CHAPTER 3 LOADS AND MATERIALS. 3.1 Introduction

Transcription

1 CHAPTER 3 LOADS AND MATERIALS 3.1 Introduction Loads and properties of materials the basic parameters affecting the structural design of a Reinforced cement concrete structure. Both of them are basically of variation nature. The correct assessment of loads/forces on a structure is a very important step for the safe and serviceable of structure. 3.2 Types of Loads. Broadly classification of loads is done as horizontal loads, vertical loads and longitudinal loads. The horizontal loads consist of earthquake load and wind load.the vertical loads contains dead load, live load and impact load. Longitudinal loads. (viz Tractive and braking forces are considered are special cases of design of bridges, design of gantry girder etc) Dead load: These are the stationary or permanent loads which are transmitted to structure all over life span. Dead loads are primarily due to structural members self weight, fixed permanent equipments, permanent partition walls, and different materials weight. The dead weight of materials are given Appendix.- A, Table A Live loads or Imposed Loads: Live loads are either moving loads or movable without any impact or acceleration. These are supposed to be formed by occupancy or intended use of building including weights of furniture or movable partitions etc. The imposed loads to be assumed in buildings are given in Appendix-A Table A-2 as per IS: 875 (part-2) The design of floor slabs have to be done to carry either concentrated loads or uniformly distributed loads whichever create greater stresses on part under consideration. Because at any particular time it is unlikely that all the

2 floors will not be carrying simultaneously maximum loading, for this purpose code permits some sort of reduction within imposed loads for designing the columns, piers supports and foundations,load bearing walls,. They are given in Fig.3.1 Fig.3.1 Reduction in Imposed Loads Impact loads: Impact load which is created by vibration or acceleration or impact. A person walking produces a live load but soldiers marching of frames supporting lifts and hoists produce impact loads. Therefore, impact load is

3 equivalent to imposed load incremented in some percentage (called impact allowance or impact factor depending on the impact intensity) Wind loads: These are the loads which are chiefly horizontal loads created by movement of air with the relation to earth. Details of design wind load are given in IS : 875 (Part - 3 )2.2 Wind load which is required to be taken into consideration in the design particularly when the height surpass two times the dimensions transverse to exposed wind face. With respect to low rise structures or building say up to 4 to 5 storey's wind load is not significant or not critical since provided moment of resistance by the continuation of floor with column connection as well as walls provided amid columns are enough to house the effect of these forces' Further the design load factor in limit state method is decreased to 1.2 (DL+LL+WL) while wind is taken into consideration as against factor of 1.5(DL+LL) while wind is not taken into consideration Earthquake Load These are the type of loads which are horizontal in direction caused by earthquake also shall be calculated by utilising IS: For reinforced concrete structures which are monolithic located in seismic zone II, and III with not greater than 5 storey height possessing importance factor lesser than 1, for these cases seismic forces are not critical (See IS:13920sec1.1) 3.3 Characteristic Load Since the loads are available in nature they are determined based on statistical approach. Bur it is a impossible to give a guarantee that the loads cannot exceed during the life span of the structure. Thus, the characteristic values of the load is obtained based on statistical probabilistic principles from mean value and standard deviation.

4 The characteristic load is defined as that value of that load which has 95% probability of being exceeded during the service span of the structure. However this requires large amount of statistical data. But, since such data are not available. Code recommends to take the working loads are service loads based on past experience and judgment and are to be taken as per IS:87521 andis: Codes. 3.4 Design Load The variation in loads due to unforeseen increase in loads, constructional inaccuracies, type of Limit are taken into account to define the design load. The design load is given by : Design load = ϒ f x characteristic load Where ϒ f = loads given in Table 3.1. Table γ.1 : partial safety factor (Ȗ f ) for loads (according to IS: ) Load combination Limit State of collapse Limit State of serviceability DL IL WL DL IL WL DL + IL DL + WL 1.5 or DL + IL + WL * This value is to be considered when stability against overturning or stress reversal is critical. Notes : (1) DL = dead load IL = Imposed load or live load WL = Wind load (2) While considering earthquake effects substitute EL for WL. (3) Since the serviceability relates to the behaviour of structure at working load the partial safety factors for limit state of serviceability are unity.

