Week 4 Challenge

Aim: 

To calculate the Earthpressure acting on the abutṁent wall and apply it on STADD Pro.

Given:

Abutment wall height = 5m

Backfill soil height = 7m

Ground level = 3m

The thickness of foundation = 1m

Procedure:

Step 1: To find the Earth pressure of backfill and ground-level soil on either side of the pier respectively.,

Condition 1:

Since the water table is at ground level,

K1= k1 x ( Γsat - Γw )x h

where,

K1 = Earth pressure of the ground-level soil located on the exterior side of the pier,

k1 = Active earth pressure coefficeint,

Γsat = Unit weight of the saturated ground-level soil located on the exterior side of the pier,

Γw = Unit weight of the water,

h = height of the soil from the top face of the foundation.

Assume that k1 = 0.35, Γsat = 19 kN/m3, Γw = 10 kN/m3.

K1 = 0.35 x (19-10) x 3

K1 = 9.45 kN/m2.

Condition 2:

Since the water table is at ground level,

K2= k2 x ( Γsat - Γw )x h

where,

K2 = Earth pressure of the backfill soil located on the inner side of the pier,

k2 = Passive earth pressure coefficeint,

Γsat = Unit weight of the saturated backfill soil located on the inner side of the pier,

Γw = Unit weight of the water,

h = height of the soil from the top face of the foundation.

Assume that k2 = 0.5, Γsat = 19 kN/m3, Γw = 10 kN/m3.

K2 = 0.5 x (19-10) x 3

K2 = 13.5 kN/m2

Condition 3:

Above the water table on the inner side of the pier,

K3 = k3 x Γ x h

where,

K3 = Earth pressure of the backfill soil located on the inner side of the pier,

k3 = Passive earth pressure coefficeint,

Γ = Unit weight of the backfill soil located on the inner side of the pier,

h = height of the soil from the top face of the foundation.

Assume that k2 = 0.5, Γ = 18 kN/m3.

K3 = 0.5 x 18 x 4

K3 = 36 kN/m2.

The backfill earth pressures are added to obtain a final load.,

K2 + K3 = K4 

where K4 is the final load of the backfill.,

K4 = 13.5 + 36 

K4 = 49.5 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 7 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 bottom node using the node cursor (z=0 and y=0) -> Translational repeat that node in the z-direction and minus z-direction & x-direction and minus x-direction for a spacing of 0.5m. Select the newly created nodes along x-directions and translate repeat in the z-direction and minus z-direction for a spacing of 0.5m. The reason for creating 0.5 on all sides from the centre node is that assuming the pier is 1m wide and 1m long, for load application that plate can be neglected and other plates can be easily loaded. 

                                                                               Figure 1 

The above image represents the first created four nodes (highlighted nodes)., This is done to prevent the software from recognizing multiple structures. Multiple structures can be checked from the 'Utilities' tab under 'structure tools'.

                                                                               Figure 2

In the image above, the foundation length is 5m as per the given data, and the foundation's width is assumed to be 3m wide.

Step 5: Select add plate command from the geometry tab and create a four-noded plate over the created four nodes. These four nodes are highlighted in the image below.,

                                                                               Figure 3

Step 6: Select the plate using the plate cursor from the select tab -> Translational repeat the created plate over the X and minus X directions for 2 steps with a with 1m spacing and select all the generated plates and translational repeat them in the Z and minus Z directions for 1 step with a 1 m spacing respectively. Refer to figure 2 for clarity. 

Step 7: Specification tab -> Select foundation and select plate mat -> Assume Subgrade modulus as 12000 kN/m2/m -> Assign this plate mat foundation to the created nodes except the four cross nodes highlighted in figure 1.

Step 8: Insert a node at a 3m distance from the bottom of the pier to differentiate the load applications. 

Step 9: Pier - In the Properties tab -> select define -> rectangle -> 1m in both directions -> Assign -> close.

Step 10: Plate mat - In the Properties tab -> select thickness -> 1m on all sides -> Assign -> close.

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

Step 12: Select the Pier beams using the beam cursor from the select tab -> In property tab -> assign the Rect 1m for Pier.

Step 13: Select the Deck slab plates using the plate cursor from the select tab -> In property tab -> assign the Thickness 1m for the deck slab.

Step 14: In the loading tab -> load case details, click add -> Member load -> uniformly varying load -> enter 9.45 in W1 with z local axis which is the earth pressure on the exterior side of the pier as per calculations.

Step 15: In the loading tab -> load case details, click add -> Member load -> hydrostatic load -> select the members and enter -49.5 in W1 with z local axis in W1 which is the earth pressure on the inner side of the pier as per calculations.

                                                                                Figure 4

The blue portion of the load is K1, which is the load due to the earth-pressure on the exterior side of the pier.,

The green portion of the load is K4, which is the load due to the earth-pressure on the inner side of the pier.

Step 16: 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.

Thus the structural analysis of the given data has been done and the results are interpreted below.

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 = 1.268 mm.

                                                                                Figure 5

 The Reaction of the Plate mat can be seen below.,

                                                                                Figure 6

Bending Moment in Z direction -  Critical Bending Moment = 0 kN/m. Since the loads are acting as horizontal thrusts.

                                                                                Figure 7

Bending Moment in Y direction - Critical Bending Moment = -390.075 kN/m, the minus symbol indicates the bending moment in the opposite direction of the load axis.

                                                                                Figure 8

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

Bending Moment in X direction, Critical Bending Moment = 18.742 kN-m/m

                                                                                Figure 9

Bending Moment in Y direction, Critical Bending Moment = 136.179 kN-m/m

                                                                                Figure 10

Shear Force in X direction, Critical Shear Force = 0.230 N/mm2

                                                                                Figure 11

Shear Force in Y direction, Critical Shear Force = 0.235 N/mm2