# Structural Design of Corrugated Steel Pipe (AASHTO Method)

Corrugated Steel Pipe is a flexible structure, meaning that the strength of the culvert is dependent on the strength of the surrounding backfill.  Even if an average person were to stand directly on top of a CSP before it’s backfilled it would deflect an inch or two, so you can imagine that the structure alone is not made to handle highway traffic.  Of course, with structural characteristics like this, you would wonder about the viability of this type of structure, but the reality is that the economics have necessitated a good look at them.  Over the last 30 years, many tests have been performed by various agencies, and we have indeed become very good at designing them structurally so that the engineer need not worry if the calculations are done correctly.

There are several structural design standards in use today, but the AASHTO Bridge Design Specifications, Section 12, “Buried Structures,” are considered the primary one for most jurisdictions.  This is an updated version of the structural design standards produced much earlier by the American Institute of Steel Construction (AISI) and the American Society for Testing of Materials (ASTM).  Also, in Canada the Canadian Highway Bridge Design Code, Section 7, “Buried Structures,” (basically the equivalent of AASHTO) is based on the same basic structural design concepts but expands on them, therefore it can be used for a more in-depth analysis.

If you prefer a structural design “guide” rather than the codes, a good book to get would be the Corrugated Steel Pipe Design Manual produced by the National Corrugated Steel Pipe Association.

In the following, I will go through the basic design steps but I do not recommend that a structural design be performed on this information alone.

1. Backfill Density

The first step is to select a backfill compaction level to be used in the design and eventually specified for the project.  This will be in the form of a percentage of standard proctor dry density (the definition is beyond the scope of this article, but suffice it to say this is the standard way of specifying backfill compaction in engineering projects).  As a rough guide, you can use 90% unless your fill above the culvert is below 5 ft (1.5 m) or above 12 ft (4 m), approximately.  This middle zone is the safe zone, where the backfill is high enough that traffic and dead loads are spread out, but not too high that the dead loads over the pipe will be greater than the fill beside it.

As far as the type of backfill is concerned, it should be well graded gravel.  It doesn’t even need to be high quality (pit run will usually suffice) but if a well graded gravel is specified with the compaction level above, this is adequate backfill for a CSP.

2.  Design Pressure

At this stage, you determine the soil pressure acting on the culvert from dead and live loads.

$P_{L} = 1.95DL + 1.75LL$

$P_{L}$ = Factored crown pressure, the soil pressure from live and dead loads at the level of the culvert crown (psf or kPa),
DL = Hγ, where
H = height of cover above pipe (ft or m), and
γ = Unit Weight of the backfill.  For gravel a good number is around 120 lbs/ft³ (1900 kg/m³)
LL = the maximum calculated live load, in psf or kPa, at the elevation of the top of the culvert, from the applicable design vehicle.

3. Ring Compression

From the soil pressure, the next calculation takes you to the compression stress in the culvert wall.

$T_{L} = P_{L} (S/24)$

$T_{L}$ = Factored compressive stress in the culvert wall per unit length of pipe (lbs/ft or kN/m),
$P_{L}$ = Factored crown pressure (psf or kPa)
S = Span (ft or m)

4. Allowable Wall Stress

Now that you’ve calculated the stress in the culvert wall, it’s time to calculate the resistance.

$R_{n} =$ φ$F_{y}A$

$R_{n}$ = Factored axial resistance per unit length of wall (kips/ft or kN/m)
φ = 1.0 for most CSP installations.  Check with table 12.5.5.
Fy = Yield strength of metal.  Depends on the manufacturer, but usually 33,000 psi or 230 MPa.
A = Wall area (in.²/ft or mm²/mm).  This is found on tables provided by the manufacturer, and this is your chance to choose a required wall thickness to resist the applied loads.

You must also check for buckling, for which the calculations are found in section 12.7.2.4.

5. Handling Stiffness

One last check.  The flexibility factor is calculated as follows:

$FF = S^{2}/EI$

FF = Flexibility Factor
E = Modulus of Elasticity of Steel (30,000,000 psi or 200,000 MPa)
I = Moment of Inertia of the pipe wall, in mm4/mm

Maximum values of FF are given in the tables in section 12.5.6.