5 (4) For limit state of serviceability the values given in this table are applicable for short term effects. While assessing the long-term effects due to creep, the dead load and that part of the live load likely to be permanent may only be considered. 3.5 Critical Load combinations While designing a structure, all load combinations, in general, considered and the structure, is designed for the most critical of all. As discussed in the earlier section, since for buildings up to 4wind load is not considered the elements are required to be designed for critical combination of dead load and live load only. For deciding load arrangements. We are required to use maximum and minimum loads for this. Code prescribes different load factors as given below: Maximum load = w max = 1.5 (DL+LL) Minimum load = w min = DL

6 The maximum positive moment producing tension at the bottom will occur when the deflection is maximum or curvature producing concavity upwards is maximum. This condition will occur when maximum load (i.e. both DL and LL) covers the whole span while minimum load (i.e. only DL) is on adjacent spans. The negative moments producing tension at the top will be maximum when the curvature at support producing convexity upwards is maximum which requires maximum load should be applied on adjacent spans. Accordingly, IS:456 recommends the following loading arrangements on structural frames: a) Consideration may be limited to combination of : 1. Design dead load on all spans with full design live on two adjacent spans (for obtaining maximum hogging moment) 2. Design dead load on all spans with full design imposed load and on alternate spans (to get maximum span moment) 3. When design imposed load does not exceed three-fourths of the design dead load, the load arrangement may be design dead load and design imposed load on all the spans. The loading arrangement giving maximum span moment, say span AB is shown in figure and it gives the loading arrangements for maximum negative load on all the spans. 3.6 Generalized procedure for calculation of maximum span moment and point flexures When the loading arrangement specified by the code is considered for the analysis of a continuous beam simply supported at ends and by UDL, the maximum bending moment does not occur at the mid-span of penultimate span but it occurs at a small distance away from the mid-span towards the simply supported end. In general, the analysis of a structure using any method of analysis gives the end forces consisting of axial force bending moment and shear force

7 (or reaction). The next step is to analyze the beam to determine the maximum span moment and points of contra flexures if any, and then to design the beam at different sections. The end sections subjected to hogging moments require provision of steel at top while the mid span section will require steel at bottom face to resist sagging moment. In some cases the end moments are so large that the negative (or hogging moment may prevail over the whole span and it would be necessary to provide steel at top only or on some cases even negative reaction may develop a tone of the ends for which proper anchoring arrangements may become necessary. Further, in some cases the end moments may be zero or only one end maybe subjected to moment because of the other end being simply supported (e.g. penultimate span of a continuous beam) or end moments having the same or different magnitudes may act at both ends (e.g. intermediate span of a continuous beam). In order to consider all these probabilities it is necessary to derive generalized equations for calculation of span moment and points of contra flexures for a beam loaded by a uniformly distributed load subjected to end moments. Consider a beam AB of span L loaded by a uniformly distributed load of intensity w, and subjected to end moments M A and M B as shown in Fig It is assumed that M A is greater than M B. x 1, x 2 = distances of the points of contra flexures from end A. L o = Length of beam between points of contra flexures x max = distance of the section from A at which sagging moment is maximum. M max =maximum sagging moment occurring at distance x max from end A. R A R B = end shear forces.

8 Fig 3.2 Sagging and Hogging Moment in beam xmax = x1 + L 0 /2 = R A /w or R A = w x max M max = R A x max /2 MA = wl 2 /8 o L o = 2 x 2 max 2M A w 2 2 R A R A 2M A x 1 = x max + x 2 M A w max = w w w 2 x 2 2M A R A x 2 = x max max = w R A 2M + A w w w

9 Fig-3.3 Negative Moments in beam The bending moment will be negative throughout the span, See Fig 3.3 if one of the following conditions is satisfied : 2 RA 2M A Condition -1: if w w is negative. Condition 2 : if either R A or R B acts in the downward direction irrespective of condition -1 is satisfied or not. In these cases the span moment is calculated at mid-span at a distance L/2 from the support for details of derivation of equations. 3.7 Properties of Concrete

