse of the column, though the strains throughout the depth is compressive and zero at the left edge. The strain profile JK has the maximum compressive strain at the right edge between 0.002 and 0.0035 and the minimum compressive strain at the left edge. This strain profile JK also causes collapse of the column since the maximum compressive strain at the right edge is a limiting strain.
The four strain profiles, IN, EF, JK and IH of Figs.b and c, separately cause collapse of the same column when subjected to four different pairs of Puand Mu. This shows that the column may collapse either due to a uniform constant strain throughout (= 0.002 by EF) or due to the maximum compressive strain at the right edge satisfying assumption irrespective of the strain at the left edge (zero for IH and tensile for IN). The positions of the neutral axis and the eccentricities of the load are widely varying as follows: (i) For the strain profile EF, kDis infinity and the eccentricity of the load is zero. (ii) For the strain profile JK, kDis outside the section (D
It is evident that gradual increase of the eccentricity of the load Pufrom zero is changing the strain profiles from EF to JK, IH and then to IN. Therefore, we can accept that if we increase the eccentricity of the load to infinity, there will be only Mu acting on the column. Designating by Po as the load that causes collapse of the column when acting alone and Mo as the moment that also causes collapse when acting alone, we mark them in Fig. in the vertical and horizontal axes. These two points are the extreme points on the plot of Puversus Mu, any point on which is a pair of Puand Mu (of different magnitudes) that will cause collapse of the same column having the neutral axis either outside or within the column.
The plot of Puversus Mu of Fig. is designated as interaction diagram since any point on the diagram gives a pair of values of Puand Mu causing collapse of the same column in an interactive manner. Following the same logic, several alternative column sections with appropriate longitudinal steel bars are also possible for a particular pair of Puand Mu. Accordingly for the purpose of designing the column, it is essential to understand the different modes of failure of columns, as given in the next section. 4.4.2 Modes of Failure of Columns The two distinct categories of the location of neutral axis, mentioned in the last section, clearly indicate the two types of failure modes: (i) compression failure, when the neutral axis is outside the section, causing compression throughout the section, and (ii) tension failure, when the neutral axis is within the section developing tensile strain on the left of the neutral axis. Before taking up these two failure modes, let us discuss about the third mode of failure i.e., the balanced failure. (A) Balanced failure
Under this mode of failure, yielding of outer most row of longitudinal steel near the left edge occurs simultaneously with the attainment of maximum compressive strain of 0.0035 in concrete at the right edge of the column. As a result, yielding of longitudinal steel at the outermost row near the left edge and crushing of concrete at the right edge occur simultaneously. The different yielding strains of steel are determined from the following: (i) For mild steel (Fe 250): yε = 0.87fy/Es(10.12) (ii) For cold worked deformed bars: yε = 0.87fy/Es+ 0.002 (10.13)
The corresponding numerical values are 0.00109, 0.0038 and 0.00417 for Fe 250, Fe 415 and Fe 500, respectively. Such a strain profile is known a balanced strain profile which is shown by the strain profile IQ in Fig. with a number 5. This number is shown in Fig. lying on the interaction diagram causing collapse of the column. The depth of the neutral axis is designated as kbDand shown in Fig.b. The balanced strain profile IQ in Fig. also shows the strain yε whose numerical value would change depending on the grade of steel as mentioned earlier. It is also important to observe that this balanced profile IQ does not pass trough the fulcrum point V in Fig., while other profiles 1, 2 and 3 i.e., EF, LM and IN pass through the fulcrum point V as none of them produce tensile strain any where in the section of the column. The neutral axis depth for the balanced strain profile IQ is less than D, while the same for the other three are either equal to or more than D. To have the balanced strain profile IQ causing balanced failure of the column, the required load and moment are designated as Pband Mb , respectively and shown in Fig. as the coordinates of point 5. The corresponding eccentricity of the load Pbis defined by the notation eb(= Mb/Pb). The four parameters of the balanced failure are, therefore, Pb, Mb, eband kb (the coefficient of the neutral axis depth kbD). (B) Compression failure
Compression failure of the column occurs when the eccentricity of the load Puis less than that of balanced eccentricity (e
of the neutral axis till kD = D. All these strain profiles having 1 >k >kb will not pass through the fulcrum point V. Neither the tensile strain of the outermost row of steel on the left of the neutral axis reaches yε. On the other hand, all strain profiles having kDgreater than D pass through the fulcrum point V and cause compression failure (Fig.b). The loads causing compression failure are higher than the balanced load Pbhaving the respective eccentricities less than that of the load of balanced failure. The extreme strain profile is EF marked by 1 in Fig.. Some of these points causing compression failure are shown in Fig. as 1, 2, 3 and 4 having k >kb, either within or outside the section. Three such strain profiles are of interest and need further elaboration. One of them is the strain profile IH (Fig.) marked by point 3 (Fig.) for which kD = D. This strain profile develops compressive strain in the section with zero strain at the left edge and 0.0035 in the right edge as explained in sec.. Denoting the depth of the neutral axis by D and eccentricity of the load for this profile by eD, we observe that the other strain profiles LM and EF (Fig.), marked by 2 and 1 in Fig., have the respective kD> D and e >D (Fig.). It is thus seen that from points 1 to 5 (i.e., from compression failure to balanced failure) of the interaction diagram of Fig., the loads are gradually decreasing and the moments are correspondingly increasing. The eccentricities of the successive loads are also increasing and the depths of neutral axis are decreasing from infinity to finite but outside and then within the section up to kbDat balanced failure (point 5). Moreover, this region of compression failure can be subdivided into two zones: (i) zone from point 1 to point 2, where the eccentricity of the load is less than the minimum eccentricity that should be considered in the actual design as specified in IS 456, and (ii) zone from point 2 to point 5, where the eccentricity of the load is equal to or more than the minimum that is specified in IS 456. It has been mentioned also that the first zone from point 1 to point 2 should be avoided in the design of column. (C) Tension failure
Tension failure occurs when the eccentricity of the load is greater than the balanced eccentricity eb. The depth of the neutral axis is less than that of the balanced failure. The longitudinal steel in the outermost row on the left of the neutral axis yields first. Gradually, with the increase of tensile strain, longitudinal steel of inner rows, if provided, starts yielding till the compressive strain reaches 0.0035 at the right edge. The line IR of Fig represents such a profile for which some of the inner rows of steel bars have yielded and compressive strain has reached 0.0035 at the right edge. The depth of the neutral axis is designated by (kminD). It is interesting to note that in this region of the interaction diagram (from 5 to 6 in Fig.), both the load and the moment are found to decrease till point 6 when the column fails due to Mo acting alone. This important behaviour is explained below starting from the failure of the column due to Mo alone at point 6 of Fig. At point 6, let us consider that the column is loaded in simple bending to the point (when M = Mo) at which yielding of the tension steel begins. Addition of some axial compressive load P at this stage will reduce the previous tensile stress of steel to a value less than its yield strength. As a result, it can carry additional moment. This increase of moment carrying capacity with the increase of load shall continue till the combined stress in steel due to additional axial load and increased moment reaches the yield strength. 4.5 Design of Isolated footings
Most of the structures built by us are made of reinforced concrete. Here, the part of the structure above ground level is called as the superstructure, where the part of the structure below the ground level is called as the substructure. Footings are located below the ground level and are also referred as foundations. Foundation is that part of the structure which is in direct contact with soil. The R.C. structures consist of various structural components which act together to resist the applied loads and transfer them safely to soil. In general the loads applied on slabs in buildings are transferred to soil through beams, columns and footings. Footings are that part of the structure which are generally located below ground Level. They are also referred as foundations. Footings transfer the vertical loads, Horizontal loads, Moments, and other forces to the soil. The important purpose of foundation is as follows; 1. To transfer forces from superstructure to firm soil below. 2. To distribute stresses evenly on foundation soil such that foundation soil neither fails nor experiences excessive settlement. 3. To develop an anchor for stability against overturning. 4. To provide an even surface for smooth construction of superstructure. Due to the loads and soil pressure, footings develop Bending moments and Shear forces. Calculations are made as per the guidelines suggested in IS 456 2000 to resist the internal forces.
4.5.1. Types of Foundations Based on the position with respect to ground level, Footings are classified into two types; 1. Shallow Foundations 2. Deep Foundations Shallow Foundations are provided when adequate SBC is available at relatively short depth below ground level. Here, the ratio of Df / B < 1, where Df is the depth of footing and B is the width of footing. Deep Foundations are provided when adequate SBC is available at large depth below ground level. Here the ratio of Df / B >= 1. 4.5.1.1 Types of Shallow Foundations The different types of shallow foundations are as follows: • Isolated Footing • Combined footing • Strap Footing • Strip Footing • Mat/Raft Foundation •
Wall footing
Some of the popular types of shallow foundations are briefly discussed below. 4.5.1.a) Isolated Column Footing These are independent footings which are provided for each column. This type of footing is chosen when • SBC is generally high • Columns are far apart • Loads on footings are less The isolated footings can have different shapes in plan. Generally it depends on the shape of column cross section Some of the popular shapes of footings are; • Square • Rectangular • Circular
The isolated footings essentially consists of bottom slab. These bottom Slabs can be either flat, stepped or sloping in nature. The bottom of the slab is reinforced with steel mesh to resist the two internal forces namely bending moment and shear force. The sketch of a typical isolated footing is shown in Fig. 1.
Fig. 1 Plan and section of typical isolated footing
4.5.1.b) Combined Column Footing These are common footings which support the loads from 2 or more columns. Combined footings are provided when
• SBC is generally less • Columns are closely spaced • Footings are heavily loaded
In the above situations, the area required to provide isolated footings for the columns generally overlap. Hence, it is advantageous to provide single combined footing. In some cases the columns are located on or close to property line. In such cases footings cannot be extended on one side. Here, the footings of exterior and interior columns are connected by the combined footing.
Fig. 2 Plaan and sectioon of typicall combined ffooting Combineed footings essentially e c consist of a common sllab for the ccolumns it is i supporting. These slaabs are geneerally rectan ngular in plaan. Sometim mes they cann also be trapezoidal t i in plan (reefer Fig. 2). Combined d footings can c also hav ve a conneccting beam m and a slaab arrangem ment, which is i similar to an inverted T – beam slab.
