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 are 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 ultimate strength of concrete and yield strength or 0.2% proof stress of steel are divided by factors of safety to obtain permissible stresses. These factors of safety take into account the uncertainties in manufacturing of these materials. As per IS456, a factor of safety of 3 is to be used for bending compressive stresses in concrete and 1.78 for yield/proof strength of steel.
The main drawbacks of the working stress method of design are as follows :
(i) It assumes that concrete is elastic which is not true as the concrete behaves in-elastically even on low level of stresses.
(ii) It uses factors of safety for stresses only and not for loads. Hence, this method does not give true margin of safety with respect to loads because we do not know the failure load.
(iii) It does not use any factor of safety with respect to loads. It means, there is no provision for the uncertainties associated with the estimation of loads.
(iv) It does not account for shrinkage and creep which are time dependent and plastic in nature.
(v) This method gives uneconomical sections.
(vi) It pays no attention to the conditions that arise at the time of collapse.
The working stress method is very simple and reliable but as per IS 456:2000 the working stress method is to be used only if it is not possible to use limit state method of design. Working stress method is the basic method and its knowledge is essential for understanding the concepts of design.
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…
Types of problem in T Beam
Learn : Types of problem in T Beam : Procedure for Determining the Moment of Resistance of the Given Section in T beam,Find Stresses in Steel and Concrete in T beam,To design the section for given loads.Design of T beam TYPES OF PROBLEM IN T BEAM To determine the moment of resistance of the given section in T beam. To Find Stresses in Steel and Concrete in T beam. To design of T beam. Procedure for Determining the Moment of Resistance of the Given Section in T beam Given : Dimensions of the section i.e., bw, bf, Df, d. Area of steel Ast Material - grade of concrete and steel (i) Determine σcbc and σst from the Tables 2.1 and 2.2 for given grades of concrete and steel Calculater modular ratio (m) \[m=\frac{280}{3\sigma_{cbc}}\] (ii) Determine critical neutral axis (nc) \[\frac{m.\sigma_{cbc}}{\sigma_{st}}=\frac{n_{c}}{d-n_{c}}\] (iii) Determine actual neutral axis (n) : To reduce the trial…
Analysis of T beam working stress method
Learn : Analysis of T beam working stress method : Neutral Axis is Within the Flange (n < Df), Neutral Axis Lies in the Web of the Beam (n >Df) ANALYSIS OF T BEAM Consider the section of a T-beam shown in Fig. 2.14 (a). The analysis of a T-beam comprises of following two cases : (i) Neutral axis is within the flange. (ii) Neutral axis is in the web. Case 1 : Neutral Axis is Within the Flange (n < Df) Equivalent or Transformed Section The equivalent section of the T-beam in terms of concrete is shown in Fig. 2.13 (b). The concrete below the neutral axis is assumed to be cracked and the area of steel is replaced by an equivalent concrete area which is equal to m.Ast. The compression area is rectangular in shape as n < Df. Thus, this flanged beam can be analyzed exactly as…
T beams and terms used in T beams : Breadth of Web (bw),Thickness of the Flange (Df),Overall Depth of the Beam (D),Effective Width of the Flange (bf),Effective width of the compression flange of the flanged beam in Reinforced cement concrete T beams and terms used in T beams in Reinforced cement concrete T BEAMS In RCC construction, slabs and beams are cast monolithic-ally. In such construction, a portion of the slab act integrally with the beam and bends along with the beam under the loads. This phenomenon is seen in the beams supported slab system as shown in Fig. 2.11. The portion of the slab which acts integrally with the beam to resist loads is called as Flange of the T-beam or L-beam. The portion of the beam below the flange is called as Web or Rib of the beam. The intermediate beams supporting the slab are called as T-beams and the…
Steel beam theory is used to find the approximate value of the moment of resistance of a doubly reinforced beam specially when the area of compression steel is equal to or more than the area of the tensile steel. Steel beam theory moment of resistance of a doubly reinforced beam The moment of resistance of a doubly reinforced beam consists of : (i) Moment of resistance of compression concrete and the corresponding tensile steel (Ast1) i.e., moment of resistance of balanced section (M1). (ii) Moment of Resistance M' of the compression steel (Asc) and the additional tensile steel (Ast2). In the steel beam theory : (i) Concrete is completely neglected. (ii) The moment of resistance is taken equal to the amount of the couple of compressive and tensile steel. (iii) The permissible stress in compressive steel is taken as equal to the permissible stress in tensile steel. \[\therefore M _{r}=\sigma…
