Project 2

Aim: 

 

To calculate the Water current load, Centrifugal loads, Wave load, wind load, Snow load, Temperature load and Barge impact loads for the bridge structure shown in the figure. 

 

Given: 

 

The span of the bridge = 10 m

The Width of the carriage way = 9 m 

The size of the Pier = 1.2 m x 1.2 m 

The maximum crest elevation for the wave = 3 m

The deck of the slab is supported by four I Girders

Each I Girder = 1.6 m

A top and bottom flange width = 2 m

The thickness of the flange and web = 0.3 m

Assume constant r = 5

Assume Cva = 3

The Storm elevation = 8.5 m

The constant Cr = 0.4

The high flood level = 4 m above the Bottom of the foundation level

The mean velocity of the river = 2.5 m/s

The bridge is subjected to a live load of Class 70R tracked vehicle 

The radius of curvature in the bridge = 2 m

The design speed of the vehicles = 50 km/hr

The width of the deck slab = 10.5m

The thickness of the deck slab = 1.5 m

The deck of the bridge = flat with B <30 degrees

The depth of accumulation of snow = 1250 mm

The Dead weight tonnage of the Panamax vessel = 25000 DWT

The Ship can accommodate a maximum of 1500 containers

Each container is of standard 6.1 TEU

 

Introduction:

 

Water current force:

Water current forces are the forces caused by the ocean. Whenever a pier is located in a water body in which the water is moving, it possesses a force. This force can cause deflection and bending moments in the bridge structure. The direction, intensity and velocity of the current and the size and shape of the pier influence the load. Thus adequate design approach must be carried out. 

 

Centrifugal forces:

The movement 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. 

 

Wave load: 

Waves are caused due to disturbances over and under the water's surface such as wind, changes in temperatures, earth slides underwater and water current. These waves in turn generate force acting on the substructure and substructure of the bridge all around the year causing catastrophic damage. These loads are termed wave loads.

 

Snow load:

Bridge structures are subjected to snow load when the bridge is located in snowy regions. The type of snow resting on the structure is a major factor since the snow's age, dampness, sturdiness and slope determine the load. The snow load can be calculated as per IS 875 Part IV and IRC 6. Snow loads must be considered during the design phase in geographical locations where the structure is incidental to snow. 

 

Temperature load:

Temperature loads are caused due to fluctuations in the shade air temperature and solar radiation this in turn causes differential temperatures in the bridge. This differential temperature causes the bridge to expand and contract. When the bridge structure is effectively restrained against movement, expansion and contraction due to the temperature differential are not allowed causing the bridge to experience internal stress leading to cracks and distress of the structure. This phenomenon is called temperature loading. The differential temperature can be calculated per IRC 6 - 2017. 

 

Barge Impact load:

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: 

 

I: Calculation of loads:

 

Part I: Manual Calculation of Water forces acting on the Bridge: 

 

 

Step1: Maximum Velocity of the River

 

V = √2 x V mean 

 

where, 

V = Maximum Velocity of the River

V mean = Mean Velocity of the River

 

  = √2 x 2.5

 V = 3.53 m/s

 

Step2: Water Current

 

P = 52 x K x V²

 

where,

P = Water current

K = Shape factor

V = Maximum Velocity of the River

 

P = 52 x 1.5 x 3.53²

P = 971.95 kN/m²

 

The water forces acting on the bridge's pier were calculated as 971.95 kN/m².

 

Part II: 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 50² ) / 127 x 2

 

C = 688.97 kN

 

The Centrifugal load acting on the bridge is calculated as 688.97 kN.

 

 

Part III: Calculation of wave load acting on the Bridge:

 

Δzh = ╖max - Centroid of I girder 

 

where, 

Δzh = Difference between the elevation of the maximum wave crest and centroid of I girder

╖max = Maximum height of the wave

 

Δzh = 3 - (1.6/2) 

 

Δzh = 2.2 m

 

Δzv = ╖max - Elevation of the bottom deck

 

where, 

Δzv = Difference between the elevation of the maximum wave crest and elevation of the underside of the bridge deck

╖max = Maximum height of the wave

 

Δzv = 3 - 1.5

 

Δzv = 1.5 m

 

Vertical load, Fv = Γ x Δzv x Av

 

where, 

 

Γ = Unit weight of water

Δzv = Difference between the elevation of the maximum wave crest and elevation of the underside of the bridge deck

╖max = Maximum height of the wave

Av = Area of bridge contributing to vertical uplift

 

Fv = 10 x 1.5 x ( 10.5 x 1.6/2)

 

Fv = 126 kN

 

Horizontal load, Fh = r x Δzh x Ah

 

where, 

 