4.5.1.c) Strap Footinng An alternnate way off providing combined c foooting locateed close to pproperty linne is the straap footing. In strap fo ooting, indeppendent slabbs below coolumns are pprovided whhich are theen connected by a strap beam. The strap beam does d not rem main in contaact with the soil and doees not transfer any pressure to the soil. Generaally it is used to combinne the footing of the outeer column to t the adjaceent one so thhat the footiing does nott extend in thhe adjoining g property. A typical sttrap footing is shown in Fig. 3.
Fig. 3 Plaan and sectioon of typicall strap footinng
4.5.1.d) Strip S Footingg Strip foooting is a co ontinuous footing f provvided underr columns or walls. A typical striip footing for f columns is shown in Fig. 4.
Fig. 4 Plaan and sectioon of typicall strip footinng
4.5.1.e) Mat Foundaation
Mat founndation cov vers the whole plan area of structture. The deetailing is siimilar to tw wo way reinforced solidd floor slabss or flat slabs. It is a com mbined footiing that cov vers the entirre area beneeath a structuure and suppports all the walls and coolumns. It iss normally prrovided wheen
w • Soil prressure is low • Loads are very heaavy • Spread d footings coover > 50% area a
A typicall mat foundaation is show wn in Fig. 5.
Fig. 5 Plaan and sectioon of typicall strip footinng
4.5.2.2 Types T of Deeep Foundatioons Deep fou undations arre provided when adequuate SBC is available att large depthh below GL L. There arre different types of deep d founddations. Som me of the ccommon tyypes of deeep foundatioons are listeed below. • Pile Fo oundation • Pier Fooundation • Well Foundation F 4.5.2.3. Bearing B Cappacity of Soiil The safee bearing capacity c of soil is the safe extra load soil can withstaand withouut experienccing shear failure. f The Safe Beariing Capacityy (SBC) is considered unique at a particularr site. But it also dependds on the folllowing facto ors: • Size off footing • Shape of footing • Inclinaation of footiing • Inclinaation of grouund • Type of o load • Depth of footing ettc.
SBC alone is not sufficient for design. The allowable bearing capacity is taken as the smaller of the following two criteria
• Limit states of shear failure criteria (SBC) • Limit states of settlement criteria Based on ultimate capacity, i.e., shear failure criteria, the SBC is calculated as SBC = Total load / Area of footing Usually the Allowable Bearing Pressure (ABP) varies in the range of 100 kN/m2 to 400 kN/m2. The area of the footing should be so arrived that the pressure distribution below the footing should be less than the allowable bearing pressure of the soil. Even for symmetrical Loading, the pressure distribution below the footing may not be uniform. It depends on the Rigidity of footing, Soil type and Conditions of soil. In case of Cohesive Soil and Cohesion less Soil the pressure distribution varies in a nonlinear way. However, while designing the footings a linear variation of pressure distribution from one edge of the footing to the other edge is assumed. Once the pressure distribution is known, the bending moment and shear force can be determined and the footing can be designed to safely resist these forces 4. Design of Isolated Column Footing The objective of design is to determine • Area of footing • Thickness of footing • Reinforcement details of footing (satisfying moment and shear considerations) • Check for bearing stresses and development length This is carried out considering the loads of footing, SBC of soil, Grade of concrete and Grade of steel. The method of design is similar to the design of beams and slabs. Since footings are buried, deflection control is not important. However, crack widths should be less than 0.3 mm. The steps followed in the design of footings are generally iterative. The important steps in the design of footings are; • Find the area of footing (due to service loads) • Assume a suitable thickness of footing • Identify critical sections for flexure and shear
• Find the bending moment and shear forces at these critical sections (due to factored loads) • Check the adequacy of the assumed thickness • Find the reinforcement details • Check for development length • Check for bearing stresses
Limit state of collapse is adopted in the design pf isolated column footings. The various design steps considered are;
• Design for flexure • Design for shear (one way shear and two way shear) • Design for bearing • Design for development length
The materials used in RC footings are concrete and steel. The minimum grade of concrete to be used for footings is M20, which can be increased when the footings are placed in aggressive environment, or to resist higher stresses.
Cover: The minimum thickness of cover to main reinforcement shall not be less than 50 mm for surfaces in contact with earth face and not less than 40 mm for external exposed face. However, where the concrete is in direct contact with the soil the cover should be 75 mm. In case of raft foundation the cover for reinforcement shall not be less than 75 mm.
Minimum reinforcement and bar diameter: The minimum reinforcement according to slab and beam elements as appropriate should be followed, unless otherwise specified. The diameter of main reinforcing bars shall not be less 10 mm. The grade of steel used is either Fe 415 or Fe 500. 4.6. Specifications for Design of footings as per IS 456 : 2000
The important guidelines given in IS 456 : 2000 for the design of isolated footings are as follows: 4.6.1 General
Footings shall be designed to sustain the applied loads, moments and forces and the induced reactions and to ensure that any settlement which may occur shall be as nearly uniform as possible, and the safe bearing capacity of the soil is not exceeded (see IS 1904). 4.6.1.1 In sloped or stepped footings the effective cross-section in compression shall be limited by the area above the neutral plane, and the angle of slope or depth and location of steps shall be such that the design requirements are satisfied at every section. Sloped and stepped footings that are designed as a unit shall be constructed to assure action as a unit. 4.6.1.2 Thickness at the Edge of Footing In reinforced and plain concrete footings, the thickness at the edge shall be not less than 150 mm for footings on soils, nor less than 300 mm above the tops of piles for footings on piles. 4.6.1.3 In the case of plain concrete pedestals, the angle between the plane passing through the bottom edge of the pedestal and the corresponding junction edge of the column with pedestal and the horizontal plane (see Fig. 20) shall be governed by the expression:
where = calculated maximum bearing pressure at the base of the pedestal in N/mm2 = characteristic strength of concrete at 28 days in N/mm2. 4.6.2 Moments and Forces 4.6.2.1 In the case of footings on piles, computation for moments and shears may be based on the assumption that the reaction from any pile is concentrated at the centre of the pile. 4.6.2.2 For the purpose of computing stresses in footings which support a round or octagonal concrete column or pedestal, the face of the column or pedestal shall be taken as the side of a square inscribed within the perimeter of the round or octagonal column or pedestal. 4.6.2.3 Bending Moment 4.6.2.3.1 The bending moment at any section shall be determined by passing through the section a vertical plane which extends completely across the footing, and computing the moment of the forces acting over the entire area of the footing on one side of the said plane. 4.6.2.3.2 The greatest bending moment to be used in the design of an isolated concrete footing which supports a column, pedestal or wall, shall be the moment computed in the manner prescribed in 4.6.2.3.1 at sections located as follows: a) At the face of the column, pedestal or wall, for footings supporting a concrete column, pedestal or wall;
b) Halfway between the centre-line and the edge of the wall, for footings under masonry walls; and c) Halfway between the face of the column or pedestal and the edge of the gussetted base, for footings under gussetted bases. 4.6.2.4 Shear and Bond 4.6.2.4.1 The shear strength of footings is governed by the more severe of the following two conditions: a) The footing acting essentially as a wide beam, with a potential diagonal crack extending in a plane across the entire width; the critical section for this condition shall be assumed as a vertical section located from the face of the column, pedestal or wall at a distance equal to the effective depth of footing for footings on piles. b) Two-way action of the footing, with potential diagonal cracking along the surface of truncated cone or pyramid around the concentrated load; in this case, the footing shall be designed for shear in accordance with appropriate provisions specified in 31.6. 4.6.2.4.2 In computing the external shear or any section through a footing supported on piles, the entire reaction from any pile of diameter Dp whose centre is located DP/2 or more outside the section shall be assumed as producing shear on the section; the reaction from any pile whose centre is located DP/2 or more inside the section shall be assumed as producing no shear on the section, For intermediate positions of the pile centre, the portion of the pile reaction to be assumed as producing shear on the section shall be based on straight line interpolation between full value at DP/2 outside the section and zero value at DP/2 inside the section. 4.6.2.4.3 The critical section for checking the development length in a footing shall be assumed at the same planes as those described for bending moment in 4.6.2.3 and also at all other vertical planes where abrupt changes of section occur. If reinforcement is curtailed, the anchorage requirements shall be checked in accordance with 26.2.3. 4.6.3 Tensile Reinforcement The total tensile reinforcement at any section shall provide a moment of resistance at least equal to the bending moment on the section calculated in accordance with 4.6.2.3. 4.6.3.1 Total tensile reinforcement shall be distributed across the corresponding resisting section as given below: a) In one-way reinforced footing, the-reinforcement extending in each direction shall be distributed uniformly across the full width of the footing; b) In two-way reinforced square footing, the reinforcement extending in each direction shall be distributed uniformly across the full width of the footing; and
c) In two-way reinforced rectangular footing, the reinforcement in the long direction shall be distributed uniformly across the full width of the footing. For reinforcement in the short direction, a central band equal to the width of the footing shall be marked along the length of the footing and portion of the reinforcement determined in accordance with the equation given below shall be uniformly distributed across the central band:
whereβ is the ratio of the long side to the short side of the footing. The remainder of the reinforcement shall be uniformly distributed in the outer portions of the footing. 4.6.4 Transfer of Load at the Base of Column The compressive stress in concrete at the base of a column or pedestal shdlbe considered as being transferred by bearing to the top of the supporting Redestal or footing. The bearing pressure on the loaded area shall not exceed the permissible bearing stress in direct compression multiplied by a value equal to
but not greater than 2, where A1 = supporting area for bearing of footing, which in sloped or stepped footing may be taken as the area of the lower base of the largest frustum of a pyramid or cone contained wholly within the footing and having for its upper base, the area actually loaded and having side slope of one vertical to two horizontal; and A2 = loaded area at the column base. 4.6.4.1 Where the permissible bearing stress on the concrete in the supporting or supported member would be exceeded, reinforcement shall be provided for developing the excess force, either by extending the longitudinal bars into the supporting member, or by dowels (see 4.6.4.3). 4.6.4.2 Where transfer of force is accomplished by, reinforcement, the development length of the reinforcement shall be sufficient to transfer the compression or tension to the supporting member in accordance with 26.2. 4.6.4.3 Extended longitudinal reinforcement or dowels of at least 0.5 percent of the crosssectional area of the supported column or pedestal and a minimum of four bars shall be provided. Where dowels are used, their diameter shall no exceed the diameter of the column bars by more than 3 mm. 4.6.4.4 Column bars of diameters larger than 36 mm, in compression only can be dowelled at the footings with bars of smaller size of the necessary area. The dowel shall extend into the
column, a distance equal to the development length of the column bar and into the footing, a distance equal to the development length of the dowel. 4.6.5 Nominal Reinforcement 4.6.5.1 Minimum reinforcement and spacing shall be as per the requirements of solid slab. 4.6.5.2 The nominal reinforcement for concrete sections of thickness greater than 1 m shall be 360 mm2 per metre length in each direction on each face. This provision does not supersede the requirement of minimum tensile reinforcement based on the depth of the section. 4.7 Basic Concept of Prestressed Concrete
4.7.1 Introduction
The prestressing and precasting of concrete are inter-related features of the modern building industry. Through the application of imaginative design and quality control, they have, since the 1930’s, had an increasing impact on architectural and construction procedures. Prestressing of concrete is the application of a compressive force to concrete members and may be achieved by either pretensioning high tensile steel strands before the concrete has set, or by post-tensioning the strands after the concrete has set. Although these techniques are commonplace, misunderstanding of the principles, and the way they are applied, still exists. This paper is aimed at providing a clear outline of the basic factors differentiating each technique and has been prepared to encourage understanding amongst those seeking to broaden their knowledge of structural systems. 4.7.2. Definitions 4.7.2.1 Prestressed Concrete
Prestressing of concrete is defined as the application of compressive stresses to concrete members. Those zones of the member ultimately required to carry tensile stresses under working load conditions are given an initial compressive stress before the application of working loads so that the tensile stresses developed by these working loads are balanced by induced compressive strength. Prestress can be applied in two ways - Pre-tensioning or Posttensioning.
