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.