Challenge

Project 2

SSmarak Priyaranjan25 Mar 2023

AIM OF THE EXPERIMENT:-

To calculate the water current forces, centrifugal forces, wave forces, snow loads, temperature loads, Barge Impact load for the bridge structure shown below

DATA GIVEN:-

Maximum Crest elevation for the wave = 3.0 m

Number of Main Girder = 4

Size of Main I Girder = Flange as 2.0 x 0.3m and Depth as 1.6 x 0.3m

Constant r = 5

C_va= 3

Storm Elevation = 8.5 m

C_r = 0.4

Highest Flood Level = 4 m above the Bottom of foundation

Span of bridge = 10.0 m

Mean velocity of river = 2.5 m/s

Width of carriage way = 9.0 m

Live load on Bridge = 70R Tracked vehicle

Radius of curvature (R) = 2.0 m

Design speed of vehicle = 50 km/hr

Size of Pier = 1.2 x 1.2 m

Width of deck slab = 10.5 m

Thickness of the deck slab = 1.5 m

Deck slab is flat.

Depth of snow = 1250 mm = 1.25 m

Dead Weight tonnage of Panamax vessel = 25000 Tons

No. of containers shipped by ship = 1500 containers

Each container = 6.1 TEU

ASSUMPTIONS:-

Depth of Foundation = 2.0 m

Speed of Barge vessel = 60 km/hr

Delhi

Coefficient of Thermal Expansion (α) = 12.0 x 10^-6/^oC

Compressive strength of concrete = 40 N/mm²

Modelling of the Structure by Staad Pro. V8i

Modelling of structure is done as per given questions

Size of Cross beam = 1.0 m x 1.4 m

Hydrodynamic Coefficient (C_H) = 1.25

Type of Snow = Damp New Snow

Location of bridge = New Delhi

Property of the elements will be assigned as per given question

THEORY FOR WATER CURRENT LOADS:-

Water Current Loads:-

As per IRC 6:-2017, P=52KV²

Calculations of water current loads

For Sqaure piers,

Shape factor K = 1.50

Height of H.F.L from foundation is 4m so water forces will be acting at 4m height of piers so,

Maximum Velocity, V = √2x Vmean

Mean Velocity = 2.5 m/sec (Given)

V= 3.53

Water Current Force, P = 52 x K X V2

= 52 x 1.50 x 3.53 x 3.53

P = 971.9 kN/m2

As Pier size is 1.2m x 1.2m, so final P = 1.2 X 971.9 = 11.66kN/m

Calculation of Centrifugal Loads:

Live Load due to 70R Tracked vehicle (W) = 70KN

Design Speed of vehicles (V) = 50 km/hr

Radius of Curvature (R) = 2.0 m

Centrifugal Loads (Fc) = (W x V²)/(127 x R) = (70 x 50²)/(127 x 2) = 688.98KN

a= 1.8m

For Inner wheel

(W/2)-1.2C/a

= (70/2)-1.2*(688.97)/1.8

=-424.313

For Outer wheel

(W/2)+1.2C/a

= (70/2)-1.2*(688.97)/1.8

=494.313

Calculation of Wave Loads:

Maximum elevation of wave crest, η_max = 3.0 m

Depth of Superstructure = 1.5 m

ΔZh = η_max – Centroid of superstructure = 3 – (1.5/2) = 2.25 m

ΔZv = η_max – elevation of upside of deck = 3 – 1.5 = 1.5 m

Number of girders supporting bridge deck (N) = 4

Vertical load (Fv) = r x ΔZv x Av = 5 x 1.5 x (10.5 x (1.5/2)) = 59.063 KN

Horizontal load (Fh) = r x ΔZh x Ah = 5 x 2.25 x (10 x 1.5) = 168.75 KN

Maximum wave induced vertical load (Fv_max) = Cva x Fv = 3 x 59.063 = 177.189 KN

Maximum wave induced horizontal load (Fh_max) = (1+Cr x (N-1)) x Cva x Fh = (1 + 0.4 x (4-1)) x 3 x 177.189 = 1169.4474 KN

Calculation of Snow Loads:

Density of settled snow (ρ) = 200 Kg/m³

Depth of snow accumulation (D) = 1250 mm = 1.25 m

Slope of floor/roof (β) = 0

Snow Load, S₀ = β x D x ρ = 2 x 1.25 x 10 = 25 KN/m

Shape Coefficient from IS 875 Part 4,

For angle β < 30⁰, μ = 0.8

Design Snow Load,

S = μ x S₀ = 0.8 x 25 = 20 KN/m

Calculation of Temperature Loads:

Maximum temperature at Delhi C.H.O. as per IRC 6 2017 = 47.8^oC

Minimum temperature at Delhi C.H.O. as per IRC 6 2017 = -0.4^oC

Effective temperature difference (T_eff) = [(47.8 - (-0.4))/2] + 10 = 34.1^oC

Coefficient of Thermal Expansion (α) = 12.0 x 10^-6/^oC

Young Modulus of concrete (E) as per IS 456 = 5000√fck = 5000 x √40 = 31622.777 KN/m²

Stress due to Temperature (σ_temp) = α x T_eff x E = 12.0 x 10^-6 x 34.1 x 31622.777 = 12.94 KN/m²

Maximum Permissible Stress (σ_perm) = (2/3) x 0.7 x √fck = (2/3) x 0.7 x √40 = 2.952 KN/m²

So, Stress is reduced 3 KN/m².

Positive Temperature Differences:

Temperature at top of deck = 47.8^oC

Temperature at bottom of deck = (2.1/17.8) x 47.8^oC = 5.64^oC

Reverse Temperature Differences:

Temperature at top of deck = 47.8^oC

Temperature at bottom of deck = (6.6/10.6) x 47.8^oC = 29.762^oC

Calculation of Barge Impact Loads:

Hydrodynamic Coefficient (C_H) = 1.25

Barge Displacement Tonnage = 25000 DWT

Barge Impact Speed (V) = 60 km/hr. = 16.67 m/s

Barge Collision Energy (KE) = 500 x C_H x W x V² = 500 x 1.25 x 25000 x (16.67)²= 260468750 N-m = 2.61 x 10⁸ N-m

Barge Damage Depth, a_B = 3100 x ([1 + 1.3 x 10^-7 KE]^0.5 -1) = 3100 x ([1 + (1.3 x 10^-7 x 2.61 x 10⁸)]^0.5 -1) = 15221.5 mm

Since a_B > 100 mm

Then, Barge Collision Impact Force (P_B)

P_B = 6.0 x 10⁶ + 1600 x a_B = 6.0 x 10⁶ + 1600 x 15221.5 = 30354400 N = 30354.4 KN

PROCEDURES:-

STEP 1:-

Application of Loadings:-

Water current loads

Go to load and definition
Select on load case details, click add
Rename as water current load,click add
Go to water current loads, select add
Go to trapezoidal loadings, ;put the loading value as calculated above and assign it to the required structure

2. Application of Centrifugal Loads

Go to Vehicle definations
Select vehicle width = 1.8m
Annotate the vehicle loads and the distance between the axle
Go to Load case details, click add
Go to load Generation
of loads to be generated=45 (say)
Assign vehicle start node

3. Application of wave loading to the structure

Go to load cases details
Select add
Rename as wave loads
Click on wave load, select add
Go to nodal loads,
Give the calculated load values in FY and FZ direction

4. Application of Snow loads to the structure

Go to load cases details
Rename as snow load
Go to member loads, put the calculated value and assign to the cross girders of the structure
Another Live load of 500kg/m3 was assigned to the deck slab of the structure