4.7.2.2 Pre-tensioning
Pre-tensioning is the application, before casting, of a tensile force to high tensile steel tendons around which the concrete is to be cast. When the placed concrete has developed sufficient compressive strength a compressive force is imparted to it by releasing the tendons, so that the concrete member is in a permanent state of prestress.
4.7.2.3 Post-tensioning
Post-tensioning is the application of a compressive force to the concrete at some point in time after casting. When the concrete has gained strength a state of prestress is induced by tensioning steel tendons passed through ducts cast into the concrete, and locking the stressed tendons with mechanical anchors. The tendons are then normally grouted in place.
4.7.3.Advanages of Prestressing
4.7.3.1 General Advantages
The use of prestressed concrete offers distinct advantages over ordinary reinforced concrete. These advantages can be briefly listed as follows: 1. Prestressing minimises the effect of cracks in concrete elements by holding the concrete in compression. 2. Prestressing allows reduced beam depths to be achieved for equivalent design strengths. 3. Prestressed concrete is resilient and will recover from the effects of a greater degree of overload than any other structural material. 4. If the member is subject to overload, cracks, which may develop, will close up on removal of the overload. 5. Prestressing enables both entire structural elements and structures to be formed from a number of precast units, e.g. Segmented and Modular Construction. 6. Lighter elements permit the use of longer spanning members with a high strength to weight characteristic. 7. The ability to control deflections in prestressed beams and slabs permits longer spans to be achieved. 8. Prestressing permits a more efficient usage of steel and enables the economic use of high tensile steels and high strength concrete.
4.7.3.2 Cost advantages of Prestressing
Prestressedsconcrete can provide significant cost advantages over structural steel sections or ordinary reinforced concrete.
4.7.4. Limitations of Prestressing
The limitations of prestressed concrete are few and really depend only upon the imagination of the designer and the terms of his brief. The only real limitation where prestressing is a possible solution may be the cost of providing moulds for runs of limited quantity of small numbers of non-standard units.
4.7.5. Fundamentals of Prestressing
5.1 The Tensile Strength of Concrete
The tensile strength of unreinforced concrete is equal to about 10% of its compressive strength. Reinforced concrete design has in the past neglected the tensile strength of unreinforced concrete as being too unreliable. Cracks in the unreinforced concrete occur for many reasons and destroy the tensile capability. See Fig.1.With prestressed concrete design however, the tensile strength of concrete is not neglected. In certain applications it is used as part of the design for service loadings. In ordinary reinforced concrete, steel bars are introduced to overcome this low tensile strength. They resist tensile forces andlimit the width of cracks that will develop under design loadings. Reinforced concrete is thus designed assuming the concrete to be cracked and unable to carry any tensile force. Prestressing gives crack-free construction by placing the concrete in compression before the application of service loads. 4.7.5.2 The Basic Idea
A simple analogy to prestressing will best explain the basic idea. Consider a row of books or blocks set up as a beam. See Fig.2(a). This "beam" is able to resist compression at the top but is unable to resist any tension forces at the bottom as the "beam" is now like a badly cracked concrete member, i.e. the discontinuity between the books ensures that the "beam" has no inherent tension resisting properties. If it is temporarily supported and a tensile force is applied, the "beam’’ will fail by the books dropping out along the discontinuities. See Fig.2(b). For the beam then to function properly a compression force must be applied as in Fig.2(c). The beam is then "prestressed" with forces acting in an opposite direction to those induced by loading. The effect of the longitudinal prestressing force is thus to produce pre-compression in the beam before external downward loads are applied. The application of the external downward load merely reduces the proportion of precompression acting in the tensile zone of the beam.
4.7.5.3 The Position of the Prestressing Force
Prestressing can be used to best advantage by varying the position of the prestress force. When the prestress is applied on the centroid of the cross-section a uniform compression is obtained. Consider the stress state of the beam in Fig.3(b). We can see that by applying a prestress of the right magnitude we can produce pre-compression equal and opposite to the tensile force in Fig.3(b).Then by adding the stress blocks we get: i.e. zero stress towards the
bottom fibres and twice the compressive stress towards the top fibres. Now apply the precompression force at 1/3 the beam depth above the bottom face. As well as the overall compression we now have a further compressive stress acting on the bottom fibre due to the moment of the eccentric prestress force about the neutral axis of the section. We then find it is possible to achieve the same compression at the bottom fibre with only half the prestressing force. See Fig.3(d). Adding now the stress blocks of Fig.3(b) and 3(d) we find that the tensile stress in the bottom fibre is again negated whilst the final compressive stress in the top fibre is only half that of Fig.3(c). See Fig.3(e). Thus by varying the position of the compressive force we can reduce the prestress force required, reduce the concrete strength required and sometimes reduce the cross sectional area. Changes in cross sections such as using T or I or channel sections rather than rectangular sections can lead to further economies.
4.7.5.4 The Effect of Prestress on Beam Deflection
From 5.3 it is obvious that the designer should, unless there are special circumstances, choose the eccentrically applied prestress. Consider again the non-prestressed beam of Fig.1(a). Under external loads the beam deflects to a profile similar to that exaggerated in Fig.4(a). By applying prestress eccentrically a deflection is induced. When the prestress is applied in the lower portion of the beam, the deflection is upwards producing a hogging profile. See Fig.4(b). By applying the loads of Fig.4(a) to our prestressed beam, the final deflection shape produced is a sum of Figs.4(a) and 4(b) as shown in Fig.4(c). Residual hogging, though shown exaggerated in the Fig.4(c), is controlled within limits by design code and bylaw requirements. Such control of deflection is not possible with simple reinforced concrete. Reductions in deflections under working loads can then be achieved by suitable eccentric prestressing. In long span members this is the controlling factor in the choice of the construction concept an technique employed.
4.7.5.5 Prestress Losses
Most materials to varying degrees are subject to "creep", i.e. under a sustained permanent load the material tends to develop some small amount of plasticity and will not return completely to its original shape. There has been an irreversible deformation or permanent set. This is known as "creep" Shrinkage of concrete and "creep" of concrete and of steel reinforcement are potential sources of prestress loss and are provided for in the design of prestressed concrete. Shrinkage:The magnitude of shrinkage may be in the range of 0.02% depending on the environmental conditions and type of concrete.With pre-tensioning, shrinkage starts as soon as the concrete is poured whereas with post-tensioned concrete there is an opportunity for the member to experience part of its shrinkage prior to tensioning of the tendon, thus pre-compression loss from concrete shrinkage is less.
Creep:With prestressing of concrete the effect is to compress and shorten the concrete. This shortening must be added to that of concrete shrinkage. In the tensioned steel tendons the effect of "creep’’ is to lengthen the tendon causing further stress loss. Allowance must be made in the design process for these losses. Various formulae are available.
Pull-in: With all prestressing systems employing wedge type gripping devices, some degree of pull-in at either or both ends of a pre-tensioning bed or post-tensioned member can be expected. In normal operation, for most devices in common use, this pull-in is between 3mm and 13mm and allowance is made when tensioning the tendons to accommodate this.
4.7.5.6 Materials
4.7.5.6.1 Steel
Early in the development of prestressing it was found that because of its low limit of elasticity ordinary reinforcing steel could not provide sufficient elongation to counter concrete shortening due to creep and shrinkage. it is necessary to use the high tensile steels which were developed to produce a large elongation when tensioned. This ensures that there is sufficient elongation reserve to maintain the desired pre-compression. The relationship between the amount of load, or stress, in a material and the stretch, or strain, which the material undergoes while it is being loaded is depicted by a stress-strain curve. At any given stress there is a corresponding strain. Strain is defined as the elongation of a member divided by
the length of the member. The stress-strain properties of some grades of steel commonly encountered in construction are shown in Fig.5. It is apparent from these relationships that considerable variation exists between the properties of these steels. All grades of steel have one feature in common: the relationship between stress and strain is a straight line below a certain stress. The stress at which this relationship departs from the straight line is called the yield stress, and is denoted by the symbol fy in Fig. 5. A conversion factor may be used to convert either stress to strain or strain to stress in this range. This conversion factor is called the modulus of elasticity E. Structural grade steels which are commonly used for rolled structural sections and reinforcing bars, show a deviation from this linear relationship at a much lower stress than high strength prestressing steel. High strength steels cannot be used for reinforced concrete as the width of cracks under loading would be unacceptably large. These high strength steels achieve their strength largely through the use of special compositions in conjunction with cold working. Smaller diameter wires gain strength by being cold drawn through a number of dies. The high strength of alloy bars is derived by the use of special alloys and some working.
