Challenge 3

Ans 1

Sectional properties required for designing a metro viaduct:-

1. Cross sectional area of the girder

2. Centre of Gravity (C.G) of the section

3. Moment of Inertia about major and minor axis

4. Sectional modulus of the section

AutoCAD software from Autodesk can be used as a supporting software to arrive at the sectional properties of a metro viaduct girder. This is mainly since the shape of U-girder or box girder is non-standard and hence deriving the sectional properties by traditional methods can be cumbersome and time consuming.

Ans 2

Steps involved in creating elements in Staad Pro:-

Step 1: Note the dimensions between the two end nodes of the structure as per actual. Engineer needs to note the centre to centre between bearings as well as offset outside bearings towards pier centreline for exact girder end support nodes. Create the nodes in Staad as per this data in global X-direction from the GEOMETRY tab. After creating the nodes check its correctness by measuring node to node distance to avoid any error and be sure.

Step 2: In GEOMETRY tab, using the ADD BEAM command, connect the 2 nodes between which we want to create a beam and an element will be formed. Other options to add beams can be found in the translational repeat command if similar existing beams need to be added in the model or we can directly enter the 2 node numbers connecting the beam in the beam table to create a beam.

Step 3: For assigning the sectional properties to the elements created, there are multiple options in the PROPERTIES tab. Options are available from the in-built SECTION DATABASE as per numerous codes. Also we can DEFINE a section whether circular, rectangular, T-beam, trapezoidal, general, etc. For the case of metro viaduct, we have to assign properties using the DEFINE-GENERAL command and assign the sectional properties derived from AutoCAD by converting the same as per Staad Pro Units.

Ans 3

SLS (Serviceability Limit State) are combinations of loads where design criteria related to deflections, crack widths, etc are checked.

For Live Loads and SIDL, the SLS Combination 1 = 1.0*DL +1.2*SIDL + 1.1*LL*I

where, I (Impact factor for live load) = 1 + [ 0.15 + 8/(6+L) ] and L = span length.

Above formula is for broad gauge and a velocity correction factor is used to derive the actual Impact factor for meter gauge based on design speed of metro.

In STAAD Pro, the above SLS combination can be assigned in Load Combination command after the individual dead loads, SIDL and Live Loads are applied to the metro viaduct elements. Post analysis, the maximum bending moment values can be found in the RESULTS / REPORTS tab for the said combination.

Ans 4

Prestressing in girders means the application of eccentric axial compressive force to a concrete cross section such that it creates a stress distribution opposite to the stress distribution of the girder in service stage (SIDL, LL, etc). Compressive forces are applied with the use of hightensile steel tendons and jacking. Pre-stressing can be done in two methods - pre-tensioning or post tensioning.

Advantages of prestress:-

1. Since the permanent loads are known, we can pre determine the amount of prestress required to resist these loads and the section can thus get better utilized.

2. The qualtiy of the girder is far better as the prestress is applied before the girder goes into service and hence issues if any during inspection can be rectified at the time of casting itself.

3. As compared to RCC section where engineer needs to neglect the concrete strength in tension zone, a pre-stressed concrete section can be used effectively, thus the depth of the girder is reduced.

4. Lesser depth of girders leads to reduction in weight and subsequently the cost and time of erection and casting at site.

5. Pre-stressing in pretensioned girder is done by bonded and/or unbonded tendons whereas in post-tensioned girder by profiling the cables.

Ans 5

Pre-stressing losses means the reduction in the prestressing force of a girder after its application due to different reasons listed below. The initial prestress force is never available during the service life of a girder.

Following are the classification of losses:-

1. Immediate losses - occur immediately after application of pre-stress force

2. Time dependent losses - occur in due course of time when the girder is in service

Immediate losses are as follows:-

Elastic Shortening of Concrete - When the pre-stressing steel strands in the concrete girder are pulled by jacks for applying compression to the concrete, the concrete cross section along with the strands starts to deform due to its elastic property. This phenomena in turn causes the strands to relax and this leads to loss of pres-stress force.

Anchorage Slip loss - As the name suggests, this loss is due to the slipping of anchors/wedges in case of post-tensioning. The anchors/wedges need to get locked after the strands are pulled by the jacks. Before getting locked into the final postition, there is slippage in these wedges/anchors and hence a loss of pre-stressing force equivalent to it.

Frictional Losses - The steel strands (cables) are laid inside the ducts in the concrete section. At the time of stressing of the cables, there is friction between cables and ducts due to physical contact and thus the pre-stress force gets reduced as it travels through the cables till it reaches the other end. Depends upon co-efficient of friction and cable profile.

