Week 5 Challenge

1. Basic Design Data: ( For Pier  Foundation) using IRC:6,112,78

Basic Designdata: -
Span and Cross Section Data
C/C of expansion gap@ Left Span				=	13.30	m	(Sq.)
C/C of Bearing@ Left Span				=	12.30	m	(Sq.)
Distance of Bearing to expansion gap @ Left Span				=	0.50	m	(Sq.)
Girder Overhang beyond bearing@ Left Span				=	0.35	m
C/C of expansion gap@ right Span				=	13.30	m	(Sq.)
C/C of Bearing@ right Span				=	12.30	m	(Sq.)
Distance of Bearing to expansion gap				=	0.50	m	(Sq.)
Girder Overhang beyond bearing@ right Span				=	0.35	m
Carriage way width				=	11.00	m
Total Width				=	12.00	m
No of Longitudinal Girders				=	4.00	Nos
C/C spacing of the  Longitudinal girder				=	3.00	m
Footpath width (left Side) or Parapet				=	0.50	m
Footpath width (right Side)				=	1.50	m
Crash Barrier (Left Side)				=	0.50	m
Crash barrier (Right Side)				=	0.50	m
CG of Crash Barrier				=	0.373	m
Handrail width (Left Side)				=	-	m
Handrail (right Side)				=	-	m
Wearing Coat thickness				=	0.065	m
Super-Structure Details:
Depth of Superstructure @Left Span				=	1.320	m
Depth of Superstructure @Right Span				=	1.320	m
CG of Super-structure from @Left Span				=	0.880	m
CG of Super-structure from @Right Span				=	0.880	m
Height of Crash Barrier				=	0.900	m
Bearing Thickness (Max)				=	0.065	m
Height of Pedestal				=	0.250	m	Min
Expansion Joint				=	0.040	m
Skew Angle				=	-	o	00.00 radians
Super_Elevation/Camber				=	2.50%	m
Type of Super-Structure				=	RCC Girder & Deck
Typical Levels:-
Formation Level FRL			FRL	=	230.115	m
Bearing Level			BRL	=	228.458	m
Pier Cap Top Level			CTL	=	228.143	m
Footing top level			FTL	=	217.262	m
Footing bottom level			FBL	=	216.262	m
Lowest Bed Level			LBL	=	224.178	m
Max. Scour Level			MSL	=	218.262	m
Height Flood Level			HFL	=	227.105	m
Lowest Water Level			LWL	=	224.178	m
Founding Level (Actual)			FL	=	216.262	m
Founding Level (Actual)			FL	=	216.260	m
Water Current Data
Max. Mean Velocity				=	0.98	m/s
Constant K for Pier in transverse Direction				=	0.66
Constant K for Pier in Longitudinal Direction				=	1.50		Cl.210.2,IRC:6-2014
% of Uplift Considered				=	100%
Material Data:-
For Pier Cap, Pier & Footing
Grade of Concrete			fck	=	M 35
Design strength of Concrete			fcd	=	15.63	MPa	(Cl.6.4.2.8,IRC:112-2020,Page-38)
Modulus of elasticity  of steel			Es	=	2.00E+05	MPa
Modulus of elasticity  of Concrete			Es	=	3.20E+04	MPa
Mean Axial Tensile strength of concrete			fctm	=	2.80	MPa
Grade of steel			fyk	=	Fe 500
Design strength of Steel			fyd	=	434.78
Density of concrete				=	2.50	t/m3	Cl.203(6),IRC:6-2010
Density of wearing coat				=	2.20	t/m3
Co-efficient of thermal expansion of concrete				=	1.20E-05	/oC	(Cl.215.4,IRC:6-2014)
Shrinkage Strain for Concrete				=	2.00E-04		(Cl.217.3,IRC:6-2014)
Soil Parameters:-
Angle of shear resistance “				=	30	o
Density of dry backfill “				=	2.00	t/m3
Density of submerged backfill, “				=	1.00	t/m3
HFL Case
Net Bearing Capacity at founding Level				=	25.00	t/m2
Gross  bearing capacity				=	29.00	t/m2
Net Safe Bearing SBS Seismic Case				=	31.25	t/m2
Gross Bearing SBS Seismic Case				=	33.25	t/m2
