Project 2

AIM AND INTRODUCTION :

To calculate the wave-current forces, centrifugal forces, wave forces, snow loads, Temperature loads, Barge impact loads for the given bridge structures.

water current loads: The deep ocean currents are driven by density and temperature gradients, The major ocean currents are:

• 1. North equatorial current.
• 2. Equatorial counter current
• 3. Atlantic currents,
• 4. North Pacific currents.
• 5. south Indian currents.

water current loads are calculated as per IRC as follows:

• P= 52 * K * V * V
• P= pressure intensity due to the water current.
• v maximum velocity of water current.
• where K is constant, based on shape of the pier.
• The maximum velocity v = (2)^0.5 * Vmean.

Centrifugal force:

• The centrifugal force is an outward pushing force that exerts a load on structural elements of the bridge.
• C = W * V * V / 127 R
• C is point load or udl.
• W= live load of the vehicle class 70 R loading.
• V= design speed of the vehicle in km/hr.
• R is the radius of curvature.

wave forces:

• wave load is caused due to the disturbance of the water surface.
• Based on the intensity of the wind, the wave generates a force on the bridge substructure like piers and abutments. These wave loads will cause damages to the structure and have a tendency to uplift the superstructure.
• wave loads have two components

1. The crust - The highest point of the wave.
2. The trough- The lowest point of the wave.

Wave Load, Fv* = Y * ΔZv * Av

where, Av= projection of bridge deck onto hizontal plane.

ΔZv= difference between elevation of crest of maximum wave and elevation of underside of bridge deck.

Y = Unit weight of water.

Fh*= Y * ΔZh * Ah

where, Ah= projection of bridge deck onto vertical plane.

ΔZh = difference between elevation of trough of maximum wave and elevation of underside of bridge deck.

Snow loads:

• Snow loads are more common in regions where snowfall occurs and regions where colder climate prevails.
• snow load is calculated as per IS 875 part 4 and also loads are applied as per IRC 6
• The minimum load considered should be 900kg/m3 as per clause 224 IRC 6.
• The design snow load S = μ * So.
• The density of snow load varies according to its settlement over structure.
• Based on the slope condition the snow load classified into

>> Positive roof slope.

>> Negative roof slope.

>> Multilevel roof slope.

Temperature loads:

• Daily and seasonal fluctuations in shade air temperature by solar radiation cause temperature loads.
• The variation of maximum and minimum temperature due to seasonal changes causes temperature load on the bridge.
• This load causes temperature restraint which causes thermal expansions or contraction at joints, which accelerates material degradation and increases stress in the structure.
• The difference of temperature in the top and bottom surface of the superstructure needs to be applied as load in staad pro for analyzing the structure.
• IS 875 part five deals with temperature load.

Barge impact loads:

• Barge refers to the ships or vessels crossing the bridges constructed in rivers, canals, sea causes collision on the bridge structure.
• IRC 6 2017 gives the details for barge impact load
• Barge collision energy is given by KE = 500 * ch * w * v2
• CH is a hydrodynamic coefficient.
• W is barge displacement in tonnage.
• V is barge impact speed.

PROCEDURE :

Given data:

Maximum crest elevation of wave = 3m

No. of I girder supporting bridge deck = 4

r = 5, Cva = 3, Cr= 0.4, B<30degree

Storm elevation = 8.5

High flood level is 4m above foundation level

bridge span = 10m

mean velocity of river= 2.5m/s

width of carriageway = 9m

Radius of curvature = 2m

Design speed of vehicle = 50 KM/hr

Depth of snow accumulation = 1250 mm

Dead weight of panamax vessel = 25000 DWT

Pier size = 1.2m * 1.2m

deck slab width = 10.5m

deck slab thickness = 1.5m

I girder: height = 1.6m, top and bottom flange width = 2m,

thickness of flange and web = 0.3m

• Water Current Forces:

water current load = 52 * K * V * V ( For square ended pier K= 1.5, Vmean= 2.5m/s)

= 52 * 1.5 * (1.414 * 2.5)^2 = 974.70 KN/m2.

water current load = 974.70 KN/m2.

• Centrifugal forces:

Centrifugal load = W * V * V / 127R

= 70 * 50 * 50 /127 * 2 , (W= 70tonne, live load of class 70R loading, design speed, v=50km/hr, radius of curv. = 2m)

centifugal load = 688.97 KN/m2

• Wave load :

Maximum crest elevation,(η)max = 3m

No. of girders supporting bridge deck = 4

I girder, H= 1.6m, flange width = 2m, flange thickness = 0.3

Bridge span = 10m, deck slab width = 10.5m, deck slab thickness = 1.5m

r = 5, Cva= 3, Cr= 0.4, storm elevation = 8.5

ΔZh= (η)max - centre of I girder= 3- 1.6/2 = 2.20

ΔZv= (η)max - elevation of bottom deck = 3-1.5= 1.5m

Wave load, Fv* = Y * ΔZv * Av

Fv* = 10 * 1.5 * (9 * 1.5/2) = 101.25 KN

Fh* = Y * ΔZh * Ah = 10 * 2.20 * (10.5*3)

Fh* = 693 KN

Max vertical load, (Fv)max = Cva * Fv = 3 * 101.25 = 303.75 KN

Max horizontal load, (Fh)max = (1+Cr(N-1)) *Cva * Fh = (1+0.4(4-1)) * 3 * 693

(Fh)max = 4573.8 KN

• Snow Loads:

