Flexural Strength

For both the LRFD and the STND Specifications, the following procedure is used to compute the required area of steel at three critical sections of each member (left/bottom end, midpoint, and right top end). At the ends of the member, the critical section for the following flexure calculations may be taken at the face of the intersecting members, within a haunch (LRFD C5.7.3.2/C5.6.3.2 and STND 8.8.2), and at the toe of a 45 degree haunch (LRFD 12.11.4.2 and STND 16.7.4.5).

1.) Compute the loading using the code specified load factors (see Section 5.4 of this manual).

2.) A concrete stress of 0.85f’ will be assumed uniformly distributed over an equivalent compression zone bounded by the edges of a cross section and a straight line located parallel to the neutral axis at a distance a = Β₁ (c) from the fiber of maximum compressive strain.

3.) No compression steel is considered and all tension steel is assumed to be in 1 layer

4.) Assume A_s

5.) Compute Mu (pure flexure)

(note: under LRFD, phi is excluded in the above equation for M_u, as it is present in the P-M diagram)

6.) Compute P_o (pure compression)

(note: under LRFD, phi is excluded in the above equation for P_o, as it is present in the P-M diagram)

Standard Specification:

7.) Compute P_b and M_b (balanced condition)

For slabs, phi = 0.85, for exterior walls, phi = 0.8, and for interior walls, phi = 0.7.

8.) Assume straight line relationship between pure compression and balanced condition and balanced condition and pure flexure.

LRFD:

7.) Compute Pc and Mc (limit of compression controlled section, and P_t and M_t (limit of tension controlled section). Here phi is variable, depending where on the P-M diagram you fall. For the compression controlled area, phi is 0.75. For the tension controlled area, phi is 0.9. For the transition zone, phi will vary between 0.75 and 0.9 (see LRFD Article 5.5.4.2.1/5.5.4.2).

8.) Under LRFD, there are three parts to the P-M curve, that between pure compression and the compression controlled limit, that between pure flexure and the tension controlled limit, and a third line that transitions between the two limits. As with STND, a straight line is assumed between major points on the curve.

For both codes, the program then iterates until the allowable moment is greater than the applied moment.

For both STND and LRFD, the user also has the option of using 12.10.4.2.4 to calculate the flexural resistance using:

For CHBDC, the above equation is modified as follows:

Minimum Eccentricity

Minimum eccentricity is be checked for all members.

If e is less than 1", then e is set equal to 1".

If e is less than 0.1(T), then e is set equal to 0.1(T), where T = member thickness.

Slenderness

Slenderness is checked for walls only.

Slenderness may be neglected if kl/r < 22, where

K = 2.0, l = box culvert clear height, and r = 0.3T / 12

Walls are designed using the factored axial load, P_u, and a magnified factored moment, M_c, defined by:

Deflections

The maximum live load deflection in the top slab is calculated for single cell boxes only. This live load deflection is compared to the deflection limitation specified in the input and, if needed, the thickness of the top slab is increased until the deflection criterion is met.

Maximum Steel

The STND Specification specifies that mild reinforced concrete members shall be designed so that the reinforcement ratio shall not exceed 0.75 of the balanced reinforcement ratio (STND 8.16.3.1). This approach is used for CHBDC as well.

LRFD uses a unified approach which is built into the P-M diagram.

Minimum Steel

Both STND and LRFD require that a sufficient amount of reinforcement be present in the culvert element to develop a moment of 1.2 times the total moment required to crack the culvert element. If the flexural resistance is at least 1/3 greater than that required by analysis, then this limit may be ignored. Minimum flexural reinforcement (parallel to the span) is calculated as 0.002bh for all specifications.