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Section calculation of RC member receiving bending load (Design of allowable stress level)

1. Section calculation policy

Follow the normal bending strength calculation method for reinforced concrete member based on the assumptions below:
Assumptions for calculation:

  1. (1) Compressive stress generated by concrete has a triangular distribution.
  2. (2) Tensile strenth of concrete is ignored.
  3. (3) Navier hypothesis is established.
  4. (4) Tensile stress is received by the TORAYCA® laminate.
  5. (5) Only the stress generating after application is received by the TORAYCA® laminate.


Concept of bending reinforcement of RC member

2. Section calculation procedure

  1. 1) Calculation of neutral axis position (X)
    Assume the Trayca® laminate reinforcement amount and calculate the position of the neutral axis based on the balance of forces.
      Balance of forces: Compressive force (Cc + Tsc) = Tensile force (Ts + Tcf)
        X={-Y+√(Y2+2・b・Z)}/b
        Y=n・Asc+n・As+ncf・Acf
        Z=n・Asc・dc+n・As・d+ncf・Acf・D
  2. 2) Calculation of geometric moment of inertia (I) relating to the neutral axis
        I=b・X3/3+n・Asc(X-dc)2+n・As(d-X)2+ncf・Acf(D-X)2
  3. 3) Calculation of stress level
      Calculate the level of stress generating at the reinforced member when the design bending moment applies.
        Compressive stress level of the concrete :
          σc=DM・X/I
        Compressive stress level of the compressed reinforcing steel :
         σsc=n・DM (X-dc)/I
        Tensile stress level of the tensile reinforcing steel :
         σs=n・DM (d-X)/I
        Tensile stress level of the TORAYCA® laminate :
         σcf=ncf・DM (D-X)/I
List of symbols
n Young's modulus ratio of the reinforcing steel/concrete
ncf Young's modulus ratio of the TORAYCA® laminate/concrete
Lx Effective span of the short side of the rectangular slab
Ly Effective span of the long side of the rectangular slab
λ Side length ratio of the slab (Ly/Lx)
B Unit width of the slab
t Thickness of the slab
dc Distance from the compressed edge to the center of gravity of the compressed reinforcing steel
dt Distance from the tensile edge to the center of gravity of the tensile reinforcing steel
ac Cross-section area of the compressed reinforcing steel
at Cross-section area of the tensile reinforcing steel
DL Fixed load
LL Loading capacity
MDL Bending moment under fixed load
MLL Bending moment under loading capacity
MTL Bending moment under (fixed load + loading capacity)
Msy Bending yield strength of the non-reinforced member at yielding of the reinforcing steel
Msy=at・σy・(t-dt)・7/8 
X Distance from the compressed edge to the neutral axis
I Geometric moment of inertia relating to neutral axis
σc Compressive stress level of the concrete
σsc Compressive stress level of the compressed reinforcing steel
σst Tensile stress level of the tensile reinforcing steel
σcf Tensile stress level of the TORAYCA® laminate