Balanced sections,under reinforced section and over reinforced section

  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…

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Analysis of singly reinforced beam Working stress method

Learn : Analysis of singly reinforced beam Working stress method,Equivalent or Transformed Section,Strain Diagram,Stress Diagram,Neutral Axis,Stresses in Concrete and Steel , Dimensions of the Beam and Area of Steel,Percentage of Steel,Lever arm, moment of resistance Analysis of singly reinforced beam Working stress method Analysis of singly reinforced beam Working stress method : A singly reinforced beam section is shown in Fig. 2.3(a). To analyse this section, it is necessary to convert it into a transformed or equivalent section of concrete. Equivalent or Transformed Section As per the assumption (3), all the tensile stresses are taken by steel and none by concrete i.e., concrete in the tensile zone is cracked. So, the concrete area below the neutral axis is neglected and the effective area or the equivalent area of the section in terms of concrete is shown in Fig. 2.3(b). The equivalent area is equal to the area of concrete in…

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Concept of transformed or equivalent section of a RCC beam

Learn : Concept of transformed or equivalent section of a RCC beam,load carried by steel.load carried by concrete,section in terms of concrete CONCEPT OF TRANSFORMED OR EQUIVALENT SECTION Consider an R.C.C. section shown in Fig. 2.2(a) subjected to a compressive load P. Let      A         = Area of cross-section Ac        = Area of concrete Ast       = Area of steel m         = Modular ratio ss        = Stress in steel sc        = Stress in concrete es         = Strain in steel ec         = Strain in concrete Ps         = Load carried by steel Pc         = Load carried by concrete Aeqc     = Equivalent area of section in terms of concrete Es        = Yong's modulus of elasticity of steel Ec        = Young's modulus of elasticity of concrete P          = Ps + Pc \[ P          = \sigma _{s}A_{st}+\sigma _{c}A_{c}  \] The bond between steel and concrete is assumed to be perfect so the strains in steel and…

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