Challenge 9

Q1)Explain in detail the steps involved in calculation of the loads considered in piers.

Answer:-

• Pier is a component which basically carries compression member of the bridge or convert all types of load into direct compression & transfer it into the piles.
• Piers support the superstructure of the bridge by transferring the load to the foundation.
• They are subjected to loads like Bi-axial moment in both longitudinal and transverse direction. Axial loads and shear force.

Following are the details of the Loads considered in piers:

• Dead Load:
  • This load plays the most important role majority comprises dead load (selfweight) of the superstructure and substructure.
• Superimpose Dead Load:
  • This load majority comprises the dead weight of super imposed dead load like track load, track base, cable trays, handrails, parapets etc.
• Live Load:
  • This load basically the train load that runs on the superstructure.

• Four Cases of train loadings
  • One Track One Side Loaded (OTOS)
  • One Track Both Side Loaded (OTBS)
  • Both Track One Side Loaded (BTOS)
  • 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 locations spans.
  • It is calculated with the actual maximum allowed speed of the train in a curve according to the planned radius of curvature.

Coefficient of CF = xR

• Wind Load (without Live Load):
  • This type of load exerted 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 kind of load acts on the structure 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 type of load acts on the structure 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.

Ans:-

Seismic Check

Seismic Calculation
Seismic Acceelaration -
	Ah	=	(Z/2) * (I/R) * (Sa/g)
		Ah	= Horizontal seismic co-ifficient to be considered in design
		Z	= Zone Factor
		I	= Importance Factor
		R	= Response reduction factor
			= 4 , For Pier
	Sa/g being computed as per /iRC 6:2017 fir medium Soil sites.
	Mathematical expressions are:
	Sa/g	=	1 + 1.5T for		0.0 < T < 0.10
	Sa/g	=	2.5 for		0.10 < T < 0.55
	Sa/g	=	1.36/T for		0.55 < T < 4.00

Shear Check for enhancement factor

Shear Stress Enhancement Factor,					d =	1+0.05P
						Ac
	Where,
	P	=	Ultimate axial loads in Newton		=	7577780	N
	Ac		Area of entire concrete section in mm2		=	2269801	mm2
	Fck				=	50	N/mm2

Taking an example

Shear Stress Enhancement Factor,

d =

1.167

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

Then it need to be checked wheather shear reinforcement is required or not. Then the following conditions need to be checked accordingly.

Shear Reinforcement
1.	If V <= S Vc			Asv	=	0.4*b*Sv/0.87*fy
2.	If V > S Vc			Asv	=	b*Sv*(V+0.4-SVc)/0.87*fy
Where,
ASV	=	c/s area of all the legs of the stirrup/links at a particular cross section
Sv	=	Spacing of the stirrups along the member
b	=	Breadth of the section

Confing Reinforcement (For Circular Section)
Max of
	Ash	=	0.09 x S x Dk x (Ag/Ac-1) x fck / f y
	or
	Ash	=	0.24 x S x Dk x fck/fy

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
As per Cl 15.6.5 of IRS CBC, A slender column of constant cross section shall be designed for its ultimate axial load, P, together with the moment, Mty
	Mty	=	Miy +	Phx	(Ie/hx)2	(1-	0.0035Ie	)
				1750			hx
	Mty	=	Miy + P x e
Additional Moment, Me (=P xe)						P x e