Week 7 Challenge

Aim: 

To calculate the water current forces for the bridge shown in the figure.

Given: 

The high flood level is 2 m above the foundation level.

The span of the bridge is 45m. 

The mean velocity of the river is 3 m/s. 

The diameter of the pier is 1065 mm.

Assume the Uniform pier height as 6m.

 Assume that the river is flowing only in one direction. 

Procedure: 

Part I: Manual Calculation of Water forces acting on the Bridge: 

Step1: Maximum Velocity of the River

V = √2 x V mean 

where, 

V = Maximum Velocity of the River

V mean = Mean Velocity of the River

  = √2 x 3

 V = 4.24 m/s

Step2: Water Current

P = 52 x K x V²

where,

P = Water current

K = Shape factor

V = Maximum Velocity of the River

P = 52 x 0.66 x 4.24²

P = 616.99 kN/m²

The water forces acting on the bridge's pier were calculated as 616.99 kN/m².

Part II: Model creation and Analysis in Stadd Pro. : 

Step 1: Open Stadd Pro connect edition software -> create a new file with the units set to metric standards.

Step 2: Create a node and translational repeat this node in the X direction for a step of 5m distance -> Select both these nodes using the select node cursor and translational repeat these two nodes in the Z direction for a step of 5m distance creating four nodes of 5 m equal distance from each other as a square.

Step 3: Using Add plate command -> draw the plate over these four nodes creating a plate -> Using Add beam command draw four beams on the edges of this plate.

Step 4: Translational repeat this plate in the X direction for 8 steps (45m long) and in the Z direction for 6 steps (26m wide) -> Translational repeat the highlighted nodes in the below figure for a single step in the Y direction for -6m, thus creating the piers of the bridge. 

                                                                          Figure 1

Step 5: Specification tab -> Select fixed and create foundation -> Assign this fixed foundation to the four nodes under the pier.

Step 6: Pier - In the Properties tab -> select define -> circle -> 1.065m -> Assign to the highlighted beam in figure 2 -> close.

                                                                          Figure 2

Step 7: Main Girder - In the Properties tab -> select define -> tapered -> F1=1.2m F2=0.5m F3=1.5m F4=0.5m F5=0.3m F6=0.5m F7=0.3m -> Assign to the highlighted beam in figure 3 -> close.

                                                                          Figure 3

Step 8: Cross Girder - In the Properties tab -> select define -> rectangle-> YD=1m ZD=0.5m-> Assign to the highlighted beam in figure 4 -> close. 

                                                                          Figure 4

Step 9: Deck - In the Properties tab -> select Thickness -> 0.35m -> Assign to the highlighted beam in figure 5 -> close.

                                                                          Figure 5

Step 10: In the Materials tab -> Select concrete and assign it to view.

Step 11: In the loading tab -> Load case details -> Click New -> Primary, Name it as WATER CURRENT LOADS ->  Click water current loads and click add -> Under Member load in Trapezoidal load, Enter the following details in Figure 6, The load only acts up to 2m height since the Maximum flood level is 2m above the foundation. 

                                                                          Figure 6

The calculated water current load manually is 616.99 kN/m², This load acts on the surface of the pier along the Z Global axis ( assumption ), thus multiplying the force on the width of the pier 1.065m, we get 657.09 kN/m. 

Enter this load in W1, and Enter d1 = 4m, and d2 = 6m. Since HFL = 2m above the foundation level. 

Step 12: Save the file and Run the analysis by -> Click analysis and design tab -> click define commands -> no print, click add -> click run analysis and check for errors after computation.

Thus the structural analysis of the given data has been done and the results are interpreted below.

Results: 

The results can be obtained after analysis of the model and can be viewed in the post-processing tab under the workflow section.,

The loading pattern of the water current forces is shown in the figure below, the green indications on the pier are the water current forces., Refer to Figure 7.,

                                                                          Figure 7

The deflection of the Model can be seen below and the critical displacement is highlighted below., Critical Displacement = 1.699 mm.

                                                                          Figure 8

The Reaction of the Model can be seen below.,

                                                                          Figure 9

Bending Moment in Z direction - Main girder., Critical Bending Moment = 47.051 kN/m

                                                                          Figure 10

 Bending Moment in Y direction -  Critical Bending Moment = 803.126 kN/m

                                                                          Figure 11

The Plate results of the Model can be seen below.,

Bending Moment in the X direction, Critical Bending Moment = 0.457 kN-m/m

                                                                          Figure 12

Bending Moment in the Y direction, Critical Bending Moment = 1.888 kN-m/m

                                                                          Figure 13

Shear Force in X direction, Critical Shear Force = 0.003 N/mm2

                                                                          Figure 14

Shear Force in Y direction, Critical Shear Force = 0.0 N/mm2 ., since the load is uni-directional. 

                                                                          Figure 15

These results are the representation of the critical deflection, reactions of supports, critical moment across X, Y, Z, and Axial load caused due to the water current loads acting on the piers of the bridge along Global Z direction.