Project 2

Aim : To calculate the water current forces, centrifugal forces, wave forces, snow load, temperature load, barge impact load on the bridge.

Given data :

• Dead weight tonnage of panamax vessel is 25000 DWT.
• Span of bridge is 40 m
• Width of bridge is 10.5 m
• The pier of size is 1.2 x 1.2 m
• The girder size is 1.6 x 2 m
• Thickness of flange and web is 0.3m
• C_r = 0.4, C_va = 3
• Storm elevation is 8.5 m

Calculation :

1. Water current forces

High flood level – 4 m

Mean velocity of river – 2.5 m/s

Maximum velocity, V = √2 x V_mean

= √2 x 2.5

V = 3.53

Water current, P = 52 x K x V²

= 52 x 1.5 x 3.53²

P = 971.95 KN/m²

2. Centrifugal forces

Design speed of vehicle = 50 km/hour

Radius of curvature = 2 m

Live load , W = 70 KN

Centrifugal force = ( W x V² ) / (127 x R )

= ( 70 x 50² ) / ( 127 x 2 )

Centrifugal force = 729.16 KN

3. Wave force

Δ Z_h = η_max – centroid of girder

= 3 – ( 1.6 / 2 )

Δ Z_h = 2.2 m.

Δ Z_v = η_max - elevation of bottom deck

= 3 – 1.5

Δ Z_v = 1.5 m

Number of girder , N = 4

Vertical load, F_v = r x Δ Z_v x A_v

= 5 x 1.5 x ( 105 x ( 1.6/2))

F_v = 63 KN

Horizontal load, F_h = r x Δ Z_h x A_h

= 5 x 2.2 x ( 3 x 40))

F_h = 1320 KN

Max vertical load , F_{v max} = C_va x F_v

= 3 x 63

F_{v max} = 189 KN

Max horizontal load , F_{h max} =[ 1 + C_r ( N – 1 ) ] C_va x F_h

= [ 1 + 0.4 ( 4 – 1 )] 3 x 1320

F_{h max} = 8712 KN

4. Snow load

The snow is damped new snow = 2 KN/m³

The deck of bridge is flat with β < 30°

The depth of accumulation of snow is 1250 mm

Snow load, S­­­­­_° = density x area

= 2 x 1.2 x 40

Snow load, S­­­­­_° = 96 KN/m

Shape coefficient from I.S 875 part 4

For β < 30^° , µ = 0.8

Design snow load, S = µ x S­­­­­_°

= 0.8 x 96

Design snow load, S = 76.8 KN/m

5. Temperature load

Max temperature in location as per IRC 6 at the location is 48.4°

Min temperature in location as per IRC 6 at the location is -2.2°

Effective temperature difference = ( 48.4 – ( -2.2) ) / 2 + 10 = 35.3°

Stress due to temperature = ɑ x Δ T x E

= 11.27 x 10^^-6 x 35.3 x 5000 ( 40 )^0.5

Stress due to temperature = 12.58 kn/m^2

Max permissible stress = ( 2/3 ) x 0.7 x (40)^0.5 = 2.92 kn/m²

Positive temperature difference

Temperature at top = 48.4°

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

6. Barge impact load

Hydrodynamic coefficient 1.25

KE = 500 x C­­­­­_H x W x V²

= 500 x 1.25 x 25000 x 13.85²

KE = 299.7 x 10⁷

ɑ_β = 3100 x [ 1 + ( 1.3 x 10^-7 x 299.7 x 10⁷]^0.5 -1)

ɑ_β = 58167.95

P_β = 6 x 10⁶ + ( 1600 + 58167.95)

P_β = 3.58 x 10¹¹ N

Aim : To prepare the model in a STAAD Pro and perform the analysis and justify with the results.

Theory : The general steps to be create a STAAD Pro model is given below,

Step 1 : Create the nodes by using the nodes cursor.

Step 2 : Joining the nodes by using the respective beam plate cursor.

Step 3 : Supports given to the nodes whether its pinned or fixed or any other custom supports

Step 4 : specifications given to the respective beams plates

Step 5 : Assign the dead load as per calculation

Step 6 : Save the model and perform the analysis

Step 7 : The results are obtained and discuss with the results

Step 8: Take the print out of report of necessary results.

Creating the nodes by using node cursor.

Open the STAAD Pro window > Select > Node cursor > enter the value with respect to X Y Z axis > click enter

Join the nodes by using beam cursor.

Select > beam cursor > join by dragging the mouse or enter the node numbers > click enter

Supports are given to the respective nodes.

Specifications > Supports > select the supports > click enter

deck slab has been created by using mesh like structures.

Assigning the properties to the beam .

Specification > Prismatic > Rectangle > enter dimensions > select the beam > assign the properties to selected beams.

Specification > Plate thickness > enter the dimension > select plates > ok

Defining the load cases .

Loading > Load case detail > water current load > Add

Add > plate load load > hydrostatic load > enter the value > ok

define > vehicular load > define > add

load case detail > load generation > add

add > enter the ranges > ok

load case detail > wave load > add

add > plate load > hydrostatic pressure > add

load case detail > add > snow load > plate load > ok

load case detail > temperature load > click add > assigned to view

load case detail > barge impact load > add

Add > point load > enter the value > ok

Run analysis > go to post processing mode > Results

The reactions are generated at the end of the nodes .the reaction value is 176.5 KN

• The maximum deflection in X direction is 30.71 mm barge impact load
• The minimum deflection in X direction is -30.97 mm barge impact load
• The maximum deflection in Y direction is 41.39 mm barge impact load
• The minimum deflection in Y direction is -41.37 mm barge impact load
• The maximum deflection in Z direction is 2.142 mm barge impact load
• The minimum deflection in Z direction is -0.142 mm due to load case 5

• The maximum shear force in X direction is 15.64 KN barge impact load
• The minimum shear force in X direction is -15.64 KN barge impact load
• The maximum shear force in Y direction is 2.101 KN barge impact load
• The minimum shear force in Y direction is -14.11 KN barge impact load
• The maximum shear force in Z direction is 8.33 KN barge impact load
• The minimum shear force in Z direction is -8.33 KN barge impact load

• The maximum bending moment in X direction is 2.07 KN-m barge impact load
• The minimum bending moment in X direction is -2.17 KN-m barge impact load
• The maximum bending moment in Y direction is 45.6 KN-m barge impact load
• The minimum bending moment in Y direction is -44.11 KN-m barge impact load
• The maximum bending moment in Z direction is 30.78 KN-m barge impact load
• The minimum bending moment in Z direction is -30.78 KN-m barge impact load

• The maximum shear stress in X direction is 1.93 KN/m²
• The minimum shear stress in X direction is -15.26 KN/m²

• The maximum shear stress in X direction is 3.9 KN/m²
• The minimum shear stress in X direction is -6.67 KN/m²
• Reports are taken printout which ever is necessary by using report
• In the report option we obtain the results of section forces, displacement, reactions, plate
• The exact report is to be taken further move to design