Week 12 Challenge

Aim:

 

To calculate the Barge Impact load of the Panamax vessel on the bridge shown in the figure.

 

Given:

 

Dead-weight = 52500 Tonnes

Capacity of ship = 4500 containers

Container = 6.1 TEU ( Twenty-foot equivalent unit)

Speed of the barge = 60 km/hr

Width of barrage = 32m

Length of barrage = 294m 

Draft of barrage = 12m

Span of the bridge = 12m

Width of the bridge = 7m

Size of pier = 2.5 m x 2.5 m 

Rise of the bridge = 5m

Deck slab thickness = 0.5m 

Cross girder = 0.75 m x 1.8 m 

Hydrodynamic co-efficeint = 1.25

 

Introduction:

Bridges located in navigable water channels and oceans must be designed for barge impact loads as there is a possibility of ongoing ships hitting the bridge causing a range of structural to catastrophic failures. In Indian codes, IRC - 6 2017 describes the load calculation of barge impact loads and the with the data from the IWAI authority, one can calculate the design barge impact collision energy. The Size and type of barge influence the load acting on the bridge during impact, velocity also plays a major role. The IRC 6 - 2017 gives a detailed description of Barge Impact loads on the bridge structure. 

 

Procedure:

 

Part I: Calculation of Barrage Impact load: 

 

The formula used for calculating barrage impact load is as follows., As per IRC - 6, 2017, Clause 219.5

 

Barge collision energy., As per IRC - 6, 2017, Clause 219.5

 

KE = 500 x Cʜ x W X V² ., 

 

where.,

 

KE = Barge collision energy in N/m

Cʜ = Hydrodynamic co-efficient

W = Barge dispalcement in T

V = Barge Impact speed in m/s

 

Assume the speed at which the barge impacts the bridge deck is 60 km/hr

 

To convert the km/hr to m/s 

= 60 x 1000 / 3600 

= 16.66 m/s

 

To convert Tonnes to kN 

= 52500 x 9.80665

= 514849.125 kN

 

KE = 500 x 1.25 x 52500 x 16.66²

 

KE = 9.107 x 10⁹

 

Barge damage depth, As per IRC - 6, 2017, Clause 219.6.,

 

Barge damage depth = aʙ = 3100 x ( [ 1 + 1.3 x 10⁻⁷ KE ]⁰·⁵ - 1 ) 

 

= 3100 x ([ 1 + 1.3 x 10⁻⁷ x 9.107 x 10⁹ ]⁰·⁵ - 1 )

= 3100 x 33.42

 

aʙ = 103611.53 mm

 

Barge collision impact force Pʙ, As per IRC - 6, 2017, Clause 219.7.,

 

since aʙ > 100 mm

 

Pʙ = 6 x 10⁶ + 1600 x aʙ 

 

= 6 x 10⁶ + 1600 x 103611.53

 

= 1.7177 x 10⁸ N 

 

Pʙ = 1.7177 x 10⁵ 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 8 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 X direction for 12m creating one more pier at the other end of the bridge -> translate the beams for a step in the Z direction for 7m -> Connect the top nodes of the piers using add beam command in geometry 

Step 4: Select the longitudinal piers of the bridge -> insert node command -> under insert n number of nodes, enter the value 9 -> thus 10 bays are created as per the given figure. 

Step 5: The rise of the bridge as per the given is 5m and 10 vertical members support the arch on either side of the bridge. The height of the vertical members are derived using Auto-Cad drafting of a simple two-dimensional bridge arch. As we know the rise of the bridge is 5m, and the centre vertical member is 5m in height, followed by other heights of vertical members derived in auto-cad. Refer to figure 1. 

                                                                             Figure 1

Step 6: Translation repeats the nodes of either side of the longitudinal beam according to the height in the above figure -> Connect the nodes using add beam cursor forming vertical members of the bridge. Refer to figure 2.

                                                                             Figure 2

Step 7: Using add beam cursor -> connect all the top nodes of the vertical members along the longitudinal direction forming the arch of the bridge. Also, connect the bracings of the vertical members as shown in the figure in question. 

Step 8: Translational repeat -> select the highlighted node in Figure 3 and translational repeat it along the X direction for a step of 0.25 length -> Select both these nodes and translational repeat them along the Z direction for a step of 0.25 length -> Using add plate cursor connect these four nodes and create a plate. Refer to figure 4.

                                                                              Figure 3

                                                                              Figure 4

Step 9: Select the plate -> translational repeat that plate along the X direction for 35 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 27 steps of 0.25 length each ( 7/0.25 = 28 since one plate is there, 27 steps ). Refer to Figure 5.

                                                                              Figure 5

Step 10: Specification tab -> Select fixed and create foundation -> Assign this fixed foundation to the 4 nodes under the piers.

Step 11: Pier - In the Properties tab -> select define -> Rectangle -> 2.5 x 2.5 -> Assign to the piers -> close.

Step 12: Vertical members - In the Properties tab -> select define -> tapered / steel-> F1 = 0.4m,  F2 = 0.2m, F3 = 0.4m, F4 = 0.3m, F5 = 0.2m, F6 = 0.3m, F7 = 0.2m -> Assign to the highlighted beams in figure 6 and refer to figure 7 -> close.

                                                                              Figure 6

                                                                              Figure 7

Step 13: Girder -  In the Properties tab -> select define -> rectangle / concrete -> 0.75 m x 1.8 m  -> Assign to the highlighted beams in figure 8 -> close.

                                                                              Figure 8

Step 14: Girder -  In the Properties tab -> section database -> India -> ISA200X200X20 -> Assign to the highlighted beams in figure 9 -> close.

                                                                              Figure 9

Step 15: Deck - In the Properties tab -> select Thickness -> 0.5m -> Assign to all of the plates  -> close. The model in 3D is shown in figure 10. 

                                                                              Figure 10

Step 16: In the loading tab -> Load case details-> click add -> Enter Barge Impact load -> Click Barge Impact load and add -> Select Nodal load and enter in Fy = - 171770 kN and click add. -> Apply it to the highlighted node below using the node cursor in the select window -> Assign to selected node -> close. Refer to figure 11. 

                                                                              Figure 11

Step 17: Thus Barge Impact 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 = 120.021 mm. Refer to Figure 12.,

                                                                             Figure 12

 The Reaction of the Foundation can be seen below., Refer to Figure 13., 

                                                                             Figure 13

Bending Moment in Z direction -  Critical Bending Moment = 19943.094 kN/m. Refer to Figure 14.,

                                                                             Figure 14

Bending Moment in Y direction - Critical Bending Moment = 37244.984 kN/m, Refer to Figure 15.,

                                                                             Figure 15

Shear Force in Z direction - Critical Shear Force = 42977.898 kN, Refer to Figure 16.,

                                                                             Figure 16

Shear Force in Y direction - Critical Shear Force = 8350.063 kN, Refer to Figure 17.,

                                                                             Figure 17

 

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

Bending Moment in X direction, Critical Bending Moment = 3028.822 kN-m/m., Refer to Figure 18.,

                                                                             Figure 18

Bending Moment in Y direction, Critical Bending Moment = 1523.412 kN-m/m., Refer to Figure 19.,

                                                                             Figure 19

Shear Force in X direction, Critical Shear Force = 3.751 N/mm² ., Refer to Figure 20.,

                                                                             Figure 20

Shear Force in Y direction, Critical Shear Force = 5.711 N/mm² ., Refer to Figure 21.,

                                                                              Figure 21

 

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