﻿ Reinforcement calculation | TORAYCA® | TORAY # 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
n Young's modulus ratio of the reinforcing steel/concrete Young's modulus ratio of the TORAYCA® laminate/concrete Effective span of the short side of the rectangular slab Effective span of the long side of the rectangular slab Side length ratio of the slab (Ly/Lx) Unit width of the slab Thickness of the slab Distance from the compressed edge to the center of gravity of the compressed reinforcing steel Distance from the tensile edge to the center of gravity of the tensile reinforcing steel Cross-section area of the compressed reinforcing steel Cross-section area of the tensile reinforcing steel Fixed load Loading capacity Bending moment under fixed load Bending moment under loading capacity Bending moment under (fixed load + loading capacity) Bending yield strength of the non-reinforced member at yielding of the reinforcing steel Msy=at･σｙ･(t-dt）･7/8 Distance from the compressed edge to the neutral axis Geometric moment of inertia relating to neutral axis Compressive stress level of the concrete Compressive stress level of the compressed reinforcing steel Tensile stress level of the tensile reinforcing steel Tensile stress level of the TORAYCA® laminate