Crack Control

LRFD

Under the LRFD Specification the stress in the spacing of the individual tension steel bars must be less than a required value as specified LRFD 5.7.3.4/5.6.4.3. First, the stress in the tension steel is calculated. This stress is used to calculate the required spacing of the tension steel using the following equation:

In LRFD, there is no limit on d_c (distance between the center of the layer of steel closest to the tension face and the tension face itself) in the cracking analysis. Therefore, to prevent the calculation of a negative s_reqd, the cracking analysis limits the calculation of d_c similar to that in the STND Specification, that is, an upper limit of 2 inches is placed on the concrete cover used in the calculation of d_c.

The cracking parameter γ_e is assigned by the user, however LRFD does not give any guidance as to the magnitude of this value for culverts. To bypass the cracking check, that is, to prevent cracking from controlling the design, set γ_e to a very large value.

Standard Specifications

For the STND Specification service check (16.6.4.7 and 16.7.4.7), the stress in the tensile steel is again calculated, which is then compared to an allowable stress as calculated by the following:

where β is equal to:

Where A is the effective tension area of concrete surrounding the flexural tension reinforcement and having the same centroid as that reinforcement, divided by the number of bars. The cracking parameter Z is assigned by the user. The STND Specification suggests a value of 155 for Z for CIP construction, and 98 for precast. To bypass this check, that is, to prevent cracking from controlling the design, set Z to a very large value, although keep in mind that there is still an upper limit on f_s of 0.6f_y. AREMA suggests a Z of 170 for members in moderate exposure conditions and 130 for members in severe exposure conditions.

CHBDC

Per Section 8.12.3.2, the crack width shall be calculated as follows:

where k_b shall be taken as 1.2 for components with epoxy-coated reinforcing steel and 1.0 for all other components, and β_c shall be taken as 1.7

s_rm shall be calculated as follows:

where k_c = 0.5,

d_b = diameter of bar (mm)

ρ_c = ratio of area of steel (A_s) to effective tension area of concrete (A_ct). The depth of A_ct shall be taken as the lesser of 2.5 times the distance from the extreme tensile fiber to the centroid of the tension steel, or, 1/3 the distance from the neutral axis to the extreme tensile fiber

ε_sm shall be calculated as follows:

where f_s = stress in reinforcement at the serviceability limit state (i.e., service load),

f_w = stress in reinforcement under conditions causing initial cracking

Per 8.4.1.8, the cracking strength for normal density concrete shall be taken as:

And f_w can be calculated using f_cr and the thrust in the member by first calculating:

The program then uses this moment to determine what the stress in the reinforcement (f_w) would be at this moment value.