4.7.5.6.2 Concrete
To accommodate the degree of compression imposed by the tensioning tendons and to minimise prestress losses, a high strength concrete with low shrinkage properties is required. Units employing high strength concrete are most successfully cast under controlled factory conditions.
4.8 Prestressing Methods
4.8.1 General
Methods of prestressing concrete fall into two broad categories differentiated by the stage at which the prestress is applied.That is, whether the steel is pre-tensioned or post-tensioned. From the definitions para 2.2 pre-tensioning is stated as "the application before casting, of a tensile force to high tensile steel tendons around which the concrete is cast. . ." and para 2.3 "Post-tensioning is the application of a compressive force to the concrete at some point in time after casting. When the concrete has hardened a state of prestress is induced by tensioning steel tendons passing through ducts cast into the Concrete".
4.8.2 Types of Tendon
There are three basic types of tendon used in the prestressing of concrete:
Bars of high strength alloy steel.These bar type tendons are used in certain types of post-tensioning systems. Bars up to 40mm diameter are used and the alloy steel from which they are made has a yield stress (fy Fig.5) in the order of 620 MPa. This gives bar tendons a lower strength to weight ratio than either wires or strands, but when employed with threaded anchorages has the advantages of eliminating the possibility of pull-in at the anchorages as discussed in para. 5.5, and of reducing anchorage costs. Wire, mainly used in post-tensioning systems for prestressing concrete, is cold drawn and stress relieved with a yield stress of about 1300 MPa. Wire diameters most commonly used in New Zealand are 5mm, 7mm, and 8mm.
Strand, which is used in both pre and post-tensioning is made by winding seven cold drawn wires together on a stranding machine. Six wires are wound in a helix around a centre wire which remains straight. Strands of 19 or 37 wires are formed by adding subsequent layers of wire. Most pre-tensioning systems in New Zealand are based on the use of standard seven wire stress relieved strands conforming to BS3617:"Seven Wire steel strand for Prestressed concrete." With wire tendons and strands, it may be desirable to form a cable to cope with the stressing requirements of large post-tensioning applications. Cables are formed by arranging wires or strands in bundles with the wires or strands parallel to each other. In use the cable is placed in a preformed duct in the concrete member to be stressed and tensioned by a suitable posttensioning method. Tendons whether bars, wires, strands, or made up cables may be used either straight or curved.
i.
Straight steel tendons are still by far the most commonly used tendons in pretensioned concrete units.
ii.
Continuously curved tendons are used primarily in post-tensioning applications. Castin ducts are positioned in the concrete unit to a continuous curve chosen to suit the varying bending moment distribution along the members.
4.8.3 Pre-Tensioning
As discussed, (para 2.2) pre-tensioning requires the tensile force to be maintained in the steel until after the high strength concrete has been cast and hardened around it. The tensile force in the stressing steel is resisted by one of three methods: a. Abutment method - an anchor block cast in the ground.
b. Strut method - the bed is designed to act as a strut without deformation when tensioning forces are applied. c. Mould method - tensioning forces are resisted by strong steel moulds.
It is usual in pretensioning factories to locate the abutments of the stressing bed a considerable distance apart so that a number of similar units can be stressed at the same time, end to end using the same tendon. This arrangement is called the "Long Line Process". After pouring, the concrete is cured so that the necessary strength and bond between the steel and concrete has developed in 8 to 20 hours. When the strength has been achieved tendons can be released and the units cut to length and removed from the bed.
Post-tensioning systems are based on the direct longitudinal tensioning of a steel tendon from one or both ends of the concrete member. The most usual method of post-tensioning is by cables threaded through ducts in cured concrete. These cables are stressed by hydraulic jacks, designed for the system in use and the ducts thoroughly grouted up with cement grout after stressing has occurred. Cement grouting is almost always employed where post-tensioning through ducts is carried out to: – Protect the tendon against corrosion by preventing ingress of moisture. – Eliminate the danger of loss of prestress due to long term failure of end anchorages, especially where moisture or corrosion is present. – To bond the tendon to the structural concrete thus limiting crack width under overload.
4.8.4. Resistance of Prestressed Concrete
All concrete is incombustible. In a fire, failure of concrete members usually occurs due to the progressive loss of strength of the reinforcing steel or tendons at high temperatures. Also the physical properties of some aggregates used in concrete can change when heated to high temperatures. Experience and tests have shown however that
ordinary reinforced concrete has greater fire resistance than structural steel or timber. Current fire codes recognise this by their reference to these materials. Prestressed concrete has been shown to have at least the same fire resistance as ordinary reinforced concrete. Greater cover to the prestressing tendons is necessary however, as the reduction in strength of high tensile steel at high temperatures is greater than that of ordinary mild steel.
4.8.5 Applications of Prestressing
4.8.5.1 General
The construction possibilities of prestressed concrete are as vast as those of ordinary reinforced concrete. Typical applications of prestressing in building and construction are: 1. Structural components for integration with ordinary reinforced concrete construction, e.g. floor slabs, columns, beams. 2. Structural components for bridges. 3. Water tanks and reservoirs where water tightness (i.e. the absence of cracks) is of paramount importance. 4. Construction components e.g. piles, wall panels, frames, window mullions, power poles, fence posts, etc. 5. The construction of relatively slender structural frames. 6. Major bridges and other structures.
4.8.5.2 Conclusions
Prestressed concrete design and construction is precise. The high stresses imposed by prestressing really do occur. The following points should be carefully considered: 1. To adequately protect against losses of prestress and to use the materials economically requires that the initial stresses at prestressing be at the allowable upper limits of the material. This imposes high stresses, which the member is unlikely to experience again during its working life. 2. Because the construction system is designed to utilise the optimum stress capability of both the concrete and steel, it is necessary to ensure that these materials meet the design requirements. This requires control and responsibility from everyone involved
in prestressed concrete work - from the designer right through to the workmen on the site.
We have seen that considerable design and strength economies are achieved by the eccentric application of the prestressing force. However, if the design eccentricities are varied only slightly, variation from design stresses could be such as to affect the performance of a shallow unit under full working load. The responsibility associated with prestressing work then is that the design and construction should only be undertaken by engineers or manufacturers who are experienced in this field. 4.9 Post - tensioning System
A metal tube or flexible hose following intend profile is placed inside the mould and concrete is laid. Flexible hose is then removed leaving a duct; inside the member steel cable is inserted in the duct. Anchoring the cable at one end of the member it is stretched using a hydraulic jack from the other end. After stretching the cable is anchored at the other end also. Therefore post tensioning system consists of end anchorages and jacks. The popular Posttensioning systems are the following. 1. Freyssinet System, 2. MagnelBlaton System, 3. Gifford Udall System, 4. Le Mc Call System.
4.9.1 FreyssinetSystem :-
It was introduced by the French Engineer ` FREYSSINET ‘ in 1939 and is the origin of all patented systems which came over the years. High strength steel wires of 5 mm dia in groups of 6, 8, 12, 16, or 24 and 7mm dia arranged in groups of 12 wires. The group of wires, commonly known as cable are encased in flexible tube or sheeting of 32 gauge metal sheet, with a helical spring inside the wires. The spring keeps a proper spacing between the wires and forms a channel for cement grout. The wires are anchored by being held between two reinforced concrete cones which fit one inside the other, as shown in figure. The female part of the anchorage is a conical steel wound lining heavily reinforced with high tensile steel soirals to resist bursting forces. The male cone is of mesh reinforced concrete, fluted to space evenly the requisite number of wires. A central tube pass axially through the male cone. This tube permits the grout to be injected through it. All the wires are stressed simultaneously by means of Freyssinet double acting jack, which can pull upto group of wires at a time. The wires are wedged around the casing and are stretched by the main ram. When the required tension is reached, an inner piston pushes the plug into the anchorage to secure the wires. The pressure on the main ram and that a on the inner piston are then released gradually and the
jack is removed. Since the anchoring unit is buried flush with the face of concrete, it helps to transmit the reaction of the jack as well as the prestress of the concrete. After the completion of prestressing, grout is injected through the hole at the centre of male cone. Freyssinet system of Post-tensioning 4.9.2 MagnelBlaton System :-
This method was introduced by the famous Engineer ‘ Prof. MAGNEL’ and Contractors Blaton, both of Belgium. In freyssinet system, several wires are stretched at a time. In magnelblaton system two wires are stretched at a time as shown in Fig. In this system, the anchorage device consists of sandwitch plate having grooves to hold the wires and wedgs which are also grooved. Each cable plate carried eight wires. Between the two ends, the spacing of wire is maintained by spacers. Wires of 5 mm or 7 mm are adopted. Cable consists of wires in multiples of 8 wires. Cables with as much as 64 wires are also used under special occasions. A specially deviced jack pulls two wires at a time and anchores. The wires are the sandwitch plate with tapered wedge. 4.9.3 Gifford Udall System :-
This method was developed by British Engineers is used to pull one wire at a time by hydraulic type jack. Wedges are used to anchor the prestressing wires. Introducing spacers, a multi wire cable can also be tensioned by stretching and anchoring one by one. Gifford Udall jack and the tendon are in the same alignment. The nose of the jack is spring loaded for forcing the wedges. Up to 7 mm dia wire are stretched and maximum elongation of 500 mm is possible. These jacks are operated manually for small capacities and by an electrically operated hydraulic pump for large capacities.
There are two types anchorage devices used in the system I tube anchorage II plate anchorage 4.9.3.I. Tube anchorage :-
Tube anchorage consist of a bearing plate, anchor wedges and anchor grips. anchor plate may be square or circular caplates have 8 or 12 tapered holes to accommodate the indidual prestressing wires . these wires are locked in to the tappered holes by means of anchor wedges. In addition grout entry hole is also provided in the bearing plate for grout ing . anchor wedges are split cone wedges carrying serration on its f late surface .there is a tube unit which is fabricated steel component incorporation a thrust plate steel tube with a surrounding helix . this unit attached to the end shutters and forms an efficient cast in component of the anchorage.
