Challenge

Challenge 4

Aim: Prepare a longitudinal model of I-girder and analyse for all the loads with following specifications.

Introduction:

Given Data of girder are

  1. Grillage model of 4 I-girders with span length of 27.0m.
  2. Having supports at 0.700m from both ends.
  3. Having following geometrical properties:

End Section: Area = 1.218m2

Iy = 0.32541m4

Iz = 0.05129m4

Mid Section: Area = 0.87702m2

Iy = 0.27835m4

Iz = 0.02622m4

4. Having material properties: Concrete, M60 grade

Other data's are assumed.

Procedure: Preparation of STAAD Model

Step 1: Create Nodes with span length of 27m.

Step 2: Join the Nodes to create Beams:

Step 3: To create 4 girders Translational Repeat is used in Z-direction with c/c spacing =2m

Step 4: Create internal diaphgrams at 2m distance in X-direction (assumed)

Step 5: Assign Supports:

i) Where all the moments are released

ii) To allow longitudinal movement we release FX in next support

iii) To allow transverse movement we release FZ

iv) We add roller support in X-Z plane

Step 6:Creating properties of girder and diaphgrams

Concrete is M60 therefore Compressive strength = 5000fck^0.5= 5000(60)^0.5=38729.83MPa , For Diaphgram

Step 7: Define Sectional Properties for I-girder

i) End Section

ii) Mid Section

iii) Tapering Section between end & mid girder (Avg of both)

Step 8: For Assigning Loads-->

i) Deadload--> S/W -1

ii) 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

Step 9: Applying moving loads For LiveLoad

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 DeadLoad:
Bending Moment for SIDL:
Bending Moment for Live Load:

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 = 11047.52+1.2*7603.13+1.45*1152 = 21841 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 =21841 kNm

Therefore, Stress @ bottom of girder = 1.12 n/mm2 (Since the resultant stress is positive it is compressive, as to avoid tension we are providing tendons)

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