10 3.7.1 Grade of concrete This is recognized by its grade which isÿdesignatedm15,m20,m25 etc. Within this letter M refers to Mix of concrete or Mix whereas the number 15,20,25 etc, indicates (fck) the is specified compressive strength ofÿ150mmÿsize cube after during for 28 days, and is expressed in N/mm2. Therefore concrete which is known by its compressive strength. In R.C. work, M20, M25 grades of concrete, but higher grades of concrete must be utilised for severe, very severe, extreme environment as specified Compressive Strength Like load, strength of concrete is also a quantity which differ significantly for the same mix of concrete. Consequently, a single or say solitary representative value is required, known characteristic strength, is arrived at using statistical probabilistic principles. (a) Characteristic strength It is defined as the value of strength under which not moreÿthanÿ5% of test results are likely to fall, (that is there is 95% probability exists of achieving this value, or probability of not achieving the same). (b) Characteristic strength of concrete in Flexural Member It may be noted that the strength of concrete does not truly represent the strength of concrete in flexural member because factors namely, the shape effect, the prism effect (ratio h/a of the specimen), state of stress in a member and casting and curing conditions for concrete in test specimen differ considerably from those of concrete in the member. Taking this into consideration, the characteristic strength of concrete in a flexural member is considered or taken as equal to 0.67 times the concrete cube strength. (c) Design Strength (f d ) and material strength partial safety factor (γ m ). The strength which is to be taken into consideration for purpose of design is called as design strength and is represented by

11 Design Strength (f d ) = Characteristic strength (f ck ) The value Partial safety factor for material strength (Ȗ m ) of Ȗ m depends upon the type (in fact, reliability) of material and upon the type of limit state. According to I.S Code. Ȗ m = 1.5 for concrete, and Ȗ m = 1.15 for steel. Design strength of concrete in member = 0.67f ck / 1.5 = f ck 0.45f ck Tensile Strength (f cr ) Estimation of modulus of rupture or flexural tensile strength or the concrete's cracking strength from cube's compressive strength is got from the relation. f cr = 0.7 f ck N/mm 2. In direct tension tensile strength of concrete is experimentally obtained by split cylinder strength as described in IS: 5816.which varies between 1/8 to 1/12 of compressive strength of cube. The test for flexural strength of concrete shall be carried out as per IS: Creep Creep which is nothing but the plastic deformation under sustained load. The ultimate creep strain is estimated from the creep coefficient θ given by θ = creep strain /elastic strain = ε cc / ε i Creep strain ε cc depends primarily o the duration of sustained loading. According to the code, the value of ultimate creep coefficient is 1.6 at 28 days of loading.

12 3.7.5 Shrinkage. This is defined as the property of diminishing in volume with hardening. It depends essentially on duration of exposure. If this type of strain is not permitted, it creates tensile stress in the concrete and therefore cracks will be developed in concrete. The shrinkage is measured by shrinkage strain ε cc I.S. Code prescribes the ultimate shrinkage strain ε cc = for design purposes Short-term Modules of elasticity (E c ) The secant modules obtained by testing a concrete specimen at 28specified rate of loading is known as short-term modules of elasticity because inelastic deformations under this loading are practically negligible According to the code; short-term modules of elasticity of concrete is given by E c = 5000 f ck N/mm Long term Modules of Elasticity (E ce ) Effect of shrinkage and creep is to decrease the modulus of elasticity of concrete as time passes. Therefore, the long-term modules of elasticity of concrete takes into consideration the effect of shrinkage and creep and is given by: E = ce E c 1 + θ Where, E ce = long-term modulus of elasticity E c = short-term modulus of elasticity θ= creep coefficient Effect of the reduction in E ce with time is to increase deflections and cracking with time. It, therefore, plays a very important role in limit state of serviceability and in calculations of deflection and cracking.

