Week 5 Challenge

Aim:

To calculate the design wind loads for the given bridge located at Mumbai and to be designed in Stadd Pro.

Given:

Height of the bridge = 9m

Located in Mumbai in open terrain with well-scattered obstructions of height less than 10m.

Size of the Pier = 1.5m x 1.5m

Procedure:

Step 1: Basic Wind Speed (Vb):

From IS 875 Part 3 2015 Code book, On page number 6 from Figure 1,

The basic wind speed in Mumbai can be identified as 44 m/s.

Vb = 44 m/s Refer to Figure 1 below.,

Figure 1

Step 2: Factor K1:

Referring to table 1 of IS 875 Part 3 2015, for important structures and 44 m/s,

factor K1 is determined as 1.07

K1 = 1.07

Step 3: Factor K2:

Referring to table 2 of IS 875 Part 3 2015, for height 9m and category 2 structure,

Since the height of the bridge is 9m, the least value in table 2 is adopted,

factor K2 is determined as 1.00

K2 = 1.00

Step 4: Factor K3:

As per clause 6.3.3 IS 875 Part 3 2015 for upwind slope less than 3 degrees,

factor K3 is determined as 1.00

K3 = 1.00

Step 5: Factor K4:

As per Clause see 6.3.4 of IS 875 Part 3 2015When the location is within a 60 km radius of the ocean, the cyclone factor is taken into account,

factor K4 is determined as 1.3

K4 = 1.30

Step 6: Design Wind Speed (Vz):

Vz = Vb x K1 x K2 x K3 x K4

where,

Vz = 44 x 1.07 x 1 x 1 x 1.3

Vz = 61.204 m/s

Step 6: Wind Pressure (Pz):

Pz = 0.6 x Vz²

Pz = 0.6 x 61.204²

Pz = 2.247 kN/m²

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 9 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 Copy - paste the beam creating a new beam at a distance of 20m. Now, two piers are created.

Step 5: Select both the beams using the beam cursor -> Select the translational repeat command from the geometry tab -> In the X direction for 3 steps and spacing 10m create three more piers and also select link steps. Delete the linked beam connecting the bottom nodes.

Step 6: Connect the top of piers across the Z direction using Add beam command to create cross girders for the first two piers. Select the cross girder using the beam cursor from the select tab -> Using translational repeat create cross girders across the X direction for three steps for a spacing of 10m. The model is shown below in Figure 2.

Figure 2

Step 7: Specification tab -> Select fixed and create foundation -> Assign this fixed foundation to the 8 nodes under the pier.

Step 8: Pier - In the Properties tab -> select define -> Rectangle -> 1.5m x 1.5m -> Assign -> close.

Step 9: Main Girder - In the Properties tab -> select define -> Rectangle -> Width = 1.5m & Depth = 1.8m -> Assign -> close.

Step 10: Cross Girder - In the Properties tab -> select define -> Rectangle -> Width = 1.5m & Depth = 1.8m -> Assign -> close.

Step 11: In the Materials tab -> Select concrete and assign it to view.

Step 12: Select the Main girders using the beam cursor from the select tab -> In property tab -> assign the Rectangle 1.mx1.8m for the main girders.

Step 13: Select the Cross girders using the beam cursor from the select tab -> In property tab -> assign the Rectangle 1.mx1.8m for cross girders.

Step 14: Select the Pier beams using the beam cursor from the select tab -> In property tab -> assign the Rectangle 1.5mx1.5m for Pier.

Step 15: In the loading tab -> Load case details -> Generate a load type by clicking add -> primary -> enter WIND +Z and click add.

Step 16: In the loading tab -> Load case details -> Generate a load type by clicking add -> primary -> enter WIND -Z and click add.

Step 17: In the loading tab -> Load case details -> Generate a load type by clicking add -> primary -> enter WIND +X and click add.

Step 18: In the loading tab -> Load case details -> Generate a load type by clicking add -> primary -> enter WIND -X and click add.

Step 19: In the loading tab -> Load case details -> Select WIND +Z and click add -> In Member load under Uniform forces -> enter the load as 2.247 kN/m² in the Global Z direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 3.

Figure 3

Step 20: In the loading tab -> Load case details -> Select WIND +Z and click add -> In Member load under Uniform forces -> enter the load as 4.0446 kN/m² in the Global Z direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 4.

Explanation: The depth of the main girder is 1.8m and the area exposed to the direction of wind load application is 1.8m depth across the span of the bridge,

Thus, 1.8 x 2.247 = 4.0446 kN/m²

Figure 4

Step 21: In the loading tab -> Load case details -> Select WIND -Z and click add -> In Member load under Uniform forces -> enter the load as -2.247 kN/m² in the Global Z direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 5.

Figure 5

Step 22: In the loading tab -> Load case details -> Select WIND -Z and click add -> In Member load under Uniform forces -> enter the load as -4.0446 kN/m² in the Global Z direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 6.

Explanation: The depth of the main girder is 1.8m and the area exposed to the direction of wind load application is 1.8m depth across the span of the bridge,

Thus, 1.8 x 2.247 = 4.0446 kN/m²

Figure 6

Step 23: In the loading tab -> Load case details -> Select WIND +X and click add -> In Member load under Uniform forces -> enter the load as 2.247 kN/m² in the Global X direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 7.

Figure 7

Step 24: In the loading tab -> Load case details -> Select WIND +X and click add -> In Member load under Uniform forces -> enter the load as 4.0446 kN/m² in the Global X direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 8.

Explanation: The depth of the main girder is 1.8m and the area exposed to the direction of wind load application is 1.8m depth across the span of the bridge,

Thus, 1.8 x 2.247 = 4.0446 kN/m²

Figure 8

Step 25: In the loading tab -> Load case details -> Select WIND -X and click add -> In Member load under Uniform forces -> enter the load as -2.247 kN/m² in the Global X direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 9.

Figure 9

Step 26: In the loading tab -> Load case details -> Select WIND -X and click add -> In Member load under Uniform forces -> enter the load as -4.0446 kN/m² in the Global X direction and click add -> Assign this load to the highlighted blue region loaded beams in Figure 10.

Explanation: The depth of the main girder is 1.8m and the area exposed to the direction of wind load application is 1.8m depth across the span of the bridge,

Thus, 1.8 x 2.247 = 4.0446 kN/m²

Figure 10

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 in Figure 11 and the critical displacement is highlighted below., Critical Displacement = 0.809 mm.

Figure 11

The Reaction of the foundations can be seen below in Figure 12.,

Figure 12

Bending Moment in Z direction - Critical Bending Moment = 82.469 kN/m. Refer to Figure 13.

Figure 13

Bending Moment in Y direction - Critical Bending Moment = 154.909 kN/m. Refer to Figure 14.

Figure 14

Shear in Z direction - Critical Shear Force = 40.446 kN. Refer to Figure 15.

Figure 15

Shear in Y direction - Critical Shear Force = 23.387 kN. Refer to Figure 16.

Figure 16