4.9.3.II Plate anchorage :-
In the plate anchorage system there is a bearing plate with appropriate number of holes for anchoring the wires .wires passing through the plate are anchored using steel anchorages. Anchorage consists of a steel cylinder of diameter and length about 20mm with a tapered holes ,split cone wedges passing through these holes grip the wires. Strands are also prestressed using GIFFORD UDALL SYSTEM. 4.9.4 Le Mc Call System :-
This system uses high-tensile alloy steel bars as the prestressing tendons, in the place of hightensile steel wires used in other systems. The diameter of the bar is between 12 and 28 mm bars provided with threads at the ends are inserted in the performed ducts. After stretching the bars to the required length , they are tightened using nuts against bearing plates provided at the end section of the members. This system, wires are tensioned individually. The system uses collect sleeves weding. 4.10 Post-Tensioning
This section applies to both concrete boxes and post-tensioned I-girders unless otherwise noted. 4.10.1 Integrated Drawings
A. Show congested areas of post-tensioned concrete structures on integrated drawings with an assumed post-tensioning system. Such areas include anchorage zones, areas containing embedded items for the assumed post-tensioning system, areas where post-tensioning ducts deviate both in the vertical and transverse directions, and other highly congested areas as determined by the Engineer and/or the Department. B. For all post-tensioned structures, evaluate and accommodate possible conflicts between webs and external tendons. Check for conflicts between future post-tensioning tendons and permanent tendons. C. Select the assumed post-tensioning system, embedded items, etc. in a manner that will accommodate competitive systems using standard anchorage sizes of 4-0.6” dia, 7-0.6” dia, 12-0.6” dia, 19-0.6 dia and 27-0.6” dia. Integrated drawings utilizing the assumed system must be detailed to a scale and quality required to show double-line reinforcing and posttensioning steel in two-dimension (2-D) and, when necessary, in complete three-dimension (3-D) drawings and details. 4.10.2 Prestress
A. Secondary Effects: 1. During design of continuous straight and curved structures, account for secondary effects due to post-tensioning.
2.) Design curved structures for the lateral forces due to the plan curvature of the tendons. B. Tendon Geometry: When coordinating design calculations with detail drawings, account for the fact that the center of gravity of the duct and the center of gravity of the prestressing steel are not necessarily coincidental. C. Required Prestress: On the drawings, show prestress force values for tendon ends at anchorages. D. Internal/External Tendons: External tendons must remain external to the section without entering the top or bottom slab. E. Strand Couplers: Strand couplers as described in LRFD are not allowed. 4.10.3 Material
A. Concrete (minimum 28-day cylinder strengths): 1.) Precast superstructure (including CIP joints):
5.5 ksi
2.) Precast pier stems:
5.5 ksi
3.) Post-tensioned I-girders:
5.5 ksi
B. Post-Tensioning Steel: 1.) Strand:
ASTM A416, Grade 270, low relaxation.
2.) Parallel wires:
ASTM A421, Grade 240.
3.) Bars:
ASTM A722, Grade 150.
C. Post-Tensioning Anchor set (to be verified during construction): 1.) Strand:
3/8-inch
2.) Parallel wires:
1/2-inch
3.) Bars:
0
4.10.4 Expansion Joints
A. Do not design superstructures utilizing expansion joints within the span (i.e. ¼ point hinges). B. Settings: The setting of expansion joint recesses and expansion joint devices, including any precompression, must be clearly stated on the drawings. Expansion joints must be sized and set at time of construction for the following conditions:
1.) Allowance for opening movements based on the total anticipated movement resulting from the combined effects of creep, shrinkage, and temperature rise and fall. For box girder structures, compute creep and shrinkage from the time the expansion joints are installed through day 4,000. 2.) To account for the larger amount of opening movement, expansion devices should be set precompressed to the maximum extent possible. In calculations, allow for an assumed setting temperature of 85 degrees F. Provide a table on the plans giving precompression settings according to the prevailing conditions. Size expansion devices and set to remain in compression through the full range of design temperature from their initial installation until a time of 4,000 days. 3.) Provide a table of setting adjustments to account for temperature variation at installation. Indicate the ambient air temperature at time of installation, and note that adjustments must be calculated for the difference between the ambient air temperature and the mean temperature. C. Armoring: Design and detail concrete corners under expansion joint devices with adequate steel armoring to prevent spalling or other damage under traffic. The armor should be minimum 4-inch x 4-inch x 5/8-inch galvanized angles anchored to the concrete with welded studs or similar devices. Specify that horizontal concrete surfaces supporting the expansion joint device and running flush with the armoring have a finish acceptable for the device. Detail armor with adequate vent holes to assure proper filling and compaction of the concrete under the armor. 4.11 Ducts, Tendons and Anchorages
A. Specify tendon duct radius and dimensions to duct PC and PT points on the design plans. Show offset dimensions to post-tensioning duct trajectories from fixed surfaces or clearly defined reference lines at intervals not exceeding 5 feet. When the radius of curvature of a duct exceeds one-half degree per foot, show offsets at intervals not exceeding 30-inches. In regions of tight reverse curvature of short tendon sections, show offsets at sufficiently frequent intervals to clearly define the reverse curve. B. Curved ducts that run parallel to each other or around a void or re-entrant corner must be sufficiently encased in concrete and reinforced as necessary to avoid radial failure (pull-out into another duct or void). In the case of approximately parallel ducts, consider the arrangement, installation, stressing sequence, and grouting in order to avoid potential problems with cross grouting of ducts C. Detail post-tensioned precast I-girders to utilize round ducts only.
Table 4.2 Minimum Center-to-Center Duct Spacing Post Tensioned Bridge Type
*Minimum Center To Center
Longitudinal Duct Spacing
Precast Segmental Cantilever
Balanced
8-inches, 2 times outer duct diameter, or outer duct diameter plus 4½-inches whichever is greater.
Cast-In-Place Balanced Cantilever
Spliced I-Girder Bridges
C.I.P. Voided Slab Bridges C.I.P. Multi-Cell Bridges
4-inches, outer duct diameter plus 1.5 times maximum aggregate size, or outer duct diameter plus 2-inches whichever is greater. When all ducts are in a vertical plane, 4-inches, outer duct diameter plus 1.5 times maximum aggregate size, or outer duct diameter plus 2inches whichever is greater. **For two or more ducts set side-by-side, outer duct diameter plus 3-inches.
* - Bundled tendons are not allowed. ** - The 3-inch measurement must be measured in a horizontal plane.
D. Size ducts for all post-tensioning bars ½-inch larger than the diameter of the bar coupler. E. Internal post-tensioning ducts must be positively sealed with a duct coupler or o-ring at all segment joints to eliminate cross contamination. Design and detail all internal tendon couplers with maximum deflection of 6 degrees at the segment joint. Couplers or o-ring hardware are to be mounted perpendicular to bulkhead at the segment joints. Use only approved PT systems which contain segment couplers. Theoretically, the tendon must pass through the coupler without touching the duct or coupler. See tendon alignment schematic below. Require cast-in-place closure joints to be minimum 18-inch wide.
Commentary: Couplers shall be made normal to joints to allow stripping of the bulkhead forms. Over-sizing couplers allows for standardized bulkheads and avoids curved tendons.
F. To allow room for the installation of duct couplers, detail all external tendons to provide a 1½-inch clearance between the duct surface and the face of the concrete. G. Where external tendons pass through deviation saddles, design the tendons to be contained in grouted steel pipes, cast into the deviation saddle concrete. H. Strand anchorages cast into concrete structures are not allowed. I. Use steel pipe ducts for tendons whose anchorages are embedded in the diaphragms. Design and detail shear connectors on these steel pipe ducts to transfer the tendon ultimate capacity to the surrounding concrete.
Table Minimum Tendon Radius Tendon Size
Minimum Radius
19-0.5” dia, 12-0.6” dia
8 feet
31-0.5” dia, 19-0.6” dia
10 feet
55-0.5” dia, 37-0.6” dia
13 feet
J. All balanced cantilever bridges must utilize a minimum of four positive moment external draped continuity tendons (two per web) that extend to adjacent pier diaphragms.
Table Min. Tendons Required for Critical Post-tensioned Sections Post Tensioned Bridge Element
Minimum Number of Tendons
Mid Span Closure Pour
Bottom slab – two tendons per web
C.I.P. and Precast Balanced Cantilever Bridges
Top slab – One tendon per web (4- 0.6-inch dia. min.)
Span by Span Segmental Bridges
Four tendons per web
C.I.P. Multi-Cell Bridges
Three tendons per web
Spliced I-Girder Bridges*
Three tendons per girder
Unit End Spans C.I.P. and Precast Balanced Cantilever
Three tendons per web
Bridges
Diaphragms - Vertically Post-Tensioned
Six tendons; if strength is provided by P.T. only Four tendons; if strength is provided by combination of P.T. and mild reinforcing
Diaphragms - Vertically Post-Tensioned
Four Bars per face, per cell
Segment - Vertically Post-Tensioned
Two Bars per web
* 3 girders minimum per span.
Minimum Dimensions Table Dimensions for sections containing post-tensioning tendons Post Tensioned Bridge Element
Minimum Thickness
Webs; I-Girder Bridges
8-inches or outer whichever is greater.
Regions of Slabs without longitudinal tendons
8-inches, or as required to accommodate grinding, concrete covers, transverse and longitudinal P.T. ducts and top and bottom mild reinforcing mats, with allowance for construction tolerances whichever is greater.
Regions of slabs containing longitudinal internal tendons
9-inches, or as required to accommodate grinding, concrete covers, transverse and longitudinal P.T. ducts and top and bottom mild reinforcing mats, with allowance for construction tolerances whichever is greater.
Clear Distance Between Circular Voids C.I.P. Voided Slab Bridges
Outer duct diameter plus 5-inches, or outer duct diameter plus vertical reinforcing plus concrete cover whichever is greater.
Segment Pier Diaphragms external post-tensioning
*6 feet.
containing
Webs of C.I.P. boxes with internal tendons
duct
plus
5-inches
For single column of ducts: 12-inches, or 3 times outer duct diameter whichever is
greater.
**For two or more ducts set side by side: Web thickness must be sufficient to accommodate concrete covers, longitudinal P.T. ducts, 3 -inch min. spacing between ducts, vertical reinforcing, with allowance for construction tolerances. *Post-Tensioned pier segment halves are acceptable. **The 3 -inch measurement must be measured in a horizontal plane.