LWL Case
Net Bearing Capacity at founding Level				=	25.00	t/m2
Gross  bearing capacity				=	40.84	t/m2
Net Safe Bearing SBS Seismic Case				=	31.25	t/m2
Gross Bearing SBS Seismic Case				=	33.25	t/m2
Type of soil				=	Medium Soil
Co-efficient of friction between the.				=	0.50
Load Data:-
Deal Load@ Left Span
Total Weight of Super-Structure				=	199.00	t	From staad
Deal Load@ Right Span
Total Weight of Super-Structure				=	199.00	t	From staad
SILD ( Excluding wearing Coat)
Self- weight of Crash Barrier				=	1.0	t/m
Self- weight of Railing/ Parapet(One Side)				=	-	t/m
Transverse eccentricity of crash barrier (				=	-	m
Transverse eccentricity of Railing or Para				=	-	m
Transverse eccentricity of Railing or Para				=	-	m
Transverse eccentricity of footpath/servic				=	-	m
SILD ( Including Wearing Coat)					-
Load intensity due to wearing course				=	0.14	t/m2
Transverse eccentricity of wearing course				=	-	m
FPLL:
Maximum intensity of footpath live load				=	500.00	kg/m2	Cl.206.1,IRC:6-2014
Live Load: - Cl 205, IRC:6-2014
Both Span Loaded
1 lane 70 R- wheeled
Left Span				=	41.80	t
Right Span				=	34.80	t
1 Lane Class -A
Left Span				=	9.50	t
Right Span				=	25.20	t
One Span Loaded
1 lane 70 R- wheeled
Left Span				=	-	t
Right Span				=	61.00	t
1 Lane Class -A
Left Span				=	-	t
Right Span				=	28.80	t
Reduction %				=	90%		Cl.205,IRC:6-2014
Fraction Live Load remaining in seismic case				=	1.00		For 11 m CW 3 lane is possible
Factor by which seismic force should be increased for foundation design				=	1.35		IRC:6-2014,Cl.218.8
Wind Load Data
Basic Wind Speed				=	50.00	m/s
Type of terrain				=	Plain Terrain
Parameter  for wind force on super-structure ( Except truss)						Cl.209.3.3 to 209.3.5,IRC:6-2014
		For DL+SIDL	For LL
Gust Factor,G		2.00	2.00
Drag Co-efficient,CD		1.30	1.20
Lift Co-efficient,CL		0.75	-
Parameters for wind force on sub-structure
For Pier Cap
Gust Factor			G	=	2.00		Cl.209.3.3,IRC 6-2020,P-35
t/b				=	4.59		Pier cap-Tranverse length/Pier cap Longitudinal Length
Height/ Breadth				=	0.341
Drag, Co-efficeint			CD	=	1.20
For Shaft
Gust Factor			G	=	2.00
Height/ Breadth				=	12.859
Drag, Co-efficeint			CD	=	1.20
Bearing Data:-
Type of bearing				=	Elastomeric
Elastomeric Bearing: -
length (Along traffic dim.)			l	=	500.00	mm
width (Perpendicular to traffic)			b	=	250.00	mm
Thickness of each elastomer			hi	=	10.00	mm
ber of internal elastomer layer			n	=	4	Nos
Thickness of Outer elastomer layer			he	=	6	mm
Thickness of steel plate			hs	=	3	mm
rall thickness of bearing			ho	=	65.00	mm
ar cover to steel plate (Vertical)			he	=	5.00	mm
of Steel plates			n	=	5.00	Nos
Effective thickness of the elastomeric bearing			heff	=	50.00	mm
ar modulus			G	=	1.00	Mpa
of bearing over pier on support line			n	=	8	Nos
Pier Cap Dimension
Rectangular Part
Length (T_T)				=	10.10	m
Length (L_L)				=	2.20	m
Height				=	0.25	m
Trapedoidal  Part
Length (T_T)				=	8.50	m
Length (L_L)				=	0.60	m
Height				=	0.50	m
Pier Shaft
Dimension along Traffic				=	0.70	m
Dimension Perpendicular to  Traffic				=	8.50	m
Foundation Data