Γ = Unit weight of water

Δzh = Difference between the elevation of the maximum wave crest and centroid of I girder

╖max = Maximum height of the wave

Ah = Area of bridge contributing to horizontal thrust

 

Fh = 10 x 2.2 x ( 3 x 40 ) 

 

Fh = 2640 kN

 

Maximum vertical load, Fvmax = Cva x Fv 

 

 where, 

 

Cva = Empirical co-efficient for vertically varying load

 

Fvmax = 3 x 126

 

Fvmax = 378 kN

 

Maximum horizontal load, Fhmax = (1 + Cr(N-1)) x Cva x Fh

 

 where, 

 

Cva = Empirical co-efficient for horizontally varying load

Cr = Reduction co-efficient for reduced horizontal load on interval girders

 

Fhmax = (1 + 0.4 ( 4-1 )) x 3 x 2640

 

Fhmax = 17424 kN

 

 

Part IV: Calculation of snow load: 

 

As per IS 875 Part IV and IRC 6,  with the given data following is determined,

 

Γ = 3 kN/m³ ( assume that the snow is settled snow )

Since the deck bridge is flat, ß < 30°, the shape coefficient µ = 0.8

 

S₀ = Γ x depth of snow x span of the bridge 

 

where, 

Γ = unit weight of snow on the bridge

S₀ = snow load

 

S₀ = 3 x 1.25 x 40 

 

S₀ = 150 kN/m

 

S = µ x S₀

 

where, 

S = Design Load due to snow

S₀ = Load due to snow

µ = shape coefficient

 

S = 0.8 x 150

 

S = 120 kN/m

 

Part V: Calculation of temperature load: 

 

Assuming that the bridge is located in Delhi, from IRC 6 - 2017, Annexure F, the maximum temperature and minimum temperature of the given location can be determined. Refer to figure 1.,

 

The maximum temperature in Delhi is 48.4 °

The minimum temperature in Delhi is -2.2 °

                                                                            Figure 1

 

The effective temperature difference = ( Tmax - Tmin) / 2 + Range of bridge temperature. 

 

where, 

 

Tmax = The maximum temperature,

Tmin = The minimum temperature.

 

The effective temperature difference = ( 48.4 - 2.2 )/2 + 10 

Though the minimum temperature is minus, in the formula it shall be substituted as value only.

 

The effective temperature difference = 33.1 °

 

The stress due to temperature = α x ▲T x E 

 

The stress due to temperature = α x ▲T x 5000 √fck

 

where, 

α = Coefficient of thermal expansion

▲T = Effective temperature difference

fck = Compressive strength of concrete

 

Assume the compressive strength of concrete as 40 N/mm²

 

The stress due to temperature = 11.27 x 10⁻⁶ x 33.1 x 5000 √40

The stress due to temperature = 11.79 kN/m²

 

Maximum permissble stress = (2/3)  x 0.7 x √fck

 

where, 

fck = Compressive strength of concrete

 

Maximum permissble stress = (2/3)  x 0.7 x √40

 

Maximum permissble stress = 2.95 kN/m²

 

Hence the stresses are restricted to 3 kN/m²

 

As per IRC 6, with the given details, 

 

Temperature at top = 48.4 °

Temperature at bottom = (2.1/17.8) x 48.4 ° = 5.71 °

 

Part VI: 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

 

KE = 500 x 1.25 x 25000 x 16.66²

 

KE = 4.336 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 4.336 x 10⁹ ]⁰·⁵ - 1 )

= 3100 x 22.76

 

aʙ = 70565.28 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 70565.28

 

= 1.189 x 10⁸ N 

 

Pʙ = 1.189 x 10⁵ kN

 

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 12 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 3 steps in the Z direction for 3.5m creating three more piers of the bridge -> Connect all the top nodes of the piers using add beam command in geometry.

Step 4: Select all the beams using the beam cursor -> translational repeat in geometry tab -> translate the beams for 4 steps in the X direction for 10m creating piers on the other end of the bridge. Connect all the top nodes of the piers in a longitudinal manner using add beam command in geometry. Refer to figure 1.,

                                                                            Figure 1

Step 5: Translational repeat -> select the highlighted node in Figure 2 and translational repeat it along the X direction for a step of 0.5 length -> Select both these nodes and translational repeat them along the Z direction for a step of 0.5 length -> Using add plate cursor connect these four nodes and create a plate. Refer to figure 2.

                                                                            Figure 2

                                                                            Figure 3

Step 6: Select the plate -> translational repeat that plate along the X direction for 79 steps of 0.5 length each ( 40/0.5 = 80 since one plate is there 79 steps ). Select the created plates and translational repeat them along the Z direction for 20 steps of 0.5 length each ( 10.5/0.5 = 21 since one plate is there 20 steps ) Refer to Figures 4 and 5.

