Method of Analysis and Design
- Becca Alford (Unlicensed)
Analytics
Load Cases
Eriksson Pipe performs a separate structural analysis for each of the load conditions. These include:
Pipe culvert dead weight .
Soil weight
Gravity weight of internal fluid
Internal pressure
· Live load vehicle weight
Culvert dead weight is computed based on the user ·specified wall thickness and concrete density. The program default for support of the pipe weight is a line support at the invert as shown in Figure 5-1. This assumes that the pipe is laid directly on a flat bedding. The user may override the. program default by specifying a pipe bedding angle. The installation designer is responsible for assuring that the assumed bedding angle can be achieved in the field.
Vertical soil load is computed as the soil prism load times a ·soil structure interaction factor (also known as an arching factor). The soil prism load is the weight of the column of earth directly above the pipe, computed as the product of the soil density, the outside diameter of the pipe and the depth of fill. AASHTO Section 17.4.4.2 provides a method for computing the soil structure interaction factor. The vertical soil load is supported by a soil reaction over a user specified width. Lateral soil pressure is considered as part of the same load case as the vertical soil pressure. The Design Code and Install Conditions dialog box in Section 3.3 on Pressure Distribution discusses the user input variables for determining the vertical and lateral soil pressures.
As an alternate to the soil load condition the user may specify vertical and lateral loads directly in pounds per square foot using the uniform/manual load condition.
The internal fluid load is computed from the user specified depth of fluid in the culvert and the density of the fluid. The weight of fluid is supported by an external soil reaction which is the same width as specified to support vertical soil load. The internal fluid load condition is for the gravity weight of the internal fluid only.
Internal pressures may be considered for circular pipe only. The analysis assumes that the internal pressure creates a pure tension force in the pipe wall equal to the inside radius times the specified pressure. This tension force is assumed to be uniform around the perimeter of the pipe.
The user may specify a live load as an AASHTO HS series truck, the AASHTO Alternate Military Loading (called the interstate truck herein), an AREMA Cooper series locomotive or "Other” which allows input of the live load magnitude and the length and width over which the load is distributed at the top of the pipe. Wheel loads are distributed through earth fills in accordance with the requirements of AASHTO Section 6.4 or AREMA Chapter 8, Part 10, as appropriate. The pressure distribution neglects any effects of pavement. Impact factors are applied to live loads in accordance with the appropriate standard. No impact factor is applied when neither is specified. Live load vehicles are assumed to be located directly over the crown of the pipe, and live loads are computed and applied at all depths unless the user specifies no live load. For the HS-series truck, the user may specify the magnitude (i.e. HS-20, HS-15, etc.). When the interstate truck is specified, Eriksson Pipe also checks the HS-20 truck and designs for the most conservative condition. Eriksson Pipe distributes truck loads through earth fills in accordance with AASHTO Section 6.4. Two conditions are considered to allow for passing trucks:
Condition A- Condition A is a single lane with a fully overloaded truck.
Condition B - Condition B is a four lane road with a truck in each lane; however, to consider the low probability of overloaded trucks being in each lane at the same time, the beta factor (see AASHTO Section 3.22) is taken as 1.0.
Condition B controls service loads at all depths. Condition A controls the ultimate loads to a depth of about 10 ft.
Pressure Distribution
Eriksson Pipe allows the user to select from two pressure distributions that are commonly used in the direct design of pipe.
Radial Load System
The radial load system is developed from the pressure distribution first proposed by Olander (see References). It assumes that all external loads are applied normal to the pipe wall, i.e. no load is applied to the pipe by tangential shear forces. Figure 5.1a shows how this load system is used for the four load conditions used in Eriksson Pipe.
The distribution of the applied load and supporting forces are determined by simple sinusoidal functions:
reaction pressure:
where:
Pt = applied load pressure (psi) at angle e from ;nvert
Po = applied load pressure (psi) at crown of pipe
Js = angle over which applied load is distributed
fJ = angle from invert
Pb = applied reaction pressure (psi) at angle 8 from invert
Pi = applied reaction pressure (psi) at invert of pipe
fJs = angle over which reaction is distributed
As proposed by Olander, the sum of the load and reaction angles (fJs + fJs) always add up to 360 degrees. Eriksson Pipe allows the user to specify load and reaction angles that total less than 360 degrees, allowing consideration of the condition of poor. support to the pipe haunches.
The load angle over which a live load is distributed (fJuJ is a· function· of the depth of the pipe and the surface distribution of the live load. The live load angle is 180 degrees for deeply buried pipe.
Uniform Load System
The uniform load system, sometimes called the Paris distribution because of the common use of tables of moment coefficients published by Paris (see references), consists of uniformly distributed vertical and horizontal pressures, as shown in Figure 5-1b. In the automatic mode the total vertical earth load is computed as the soil prism load times the soil structure interaction factor and is applied to the top 180 degrees of the pipe. The lateral pressure is taken as the vertical soil prism pressure times the user input lateral pressure coefficient. The lateral pressure is applied over the entire height of the pipe. The bedding reaction is equal in magnitude to the vertical applied load and is spread over the user specified bedding width.
As an alternative to the automatic mode, the user may apply earth pressures using the “manual” mode, which allows specifying the vertical and lateral applied pressures directly in pounds per square foot. When using this mode the user may also specify the vertical load width, which may be less than 180 degrees; the supporting reaction width (just like the reaction width in the automatic mode) and the location and distribution of the lateral pressures, as shown in Figure 5-2.
The treatment of pipe weight, internal fluid and vehicle weight are the same whether the manual or automatic modes of the uniform load system are specified, as shown in Figure 5-1b.