13 It is further noted that as E c changes, modular ration E s /E c charges with time. Thus, the working stress method which takes a single value of modular Table 3.2. : Modular Ratio for different Grades of Concrete ration m does not represent the true strength and behavior of concrete members Modular Ratio Short-term modular ratio is nothing but the modulus of elasticity of steel to modulus of elasticity of concrete. Short term modular ratio = E s /Ec Where, E s = modulus of elasticity of steel = 2 x 10 5 N/mm 2 E c = 5000 f ck N/mm 2 As the of concrete changes with age at loading, time, etc, modular ratio too changes accordingly. I.S. Code provides the following expression with respect to Long-term modular ratio, by taking into consideration the creep's effects and shrinkage partially Long-term modular ratio = m = 280 3σ cb c Where, σ cb c = permissible compressive stress due to bending in concrete in N/mm 2. Therefore this modular ratio is useful only in the working stress design. It is also required for calculating the properties of a transformed section of a R.C member for the serviceability calculations. The values of modular ratio based on short term and that based for different grades of concrete are given in Table 3.2.Table 3.2

14 Grade of concrete Modular Ration m Short-term Long-term M M Poisson's Ratio Poisson's ratio varies betweenÿ0.1 for concrete of high strengthandÿ0.2 fir weak mixes. It is normally taken equal to 0.15 for strength design and 0.2 for serviceability criteria. Many times the poison's totally neglected with little error in strength calculations Durability Durability of concrete which is its capability to resist its plus decay. One of the principal characteristics affecting durability of concrete is its permeability to entrance of water as well as other materials which are deleterious. The desired lower permeability within concrete is reached or achieved by including an adequate cement, sufficiently low water/cement ration, by doing compaction full in concrete and by sufficient cement. Hence, according to exposure conditions minimum cement content and maximum water/cement ratio, have been specified by IS: 456 in table 5. The exposure conditions in working life, nominal cover an minimum grade of concrete for R.C.C. work are given in Table C-1 in Appendix C Unit weight of concrete: The unit weight of reinforced concrete depends on percentage of reinforcement, type of aggregate, amount of voids and varies from 23 to 26 kn/m 2 respectively.

15 stress - strain curve Stress-strain curve adopted by IS code is shown in Fig it consists of a parabola for the initial ascending part up to a strain of followed by a horizontal line terminating at an ultimate strain of Fig. 3.4 Stress-Strain Curves for Concrete The equation of an idealized stress-strain curve is given by 2 2ε ε = o for o < ε < ε o ε 0 ε 0 and = o Where ε = strain at any point

16 ı = stress at any point ε o = strain at which parabolic part ends = ı o = idealized maximum stress corresponding to ε o 3.8 Concrete Mix proportioning Structural designer properties and strength of concrete assumed within design. Engineer is must proportion the different ingredients making concrete so that the ensuing mix has appropriate workability for placing and give desired strength. Proportioning of concrete is carried out by using any of the following technique (a) (b) By designing concrete mix; This type of designed concrete is known as design mix concrete. By adopting nominal concrete mix; This type of nominally mixed concrete is known as Nominal mix concrete. The former is used for important and large works whereas the later type is used for routine concrete work of medium type construction. Normally, it is desirable to proportion the ingredients by weight. However, for small routine jobs, it is conveniently being done by volume. Mixing shall be done in mechanical mixture for at least 2 minutes till the mass uniform colour and consistency is obtained. 3.9 Curing and stripping time for striking of formwork Concrete subsequent to casting shall be cured in moist condition for minimum period of 7 days and shall be kept in forms concrete attains the strength of at least twice the quantity of stress to which concrete would ordinary Portland cement is used, forms may be removed after expiry of the periods given within Table 3.3. The props under the beams and slabs shall be disconnected in such a sequence so as to of support condition and structural

17 action as imagined in design. For example, the props beneath cantilever beam shall be separated starting from the free end of cantilever towards the fixed end sequentially. Table 3.3. Minimum Curing period and stripping time for striking of Formwork Sr. No. Members Period 1. Walls, columns and vertical faces of all structural members 2. Soffit formwork to slabs (props to be refixed immediately after removal of formwork) 3. Soffit formwork to beams (Props to be refixed immediately after removal of formwork) 16 to 24 hours 3 days 7 days 4. Removal of props under slabs : a) Spanning up to 4.5 m b) Spanning over 4.5 m 7 days 14 days 5. Removal of props under beams and arches : c) Spanning up to 6 m d) Spanning over 6 m 14 days 21 days

