Challenge 4

Procedure: Preparation of Staad model

Open Staad pro and create 1st node at 0,0,0 (X,Y,Z = Longitudinal,Vertical,Transverse)

Since the support is at 0.7m from both ends, nodes are created as at respective nodes and last node at 27m as span length is 27m

Now for creating 4girders translation repeat is used in Z direction

c/c spacing of girder = 2m(assumed)

Now we create internal diaphragms at 2m distance in X direction

Now lets assign supports

To allow longitudinal movement we release FX in next support

To allow transverse movement we release FZ in next support

Now assigning roller support for free movement in X-Z plane

Now creating properties of the girder and diaphragm

Concrete is of M60, therefore compressive strength = 5000(fck)^0.5 = 5000(60)^0.5= 38729.83 MPa

Creating Null property for diaphragms as these are to be modelled for as only connecting members and not of structural importance

End Girder property

Mid girder property

Tapering section property b/w end and mid girder(Average of both)

Diaphragm property

Now calculating and assigning loads to the girder

DEAD LOAD

It is assigned as self weight with factor Y -1 as we have given properties to the girder.

SIDL

Applied as 8.34kN/m - Load of plinth/deck, rails & rail pad

23.5 kN/m - Load of parapet

As parapet is in end, we take into consideration moment generated due to parapet - Cg of parapet = 0.5m Therefore moment = 23.5*0.5=11.75kNm

For Live Load we first define vehicle of metro, since span is 27m we define 2 bogies

Now generating moving load

No.of Load generations = (Length of vehicle + Length of span) /increment = (2.3+12.4+2.3+4.4+2.3+12.4+2.3 + 27)/0.25=261.2

Two trains are running one on left side and one on right side

Now run analysis

Results:

As the girder is simply supported beam, maximum bending moment will be at the centre of beam

Considering 1st girder beam No.60(centralbeam for design)

Summary of forces

Bending moment for DL

Bending moment for SIDL

Bending moment for LL

SLS LOAD COMBINATION = DL+1.2*SIDL+1.1*LL*I

I=Impact factor

Impact factor CDA as per IRS bridge rules will be 0.15+8/(6+L) = 0.15+8/(6+25.6) = 0.403.

Now this CDA is for broad guage as per IRS we have to calculate it for metro.

Speed for metro is 90km/hr whereas for Broadguage it is 116 km/hr

Therefore impact factor will be 0.403x(90/116)=0.313

Impact factor x Live load factor = 1.313 x 1.1 = 1.45 = factor for live load in SLS combination

Moment = 1725.9+1.2*1635.6+1.45*1152 = 5359.02 kNm

This moment is used for design

Prestress design

No.of cables =4

No.of strands (n) = (7 strands in 3 cable + 8 strands in 1 cable)= 7*3+8=29

Prestressing force applied (P) = 0.765fpu x As x n x (1-loss) / 1000 kN

fpu = Nominal ultimate stress = 1860 MPa

Maximum jacking stress = 0.765 fpu = 0.765 x 1860 = 1422.9 MPa

As = Area of strand = 140mm2

Assume loss of 17.5%

Prestressing force (P) = 4766 kN

Stress @ bottom of girder = Compressive stress due to tendons - tensile stress due to external loading

= ( P/A + P.e/Z) - (M/Z)

Z = I/y = 1.24m3

A = Sectional Area of girder = 1.04 m2 (Average)

P = 4766 kN as calculated above

e = centre of gravity of girder section @ bottom of girder- centre of gravity of tendon @ bottom of girder = 0.454m

M = moment of SLS combination from longitudinal analysis for DL, SIDL & LL combination = 5359.02 kNm

Therefore, Stress @ bottom of girder = 1.97 n/mm2 (Since the resultant stress is positive it is compressive, as to avoid tension we are providing tendons)