Structural Analysis

Eriksson Pipe analyzes one half of the pipe section using the model in Figure 5-3.  The pipe is modelled as a 36 member plane frame with· boundary supports at the crown and invert. Each member spans 5 degrees and is located at mid depth of the pipe wall.  For each member of the frame, a member stiffness. matrix is formed, and then transformed into a global coordinate system.  The loads on the pipe are calculated as pressures applied normal and tangential to each of the 36 members.  These pressures are converted into nodal pressures that act radially and tangentially to the pipe.  Loads at each joint are assembled into a joint load matrix and a solution is obtained by a recursion algorithm from which member end forces are obtained at each joint.  Analysis is completed separately for each load condition.

After the structural analysis is completed for each load condition, Eriksson Pipe combines the moments, thrust and shears as required to obtain the governing forces at the five design locations shown on Figure 5-4.       Locations 1, 3 and 5 are for the design of flexural reinforcement, and locations 2 and 4 are for evaluation of diagonal tension.

Because of the symmetry in all the load conditions, Eriksson Pipe assumes that maximum positive moments always occur at the crown (design location 5) and invert (design location1). These moments are used to design the top inside and bottom inside reinforcement, respectively. Eriksson Pipe searches for the location of the maximum negative moment in the springline area (design location 3) and uses this moment to design the springline outside reinforcement.  Users should note that if too much lateral load is applied to the pipe then there may not be any positive moment at the crown or invert or there may not be any negative moment at the springline. If this occurs, the program will stop execution and print an error message to the screen.

Based on AASHTO requirements, shear is assumed to be critical in the positive moment regions where the ratio M/V¢d is equal to 3, which occurs near the crown (design location 4) and invert (design location 2).  Eriksson Pipe determines these locations and calculates the design forces.

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Flexure Design Locations:

Shear  Design  Locations:

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