Week 8 Challenge

Aim: 

To calculate the centrifugal load of the given bridge for the following load data and to apply and analyse it in Stadd Pro.

Given: 

Span of the bridge = 12m

Width of the carriage way = 7m

Live load class according to IRC = Class 70R tracked vehicle

The design speed of the vehicles = 75 km/hr

The radius of curvature in the bridge = 3 m

Introduction: 

The moving of a vehicle in a curve produces an outward pushing force from the bridge which exerts a load on the structural members of the bridge termed centrifugal loads. 

Procedure:

Part I: Calculation of Centrifugal load due to IRC Class 70R tracked vehicle:

C = WV² / 127R

where,

W = Live load of the IRC Class moving on the bridge,

V = Velocity of the moving vehicle, 

R = Radius of Curvature. 

C = ( 70 x 75² ) / 127 x 3

C = 1033.46 kN

Part II: Design and Analysis:

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.

Step 3: Select add beam cursor and connect the two nodes creating a beam, this beam is one of the piers of the bridge.

Step 4: Select the beam cursor in the Select window -> Select the beam and translational repeat the beam along Z direction for a step of 7m creating a new beam. Now, two piers are created. Repeat the same process by selecting both beams to create two more piers at a distance of 12m for a step creating a total of four piers.

Step 4: Connect the upper four nodes of the four piers using add beam command in geometry -> Thus creating the main four girders of the bridge

Step 5: Select the upper leftmost node ( Node 2 ) -> translational command in geometry -> translate this node along Z direction for a step of 0.5m spacing. Select these two nodes using select node cursor -> translational repeat these nodes along X direction for a step of 0.5m spacing. Refer to Figure 1 for clarity. 

                                                                           Figure 1

Step 6: Connect these four nodes by adding beams and a plate over them using Add beam and Add plate commands.

Step 7: Select the upper leftmost plate ( Plate 1 ) -> translational command in geometry -> translate this plate along Z direction for 13 steps of 0.5m spacing -> translational repeat the Plate 1 along X direction for 23 steps of 0.5m spacing. Refer to Figure 2 for clarity. 

                                                                            Figure 2

Step 8: Select the highlighted plates in figure 3 -> translational repeat them along the X direction for 23 steps for a spacing of 0.5m. 

The Span of the bridge is 12m thus 24 plates of 0.5m along the X direction and the width of the bridge is 7m thus 14 plates of 0.5m in the Z direction. 

                                                                            Figure 3

Step 9: Specification tab -> Select fixed and create foundation -> Assign this fixed foundation to the 4 nodes under the piers.

Step 10: Pier - In the Properties tab -> select define -> Rectangle -> 2m x 2m -> Assign -> close.

Step 11: Main Girder - In the Properties tab -> select define -> tapered -> F1=1.8m F2=0.5m F3=1.8m F4=2m F5=0.3m F6=2m F7=0.3m -> Assign to the highlighted beam in figure 4 -> close.

                                                                            Figure 4

Step 12: Cross Girder - In the Properties tab -> select define -> tapered -> F1=1.6m F2=0.4m F3=1.6m F4=2m F5=0.4m F6=2m F7=0.4m -> Assign to the highlighted beam in figure 5 -> close. 

                                                                            Figure 5

Step 13: Deck - In the Properties tab -> select Thickness -> 0.3m -> Assign to all of the plates  -> close.

Step 14: In the loading tab -> Definitions -> Vehicle definition, click add -> Width= 2.05m, Calculated centrifugal load of Class 70R tracked load details from IRC guidelines as 1033.46kN - 0m, 1033.46kN - 3.6m. Refer to Figure 6 below.,

                                                                            Figure 6

Step 15: In the loading tab -> Load case details -> Generate a load type by clicking add -> load generation -> click add -> Enter the number of loads to be generated as 24

12  / 0.5 = 24

( [span of bridge/increment length] )

The number of loads to be generated is 24

Step 16: Click the generated load  -> add -> enter the coordinates as X=0, Y=8, Z=1.5 as the initial position and load increment in the X direction as 0.5 m and the range in the Z axis as 10m. The coordinates as the nodal points of the I - girder from where the Centrifugal load will start and move along its length. Refer to figure 7., Thus the Centrifugal load is assigned to the structure. ,

                                                                            Figure 7

Step 17: Thus Centrifugal load 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 = 0.604 mm. Refer to Figure 8.,

                                                                             Figure 8

 The Reaction of the Foundation can be seen below., Refer to Figure 9., 

                                                                             Figure 9

Bending Moment in Z direction -  Critical Bending Moment = 787.371 kN/m. Refer to Figure 10.,

                                                                             Figure 10

Bending Moment in Y direction - Critical Bending Moment = 366.034 kN/m, Refer to Figure 11.,

                                                                             Figure 11

Shear Force in Y direction - Critical Shear Force = 741.758 kN, Refer to Figure 12.,

                                                                             Figure 12

Shear Force in Z direction - Critical Shear Force = 61.747 kN, Refer to Figure 13.,

                                                                             Figure 13

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

Bending Moment in X direction, Critical Bending Moment = 1.495 kN-m/m., Refer to Figure 14.,

                                                                             Figure 14

Bending Moment in Y direction, Critical Bending Moment = 1.401 kN-m/m., Refer to Figure 15.,

                                                                             Figure 15

Shear Force in X direction, Critical Shear Force = 0.272 N/mm² ., Refer to Figure 16.,

                                                                             Figure 16

Shear Force in Y direction, Critical Shear Force = 0.395 N/mm² ., Refer to Figure 17.,

                                                                              Figure 17

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