Week 9 Challenge

Aim: 

 

To calculate the wave load acting on the given bridge and to apply and analyse in the Stadd Pro. 

 

Given: 

 

Maximum crest elevation = 3m

Height of I girder = 1.7m

Width of top and bottom flange = 2.5m

The thickness of top, bottom flange and web = 0.5m

Span of bridge = 12m

Width of bridge = 9m

The thickness of bridge deck = 2m

Constant r = 5 

Cva = 3

Storm elevation = 8.5m

Cr = 0.4

 

Introduction: 

Waves are caused due to disturbances over and under the water's surface such as wind, changes in temperatures, earth slides underwater and water current. These waves in turn generate force acting on the substructure and substructure of the bridge all around the year causing catastrophic damage. These loads are termed wave loads.

 

Procedure: 

 

Part I: Calculation of wave load due:

 

Δzh = ╖max - Centroid of I girder 

 

where, 

Δzh = Difference between the elevation of the maximum wave crest and centroid of I girder

╖max = Maximum height of the wave

 

Δzh = 3 - (1.7/2) 

 

Δzh = 2.15 m

 

Δzv = ╖max - Elevation of the bottom deck

 

where, 

Δzv = Difference between the elevation of the maximum wave crest and elevation of the underside of the bridge deck

╖max = Maximum height of the wave

 

Δzv = 3 - 2

 

Δzv = 1 m

 

Vertical load, Fv = Γ x Δzv x Av

 

where, 

 

Γ = Unit weight of water

Δzv = Difference between the elevation of the maximum wave crest and elevation of the underside of the bridge deck

╖max = Maximum height of the wave

Av = Area of bridge contributing to vertical uplift

 

Fv = 10 x 1 x ( 9 x 1.7/2)

 

Fv = 76.5kN

 

Horizontal load, Fh = r x Δzh x Ah

 

where, 

 

Γ = Unit weight of water

Δzh = Difference between the elevation of the maximum wave crest and centroid of I girder

╖max = Maximum height of the wave

Ah = Area of bridge contributing to horizontal thrust

 

Fh = 10 x 2.15 x ( 3 x 12 ) 

 

Fh = 774 kN

 

Maximum vertical load, Fvmax = Cva x Fv 

 

 where, 

 

Cva = Empirical co-efficient for vertically varying load

 

Fvmax = 3 x 76.5

 

Fvmax = 229.5 kN

 

Maximum horizontal load, Fhmax = (1 + Cr(N-1)) x Cva x Fh

 

 where, 

 

Cva = Empirical co-efficient for horizontally varying load

Cr = Reduction co-efficient for reduced horizontal load on interval girders

 

Fhmax = (1 + 0.4 ( 2-1 )) x 3 x 774

 

Fhmax = 3250.8 kN

 

Part II: Modelling and Analysis of Bridge in Stadd Pro. :

 

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

Step 2: Select the geometry tab and enter the values of the node in the y column in the node table as 0 and 7 respectively which will create two nodes. Add beam cursor in geometry tab -> connect these nodes creating a pier. 

Step 3: Select the beam using the beam cursor -> translational repeat in geometry tab -> translate the beam for a step in the Z direction for 6m creating an adjacent second pier of the bridge.

Step 4: Select both the beams using the beam cursor -> translational repeat in geometry tab -> translate the beams for a step in the X direction for 12m. Thus four piers of the bridge are now created.

Step 5: Using add beam cursor connect the adjacent nodes along the width of the bridge and not along the span. Select the left-side top nodes ( 2 and 6 in the Stadd pro file ) -> translational repeat them along -Z direction for a step of the length of 0.75m. Similarly, select nodes 4 and 8 and translational repeat them in the Z direction for a step of the length of 0.75m. Connect nodes 9 and 11 using add beam cursor and Connect nodes 10 and 12 using add beam cursor. Refer to figure 1. 

                                                                            Figure 1

Step 6: Select add beam cursor -> Connect the nodes and form the beams as highlighted in figure 2 below creating the I girders of the bridge., 

                                                                            Figure 2

Step 6: Translational repeat -> select the highlighted nodes and translational repeat them along X direction for a step of 0.25 length. Using add plate cursor connect these four nodes and create a plate. 

Step 7: Select the plate -> translational repeat that plate along the X direction for 47 steps of 0.25 length each ( 12/0.25 = 48 since one plate is there 47 steps ). Select the created plates and translational repeat them along the Z direction for 16 steps of 0.25 length each ( 8.25/0.25 = 17 since one plate is there 16 steps ) and in -Z direction for 3 steps. Thus adding the distance between end nodes along width we have 9m. Refer to Figures 3,4,5 and 6.

                                                                            Figure 3

                                                                            Figure 4

                                                                            Figure 5

                                                                            Figure 6

Step 8: Specification tab -> Select fixed and create foundation -> Assign this fixed foundation to the 4 nodes under the piers.

Step 9: Pier - In the Properties tab -> select define -> Circle -> 2 -> Assign -> close.

Step 10: Girders - In the Properties tab -> select define -> tapered -> F1=1.7m F2=0.5m F3=1.7m F4=2.5m F5=0.5m F6=2.5m F7=0.5m -> Assign to the highlighted beam in figure 7 and refer to figure 8 -> close.

                                                                            Figure 7

                                                                            Figure 8

Step 11: Deck - In the Properties tab -> select Thickness -> 2m -> Assign to all of the plates  -> close.

Step 12: In the loading tab -> Load case details-> click add -> Enter Wave load -> Click wave load and add -> Select Nodal load and enter in Fz = 3250.8 kN and click add, again in nodal load in Fy = 229.5 kN.

Step 13: These loads act on the central node of the bay, totally there are four bays and the loads will act on the highlighted nodes in figure 9., Refer to figure 10.,

                                                                            Figure 9

                                                                            Figure 10

Step 14: Thus wave loads has been applied to the structure. 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.

 

Part III: 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 deflection of the Model can be seen below and the critical displacement is highlighted below., Critical Displacement = 8.761 mm. Refer to Figure 11.,

                                                                             Figure 11

 The Reaction of the Foundation can be seen below., Refer to Figure 12., 

                                                                             Figure 12

Bending Moment in Z direction -  Critical Bending Moment = 6538.936 kN/m. Refer to Figure 13.,

                                                                             Figure 13

 

Bending Moment in Y direction - Critical Bending Moment = 12703.89 kN/m, Refer to Figure 14.,

                                                                             Figure 14

Shear Force in Z direction - Critical Shear Force = 478.527 kN, Refer to Figure 15.,

                                                                             Figure 15

Shear Force in Y direction - Critical Shear Force = 201.94 kN, Refer to Figure 16.,

                                                                             Figure 16

 

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

Bending Moment in X direction, Critical Bending Moment = 1056.314 kN-m/m., Refer to Figure 17.,

                                                                             Figure 17

Bending Moment in Y direction, Critical Bending Moment = 3040.746 kN-m/m., Refer to Figure 18.,

                                                                             Figure 18

Shear Force in X direction, Critical Shear Force = 1.51 N/mm² ., Refer to Figure 19.,

                                                                             Figure 19

Shear Force in Y direction, Critical Shear Force = 0.356 N/mm² ., Refer to Figure 20.,

                                                                              Figure 20

 

Thus Load calculation manually is done and analysis and result interpretation is done in Stadd Pro.