Type of Foundation				=	Open
Width of Footing (L_L)				=	6.50	m
Width of Footing (T_T)				=	9.40	m
Thickness of Footing at Top				=	1.00	m
Thickness of Footing at End				=	0.30	m
Clear Cover:-
Pier Cap				=	50.00	mm
Pier Shaft				=	50.00	mm
Foundation				=	75.00	mm
Seismic Data:-
Seismic Zone				=	III
Importance factor				=	1.20
Response Reduction factor				=	1.50		Cl219.8,IRC:6
Temperature Variation				=	50	oC
Condition of exposure				=	Moderate

• General Arrangment Drawing:

                                                                                                                    Longitudinal Sectional View

• Details of Pier :-

                                                   Pier Longitudinal View

                                                                 Transverse View of Pier

• Live load calcualtion:

Load calculations from superstructure
Deal load of superstructure
Left Span
Total weight of super structure.				=	199.00	tonne
Reaction from left Span		Total Weight/2		=	99.50	tonne
Reaction on Pier		(199/2)		=	99.50	tonne
Right Span
Total weight of super structure.				=	199.00	tonne
Reaction from left Span		Total Weight/2		=	99.50	tonne
Reaction on Pier		(199/2)		=	99.50	tonne
Total Reaction on Pier					199.00	tonne
Distance between bearing & Cl of Pier shaft				=	0.50	m
Longitudinal moment		(99.5*0.5)-(99.5*0.5)		=	-	t-m
Transverse eccentricity of dead load from c/l of Pier				=	-	m
Transverse moment.		(199*0)		=	-	t-m
SIDL(Crash barrier,railing,footpath)-Excluding Wearing Course
Left Span
Crash barrier Weight		Weight of C/B*Span*2		=	26.3	t
Raling weigth				=	-	t
Footpath/services weight				=	-	t
Right Span
Crash barrier Weight		Weight of C/B*Span*2		=	26.3	t
Raling weigth				=	-	t
Footpath/services weight				=	-	t
Total reaction on pier (SIDL Excl. W/C)				=	26.33
Longitudinal moment (Crash Barrier)				=	-	t-m
Longitudinal moment (Railing)				=	-	t-m
Longitudinal moment (footpath/services)				=	-	t-m
Total Longitudinal moment(SIDL Excl. W/C)				=	-	t-m
Transverse eccentricity of C/B				=	-	m
Transverse moment of C/B				=	-	t-m
Transverse eccentricity of Railing				=	-	m
Transverse moment of Railing				=	-	t-m
Transverse eccentricity of  footpath/services				=	-	m
Transverse moment of  footpath/services				=	-	t-m
Total Transverse moment(SIDL Excl. W/C)				=	-	t-m
SIDL(Including Wearing Course
Left Span
Load Intensity due to wearing course			Weight of wc*span*cw	=	0.14	t/m2
DL of Wearing Course				=	20.92	t
Right Span
DL of Wearing Course				=	20.92	t
Total reaction on abutment (SIDL excluding W/c)			(20.92/2)+(20.92/2)	=	20.92	t
Longitudinal Moment( wearing Course)				=	-	t-m
Transverse eccentricity of wearing Course				=	-	m
Transverse moment( wearing Course)				=	-	t-m
Summary of loads from superstructure
At Bearing Level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t-m	t-m
Deal Load	199.00	199.00	-	-	-	-
SIDL-Excluding W/C	26.33	26.33	-	-	-	-
SIDL-including W/C	20.92	20.92	-	-	-	-
At Pier shaft bottom level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t-m	t-m
Deal Load	199.00	199.00	-	-	0	0
SIDL-Excluding W/C	26.33	26.33	-	-	0	0
