Let’s start with the following design scenario:

- Design Flow: 405 cfs
- Tailwater Depth: 5.70 feet
- Road Elevation: 10.25 feet above streambed
- Avg. Stream Gradient: 0.0106 ft/ft
- Design Criteria: The design flow of 405 cfs should not exceed the top of the culvert, and the structural design should to be according to AASHTO LRFD Bridge Design Specifications.

Design a precast concrete box culvert for the site.

**Hydraulics**

First, let’s figure out the size. I will be using CulvertPro’s hydraulics calculator, but you can also use HY-8 or CulvertMaster if you like. Since the headwater depth is just below 6 feet, let’s try two side-by-side 6 foot x 5 foot boxes, standing on end (See ASTM C1433 or Manufacturer’s size lists). The screenshot is on the right and can be clicked on to make it bigger.

**Culvert Shape:** Box

**Rise:** 72 inches

**Span:** 60 inches

**Culvert Length:** 80 feet (Estimated. This doesn’t make much difference).

**Flow:** 202.5 cfs

**Tailwater Depth:** 5.70 feet

**Upstream Invert Elevation:** 1000.85 feet

**Downstream Invert Elevation:** 1000.00 feet

**Culvert Burial:** 0 feet (Boxes are not normally buried as they already conform to the channel quite well).

**Manning’s n of Culvert:** 0.01 (from the Information Panel)

**Entrance Loss Coefficient:** 0.9 (also from the Information Panel)

**End Section:** Square Edge with Headwall

The Headwater elevation is 1007.162 ft, which is above the top of the culvert (Upstream Invert Elevation + Rise). This does not satisfy the design criteria.

Let’s put three of them side by side. The only difference now is that the flow is divided into thirds instead of in half. Now the headwater is 1006.332 which is 6 inches below the top of the culvert. The velocities are 4.5 ft/s upstream and 4.74 ft/s downstream, which is not excessive and easily within the range of simple scour protection measures like rock riprap.

**Structural Design**

For this exercise, I will use the design tables in ASTM Specification C1577 rather than calculating it all out by hand. Hand calculations will require analysis of the live load, dead load and earth load and subsequent design as a concrete beam and column. Since the only major variable involved is the cover over the pipe, the design tables are adequate. There are other variables such as concrete strength and soil unit weight, but broad assumptions have been made which apply to most designs. The assumptions are all clearly listed in Table 21.1 of the spec.

For a 6 ft x 5 ft precast concrete box with earth cover of 3 feet 8 inches (10.25 feet – 6 feet – 8 inches top slab thickness), A_{s1} = 0.17, A_{s2} = 0.23, A_{s3} = 0.21, and A_{s4} = 0.17.

Figure 1 on page 9 of the spec shows you where each of the steel areas applies. A_{s1} and A_{s4} are the inner and outer levels of reinforcing on the sidewalls, A_{s2} is the lower level of reinforcement for the top slab and A_{s3} is the upper level of reinforcement for the bottom slab.

All of the individual reinforcing details at the corners are also given in Figures 2 – 6. All that’s left is to choose a wire reinforcement size for each of the sections.

That’s it!

For a bit more background, check out my previous post, How to Design a Concrete Box Culvert.

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