4.11.1 Corrosion Protection
A. Detail all post-tensioned bridges consistent with the Specifications and Standards and include the following corrosion protection strategies: 1.) Enhanced Post-tensioned systems. 2.) Fully grouted tendons. 3.) Multi-level anchor protection. 4.) Watertight bridges. 5.) Multiple tendon paths. B. Three Levels of Strand Protection: Enhanced post-tensioning systems require three levels of protection for strand and four levels for anchorages. Deck overlays are not considered a level of protection for strands or anchorages. 1.) Within the Segment or Concrete Element: a.) Internal Tendons. i.) Concrete cover. ii.) Plastic duct. iii.) Complete filling of the duct with approved grout. b.) External Tendons. i.) Hollow box structure itself. ii.) Plastic duct.
iii.) Complete filling of the duct with approved grout. 2.) At the segment face or construction joint (Internal and External Tendons) a.) Epoxy seal (pre-cast construction) or wet cast joint (cast-in-place construction.) b.) Continuity of the plastic duct. c.) Complete filling of the duct with approved grout. C. Four Levels of Protection for Anchorages on interior surfaces (interior diaphragms, etc.). 1.) Grout. 2.) Permanent grout cap. 3.) Elastomeric seal coat. 4.) Concrete box structure. D. Four Levels of Protection for Anchorages on exterior surfaces (Pier Caps, expansion joints, diaphragms etc.) 1.) Grout. 2.) Permanent grout cap. 3.) Encapsulating pour-back. 4.) Seal coat (Elastomeric/Methyl Methacrylate on riding surface.) 4.12 Pre-tensioning
Prestressing systems have developed over the years and various companies have patented their products. Detailed information of the systems is given in the product catalogues and brochures published by companies. There are general guidelines of prestressing in Section 12 of IS:1343 - 1980. The information given in this section is introductory in nature, with emphasis on the basic concepts of the systems. The prestressing systems and devices are described for the two types of prestressing, pretensioning and post-tensioning, separately. This section covers pre-tensioning. Section 1.4, “Post-tensioning Systems and Devices”, covers post-tensioning. In pre-tensioning, the tension is applied to the tendons before casting of the concrete. The stages of pre-tensioning are described next. Stages of Pre-tensioning
In pre-tensioning system, the high-strength steel tendons are pulled between two end abutments (also called bulkheads) prior to the casting of concrete. The abutments are fixed at the ends of a prestressing bed.
Once the concrete attains the desired strength for prestressing, the tendons are cut loose from the abutments.
The prestress is transferred to the concrete from the tendons, due to the bond between them. During the transfer of prestress, the member undergoes elastic shortening. If the tendons are located eccentrically, the member is likely to bend and deflect (camber). The various stages of the pre-tensioning operation are summarised as follows. 1) Anchoring of tendons against the end abutments 2) Placing of jacks 3) Applying tension to the tendons 4) Casting of concrete 5) Cutting of the tendons.
During the cutting of the tendons, the prestress is transferred to the concrete with elastic shortening and camber of the member. The stages are shown schematically in the following figures.
4.12.1 Advantages of Pre-tensioning
The relative advantages of pre-tensioning as compared to post-tensioning are as follows. • Pre-tensioning is suitable for precast members produced in bulk. • In pre-tensioning large anchorage device is not present. 4.12.2 Disadvantages of Pre-tensioning
The relative disadvantages are as follows. • A prestressing bed is required for the pre-tensioning operation. • There is a waiting period in the prestressing bed, before the concrete attains sufficient strength. • There should be good bond between concrete and steel over the transmission length.
4.12.3 Devices The essential devices for pre-tensioning are as follows.
• Prestressing bed • End abutments • Shuttering / mould • Jack • Anchoring device • Harping device (optional)
4.12.3 Prestressing Bed, End Abutments and Mould
The following figure shows the devices.
Figure Prestressing bed, end abutment and mould
An extension of the previous system is the Hoyer system. This system is generally used for mass production. The end abutments are kept sufficient distance apart, and several members are cast in a single line. The shuttering is provided at the sides and between the members. This system is also called the Long Line Method. The following figure is a schematic representation of the Hoyer system.
Figure Schematic representation of Hoyer system
The end abutments have to be sufficiently stiff and have good foundations. This is usually an expensive proposition, particularly when large prestressing forces are required. The necessity
of stiff and strong foundation can be bypassed by a simpler solution which can also be a cheaper option. It is possible to avoid transmitting the heavy loads to foundations, by adopting self-equilibrating systems. This is a common solution in load-testing. Typically, this is done by means of a ‘tension frame’. The following figure shows the basic components of a tension frame. The jack and the specimen tend to push the end members. But the end members are kept in place by members under tension such as high strength steel rods.
Figure A tension frame
The frame that is generally adopted in a pre-tensioning system is called a stress bench. The concrete mould is placed within the frame and the tendons are stretched and anchored on the booms of the frame. The following figures show the components of a stress bench.
Figure Stress bench – Self straining frame
The following figure shows the free body diagram by replacing the jacks with the applied forces.
Figure Free body diagram of stress bench
The following figure shows the stress bench after casting of the concrete.
Figure The stress bench after casting concrete
4.12.4 Jacks
The jacks are used to apply tension to the tendons. Hydraulic jacks are commonly used. These jacks work on oil pressure generated by a pump. The principle behind the design of jacks is Pascal’s law. The load applied by a jack is measured by the pressure reading from a gauge attached to the oil inflow or by a separate load cell. The following figure shows a double acting hydraulic jack with a load cell.
Figure A double acting hydraulic jack with a load cell 4.12.5 Anchoring Devices
Anchoring devices are often made on the wedge and friction principle. In pre-tensioned members, the tendons are to be held in tension during the casting and hardening of concrete. Here simple and cheap quick-release grips are generally adopted. The following figure provides some examples of anchoring devices.
Figure Chuck assembly for anchoring tendons 4.12.6 Harping Devices
The tendons are frequently bent, except in cases of slabs-on-grade, poles, piles etc. The tendons are bent (harped) in between the supports with a shallow sag as shown below.
Figure Harping of tendons
The tendons are harped using special hold-down devices as shown in the following figure.
Figure Hold-down anchor for harping of tendons
4.13 Prestressing concrete
Although prestressed concrete was patented by a San Francisco engineer in 1886, it did not emerge as an accepted building material until a half-century later. The shortage of steel in Europe after World War II coupled with technological advancements in high-strength concrete and steel made prestressed concrete the building material of choice during European post-war reconstruction. North America's first prestressed concrete structure, the Walnut Lane Memorial Bridge in Philadelphia, Pennsylvania, however, was not completed until 1951. In conventional reinforced concrete, the high tensile strength of steel is combined with concrete's great compressive strength to form a structural material that is strong in both compression and tension. The principle behind prestressed concrete is that compressive stresses induced by high-strength steel tendons in a concrete member before loads are applied will balance the tensile stresses imposed in the member during service. Prestressing removes a number of design limitations conventional concrete places on span and load and permits the building of roofs, floors, bridges, and walls with longer unsupported spans. This allows architects and engineers to design and build lighter and shallower concrete structures without sacrificing strength. The principle behind prestressing is applied when a row of books is moved from place to place. Instead of stacking the books vertically and carrying them, the books may be moved in a horizontal position by applying pressure to the books at the end of the row. When sufficient pressure is applied, compressive stresses are induced throughout the entire row, and the whole row can be lifted and carried horizontally at once. 4.13.1 Compressive Strength Added
Compressive stresses are induced in prestressed concrete either by pretensioning or posttensioning the steel reinforcement. In pretensioning, the steel is stretched before the concrete is placed. High-strength steel tendons are placed between two abutments and stretched to 70 to 80 percent of their ultimate strength. Concrete is poured into molds around the tendons and allowed to cure. Once the concrete reaches the required strength, the stretching forces are released. As the steel reacts to regain its original length, the tensile stresses are translated into a compressive stress in the concrete. Typical products for pretensioned concrete are roof slabs, piles, poles, bridge girders, wall panels, and railroad ties.
In post-tensioning, the steel is stretched after the concrete hardens. Concrete is cast around, but not in contact with unstretched steel. In many cases, ducts are formed in the concrete unit using thin walled steel forms. Once the concrete has hardened to the required strength, the steel tendons are inserted and stretched against the ends of the unit and anchored off externally, placing the concrete into compression. Post-tensioned concrete is used for cast-inplace concrete and for bridges, large girders, floor slabs, shells, roofs, and pavements. Prestressed concrete has experienced greatest growth in the field of commercial buildings. For buildings such as shopping centers, prestressed concrete is an ideal choice because it provides the span length necessary for flexibility and alteration of the internal structure. Prestressed concrete is also used in school auditoriums, gymnasiums, and cafeterias because of its acoustical properties and its ability to provide long, open spaces. One of the most widespread uses of prestressed concrete is parking garages. 4.14 Aggregates
Aggregates are inert granular materials such as sand, gravel, or crushed stone that, along with water and portland cement, are an essential ingredient in concrete. For a good concrete mix, aggregates need to be clean, hard, strong particles free of absorbed chemicals or coatings of clay and other fine materials that could cause the deterioration of concrete. Aggregates, which account for 60 to 75 percent of the total volume of concrete, are divided into two distinct categories-fine and coarse. Fine aggregates generally consist of natural sand or crushed stone with most particles passing through a 3/8-inch (9.5-mm) sieve. Coarse aggregates are any particles greater than 0.19 inch (4.75 mm), but generally range between 3/8 and 1.5 inches (9.5 mm to 37.5 mm) in diameter. Gravels constitute the majority of coarse aggregate used in concrete with crushed stone making up most of the remainder. Natural gravel and sand are usually dug or dredged from a pit, river, lake, or seabed. Crushed aggregate is produced by crushing quarry rock, boulders, cobbles, or large-size gravel. Recycled concrete is a viable source of aggregate and has been satisfactorily used in granular subbases, soil-cement, and in new concrete. Aggregate processing consists of crushing, screening, and washing the aggregate to obtain proper cleanliness and gradation. If necessary, a benefaction process such as jigging or heavy media separation can be used to upgrade the quality. Once processed, the aggregates are handled and stored in a way that minimizes segregation and degradation and prevents contamination. Aggregates strongly influence concrete's freshly mixed and hardened properties, mixture proportions, and economy. Consequently, selection of aggregates is an
important process. Although some variation in aggregate properties is expected, characteristics that are considered when selecting aggregate include: •
grading
•
durability
•
particle shape and surface texture
•
abrasion and skid resistance
•
unit weights and voids
•
absorption and surface moisture
Grading refers to the determination of the particle-size distribution for aggregate. Grading limits and maximum aggregate size are specified because grading and size affect the amount of aggregate used as well as cement and water requirements, workability, pumpability, and durability of concrete. In general, if the water-cement ratio is chosen correctly, a wide range in grading can be used without a major effect on strength. When gap-graded aggregate are specified, certain particle sizes of aggregate are omitted from the size continuum. Gap-graded aggregate are used to obtain uniform textures in exposed aggregate concrete. Close control of mix proportions is necessary to avoid segregation. 4.14.1 Shape and Size Matter
Particle shape and surface texture influence the properties of freshly mixed concrete more than the properties of hardened concrete. Rough-textured, angular, and elongated particles require more water to produce workable concrete than smooth, rounded compact aggregate. Consequently, the cement content must also be increased to maintain the water-cement ratio. Generally, flat and elongated particles are avoided or are limited to about 15 percent by weight of the total aggregate. Unit-weight measures the volume that graded aggregate and the voids between them will occupy in concrete. The void content between particles affects the amount of cement paste required for the mix. Angular aggregate increase the void content. Larger sizes of well-graded aggregate and improved grading decrease the void content. Absorption and surface moisture of aggregate are measured when selecting aggregate because the internal structure of aggregate is made up of solid material and voids that may or may not contain water. The amount of water in the concrete mixture must be adjusted to include the moisture conditions of the aggregate. Abrasion and skid resistance of an aggregate are essential when the aggregate is to be used in concrete constantly subject to abrasion as in heavy-duty floors or pavements. Different minerals in the aggregate wear and polish at different rates. Harder aggregate can be selected in highly abrasive conditions to minimize wear.
