Challenge 3

1. We need the following sectional properties for designing a metro viaduct structure:

a. Area of Section b. Perimeter of Section c. Centroid of Section d. Moment of Inertia of Section about major & minor axes

We can used AutoCAD for as supporting software to arrive at these properties of U-Girder. As the Shape of U-Girder is not a standard shape and also unsymmetric, the softaware proves to be very helful in calulating various properties.

2. Following are the steps involved in creating the Line Model of Typical U-Girder Span

a. Create the nodes in Staad at desired global co-ordinates. The co-ordinates are choosen based on the geometry of actual span. It shall consider the total lenght of U-girder, the distance from Bearing centerline to edge of girder, the span of girder i.e. bearing c/c distance. The global axes in staad are shown in the viewport. We can enter the values or c-ordinates in the Node Table and generate node. We shall check if the node is created in viewport after entering the values if all the three co-ordinates in node table to avoid any error.

b. After creating the nodes, use create beam command and connect the nodes to form an element. As an alternative we can also create element by enter 2 nodes in the elements table of Staad. The elements can also be created using Traslational repeat command when 1 element is already created. In translation repeat use can select a standard lenght and number of steps. You can also edit any specific length of member from the steps table in dialogue box.

c. After creating all the elements of the structure, you have to assign the property to that element. This can be done from prperties tab. There are various section which are available in staad which can be directly applied to the elements. In case of U-Girders we have to choose, prsmatic general section and assign the properties calculated from AutoCad based on the actual geometry of our section

It is important to check the units while creating elements and entering the section properties. We can set units by searching for this option from search tab.

3. The SLS Combinations are combination of loads used for serviceability checks such as deflections, stress limits, crack width limits etc.

The SLS Combinations for Live load is DL +1.2 SIDL + 1.1 LL I

Here I is the impact factor for live load. I = 1 + [ 0.15 + 8/ (6+L) ] . Here L is span Length. The given formular is for Broad Gauge and a velocity correction factor is used to derive the actual Impact factor for metri based on design speed for given metro.

For caculating the moments for a given section the DL, SIDL & LL moment derived from the analysis are added as per the Combination formula. This can also be done in Staad by creating a load combination which will directly give the results for SLS combination under consideration.

4. Prestressing of Girders in application of compression to the concrete with use of hightensile steel in order to compensate for the tensile stresses generated in the concrete girders due to various loads such as DL,SIDL,LL. With the use of pre-stress the complete concrete section gets well utilized in resisting the load. Unlike in case of RCC girders the strenght of concrete in tension zone needs to be neglected. Pre-stressing of girders can be done as pre-tensioning or post tension. In both the methods the pre-stressing force at any given section of girder can be controlled and planned acoording to the bending moment in the section which makes is further more efficient.

In case of Pre-tensioned girder the pre-stressing can be controlled with help of bonded and unbonded tendons. In case of Post-tension girder the pre-stressing can be controlled with the help of Cable profile.

With use of complete section of concrete section the superstructure depth are optimum which is a major advantage in metro projects due to various crossings and height restrictions etc. Also the section becomes light and this helps in erection of superstructure in metro projects.

5. The pre-stressing force applied to the girder may not be fully available during the lifetime of structure. This force gets reduced and the reduction in this force is called pre-stress loss. There are 2 types of losses i. Immdediate losses which occur immediately after application of pre-stress and ii. Time Dependent/Long Term losses which happen based on the time lapsed after application of pre-stress.

a. Immediate losses are due to - i. Elastic Shortening of Concrete - This happens as concrete is elastic material and deforms under load. This deformation relaxes the steel cable and leads to pre-stress force loss.

ii. Anchorage Slip loss - This happeds in case of post-tension concrete where the Anchorage of Pre-stress cable undergoes certain slip before getting locked into the final postition. As there is slipage in anchorage there is proportionate relaxation in the pre-stress force which leads to loss of force.

iii. Frictional Losses in post-tensioned girder- These losses occur due to the friction which is geenrated between the ducts and strands. Due to this the Pre-stress and live gets reduced till the time it reaches dead end of a cable. This is function of coefficient of friction and also the profile of cable.

b. Time Dependent Losses are due to - i. Creep of Concrete - The creep of concrete i.e deformation under stsustained load leads to shortening of concrete and this leads to loss of pre-stress force.

ii. Shrikage of Concrete - Shrinkage of Concrete also leads to shortening of concrete and leads to loss of prestress force

iii. Relaxation of Pre-stressing Strands - The high tensile pre-stressing steel also undergoes some relaxation under sustained load and this leads to loss of pre-stress.

These types of losses occur in pre-tensioned as well as post-tensioned girders.