18 3.10 Requirements for determination of statistical characteristic strength a) Sampling :This is adopted to guarantee that each and every concrete batch has got reasonable chance of getting tested. The sampling shall be stretched over the whole period of concreting. The frequency of sampling will depend upon the nature of work, the volume of concrete and the importance of the location of concrete from view point of stress condition. For example, higher rate of sampling will be required for highly stressed structural member (like column). Also it will be suitable to cover higher rate of sampling and testing at the start of the work to establish the confidence level in concrete quality at the earliest. In order to establish level of confidence related to concrete quality at the earliest minimum frequency of sampling and testing at the starting of work is carried out. Minimum frequency of each grade's sampling of concrete at each time shall be decided from the volume of concrete as given in Table 3.4. Table 3.4.: Number of samples for testing Quantity of concrete in work in Above 50 m 3 Minimum number of samples x Where x is the number based ion the rate of 1 additional sample for each additional 50 m 3 or part thereof (b) Test specimen Minimum 3 specimens shall be made for each sample of concrete in order to test it at 28 days. Extra specimens may be prepared for doing other tests likeÿ7or modulus of rupture test etc. The 3 specimens average strength shall be named as sample test strength. Specimen shall be tested as mentioned in IS 516.

19 (c) Standard deviation When enough test results for a particular concrete grade are not available, then the deviation mentioned in Table 3.5 may be assumed for design of concrete mix to start with. As soon as results of the samples are available, calculated value of standard deviation should be used However, when past records of similar mix or grade exist, the standard obtained from theses records may be allowed. Table 3.5 Table 3.5 Assumed Standard Deviation Grade of Concrete Assumed Standard deviation N/mm 2 Remarks M10,M15 M20,M25 M30,M35,M40, These values have been specified assuming that there is site control. Proper storage of cement, weight, regular checking of all materials, workability and strength. Where there is deviation from the above the values of standard deviation shall be increased by 1N/mm 2 M45 and M50 D) Characteristic strength : This shall be obtained from known value of mean strength and the standard deviation Acceptance Criteria for concrete (a) Compressive Strength: The concrete shall be consider comply with strength needs when both of the following condition are met::

20 i) The mean strength is determined by any group of non overlapping successive test results comply with suitable limits in Table 3.6. ii) Any of which the individual test with appropriate limits in column B of the table Table 3.6. Characteristic Compressive strength compliance Requirement Specified Grade A The mean of the group of 4 non overlapping consecutive test results in N/mm 2 B Any individual test results in N/mm 2 M15 ( f s) or ( f + 3) N/mm 2 ck ck ck ( f 3) N/mm 2 ( f s) or ( f + 4) N/mm 2 ck ck ck ( f 4) N/mm 2 Where, s = establish standard deviation rounded off to nearest 0.5N/mm 2 Note : (i) (ii) If established standard deviation is not known, the values given in Table may be assumed. Efforts should be made to established the value of standard deviation from test results of 30 samples as early as possible.

21 (b) Flexural Strength: When both the following conditions are met the concrete complies with the specified flexural strength. (i)the mean strength determined from any group of four consecutive test results exceeds the specified characteristic strength by at least 0.3 N/mm2. (ii)the strength determined by any test result is not less than the particular characteristic strength less 0.3 N/mm Non Destructive Testing of Structures The non-destructive testing consists of following tests : (a) Core test : Minimum three cores of concrete shall be prepared and tested as per IS: 516.strength of core should not be of cube strength of concrete grade is specified for corresponding age and there is no individual core strength less than 75%. If requirements are not satisfied or where it is not possible to take cores the load test should performed. (b) Load test : The load test consists actually loading the part of the structure and observing the deflection. Details are covered in clause 17.6 of IS:456 (c) The other non-destructive tests carried out near the surface of the structural member comprises of velocity measurement at surface IS: Rebound test using hammer IS: 1311 (Part-2) 3.13 Design Strength of Concrete The characteristic design strengths of concrete for the limit state of and the limit state of serviceability for different structural actions, namely, axial tension and compression, bending tension and compression, shear bond and bearing are given in Table 3.7.