4.15 Admixtures
Chemical admixtures are the ingredients in concrete other than portland cement, water, and aggregate that are added to the mix immediately before or during mixing. Producers use admixtures primarily to reduce the cost of concrete construction; to modify the properties of hardened concrete; to ensure the quality of concrete during mixing, transporting, placing, and curing; and to overcome certain emergencies during concrete operations. Successful use of admixtures depends on the use of appropriate methods of batching and concreting. Most admixtures are supplied in ready-to-use liquid form and are added to the concrete at the plant or at the jobsite. Certain admixtures, such as pigments, expansive agents, and pumping aids are used only in extremely small amounts and are usually batched by hand from premeasured containers. The effectiveness of an admixture depends on several factors including: type and amount of cement, water content, mixing time, slump, and temperatures of the concrete and air. Sometimes, effects similar to those achieved through the addition of admixtures can be achieved by altering the concrete mixture-reducing the water-cement ratio, adding additional cement, using a different type of cement, or changing the aggregate and aggregate gradation.
4.15.1 Five Functions
Admixtures are classed according to function. There are five distinct classes of chemical admixtures: air-entraining, waterreducing, retarding, accelerating, and plasticizers (superplasticizers). All other varieties of admixtures fall into the specialty category whose functions include corrosion inhibition, shrinkage reduction, alkali-silica reactivity reduction, workability enhancement, bonding, damp proofing, and coloring. Air-entraining admixtures, which are used to purposely place microscopic air bubbles into the concrete, are discussed more fully in "Air-Entrained Concrete." Water-reducing admixtures usually reduce the required water content for a concrete mixture by about 5 to 10 percent. Consequently, concrete containing a water-reducing admixture needs less water to reach a required slump than untreated concrete. The treated concrete can have a lower water-cement ratio. This usually indicates that a higher strength concrete can be produced without increasing the amount of cement. Recent advancements in admixture technology have led to the development of mid-range water reducers. These admixtures reduce water content by at least 8 percent and tend to be more stable over a wider range of temperatures. Mid-range water reducers provide more consistent setting times than standard water reducers.
Retarding admixtures, which slow the setting rate of concrete, are used to counteract the accelerating effect of hot weather on concrete setting. High temperatures often cause an increased rate of hardening which makes placing and finishing difficult. Retarders keep concrete workable during placement and delay the initial set of concrete. Most retarders also function as water reducers and may entrain some air in concrete. Accelerating admixtures increase the rate of early strength development, reduce the time required for proper curing and protection, and speed up the start of finishing operations. Accelerating admixtures are especially useful for modifying the properties of concrete in cold weather. Super plasticizers, also known as plasticizers or high-range water reducers (HRWR), reduce water content by 12 to 30 percent and can be added to concrete with a low-to-normal slump and water-cement ratio to make high-slump flowing concrete. Flowing concrete is a highly fluid but workable concrete that can be placed with little or no vibration or compaction. The effect of superplasticizers lasts only 30 to 60 minutes, depending on the brand and dosage rate, and is followed by a rapid loss in workability. As a result of the slump loss, superplasticizers are usually added to concrete at the jobsite. Corrosion-inhibiting admixtures fall into the specialty admixture category and are used to slow corrosion of reinforcing steel in concrete. Corrosion inhibitors can be used as a defensive strategy for concrete structures, such as marine facilities, highway bridges, and parking garages, that will be exposed to high concentrations of chloride. Other specialty admixtures include shrinkage-reducing admixtures and alkali-silica reactivity inhibitors. The shrinkage reducers are used to control drying shrinkage and minimize cracking, while ASR inhibitors control durability problems associated with alkali-silica reactivity. 4.16 Pre-Stressed Steel
Although seemingly recent, pre-stressed steel is a material whose origins date back a long way. The adoption of the technique of pre-stressing is attributed to Paxton, who in 1851 utilized this technique for the realization of the Crystal Palace, unaware of the great discovery he had made. Koenen was the first to propose pre-stressing steel bars. He suggested doing this in 1907, before applying concrete, in order to avoid the formation of cracks and thus stumbled across the innovation of reinforced concrete (R.C.). Unfortunately however, his attempts failed because at that time the phenomena of fluage and shrinkage were unknown. In fact, the real “father” of pre-stressing is EugèneFreyssinet, who in 1928 defined pre-stressing as a technique which consists in subjecting a material, in his case reinforced concrete, to loads which produce stresses opposed to those in operation, through the use of cables which have first been laid in the stressed mass.
The reasons which gave rise to this material may be found in the mechanical characteristics of concrete which, in fact, shows great ability to absorb forces of compression but a low resistance to tension which is allowed to be absorbed by the metallic reinforcement. The latter, however, under the effect of tension tends to lengthen and, on account of the phenomenon of bonding, pulls the concrete along with it. Consequently, if the stresses of tension are high, the concrete will crack. The cracks do not destabilize the structure but could lead to possible further deformation and expose the reinforcement to the danger of oxidization which in turn produces a reduction of its own resistance. It can be deducted that R.C. can tolerate loads up until the cracking limit. Unlike R.C., steel is a material which has high resistance both to tension and to compression. As a consequence, by making a comparison between pre-stressed steel and reinforced concrete, we can immediately note that in the first place, this technique further raises both the quality and the resistance to tension and compression characteristics of the steel; the technique actually manages to create a state of co-action in which the tensions and deformations are opposed to those induced by the loads which will subsequently act upon the structure. In the second place it raises the resistance to tension of reinforced concrete which is, in fact, negligible. 4.16.1 Forms of Pre-stressing Steel
The development of pre-stressed concrete was influenced by the invention of high strength steel. It is an alloy of iron, carbon, manganese and optional materials. In addition to prestressing steel, conventional non-pre-stressed reinforcement is used for flexural capacity (optional), shear capacity, temperature and shrinkage requirements. Wires. A pre-stressing wire is a single unit made of steel. The nominal diameters of the wires are 2.5, 3.0, 4.0, 5.0, 7.0 and 8.0 mm. The different types of wires are as follows:
1) Plain wire: No indentations on the surface. 2) Indented wire: There are circular or elliptical indentations on the surface. Strands. A few wires are spun together in a helical form to form a pre-stressing strand. The different types of strands are as follows:
1) Two-wire strand: Two wires are spun together to form the strand. 2) Three-wire strand: Three wires are spun together to form the strand. 3) Seven-wire strand: In this type of strand, six wires are spun around a central wire. The central wire is larger than the other wires. Tendons. A group of strands or wires are placed together to form a pre-stressing tendon. The tendons are used in post-tensioned members. The following figure shows the cross section of a typical tendon. The strands are placed in a duct which may be filled with grout after the post-tensioning operation is completed (Figure 1).
Figure 1: Cross-Section of a typical tendon Cables. A group of tendons form a pre-stressing cable. The cables are used in bridges. Bars. A tendon can be made up of a single steel bar. The diameter of a bar is much larger than that of a wire. Bars are available in the following sizes: 10, 12, 16, 20, 22, 25, 28 and 32 mm.
Figure 2 shows the different forms of pre-stressing steel.
Figure 2: Forms of reinforcing and pre-stressing steel 4.16.2 Types of Pre-stressing Steel
The steel is treated to achieve the desired properties. The following are the treatment processes: •
Cold working (cold drawing) is being done by rolling the bars through a series of dyes. It re-aligns the crystals and increases the strength.
•
Stress relieving is being done by heating the strand to about 350°C and cooling slowly. This reduces the plastic deformation of the steel after the onset of yielding.
•
Strain tempering for low relaxation is being done by heating the strand to about 350°C while it is under tension. This also improves the stress-strain behavior of the
steel by reducing the plastic deformation after the onset of yielding. In addition, the relaxation is reduced. 4.16.3 Properties of Pre-stressing Steel
The steel in pre-stressed applications has to be of good quality. It requires the following attributes: 1) High strength 2) Adequate ductility 3) Bendability, which is required at the harping points and near the anchorage 4) High bond, required for pre-tensioned members 5) Low relaxation to reduce losses 6) Minimum corrosion. The tensile strength of pre-stressing steel is given in terms of the characteristic tensile strength (fpk). The characteristic strength is defined as the ultimate tensile strength of the coupon specimens below which not more than 5% of the test results are expected to fall.