SIDL-including W/C	20.92	20.92	-	-	0	0
At Foundatiion bottom level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t-m	t-m
Deal Load	199.00	199.00	-	-	-	0
SIDL-Excluding W/C	26.33	26.33	-	-	-	0
SIDL-including W/C	20.92	20.92	-	-	-	0
One Span Dislodged Consition
Dead Load of super-structure
Vertical Load on Pier				=	99.50	t
Longitudinal Moment				=	49.8	t m
Transverse Moment				=	-	t m
SIDL(Crash barrier,railing,footpath)-Excluding Wearing Course
Vertical Load on Pier				=	13.17	t
Longitudinal Moment				=	6.6	t m
Transverse Moment				=	-	t m
SIDL(Including Wearing Course
Vertical Load on Pier				=	10.46	t
Longitudinal Moment				=	5.2	t m
Transverse Moment				=	-	t m
Summary of loads from superstructure
At Bearing Level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t-m	t-m
Deal Load	99.50	99.50	49.75	-	-	-
SIDL-Excluding W/C	13.17	13.17	6.58	-	-	-
SIDL-including W/C	10.46	10.46	5.23	-	-	-
At Pier shaft bottom level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t-m	t-m
Deal Load	99.50	99.50	49.75	-	0	0
SIDL-Excluding W/C	13.17	13.17	6.58	-	0	0
SIDL-including W/C	10.46	10.46	5.23	-	0	0
At Foundatiion bottom level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t-m	t-m
Deal Load	99.50	99.50	49.75	-	-	0
SIDL-Excluding W/C	13.17	13.17	6.58	-	-	0
SIDL-including W/C	10.46	10.46	5.23	-	-	0
Live load calculation( Normal case)
Live load calculation
Following live load cases are considered
1 lane 70R-wheeled
1 lane Class A
3 lane class-A
1 lane 70R-wheeled+1 lane Class-A
Left Span
Reaction due to DL+SIDL				=	146.75	t
Right Span
Reaction due to DL+SIDL				=	146.75	t
Bearing Type		Elastomeric
1 lane 70R0 wheeled			Both Span Loaded
Live load Reactions
	Rb	(49*9.48)/(9.48+3.32-0.5)		=	37.75	t
	Rc	(51*9.61)/(9.61+3.19-0.5)		=	39.83	t
Total Load of 70R vehicle				=	77.58	t
Total Load of 70R vehicle according this span				=	77.58	t
Total Load (including Impact)			(77.58*1.25)	=	96.97	t
Live load Reactions with impact factor			Rb		47.19	t
Live load Reactions with impact factor			Rc		49.79	t
longitudinal moment				=	1.30	t-m
total length of 70R vehicle		3.96+1.52+2.13+1.37+3.05+1.37		=	13.400	m
CG Calculation	(8*0+12*3.96+12*5.48+17*7.61+17*8.98+17*12.03+17*13.4)/100			=	8.276	m
Braking Force	(96.97* of 20%)			=	19.39	t
Change in reaction due to braking force			(19.39*(1.2+230.115-228.458)/13.4)	=	4.14	t
Total Horozontal force at bearing level			Fh/2	=	9.7	t
Total Horozontal force (Longitudinal)			HL	=	9.7	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity	(12/2-(1.2+0.5+2.79/2)			=	2.905	m
Transverse Moment on abutment			MT	=	281.71	t-m
1 lane Class - A	Cl204,IRC:6-2014
Live load Reactions
Rb	(28.2*7.78)/(7.78+5.02-0.5)			=	17.83	t
Rc	(27.2*7.59)/(7.59+5.21-0.5)			=	16.79	t
Total Load of 70R vehicle				=	34.61	t
Total Load of 70R vehicle according this span				=	34.61	t
Total Load (including Impact)			(34.61*1.25)	=	43.27	t
Live load Reactions with impact factor			Rb		22.28	t
Live load Reactions with impact factor			Rc		20.98	t
longitudinal moment				=	0.65	t-m
total length of 70R vehicle				=	18.800	m
CG Calculation				=	9.091	m
