Concrete Concrete is a composite material composed of fine and coarse aggregate bonded together with a fluid cement (cement paste) that hardens (cures) over time. Concrete is the second-most-used substance in the world after water, and is the most ...

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: :

_= \epsilon_s_m

Spacing of primary cracks

Primary cracks (Figure 1) form when the

tensile stress In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...

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.

CEB-FIP code expressions for crack spacing and crack widths

In the CEB-FIP Code the following expression is used to account for the average crack spacing: :

s_m = 2(c + \frac) + k_1k_2\frac

where :

c

= clear concrete cover :

s

= maximum spacing between longitudinal reinforcing bars (shall not be taken greater than

15d_b

) :

d_b

= bar diameter :

\rho_

A_s/A_

A_s

= area of steel considered to be effectively bonded to the concrete :

A_

= area of effective

embedment Embedment is a phenomenon in mechanical engineering in which the surfaces between mechanical members of a loaded joint embed. It can lead to failure by fatigue as described below, and is of particular concern when considering the design of critical ...

zone of the concrete where the reinforcing bars can influence the crack widths. The effective embedment zone is the area of concrete around the reinforcing bar at the distance of 7.5 bar diameter :

k_1

coefficient In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves ...

that characterizes bond properties of bars ::

k_1

= 0.4 for deformed bars ::

k_1

= 0.8 for plain bars

k_2

= coefficient to account for strain

gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...

k_2 = 0.25(\epsilon_1+\epsilon_2)/2\epsilon_1

(e1 and e2 = the largest and the smallest tensile strains in the effective embedment zone)

Crack spacing of inclined cracks

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: :

_=1/(\frac + \frac)

Where

s_

is the average crack spacings that would result if the member was subjected to longitudinal tension while

s_

is the average crack spacing that would result if the member was subjected to a transverse tension. These crack spacings can be estimated from the CEB-FIP Code crack spacing expression above.

Crack spacing in shear areas

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: :

s_ = 2(c_x + \frac) + 0.25k_1\frac

s_ = 2(c_v + \frac) + 0.25k_1\frac

The above equations are suggested for better approximation of crack spacings in the shear area of the beam.

References

* * {{Refend Reinforced concrete