Figure 3(a): Test set-up
Figure 3(b): Testing of tensile strength of pre-stressing strand
The minimum tensile strengths for different types of wires as specified by the standard codes are given. Table 1: Cold Drawn Stress-Relieved Wires (IS: 1785 Part 1). The proof stress should not be less than 85% of the specified tensile strength.
Table2: As-Drawn wire (IS: 1785 Part 2). The proof stress should not be less than 75% of the specified tensile strength.
Table 3: Indented wire (IS: 6003). The proof stress should not be less than 85% of the specified tensile strength.
The minimum tensile strength of high tensile steel bars according to IS:2090 is 980 N/mm2. The proof stress should not be less than 80% of the specified tensile strength. The stiffness of pre-stressing steel is given by the initial modulus of elasticity. The modulus of elasticity depends on the form of pre-stressing steel (wires or strands or bars). IS:1343 1980 provides the following guidelines which can be used in absence of test data. Table 4: Modulus of elasticity (IS: 1343 - 1980)
4.17 PRESTRESSING DUCTS
Standard Specifications requires that the duct enclosures for prestressing steel be rigid ferrous metal, galvanized, mortar tight, and accurately placed as shown on the contract plans or as approved by the Engineer. Rigid duct is used to take advantage of the low tendon-to-duct friction inherent with rigid duct. The rigid type duct is stiff enough to eliminate horizontal
wobble, but flexible enough to bend and meet the required tendon profiles. The reduced friction coefficients associated with rigid duct as compared to that of flexible duct can result in a 10% to 50% reduction of prestressing steel required, depending on the length of the structure. Rigid duct is available in various types and diameters. One type of duct is the smooth wall type, made from strip steel held together longitudinally with a continuous resistance weld or a continuous interlocking seam. The duct is normally furnished in 20-foot lengths with one end of each length enlarged to form a slip-type connection. Another type of rigid duct is made from ribbed sheet steel with helically wound interlocking seams. This duct is generally furnished in 40-foot (12.2 m) lengths and is connected by larger rigid duct couplers. A third type of rigid duct that is approved for State use is the VSL shallow elliptical or rectangular type. This type is used occasionally for transverse deck stressing. The rigid ducts are to be field released by the structure representative. The ducts will not have release tags attached when they arrive on the jobsite. The ducts are to be checked for specification compliance and any damage that may have occurred during shipping. Damaged duct can be repaired if the damage is minor but shall be rejected if the damage is extensive. The placement of the ducts can be checked by using the “duct checker”, (Bridge Construction Records and Procedures Memo 145-7.0) or with an engineer’s rule and level. Most tendon paths are parabolic and the distance from the soffit forms to the center of gravity (CG) of the path can be calculated as shown below:
The final check for the duct alignment should be verified by visually observing a smooth tendon path. It is recommended that the taped duct joints be staggered for multiple tendon girders so that a misalignment of the ducts does not occur. Section 50-1.07, “Ducts”, of the Standard Specifications requires that waterproof tape be used at all duct connections. Once the ducts have been properly aligned, check to verify that the ducts have been properly secured to the bar reinforcing steel to prevent displacement during concrete placement. Ducts
are typically secured to the bar reinforcing steel using tie wire spaced at 5 feet intervals along the duct path. Tie wire spacing intervals should be reduced if conditions warrant. Duct vents are required on ducts with a total length of 400 feet (122 m) or more and shall be located within 6 feet (1.8 m) of a high point in the duct profile. Locating these vents on either side of the bent cap centerline may avoid possible conflicts with the top cap steel. The contractor is required to protect the ducts from any water or debris entering them prior to the placement of the stressing steel. Section 50-1.07, “Ducts”, of the Standard Specifications states that the ducts shall be covered at all times after installation into the forms. The contractor is required to prove that the ducts are free and unobstructed twice as follows: 1. Prior to placing forms for closing slabs of box girder cells, Std. Spec. 50-1.08. 2. Immediately prior to installation of prestressing steel, Std. Spec. 50-1.07. All holes or openings in a duct (large enough to let grout out or concrete in) must be repaired prior to concrete placement. Holes less than ¼ inch in diameter can be repaired with several wraps of waterproof tape. Holes or openings larger than ¼ inch should be repaired with an overlapping split metal sleeve.
4.17.1 PRESTRESSING STRANDS/BARS
The base material used to fabricate prestressing steel must conform to the requirements of ASTM Designations A416, A421, or A722, as well as Section 50-1.05, “Prestressing Steel”, of the Standard Specifications. The A416 designation covers the requirements for both 0.5” (12.70 mm) and 0.6” (15.24 mm) strand. The A421 designation gives requirements for prestressing wire. The A722 designation gives requirements for high-strength steel bars. Figures 2, 3, and 4 show typical stress-strain curves and physical properties for 0.5” (12.70 mm), 0.6” (15.24 mm) strand, and grade 150 ksi (1030 MPa) bars.
All strand is the seven wire type with a center wire enclosed by six helically placed outer wires. The center wire is slightly larger than the outer six wires. Strand is stress relieved by continuous heat treatment, a process that produces a slight bluish tint to the strands. The process of fabricating low-lax strand is schematically shown in Figure 1. The ASTM specifications allow one butt-welded wire per 150 feet (45.72 m) of strand, but only during the fabrication process. Under no circumstances should welding of joints in strands or wires be allowed in the field. The Standard Specifications allow the use of couplers for extending plain or deformed bars. The coupled unit shall have a tensile strength of not less than the manufacturer’s minimum guaranteed ultimate tensile strength of the bars. The locations of couplers are subject to approval of the Engineer and shall be shown on the contractor’s working drawings. Effective packaging of prestressing steel is necessary to protect the material from physical damage and corrosion. 4.17.1 ANCHORAGE DEVICES
Approved permanent type anchorage devices shall be shown on the pretress shop drawings. Section 50-1.06, “Anchorage and Distribution”, of the Standard Specifications requires that the final unit compressive strength stress on the concrete behind the bearing plate shall not exceed 3000 psi (21 MPa). The bending stresses in the plates shall not exceed the yield point of the material when 95% of the guaranteed ultimate tensile strength (GUTS) of the tendon is applied.
Anchorage devices must be preapproved by METS prior to their use on State contracts. The bearing plates shall be tested and released by METS. A TL-29 release form and a release tag are required prior to incorporating the bearing plates into the work. The bearing plates are to be placed perpendicular to the slope of the prestress duct. The batter of the bearing plate should be checked during the working drawing review and confirmed while the prestressblockouts are being formed. 4.17.2 STRAND WEDGES
The specifications require all permanent anchorage devices for post-tensioning to develop at least 95% of the guaranteed ultimate tensile strength (GUTS) of the prestressing steel. The anchorage systems develop the required strength through the interplay between wedges and prestressing steel, and between the wedges and anchor plate. Characteristics that effect this interplay are wedge angle, wedge teeth amplitude and spacing, type of steel, type of heat treatment, and general strand configuration in the anchor plate. The care, cleanliness, lubrication, surface condition, and finish also effect the efficiency of wedge systems. All manufacturers have quality control procedures that should eliminate obvious manufacturing defects. On-the-job care is left to the discretion of the individual field crews. The contractor must use wedges that have been approved by METS. Pulling wedges may not be used as permanent wedges. The wedge holes of the anchor block should be clean prior to placing the permanent wedges. Sand or foreign particles located in the wedge area of the anchor block can cause the wedges to fail. 4.17.3 PRESTRESSING JACKS
Jacks used in typical post-tensioning systems are generally the centerhole variety (see Figure 5 for an example). Prestressing jacks have more wearing surface, longer jack stroke, and packing than conventional jacks of the same capacity. This increases the potential of variations in the accuracy of the applied force. Other conditions which may affect accuracy and efficiency of hydraulic units are: use of unfiltered oil, exposure of the system to dust or grit, eccentric loading, type of packing, ram position, oil temperature, hydraulic valves, ram and packing maintenance, and readout equipment. Care and effort must be exercised to maintain accuracy in the jacking equipment. A condition that must be considered when using hydraulic jacks is hysteresis. Hysteresis is an energy loss due to a hydraulic pressure change inside the jack, causing inaccurate load values when the ram pressure is static or decreasing. An increase of hydraulic pressure also causes an energy loss, but this loss is taken care of by calibrating the jack and pressure gage with a load cell during this increase of pressure. Improper gage readings occur when the ram is fully extended and the hydraulic pressure is dissipated against the jack case. This condition can cause harm only if it damages the jack or gage and if the gage reading is mistaken for actual tendon stress.
The contractor should monitor the stroke of the jack. Typically, jacks have a 12-inch (300 mm) stroke and if the ram is extended beyond this limit the jack will be damaged. Fittings and valves are a common source of problems. The fittings are equipped with springloaded, self-closing ball valves that occasionally will not open when joined together. If this occurs anywhere except in the gage line, the system will not work and a high gage reading will show immediately. If the stuck valve is in the gage line, everything will work except the gage. Valves and fittings that leak or will not hold the load should be replaced. When fittings are replaced, it is imperative that high-pressure type fittings are used (e.g. Schedule 80). If there are any questions concerning high-pressure fittings, contact METS immediately. In general, jacks are about 95% efficient, but actual efficiency will vary depending on the age and condition of the jack. Be cautious of any calibration chart that shows jacking forces much greater than 95% of pressure multiplied by the piston area. Load cells and pressure gages are available to check any questionable equipment. Section 50-1.08 of the Standard Specifications requires that the jacks used to stress tendons that are permanently anchored at 25% or more of the specified minimum ultimate tensile strength of the prestressing steel, such as box girder tendons, be calibrated by METS within one year prior to use and after each repair. Jacks used to stress tendons that are permanently anchored at less than 25% of the specified minimum ultimate tensile strength of the prestressing steel, such as footing tie-downs, shall be calibrated by a private laboratory approved by METS within six months prior to use and after each repair. The Structure Construction web site, listed under “Field Resources”, has current information for jacks used with all State approved stressing systems.
Questions
1. What are long and short columns? 2. Explain behavior of RCC columns under axial load? 3. Design axially loaded short and long columns with hinged ends? 4. What is prestressed concrete? 5. What is Linear post tensioning and pre tensioning? 6. Describe Linear post tensioning system? 7. What are the materials of prestressing? 8. Describe prestressing equipment? 9. What are the special techniques of pretension?
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