Braking Force	(43.27* of 20%)			=	8.65	t
Change in reaction due to braking force				=	1.32	t
Total Horozontal force at bearing level			Fh/2	=	4.3	t
Total Horozontal force (Longitudinal)			HL	=	4.3	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity		(12/2-(0.15+0.5+2.3/2)		=	4.20	m
Transverse Moment				=	181.7	t-m
3 lane Class - A
Live load Reactions
	Ra	(3*17.83*1.25* of 90%)		=	60.17	t
	Rb	(3*16.79*1.25 of 90%)		=	56.66	t
Vertical reaction on Pier				=	116.82	t
longitudinal moment				=	1.76	t-m
Braking Force	(20% of 34.61+ 5% of 34.61%)*90%			=	6.99	t
Total Braking force at bearing level				=	1.63	t
Total Horozontal force at bearing level			Fh/2	=	3.5	t
Total Horozontal force (Longitudinal)			HL	=	3.5	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity		12/2-.5-.15-2.3-1.2-2.3/2		=	0.70	m
Transverse Moment				=	81.8	t-m
1 lane 70R +1 lane Class - A
Live load Reactions
Rb	90% of (37.75*1.25+ 17.83*1.25)			=	87.28	t
Rc	90% of (39.83*1.25+ 16.79*1.25)			=	63.69	t
Vertical reaction on Pier				=	150.97	t
Braking Force	(20% of 96.97+ 5% of 43.27%)*90%			=	19.40	t
Total Braking force at bearing level				=	4.5	t
longitudinal moment				=	54.93	t-m
Total Horozontal force at bearing level			Fh/2	=	9.70	t
Total Horozontal force (Longitudinal)			HL	=	9.70	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity of 70R-W		12/2-(0.5+1.2+2.79/2)		=	2.905	m
Transverse Eccentricity of Class-A			12/2-6.84	=	-0.84	m
Total Transverse Moment			MT	=	200.04	t-m
One Span Loaded
1 lane 70R Wheeled
Left Span
Load On Left Span				=	-	t
Right Span
Live load Reactions
Vertical Load on pier				=	78.50	t
longitudinal moment				=	39.25	t-m
Live load Reactions with impact factor			Rb		-	t
Live load Reactions with impact factor			Rc		98.12	t
Braking Force				=	15.70	t
Total braking force at bearing level				=	4.51	t
Total Horozontal force (Longitudinal)			HL	=	7.8	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity	(12/2-(1.2+0.5+2.79/2)			=	2.905	m
Transverse Moment on abutment			MT	=	228.04	t-m
1 lane Class A- Wheeled
Left Span
Load On Left Span				=	-	t
Right Span
Load On right Span include impact factor				=	48.25	t
Live load Reactions
	Rb			=	-	t
	Rc			=	22.36	t
Vertical Load on pier				=	22.36	t
longitudinal moment				=	11.18	t-m
Live load Reactions with impact factor			Rb		-	t
Live load Reactions with impact factor			Rc		27.95	t
Braking Force				=	4.47	t
Total braking force at bearing level				=	1.04	t
Total Horozontal force (Longitudinal)			HL	=	2.2	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity		(12/2-(0.15+0.5+2.3/2)		=	4.20	m
Transverse Moment on pier			MT	=	202.65	t-m
Figure:
3 lane Class - A
Live load Reactions
Ra	Include impact factor 25%			=	-	t
Rb	Include impact factor 25%			=	-	t
Rc	Include impact factor 25%		(3*0*1.25* of 90%)	=	162.84
Rd	Include impact factor 25%		(3*0*1.25 of 90%)	=	-
Vertical reaction on Pier				=	162.84	t
longitudinal moment				=	81.42	t-m
Braking Force	(20% of 38.6+ 5% of 38.6%)*90%			=	9.65	t
Total Braking force at bearing level				=	2.26	t
Total Horozontal force at bearing level			Fh/2	=	4.8	t
