Design of Beams Using Limit State Method

The working stress method gives satisfactory performance at working load but no attention is given to the conditions that arise at the time of collapse of the structure. This method does not give exact margin of safety. This drawback was taken into account in the ultimate load or load factor method of design. But load factor method leads to excessive deflection and cracking. A more rational approach is given by limit state method of design which is a balanced combination of working stress and ultimate load design method. The limit state method of design is discussed in Section 5 of IS code 456:2000.
The object of limit state design is based on the concept of achieving an acceptable probability that a structure will not become unserviceable in its lifetime for the use for which it is intended. It should be able to withstand safety all the loads that are going to act on it throughout its life alongwith satisfying the serviceability requirements. To ensure proper degree of safety and serviceability, the design must include all relevant limit states.

Singly reinforced Beam

Learn : Design of singly reinforced rectangular section for flexure, factored moment, ultimate moment of resistance, limiting moment of resistance factor, fixing dimension of the section, Area of tension steel.   Design of singly reinforced rectangular section for flexure The design problem is generally of determining dimensions (cross-sectional) of a beam (b X D) and the area of steel for a known moment or load. The basic requirement for safety at the limit of collapse (flexure) is that the factored moment Msbecause of loads should not exceed the ultimate moment of resistance Mulim of the section and the failure should be ductile. 2188ed6a96dad6de04b0dfb5853df1bee74e3d92 therefore \[M_{u}\leq M_{u lim}\] Taking equality \[M_{u}= M_{u lim}\] \[=0.36f_{ck}.\frac {x_{umax}}{d}\left ( 1-\frac {0.42 x_{u max}}{d} \right )bd^{2}\] \[M_{u}=R_{u}bd^{2}\] For the given material i.e., grade of concrete and type of steel, Ru is constant and is called as limiting moment of resistance factor. \[R_{u}=0.36f_{ck}\frac {x_{u max}}{d}\left (…

Beam Design

Learn About design of beams, effective span, effective depth, reinforcement, nominal cover to reinforcement, curtailment of tension reinforcement  BASIC RULES FOR DESIGN OF BEAMS While designing R.C.C. beams, following important rules must be kept in mind: Effective Span (CI. 22.2, IS 456) The effective span of the beams are taken as follows : (a) Simply Supported Beam or Slab The effective span of a simply supported beam or slab is taken as least of the following: (i) Clear span plus the effective depth of beam or slab. (ii)Centre to centre distance between supports. (b) Continuous Beam or Slab In case of continuous beam or slab if the width of the supports is less than \[\frac {1}{12} \]of the clear span, the effective span is taken as in (a). If the width of the support is greater than \[\frac {1}{12}\] of the clear span or 600 mm whichever is less, the…

Stress Strain relationship for concrete, Stress Strain relationship for steel,Design Strength Values for Steel Design Stresses at Specified Strains.

Learn : Stress Strain relationship for concrete, Stress Strain relationship for steel,Design Strength Values for Steel Design Stresses at Specified Strains. fe 415 and fe 500 Stress Strain relationship for concrete and Stress Strain relationship for steel Stress Strain relationship for concrete Stress Strain relationship for concrete : The experimental or actual stress strain curve for concrete is very difficult to use in design Therefore, IS code 456:2000 has simplified or idealized it as shown in Fig. 4.1. For design purpose, the compressive strength of concrete in the structure in taken as 0.67 times the characteristic strength. The 0.67 factor is introduced to account for the difference in the strength indicated by a cube test and the strength of concrete in actual structure. The partial safety factor (rmc), equal to 1.5 is applied in addition to this 0.67 factor. The initial portion of the curve is parabolic. After a strain of…

Assumptions in limit state of collapse in flexure (Bending)

Learn Assumptions in limit state of collapse in flexure (Bending),relationship between the stress strain distribution in concrete,stresses in the reinforcement are taken from the stress-strain curve Assumptions in limit state of collapse in flexure (Bending) (REFER CL. 38, IS 456) The design of reinforced concrete sections for limit state of collapse in bending, is based on the following assumptions : (a)       Plane sections normal to the axis remain plane after bending. It means that the strain at any point in the cross-section is proportional to the distance from the neutral axis. (b)       The maximum strain in concrete at the outermost compression fibre is taken as 0.0035 in bending. (c)       The relationship between the stress-strain distribution in concrete is assumed to be parabolic, as shown in Fig. 4.1. For design purpose, the compressive strength of concrete is assumed to be parabolic, as shown in Fig. 4.1. For design purpose, the compressive…

Design Strength of Materials,Partial Safety Factors for Materials,Design Loads,Values of Partial Safety Factor for Loads (Refer Clause 36,IS Code)

