Challenge 9

Aim:

Q1)Explain in detail the steps involved in 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
• Bi-axial moment in both longitudinal and transverse direction.
• Axial loads and shear force.

Following are the Loads considered in piers:

• Dead Load: 

      - This load majority comprises of selfweight of girder,pier caps and pier.

• Superimpose Dead Load: 

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

• Live Load:

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

      There are four cases:

      a. One Track One Side Loaded (OTOS)

      b. One Track Both Side Loaded (OTBS)

      c. Both Track One Side Loaded (BTOS)

      d. Both Track Both Side Loaded (BTBS)

• Breaking Load:

     - This load comes into play when the train applies brake 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 xR`

• 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 structures.

     - 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 0.8 t/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.

Q2) Elaborate the design codal provisions for piers of metro viaducts.

Answer:-

Shear Checks

Shear Enhancement Factor:

• d= 1+0.05P / Ac

     where,

• P = ultimate axial load in newtons
• Ac=area of entire column in mm^2
• fck=characteristics 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 sc/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 legs of the stirrups/links at a particular C/S.

-Sv= Spacing of the stirrups along the member.

-B= Width 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 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 ratio, Le/d (as per Cl 15.6.1.1 of IRS CBC)

   As per the below clause

  

Additional Moment, Me= P x e