Types of problem in doubly reinforced beams working stress method: Determination of moment of resistance of the given section,Determination of actual stresses in concrete and steel,Design of the section. Types of problem in doubly reinforced beams working stress method Determination of moment of resistance of the given section. Determination of actual stresses in concrete and steel. Design of the section. Determination of Moment of Resistance Given : (i) Dimension of the beam section (b and d) (ii) Area of tensile steel Ast and area of compressive steel Asc (iii) Permissible stress in concrete {σcbc) and permissible stress in steel (σst) Procedure : Calculate \[m=\frac{280}{3\sigma_{cbc}}\] Calculate critical neutral axis (nc) \[\frac{n_{c}}{d-n_{c}}=\frac{m.\sigma_{cbc}}{\sigma_{st}}\] Calculate actual neutral axis depth (nc) \[\frac{b.n^{2}}{2}+(1.5m-1)A_{sc}(n-d_{c})=m.A_{st}(d-n)\] Compare n and nc (a) If n>nc the section is under reinforced (fully stressed) Maximum tensile stress developed in steel = σst Maximum compressive stress developed in concrete \[\sigma_{cbc}(where \sigma'_{cbc})is less …
Learn : Analysis of a doubly reinforced beam working stress method : modular ratio, Equivalent section,critical neutral axis, actual neutral axis, stresses in the section, moment of resistance. Analysis of a doubly reinforced beam working stress method Modular Ratio (a) Modular ratio for tensile steel is taken as m where \[m = \frac{280}{3\sigma_{cbc}}\]. (b) Modular ratio for compressive steel is denoted by m_{c} and is taken as mc=1.5m As per IS 456 (Table 2.2) the compressive stress in steel in the compression zone is calculated by multiplying the stress in surrounding concrete (σc) by 1.5 m but this value should not exceed the permissible stress in steel bars in compression i.e. σsc} as given Table 2.2. Equivalent Section The equivalent or transformed section of the given doubly reinforced beam in terms of concrete is shown in Fig. 2.8(b). In this equivalent section (a) The tensile steel area (Ast) is replaced…
Learn : Necessity of Doubly reinforced beam, Doubly reinforced beam DOUBLY REINFORCED BEAMS The R.C.C. beams in which the steel reinforcement is placed in the tension as well as compression zone are called as doubly reinforced beams. The moment of resistance of a balanced R.C.C. beam of dimension b×d is Rbd2 Sometimes due to head room constraints or architectural considerations the size of the beam is restricted and the same beam (b×d) is required to resist a moment greater than Rbd2 There are only two ways in which it can be done. (i) By using an over reinforced section. (ii) By using a doubly reinforced section. The option (i) is not a good choice because over reinforced sections are uneconomical and the failure of these beam is sudden without warning. Therefore, it is better to use doubly reinforced beam section in such circumstances. The extra provided in the tension and…
Learn : Three types of problems in singly reinforced beam working stress method :To determine the moment of resistance of the given section,To determine the stresses developed in concrete and steel under given loading,To design the section for given loading Problems in singly reinforced beam working stress method There are three types of problems in singly reinforced beam : To determine the moment of resistance of the given section. To determine the actual stresses developed in steel and concrete under given loading. To design the section for given loading. Type 1:To determine the moment of resistance of the given section Data Given: (i) Dimensions, b and d of the section. (ii) Area of steel reinforcement in tension (Ast) (iii) Material i.e., grade of concrete and steel. Procedure: (i) For the given grade of concrete and steel, determine the permissible stresses i.e., σcbc and σstfrom the Tables 2.1 and 2.2.…
Balanced sections,under reinforced section and over reinforced section Balanced Sections A balanced sections is that in which stress in concrete and steel reach their permissible value at the same time. This means that stress diagram is as shown in Fig. 2.6(b). The percentage of steel corresponding to this section is called as balanced steel and the neutral axis is called as critical neutral axis nc \[\frac {m.\sigma_{cbc}}{\sigma_{st}}=\frac {n_{c}}{d-n_{c}}\] For a balanced sections, the moment of resistance is calculated as under : \[ M _{B}=\frac{\sigma _{cbc}}{2}b.n _{c}\left ( d-\frac{n _{c}}{3} \right )=Rbd^{2}\] Under Reinforced Section In an under reinforced section, the percentage of steel provided is less than that provided in balanced section. So the actual neutral axis will shift upwards i.e., nc > n as shown in Fig. 2.6(c). In under…
