Challenge 9

Aim:-

Que (1):- Explain in detail the steps involved in the calculation of the loads considered in piers.

Answer:-

- Pier is the compression member of the bridge

- They support the span ( superstructure) of the bridge by transferring the load to the foundation.

- They are subjected to massive loads like

• Axial loads and shear force
• Bi-axial moment in both longitudinal & transverse direction

Load Consideration

• Dead Load:

- This load majority comprises of self - the weight of the girder, pier caps, and pier.

• Superimpose Dead Load:

- This load majority comprises the weight of track plinth, rail, cable, cable trays, cable trough, handrails, parapets, etc

• Live Load:

- This load comprises the train ( rolling stock) live load that runs on the superstructure.

1. One track one side Loaded (OTOS)
2. One track with both sides Loaded (OTBS)
3. Both track one side Loaded (BTOS)
4. Both track both sides Loaded (OTOS)

• Breaking Load:

- This load comes into play when the train applied brakes while moving.

- It is taken as 18% of the unfactored vertical load.

• Traction Load:

- This load comes into play when the train starts to accelerate from rest.

- It is taken as 20% of the unfactored vertical loads.

• Centrifugal Force:

- This load acts on curved spans.

- It shall be calculated with the actual maximum allowed speed of the train in a curve according to the planned radius of curvature.

- Coefficient of CF = `V^2/(127 xx R)`

• Wind Load ( Without Live Load):

- This load comes into play when wind exerted load on the structure.

- In this case, the wind pressure will be very high, making it quite difficult to move the live load.

• Wind Load ( With Live Load):

- This load comes into play when wind applied forces on the structure.

- In this case, the wind pressure will be normal, allowing the movement of live load.

• Vz = Vb x K1 X K2 X K3

- where Vb (m/s) is the regional basic wind speed.

• Earthquake Load ( In Longitudinal Direction):

- This load comes into play during an earthquake when the structure vibrates in the longitudinal direction.

- Live load is not considered in the case as vibration doesn't have any impact on the live load as it rolls away.

• Earthquake Load ( In Transverse Direction - With live load):

- This load comes into play during an earthquake when the structure vibration is in the transverse direction.

- Live Load is considered in the case as the live load will be restrained to move in the transverse direction and would thus vibrate along with the structure.

• Earthquake Load ( In Transverse Direction - without live load):

- This load comes into play during an earthquake when the structure vibrates in the transverse direction

- In this case, the live load will not be present on the structure.

• LWR Force:

- The " Long welded rail" force acts on the structure to stress generated in the rail.

- It is generated by the expansion/contraction of rail due to an increase/decrease in temperature.

- LWR force is considered to be 0.8t|m|track.

• Derailment Load:

- This load comes into play when the live load gets derailed.

- In this case, the live load may get off the track & slide to the edge of the structure, or the live load may derail and topple on the edge.

Que (2):- Elaborate the design codal provisions for piers of metro viaducts.

Answer:-

Shear Checks

Shear stress enhancement factor:

• d = `(1+0.05 P)/(Ac)`

Where,

• P=ultimate axial load in newtons
• Ac=area of entire column section in mm^2
• Fck=characteristic compressive strength of concrete.

According to table 15 of IRS-CBC 1997 ultimate shear stress in concrete as per percentage area of tension reinforcement and grade of concrete.

Ultimate shear stress ,Vc = 0.767 N/mm2

Depth factor, S = 0.799

Enhanced ultimate shear strength of concrete, S x Vc x d = 0.715 N/mm2

Shear reinforcement is required if V>S x Vc x d

If V<=Vc x S, Asv =0.4 x b x sv/0.87xfy

If V>S x Vc, Asv =b x Sv x (V+0.4-SVc)/0.87xfy

Where,

• ASv = C/S area of all the legs of the stirrups/links at a particular C/S.
• Sv = Spacing of the stirrups along the member.
• B = Breadth of the section.

Confining reinforcement (for circular section)

Ash = 0.09 x S x Dk x (Ag/Ac-1) x Fck/fy

or

Ash = 0.024 x S x Dk x fck/fy

Take the maximum value from above.

Where,

• Concrete grade (fck)
• Reinforcement grade (fy)
• Dia of the pier (D)
• Clear cover on either side (c)
• Dia of pier core (Dk)
• Area of concrete core (Ac)
• Gross area of pier section (Ag)
• Pitch of spiral (S)

P-delta effect

Effective Length Calculation

• Diameter of the pier, d
• Cantilever Height of pier, Lo
• Effective Height of pier, Le ( = 2.3 x Lo)

Additional moment due to slenderness ratio effect

Slenderness ration, Le/d ( as per Cl 15.6.1.1 of IRS CBC)

As per the below clause

Additional momemnt, Me = P x e