Total Horozontal force (Longitudinal)			HL	=	4.8	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity		12/2-.5-.15-2.3-1.2-2.3/2		=	0.70	m
Transverse Moment				=	114.0	t-m
1 lane 70R+1 lane Class A- (Wheeled)
Live load Reactions
Rb	Include impact factor 25%			=	-	t
Rc	Include impact factor 25%			=	131.74
Vertical reaction on Pier				=	131.74	t
longitudinal moment				=	65.87	t-m
Braking Force				=	26.35	t
Total Braking force at bearing level				=	6.16	t
Total Horozontal force at bearing level			Fh/2	=	13.2	t
Total Horozontal force (Longitudinal)			HL	=	13.2	t
Total Horozontal force (transverse)			HT	=	-	t
Transverse Eccentricity of Class A				=	4.20	m
Transverse Eccentricity of 70R				=	0.455	m
Transverse Moment				=	316.5	t-m
Summary
Both Span Loaded
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t	t
1 lane 70R -W	96.97	96.97	1.30	281.71	9.70	-
I lane Class-A	43.27	43.27	0.65	181.73	4.33	-
3 lanes Class-A	116.82	116.82	1.76	81.78	3.49	-
1 lane 70R -W+I lane Class-A	150.97	150.97	54.93	200.04	9.70	-
One Span Loaded
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t	t
1 lane 70R -W	78.50	78.50	39.25	228.04	7.85	-
I lane Class-A	48.25	48.25	11.18	202.65	2.24	-
3 lanes Class-A	162.84	162.84	81.42	113.99	4.83	-
1 lane 70R -W+I lane Class-A	131.74	131.74	65.87	316.48	13.17	-
Final Summary
Normal Case
Bearing Level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t	t
LL1	150.97	150.97	82.65	200.04	9.70	0.00
LL2	162.84	162.84	95.21	113.99	4.83	-
LL3	116.82	116.82	11.74	81.78	3.49	-
Pier bottom Level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t	t
LL1	150.97	150.97	202.90	200.04	9.70	0.00
LL2	162.84	162.84	155.02	113.99	4.83	-
LL3	116.82	116.82	55.04	81.78	3.49	-
Foundation bottom Level
Load Item	Pmax	Pmin	ML	MT	HL	HT
	t	t	t-m	t-m	t	t
LL1	150.97	150.97	224.27	200.04	9.70	0.00
LL2	162.84	162.84	165.64	113.99	4.83	-
LL3	116.82	116.82	62.73	81.78	3.49	-

Water Current forces calcualation:

1	Calculation of forces due to Water Current in HFLCase
2	Max. Mean Velocity of Current					=	0.98	m/s
3	Constant "k" for circular pier in transverse direction					=	0.66
4	Constant "k" for circular pier in longitudinal direction					=	1.50
5	Constant "k" for circular Cap					=	1.50
6		Cl.210.2,IRC:6-2017,Page No-39				=
7				<!-- [if gte vml 1]> Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap <![endif]--><!-- [if !vml]--><!--[endif]-->
8
9
10
11
12
13
14
15
16
17
18
19
20	Max. intencity of pressure				P	=	52KV2	Kg/m2
21					P	=	74.91	Kg/m2
22					P	=	0.07	t/m2
23
24	Water Current force in Transverse Direction
25	Force on Pier
26	Submerged Height of pier					=	8.84	m
27
28	Intencity of pressure at pier bottom level					=	-	t/m2
29	Diameter of Circular Pier					=	0.70	m
30	Force on pier in transverse direction					=	0.23	t
31		acting RL				=	224.16	m
32
33	Transverse moment due to force on pier at pier bottom					=	1.60	t-m
34
35	Water Current in 200 from Transverse Direction
36	Force on pier in transverse direction					=	0.19	t
37		acting RL				=	224.16	m
38	Transverse moment due to force on pier at pier bottom					=	1.31	t-m
39	Diameter of Circular Pier					=	0.70	m
