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…