Concrete is a brittle material and can only withstand small amount of tensile strain due to stress before cracking. When a reinforced concrete member is put in tension, after cracking, the member elongates by widening of cracks and by formation of new cracks.
Ignoring the small elastic strain in the concrete between the cracks, we can relate the crack width to the strain of the member by:
{w}m=\epsiloncfsm
Primary cracks (Figure 1) form when the tensile stress at the outer surface of the concrete reaches the tensile strength of concrete. When a primary crack forms, the concrete in the vicinity of the crack is relieved of any tension, resulting in a stress free zone near the crack.[1]
In the CEB-FIP Code the following expression is used to account for the average crack spacing:
sm=2(c+
| s | |
| 10 |
)+k1k
|
c
s
15db
db
\rhoef
As/Ace
As
Ace
k1
k1
k1
k2
k2=0.25(\epsilon1+\epsilon2)/2\epsilon1
According to the Modified Compression Field Theory (MCFT), the spacing of inclined cracks in reinforced concrete will depend upon the crack control characteristics of both the longitudinal and the transverse reinforcement. It is suggested that the spacing is taken as:
{s}m\theta=1/(
| sin\theta | |
| smx |
+
| cos\theta | |
| smv |
)
Where
smx
smv
These crack spacings can be estimated from the CEB-FIP Code crack spacing expression above.
The above CEB expression was intended to calculate crack spacings on the surface of the member. Crack spacings become larger as the distance from the reinforcement increases. For this case, it is suggested to use the maximum distance from the reinforcement, instead of cover distance c (Collins & Mitchell). Thus, for the uniform tensile straining the above CEB expression is modified to:
smx=2(cx+
| sx | |
| 10 |
)+
| 0.25k | ||||
|
smv=2(cv+
| s | |
| 10 |
)+
| 0.25k | ||||
|
The above equations are suggested for better approximation of crack spacings in the shear area of the beam.