                                                                            Figure 4

                                                                            Figure 5

Step 7: The model is generated as per the given and refer to figure 6.

                                                                            Figure 6

Step 8: Specification tab -> Select fixed and create foundation -> Assign this fixed foundation to the 20 nodes under the piers.

Step 9: Pier - In the Properties tab -> select define -> rectangle -> 1.2 m x 1.2 m -> Assign to the piers -> close.

Step 10: Girders - In the Properties tab -> select define -> tapered -> F1=1.6m F2=0.3m F3=1.6m F4=2m F5=0.3m F6=2m F7=0.3m -> Assign to the highlighted beam in figure 7 and refer to figure 8 -> close.

                                                                            Figure 7

         

                                                                            Figure 8

Step 11: Deck - In the Properties tab -> select Thickness -> 1.5m -> Assign to all of the plates  -> close.

Step 12: In the loading tab -> Load case details -> Click New -> Primary, Name it as WATER CURRENT LOADS ->  Click water current loads and click add -> Under Member load in Trapezoidal load, Enter the following details in Figure 9, The load only acts up to 4m height since the Maximum flood level is 4m above the foundation. Apply this load to all of the piers. 

The calculated water current load manually is 971.95 kN/m², This load acts on the surface of the pier along the Z Global axis ( assumption ), thus multiplying the force on the width of the pier 1.2 m, we get 1166.34 kN/m. 

Enter this load in W1, and Enter d1 = 4m, and d2 = 0m. Since HFL = 4m above the foundation level. 

                                                                            Figure 9

 

Step 13: 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 688.97kN - 0m, 688.97kN - 3.6m. Refer to Figure 10 below.,

                                                                            Figure 10

Step 14: 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 80

40  / 0.5 = 80

( [span of bridge/increment length] )

The number of loads to be generated is 80

Step 15: Click the generated load  -> add -> enter the coordinates as X=0, Y=12, Z=3.5 as the initial position and load increment in the X direction as 0.5 m. 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 11

Step 16: In the loading tab -> Load case details-> click add -> Enter Wave load -> Click wave load and add -> Select Nodal load and enter in Fz = 17424 kN and click add, again in nodal load in Fy = 378 kN.  There are four bays along the longitudinal direction and three bays along the width of the bridge. The load acts on the centre points of these bays. Apply these loads on the highlighted nodes in figure 12, which are the centre points of these bays.

                                                                            Figure 12

Step 17: In the loading tab -> Load case details-> click add -> Enter Snow load -> Click snow load and add -> Select member load and enter in W1 = -120 kN/m³ along the global Y axis and click add. Assign to all the cross and longitudinal girders

                                                                            Figure 13

Step 18: In the loading tab -> Load case details-> click add -> Enter Temperature load -> Click Temperature load and add -> Select Temperature load and enter in Temperature change for axial elongation = 45 ° and Temperature differential from top to bottom = 45 ° and click add. Refer to figure 14. 

                                                                            Figure 14

Step 19: These loads act on the entire bridge, Apply this load to the entire bridge -> apply to view. 

Step 20: 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 Fz = - 118900 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 15. 

                                                                            Figure 15

Step 21: Thus Water current forces, Centrifugal forces, Wave forces, Snow loads, Temperature loads and Barge Impact loads have 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.

 

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 = 448.95 mm. Refer to Figure 16.,

                                                                             Figure 16

 The Reaction of the Foundation can be seen below., Refer to Figure 17., 

                                                                             Figure 17

Bending Moment in Z direction -  Critical Bending Moment = 45573.656 kN/m. Refer to Figure 18.,

                                                                             Figure 18

Bending Moment in Y direction - Critical Bending Moment = 66149.125 kN/m, Refer to Figure 19.,

                                                                             Figure 19

Shear Force in Z direction - Critical Shear Force = 15469.719 kN, Refer to Figure 20.,

                                                                             Figure 20

Shear Force in Y direction - Critical Shear Force = 12817.747 kN, Refer to Figure 21.,

                                                                             Figure 21

 

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

Bending Moment in X direction, Critical Bending Moment = 2081.111 kN-m/m., Refer to Figure 22.,

                                                                             Figure 22

Bending Moment in Y direction, Critical Bending Moment = 13298.115 kN-m/m., Refer to Figure 23.,

                                                                             Figure 23

Shear Force in X direction, Critical Shear Force = 3.496 N/mm² ., Refer to Figure 24.,

                                                                             Figure 24

Shear Force in Y direction, Critical Shear Force = 7.951 N/mm² ., Refer to Figure 25.,

                                                                              Figure 25

 

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