Design Strength of Materials :  Partial Safety Factors for Materials (rm), and Design Loads : Values of Partial Safety Factor (rf) for Loads(Refer Clause 36, IS Code)  DESIGN VALUES (REFER CLAUSE 36, IS CODE) Design Strength of Materials The strength of any material obtained in a structure is always less than the characteristic strength of the material. It is because of the workmanship or quality control in the manufacture of materials. The reduced value of strength which is obtained by applying partial safety factors to the characteristic strength is called as design strength of the material. The design strength of the material fd is given by \[f_{d}=\frac{f}{r_{m}}\] where             f = Characteristic strength of the material rm = Partial safety factors appropriate to material and limit state being considered. Partial Safety Factors for Materials (rm) The values of partial safety factors for limit state of collapse, should be taken as : rmc…

Vertical Stirrups

Types of shear reinforcement : Vertical stirrups, Bent up bars along with stirrups, Inclined stirrups, contribution of bent up bars TYPES OF SHEAR REINFORCEMENT The following three types of shear reinforcement are used : Vertical stirrups. Bent up bars along with stirrups. Inclined stirrups. Vertical Stirrups These are the steel bars vertically placed around the tensile reinforcement at suitable spacing along the length of the beam. Their diameter varies from 6 mm to 16 mm. The free ends of the stirrups are anchored in the compression zone of the beam to the anchor bars (hanger bar) or the compressive reinforcement. Depending upon the magnitude of the shear force to be resisted the vertical stirrups may be one legged, two legged, four legged and so on as shown in Fig. 5.5. It is desirable to use closely spaced stirrups for better prevention of the diagonal cracks. The spacing of stirrups near the supports is less…

Effects of Shear  Diagonal Tension, maximum bending tensile stress, tensile stress (σ) as well as shear stress (τ),

Learn : Effects of Shear  Diagonal Tension, maximum bending tensile stress, tensile stress (σ) as well as shear stress (τ),crack pattern for a simply supported beam,  The maximum bending moment in this beam will be at midspan and the maximum shear force, at the supports. EFFECTS OF SHEAR  DIAGONAL TENSION Consider a beam AB subjected to transvers loads as shown in Fig. 5.3(a). The maximum bending moment in this beam will be at midspan and the maximum shear force, at the supports. The beam is subjected to bending and shear stresses across the cross-section. Let us consider a small element (1) from the tensile zone of the beam. It is subjected to bending tensile stress (σ) as well as shear stress (τ) as shown in Fig. 5.3. (b). At the midspan, the bending moment is maximum and the shear force is zero. So the element 2 is subjected to maximum…

Shear Stresses in R.C.C. beam (Reinforced cement concrete beam), Stress Based Approach (Elastic Theory), IS Code Approach SHEAR STRESSES IN R.C.C. BEAMS Stress Based Approach (Elastic Theory) R.C.C. is a composite materials so the exact shear distribution as per elastic theory is very complex. It is shown in Fig. 5.2(b) by the hatched portion of the curve.It is parabolic in the compression zone with zero at the top and maximum at the neutral axis. The value of shear-stress is constant in the tensile zone and is equal to the maximum shear-stress (q) because the concrete, below the neutral axis (tensile zone) is assumed to be cracked and neglected. The maximum value of shear stress (q) as per elastic theory is given by \[q=\frac{V}{bjd}\] where             V = shear force at the section b and d = dimensions of the section j = Lever arm depth factor IS Code Approach As per IS code…

Characteristic Strength of Materials

Learn : Characteristic Strength of Materials :Characteristic Strength of Concrete, Characteristic Strength of Steel. and Characteristic Load or ultimate load CHARACTERISTIC VALUES  (REFER CLAUSE 36, IS CODE) Characteristic Strength of Materials The characteristic strength is based on the statistical analysis of the test results because there are variations in the strength of the material used. In order to simplify the analysis, it may be assumed that the variation in strength follows a normal distribution curve which is symmetric about the mean value as shown below in Fig. 3.1. Therefore, characteristic strength = Mean strength - k S where S is the standard deviation, k=1.64, corresponding to 5% probability \[\therefore                f_{ck}=f_{m} - 1.64 S\]  Characteristic Strength of Concrete The term characteristic strength means that value of strength of material below which not more than 5% of the test results are expected to fall. It is denoted by fck is N/mm2. The value…

Learn : comparison of working stress method and limit state method, working stress method,Drawbacks of the working stress method, Limit state method :  Limit state of collapse, Limit state of serviceability. COMPARISON OF WORKING STRESS METHOD AND LIMIT STATE METHOD Working Stress method and Drawbacks of the working stress method Working Stress method This method of design was the oldest one. It is based on the elastic theory and assumes that both steel and concrete and elastic and obey Hook's law. It means that the stress is directly proportional to strain up to the point of collapse. Based on the elastic theory, and assuming that the bond between steel and concrete is perfect, permissible stresses of the materials are obtained. The basis of this method is that the permissible stresses are not exceeded any where in the structure when it is subjected to worst combination of working loads. In this method, the…

Design of Beams Using Limit State Method

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