ABSTRACT
Using the material moduli Es and Ec, we rewrite Equation 13.4 in terms of unit strain and the modular ratio n = Es/ Ec:
ρ ε ε⋅ ⋅ = ⋅ ⋅s cn k 1 2
(13.5)
or
ε
ε ρ s
k n
=
⋅ ⋅2 (13.6)
Equating the right-hand terms of Equations 13.1 and 13.6,
2 −
=
⋅ ⋅
k k
k nρ
(13.7)
We solve for k and take the positive root to obtain the coefcient k for a rectangular section reinforced in tension only:
k n n n= ⋅ + ⋅ ⋅ − ⋅ρ ρ ρ2 2 2 (13.8)
The value of k is usually between 0.2 and 0.4. Equation 13.8 gives us a convenient vehicle to calculate the neutral axis depth in Stage II of a cracked rectangular section with tension reinforcement.