40
41	Force on pier inL_L Dir.					=	0.10	t
42		acting ar RL				=	224.16	m
43	Longitudinal moment due to force on pier at pier bottom					=	0.41	t-m
44
45	Summary of force due to water current at pier bottom level
46		Pmax	Pmin	ML	MT	HL	HT
47	Load Item	t	t	t-m	t-m	t	t
48	Water current (0o)	-	-	-	1.60	-	0.23
49	Water current (20o)	-	-	0.41	1.31	0.10	0.19
50
51	Summary of force due to water current at footing bottom level
52		Pmax	Pmin	ML	MT	HL	HT
53	Load Item	t	t	t-m	t-m	t	t
54	Water current (0o)	-	-	-	1.83	-	0.23
55	Water current (20o)	-	-	0.23	1.50	0.10	0.19
56
57	Calculation of Loads at Pier bottom level
58	Calculation of forces on Abutment and Foundation
59	Abutment Dimensions (square) as shown below:-
60	<!-- [if gte vml 1]> Bitmap <![endif]--><!-- [if !vml]--> <!--[endif]--><!-- [if !mso & vml]><![endif]-->
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76	Normal Case
77	Calcualtion of Self -Weight
78	Pedestal
79	Length					=	0.80	m
80	Breadth					=	0.80	m
81	Height					=	0.25	m
82	Nos					=	-	m
83	Total   Weight of the member					=	-	t
84
85	Pier Cap	Rectangular portion
86	Length					=	10.10	m
87	Breadth					=	2.20	m
88	Height					=	0.25	m
89	Volume					=	5.56	m3
90	Total   Weight of the member					=	13.89	t
91
92	Pier Cap	Trepezoidal Part
93	Length (Top)	10.1	Length (Bottom)	8.5		=	9.30	m
94	Width					=	0.50	m
95	Thickness					=	2.20	m
96	Volume						10.23	m3
97	Total   Weight of the member					=	25.58	t
98	Total   Weight of Pier Cap					=	39.46	t
99							z
100	Pier Shaft
101	Area of cross section part of rectangular part					=	5.95	m2
102	Height					=	10.10	m
103	Nos					=	1.00
104	Area of cross section part of semi-circular part					=	0.19	m2
105	Height					=	10.10	m
106	Nos					=	2.00
107	Total   Weight of Pier Shaft					=	159.95	t
108
109	LWL Case
110	Total   Weight of sub-structure					=	199.42	t
111	Transverse moment					=	-	t-m
112	Sub-Merged ub-structure height					=	9.84	m
113	Total   Weight of submerged structure					=	60.46	t
114	Total   Weight of Buoyancy on substructure					=	-60.46	t
115						=
116	Sumamry of forces at pier bottom level
117	Load Item	Pmax	Pmin	ML	MT	HL	HT
118		t	t	t-m	t-m	t	t
119	Substructure_Weight	199.42	199.42
120	Buoyancy on Substructure	-60.46	-60.46
121
122	Calculation of Loads at Footing bottom level
123
124	Calulation of Weight of soil on footing
125	LWL Case
126	Bed Level					=	224.18	m
127	FL Level					=	216.26	m
128	height overall from LWL to FL					=	7.92	m
129	Earth Fill Height					=	6.92	m
130	Rectanular portion
131	Length					=	9.40	m
132	Width					=	6.50	m
133	Height					=	0.30	m
134	Volume-1					=	18.33	m3
135
136	Trepezoidal Portion
137	Length						9.40	m
138	Width(Top)	6.50	Width(Bottom)	0.7		=	3.60	m
139	Height					=	0.70	m
140	Volume-2					=	23.69	m3
141	Volume of Concrete(V1+V2)					=	42.02	m3
142	Buounacy of Footing					=	-42.02	t
143	Earth fill Weight
144	Length					=	9.40	m
145	Width					=	6.50	m
146	Height					=	6.92	m
147	Volume of Earth					=	422.57	m3
148						=
149	Weight of Footing					=	105.05	t
150	Weight of Earth above footing					=	761.10	t