22 3.14 Properties of Steel Reinforcing steel is known by its grade and the reinforcement, consisting usually of round bars is known by the type of bar (whether plain order formed) Grade of steel Grade of steel which is known with its characteristic yield strength is designated as Fe 250, stands for Ferrous metal and the number following it represents yield strength in N/mm2. At present, steel is commercially available in the above three grades. Table 3.7. Characteristic Compressive strength and design strength of concrete of Limit state method Grade of Concrete Type of structural action M20 M25 Characteristic compressive strength (f ck ) N/mm N/mm 2 Design Strength in - - direct compression (0.4f ck ) - bending compression (0.446 f ck ) - flexural tension (0.7 f ck ) N/mm N/mm N/mm N/mm N/mm N/mm 2 - average bond for plain bars in tension - bearing (0.45f ck ) N/mm N/mm N/mm N/mm 2 Notes :

23 1) Direct compressive strength 0.4f ck given below is for axially loaded columns only, taking into account the effect of a minimum eccentricity. For pure axial compression, value is the same as that for bending compression, namely 0.446f ck. 2) For deformed bars confirming to IS:1786 value of the bond stress shall be increased by 60%. For bars in compression, the value of bond stress shall be increased by 25%. 3) Design strength in diagonal tension or in shear is a function of percentage of tension steel and grade of concrete. The values of design shear strength of concrete for different percentage of steel and grades of concrete have been given in Table Types of Bars Bars used as reinforcement in R.C. construction are available in the following types.: a) Plain round bars of mild steel (grade Fe250), b) (HYSD) High Yield strength deformed bars (grades Fe500 and Fe415). HYSD bars have ribs, lugs on their surfaces. They are manufactured by the process of hot rolling followed by a suitable method of cooling and/or cold working.

24 Fig. 3.5 shows typical strain curve obtained from tension test for cold worked high strength deformed bars. Fig. 3.5 Stress-Strain Curve for Fe415 The HYSD bars do not exhibit a well defined yield point, and hence 0.2% proof stress is considered as yield stress. It is that value of the stress corresponding to point intersection of stress-strain curve and line BC is drawn from residual (initial) strain of 0.00β (i.e. 0.β%) at B and parallel to line τa which is the tangent to the curve at the origin as shown in Fig. 3.6

25 Fig. 3.6 Determination of Yield Stress from Tension Test Structural Specimen The minimum yield stress 9 or 0.2% the percentage elongation at failure ultimate stress etc. for the different of available steel are given in Table 3.8. for ready reference Stress Strain Relation For steel grade Fe250, f s = ε s E s For steel grade Fe415, f s = ε s E s upto a strain of For steel grade Fe500, f s = ε s E s upto a strain of Where, E s = modulus of elasticity of steel = 2 x10 5 N/mm 2 For Fe415 for strains above , the stresses corresponding to strains are given in Table 3.9.

26 [Type the document title] Table 3.8. Types and Grades of Reinforcing bars Sr. Type of Indian Bar Diameter Yield Minim Ultimate No. steel Standard stress um stress (y.s) N/mm 2 elonga N/mm 2 tion 1. Mild steel grade I IS: 432 Part I 20 mm Over 20 mm upto % 23% and including 50 mm 2. Mild steel grade II IS: 432 Part I 20 mm Over 20 mm upto % 23% and including 50 mm 3 Medium IS: 432 Part I 16 mm % 540 Tensile steel Over 16 mm upto % 540 and including 32 mm 510 Over 32 mm up to % and including 50 mm 75

27 [Type the document title] 4. High S: 1786 All sizes % 1. 1x y.s but strength κ485σ/mm 2 deformed bars % 1.08 x y.s but κ545σ/mm x y.s 550 8% but κ5854σ/mm 2 76

28 [Type the document title]

29 [Type the document title]

30 [Type the document title]