The losees in pre-stressed girders are - Elastic Shortening of Concrete, Creep & Shrinkage of Concrete, Relaxation of Steel

The losses in Post-tensioned girders are - Elastic Shortening of Concrete if the stagewise post-tensiong of cable is done ( Elastic shortening losses can be avoided if all the cables are stressed simultaneously), Creep & Shrinkage of Concrete, Relaxation of Steel, Anchorage Slip Losses, Frictional Losses

6. The pre-tensioned girder are pre-stressed during fabrication or casting. For the purpose a casting bed is set up. With two ends which are anchor ends for strands. The casting bed is made of RCC concrete. At one ends provision of dead end of strands in made. At the other end the provision for jack and its supporting live end is made. This end anchor points are generally made with steel beams or brackets.

In the middle portion of two anchor ends, the shuttering of girders is fixed and strands are passed through shuttering at desired positions as per strand geometry. The bonded and unbonded lengths are planned. The unbonded lenght of strands are provided with 20mm dia HDPE Rigid pipes. The space in strands and pipe are to be filled with greese as per ASTM. The end of the strands are to be sealed with epoxy mortar. At junction of fixed length to unbonded length effective seal against slurry incress shall be provided.

Initital all the strands are placed in position with shuttering and reifnrocement of girder. Then the strands are stresses using jacks. After stressing of strands the girders are concreted. The strands are cut after attainment of transfer strength of concrete is achived. After cutting of strands, necessary corrosion protection or grouting is done on ends.

In case of post-tensioned girder the girders are cast with cable ducts on casting bed made of RCC concrete. After attainmenet of strength of concrete the cable can be stressed to apply prestress. This can be done in stages. First stage can be for resisting the loads due to self-weight during handling and second stage stressing can be for SIDL and other service loads. Cable Stressing Hydraulic Jacks are used for applying pre-stress.

7. The resultant pre-stress losses are calculated for various components such as shrinkage & creep, elastic shortening, friction losses, anchorage slip losses based on the applicability for the type of girder system.

The losees for pre-tensioned systems are generally 15% to 20 % and or post-tensioned system these are generally 18% to 23%.

The applied prestress for given cable is generally 75% to 80% of Braking strenght of cable based on various codes.

The prestress load after losses is calculated and then this is applied to the given section at the C.G. of Cables/Strands.

The resultant stress is calculated as Stress = P/A +/- Pe/Z

Here P is the total pre-stress after losses, A is the total cross-section area of the Concrete girder.

e is the distance between C.G. of Concrete Section to the C.G. of cables/Strands in the direction under consideration.

P.e is the moment applied on to the section due to pre-stress.

Z is the section modulus in direction under consideration Ix/ymax or Iy/xmax.

8. The transvrese analysis of open web structure of U-Girder is carried out in staad by use of plate elements. Following are the steps involved in modelling and analysis of U-Girder:

a. Finalize the geometry of the cross-section of U-Girder. The modelling of girders is done at Centerline of cross-section elements like flanges, webs and soffit slab. Hence defined the geometry of celterline of U-Girder cross-section.

b. Create the nodes at desired location as per the centerline geometry of the U-Girder. Translate the nodes as per the desired size of plate elements.

c. Create the plate elements by connecting the nodes. Follow similar orientation/sequence while creating the plate to maintain the uniformity in the local axes of the plates. This uniformity helps in load application and result extraction.

d. After creating the plate for a typical lenght of U-Girder Section, use translate plate command to create the remaining length of the U-Girder Section. The length beyond the bearing can be created by generating nodes and creating plates as per the geometry of section.

e. The various plates are assigned thicknesses as per the location of the section and actual thicknesses. The plates with varying thickness can be created by provided different values of thickness at 2 pair of nodes as per thickness variation in actual section.

f. The standard support conditions are assigned at bearing locations.

g. The Dead Load is applied as self weight to the plates. The SIDL is applied to the plates as pressure load. This is applied by providing the the co-ordinate the the load at location of rails as per geometry of structure.

f. The live load of the train is applied at critical loadtions of the axles as derived from the longitudinal analysis. These are also applied as pressure loads on plates.

g. The analysis is carried out for the U-Girder span under consideration.

h. The results for the critical sections are extracted. The various plates are grouped according to thier locations. While extracting the results we need to select only the group under consideration. And from the summary tab we can extract the maximum forces. The local axes of the plates shall be carefully checked before extractig the results. For transverse analysis results the moment in transverse direction shall be extracted.

i. These extracted value for SLS and ULS cases are then used for section check under SLS & ULS. This can be carried out with excel sheets or softwares. With this the reinforcement at top & bottom of any section can be designed. The ULS checks the section moment capacity. The SLS checks Stress limitation in Concrete, Steel and allowable Crack Widht of Section.

9. The longitudinal analysis of the U-Girder is carried out by using line elements.

The line model of a given U-Girder span is created.

The Section properties of the U-Girder are applied to the elements.

The Dead Load is applied as self weight. The SIDL is applied as ULD on the line element.

For live load a vehicle is defined with axle loads and axle spacings as per the DBR. This vehicle load is run along the span to cover all the possible cases of live loads on the span.

The load combinations are generated as per codal provisions.

After analysis the critical moments and forces for given elements and given Load combinations are extracted by selecting the same.

These moments are used along with the pre-stress loads after losses to calculate the stresses in the girder under various load comabination along from various section properties.