Week 8 Challenge
Aim: The aim of this challenge is to calculate the centrifugal force on brige superstructure. To understand the terminology used to calculate the centrifugal force.
Centrifugal force: when ever a moving object, here any vehicle encountering a curved path, a force acts on the moving body which always pushes away from the path. The force which pushes away any moving vehicle out of the path is called centrifugal force.
This force will defenitely have effect on both super structure and the substructure. The components of this force needed to be calculated and applied on the super sructure. The componenets come in to picture if the lateral slope is significant.
Introduction: The following are the procedure used to calculate the centrifugal force as per IRC - 6
Calculations
The following are the data given
Span = 12m
Width of carriage way = 9m
Design speed = 75 km/h
r = radius of curvature = 3m
Vehicle under consideration is 70 R tracked.
Procedure
FOR 70 R TRACKED THE TOTAL WEIGHT W = 700KN
Here W = 700kN
r = 3m
V= 75 km/h
C = 700x75x75/(127 x 3) = 10334.5kN
The moment applied on the slab, = 1.2x10334.5=12401.4kN-m
The centrifugal force acting on the 12m span shall be applied at the mid of the span.
The value obtained by above calculation is 10334.5kN.
And this will act at 1.2 m above the road.
Also the Class A is also considered.
W = 55.4T = 554kN
r = 3m, V= 75km/h
C= 554x75x75/(127x3)=8179.13kN
Concentrated moment = 8179.13x1.2=9814.96
The distance where the Class A vehicle to be placed in the model
= 1.2+2.9+1.2=5.3m
STADD MODEL
The following image shows the grillage model of the bridge super structure and the layout of the beam.
here the cross girders have more depth than the longitudinal girders.
The plate section is defined as concrete with thickness 0.3m
The support reactions location
LOADS TO BE CONSIDERED FOR CENTRIFUGAL FORCE ARE
SINCE HERE THE CARRIAGE WAY WIDTH ASSUMED IS 12.5 METER THE FOLLOWING IS THE CLAUSE AS PER IRC - 6 SHOWS THE LOADS TO BE CONSIDERED.
BUT IN THE CHALLENGE IS IS MENTIONED THAT 70 R TRACKED NEED TO BE CONSIDERED.
Therefore the third case from the below clause ONE LANE OF 70 R TRACKED WITH 1 CLASS A IS CONSIDERED HERE.
Loads considered on the model
The concentrated moment due to 70 R tracked
The concentrated moment due to Class - A
Results
THe following image showa the bending moment due to concentrated moments apllied due to 70 R tracked
The following image shows the two longitudianl giders were the concentrated moments due to 70 R tracked and Class A live loads are applied.
The Following Image shows the Bending moments, shear force on the longitudinal girders due to centrifugal force.
The following images show the bending moment due to Centrifugal force clculated from Class A live loads and applied as a moment
BENDING MOMENT ON THE LONGITUDINAL GIRDERS DUE TO LIVE LOAD ALONE
HERE THE BEAM SEGMENT NUMBER 771 AND 773 FORMS THE CENTER OF THE GIRDER.
AT THS PARTICULAR LOCATION THE MAXIMUM MOMENT DUE TO LIVE LAOD HAS TO BE TAAKEN
Along with the live load maximum moment the concentrated moment and it effects on the logitudianl girders are also to be considered. The results due to centrifugal forces alone are shown in the above images
The following image shows the bending and shear forces due to live load generations of both 70 R tracked and Class A.
THe following image shows the bending moment of the longitudinal girder segment 773 due to 70 R Tracked centrifugal forces.
THe following image shows the bending moment of the longitudinal girder segment 773 due to class A centrifugal forces.
Plate results
The following image shows the stress pattern in the slab
Similarly SQx SQy stress patterns can also be studied.
Due to applied forces, moments are generated and the following results show that the structure is facing heavy moements.