Snow load, So= Density of fresh snow * depth of accumulation * span

So = 2 * 1.25 * 40 = 100

Design snow load = μ * So = 0.8 * 100 = 80 KN/m2. ( μ=0.8 for 0 < B < 30 degree)

• Temp. Loads:

Assuming location chennai and grade of concrete as M40

Max temp. at the location = 45degrees, min temp. = 12.5 degrees

Effective temp. difference = (45-12.5)/2 + 10

= 26.25 degrees

Stress due to temp. = α * ΔT * E = 11.27 * 10^-6 * 26.25 * 5000(40)^0.5 = 9.35KN /m2

Max permissible stress = 2/3 * 0.7 * (40)^0.5 = 2.95 KN/m^2

Hence, the stresses are restricted to 3 KN/m2.

Positive temp. difference:

Temp. at top = 45 degree

Temp. at bottom = 2.1/17.8 * 45 = 5.30 degrees

• Barge impact loads:

KE = 500 * CH * W * V * V = 500 * 1.25 * 25000 * 60 * 60 ( Assuming, V = 60KM/hr)

= 56250 * 10^6 N/m

Barge damage depth :

aB = 3100 [(1+1.3* 10^-7 KE)^0.5 -1 ] = 3100 [(1+1.3*10^-7 * 56250*10^6)^0.5 -1]

= 3100[(1+5625)^0.5 -1] = 262.008 mm

Barge collision impact force:

For aB≥100mm

pB = 6.0 * 10^6 + 1600(262.008) = (6.0 * 10^6 + 419212.8) N

= 6419212.8 N = 6419.212 KN

Now, We apply these calculated loads on the bridge structure and perform analysis in staad pro.

A step by step procedure is follows as:

Fig. 1

• Enter the coordinates for the piers (0,0,0) and (0,10,0), the 10m is the height of the pier, connect the nodes by using add beam command.

Fig. 2

• Select the beam and copy the beam using translational repeat in z-direction for 3 steps at a spacing of 3.5m and link steps.

Fig. 3

• Select the piers and copy them in x-direction using translational repeat command at a spacing of 10m for 4 steps.

Fig. 4

• Connect the piers by using add beam command, hence the bridge of 40m span has been modelled, next step is to assign properties to the members and to add support.

Fig. 5

• Add fixed support, select the nodes of each pier and assign the support to the selected nodes of the piers.

Fig. 6

• Selected the corner nodes of the bridge and copy them in the x and z direction using the repeat command to add a plate.
• Add a plate by connecting the four nodes using add plate command,we need to copy the plates in x and y direction to form the deck slab.

Fig. 7

• select the plates, copy them in the x-direction using translational repeat command for 79 steps at 0.5m spacing

Fig. 8

• select the copied plates and copy them in z-direction for 20 steps at a spacing of 0.5m, hence the deck slab has been formed.

Fig. 9

• Next, we need to add properties to each member, select the piers and define them with a rectangular section of 1.2 * 1.2 m and assign the property to selected piers.

Fig. 10

• Add a I section for the given dimensions and select the main beam to assign the I section properties.

Fig. 11

• Add a rectangular cross-section of 1m * 0.75m, select the cross beams to assign the properties.

Fig. 12

• Add plate thickness of 1.5m and select the entire deck to assign the selected plate thickness.

Fig. 13

• The next step is to give loading to the bridge structure, add load case details and give title as water current loads.

Fig. 14

Fig. 15

• Add member load and enter the calculated load, select the pier and apply the load in the global z-direction.

Fig. 16

Fig. 17

• The next step is to give centrifugal loading add vehicular definitions and enter the calculated loading at a distance of 3.6 in define load section, after the enter the coordinates for placing of load.
• No. of load generation is taken as 20 and load is applied on the respective coordinate with x-increment = 1 at nodes having coordinate (1,10,2.5) randomly selected.

Fig. 18

Fig. 19

• Next, we need to give wave loads, add a new load case and give title as wave loads, the load needs to be applied as nodal loads at the centre, apply the calculated load fz and fy in respective directions.
• Select the corner 4 nodes in X-direction and apply the Fz load and select the middle nodes of all main beam and assign Fy load.

Fig. 20

Fig. 21

• Select the entire deck slab plate and apply the snow loads as plate loads in the global y direction.
• The negative sign shows load is applied in downward direction.

Fig. 22

• Assume the zone as Chennai and M40 as the grade of concrete for temperature loading,add a load case details and give the temperature definitions then select the plate and apply the load.

Fig. 23

Fig. 24

• The next step is to give barge impact loading, we need to apply the load as nodal loads, select the node and apply the loads in z direction for the calculate barge load values of 6419.212 KN.

RESULT:

Fig. 25

• The loads are applied to the structure next step is to analyse the structure, use the run analysis command to analyze the structure.
• Enter into post-processing mode, to analyse the structural behaviour of the bridge.

Fig. 26

• The above image is displacement of the structure due to snow load.

Fig. 27

• The shear diagram in the y-direction is shown above, due to water current load.

Fig. 28

• The bending moment diagram, Mz is shown above for the snow load.

Fig. 29

• Click on the plate stress and choose stress type as My (local), the maximum and minimum values of plate stress value will be shown as contour image.
• The bridge is designed for a given specification and calculated load has been applied over the modelled bridge structure.