Time Dependent losses are as follows:-

Creep of Concrete - Deformation of concrete cross section under the action of persistent loads leading to shortening of concrete and this leads to loss of pre-stress force.

Shrikage of Concrete - The contracting of a hardened concrete mixture due to loss of capillary water. This causes an increase in tensile stress and leads to loss of prestress force.

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.

Ans 6

Prestressing - Pretension: Pre-tensioned girders are pre-stressed before casting starts.

1. RCC casting bed is constructed onto which two anchor ends are set up for stressing strands. At one end, provision of dead anchor is designed while at the other end provision for jacking is designed (live end). Generally, ends are designed as structural steel brackets and beams.

2. Between these two ends, the reinforcement bars are tied in such a way that strands pass through them as per the designed cable profile and shutters of the girder are erected. Further, HDPE pipes (lubricated from inside) are used for the end portion length of the cables which are desired to be unbonded.

3. Once shutter geometry is checked, strands are stressed using jacks and only then girders are concreted.

4. Strands at ends are cut after attaining transfer strength of concrete before grouting (epoxy) is done at ends.

Prestressing - Post tension: Post-tensioned girders are pre-stressed after casting is completed.

1. Girders are cast in casting yard with cable ducts laid inside the shutters and reinforcement on an RCC casting bed.

2. After attainment of required strength of concrete as per design, the cable can be stressed.

3. Application of prestress can be achieved in stages.

- 1st stage stressing force calculation can be to resist moments due to selfweight and deck slab during handling and erection.

- 2nd stage stressing force calculation can be to resist moments due to other SIDL and Live Loads.

Materials used: High tension strands, HDPE pipes, Jacks, Wedge plates, Bearing plates, epoxy grout, etc.

Ans 7

Resultant pre-stress losses viz. creep, shrinkage, elastic shortening, anchorage slip, etc. are calculated.

Losses for pre-tensioned systems are 15% and for post-tensioned systems these are generally 20%. This loss of force is calculated and then this is applied in addition to the desired force for moments at the C.G of cables.

Stress in section = P/A +/- Pe/z

P = Pre-stressing force considering the losses,

A = cross sectional area of concrete,

e = eccentricity (dist. between C.G. of concrete section and C.G. of cables)

z = section modulus generally about major axis.

Ans 8

In STAAD Pro, transverse analysis of open web U-girder is done by modelling it as plate elements.

1. Create the nodes at centerline of U-Girder and then translate the nodes in X-direction or Z-direction.
2. Add plate elements by connecting the nodes. While doing so, maintain the plate orientation such that there is uniformity in its local axes which will help during applying the loads. Also create plate beyond the bearing as per geometry.
3. Further, assign plate thickness to the 4 different plate nodes as per the actual cross sectional thickness.
4. Bearings are assigned supports as per the standard rule for simply supported metro bridges.
5. Loads are then assigned as per follows - Dead Load = selfweight command, SIDL = floor load command, Live load = most critical case of the vehicle loads in the longitudinal analysis as static load in transverse analysis.
6. Run the analysis and extract results.
7. Since the plates are correctly oriented during the geometry creation, maximum moments/forces/stresses in these plates for transverse bending can be viewed and if required can be designed in separate groups.
8. Concrete and reinforcement to be provided while checking strength parameter in ULS and service parameters in SLS

Ans 9

Longitudinal analysis of the U-Girder is carried out in STAAD Pro software by modelling the girder as a line element:-

1. Add nodes at opposite bearing centres and also add nodes for the small offset outside the bearings. Connect these nodes by line elements to form a beam as per the longitudinal bridge geometry.

2. Add section properties of the U-Girder to the element in the properties tab by using DEFINE command (AutoCAD can be used for extracting properties).

3. Dead Load = SELFWEIGHT command, SIDL = Uniform Distributed Load (UDL) on beam for required length.

4. Live load is defined initially as a VEHICLE LOAD with fixed magnitude and wheel spacing as per the agreed and approved DBR. The start point of this vehicle load is defined and then load generation command is used to calculate the number of moving loads as per the steps and total span length.

5. Other transverse loads such as wind, seismic, etc. are also applied to the beam in global Z-direction.

6. Load combinations are generated as per codal provisions and the model is run, results extracted.

7. Select the beam element - go to results - go to reports - select Mz (max sagging)- select the desired ULS load combinations - get the maximum bending moments.

8. Select the beam element - go to results - go to reports - select axial force - select the desired ULS load combinations - get the maximum compression/tension.

9. The extracted results are used in the pre-stress equation P/A +/- Pe/z to calculate stresses (after losses) in the girder under respective load combination.