151	HFL case with max. scour					=
152	Earth fill Weight
153	Length					=	9.40	m
154	Width					=	6.50	m
155	Height					=	8.84	m
156	Volume of Earth					=	540.31	m3
157	Weight of Earth					=	540.31	t
158
159	Sumamry of forces at Footing bottom level			LWL
160	Load Item	Pmax	Pmin	ML	MT	HL	HT
161		t	t	t-m	t-m	t	t
162	Substructure_Weight	199.42	199.42	-	-	-	-
163	Weight of Soil on footing	761.10	761.10	-	-	-	-
164	Weigth of footing	105.05		-	-	-	-
165	Buoyancy on Substructure	-60.46	-60.46	-	-	-	-
166	Buoyancy on Footing	-42.02		-	-	-	-

Wind force Culacualtion:-

-	Calcualtion of Wind forces
-	Basic Wind Speed				=	50	m/s
-	Type of terrain				=	Plain Terrain
-	Type of Super-Structure				=	RCC Girder & Deck
-	Type of Sub-strucutre
-	The average Height in m of exposed surfacce above GL, Bed lvl. & LWL				=	H
-	Hourly Mean speed of wind in m/s at Height H				=	Vz
-	Horoizontal Wind pressure in N/m2 at Height H				=	Pz
-	Calcualtion of  wind forces on superstructure
-	Skew Angle				=	0	0	Radian
-	Left Span
-	Length of superstructure in L_L direction (sq)				=	13.30	m	Span Exp.to Exp C/C
-	Length of superstructure in L_L direction (skew)				=	13.30	m
-	Length of superstructure in T_T direction (sq)				=	12.00	m
-	Total Depth of Surestructure include Crash barrier				=	2.22	m
-	The average Height in m of exposed surfacce  from Pier cap to MSL				=	9.131	m
-	From IRC:6-2017, Table 12, page no 33			Vz	=	42.1	m/s
-				Pz	=	1064.5	N/m2
-	Wind Forces on DL+SIDL
-	Gust Factor			G	=	2	Cl.209.3.3
-	Drag Co-efficeint			CD	=	1.3
-	Expossed Solid Area			A1	=	29.526	m2
-	Force intransverse Direction			FT	=	Pz*A1*G*CD
-					=	81,719.11	N
-					=	81.72	kN
-				FT	=	8.17	t
-				acting at RL	=	229.568	m
-
-	Force  in Longitudinal Direction			FL	=	2.04	t
-	25 % of Transverse Force(FT)			IRC 6-2020,Cl.209.3.4
-				acting at RL	=	229.568	m
-
-	Plan Area			A2	=	159.60	m2
-	Lift Co-efficient			Fuplift	=	0.75	Cl.209.3.5,IRC6
-
-	Force  in Vertical l Direction			FL	=	Pz*A1*G*CL
-				FL	=	-2,54,841.30	N
-						-25.48413	t
-	Wind forces on Live load
-	height fo ddeck surface from GL				=	5.937	m
-	Wind speed at deck Level			VZ	=	42.1	m/s	Cl.209.3.7,IRC6
-				No live load should be considered on deck
-	height of live load above roadway surface				=	3	m/s	Cl.209.3.6,IRC6
-	Gust Factor			G	=	2
-	Drag Co-efficeint			CD	=	1.2
-	Expossed Solid Area			A1	=	0	m2
-
-	Force in transverse Direction			FT	=	Pz*A1*G*CD		Cl.209.3.3,IRC6
-					=	0	t
-				Acting at RL	=	231.615	m
-	Total Wind forces at bearing level from superstructure
-	Both Span					One Span (RHS Span)
-	FT	=	8.2	t	FT	4.09	t
-	FL	=	2.04	t	FL	1.02	t
-	Fuplift	=	-25.48	t	FL	-12.74	t
-
-
-	Force at bearing Level ( BS Span)
-
-	HL Wind	=	FL cos𝜃-FT sin𝜃
-	HT Wind	=	FL sin𝜃+FT cos𝜃
-	P wind	=	Fuplift
-
-	Both Span			One Span (RHS Span)
-	HL Wind	=	2. t	HL Wind	=	1. t
-	HT Wind	=	8.2 t	HT Wind	=	4.1 t
-	P wind	=	-25.5 t	P wind	=	-12.7 t
-
-	Forces at pier shaft bottom level due to wind forces on superstructure
-	Both Span present			One Span (RHS Span present)
-	P wind	=	-25.5 t	P wind	=	-12.7 t
-	HL Wind	=	2. t	HL Wind	=	1. t
-	HT Wind	=	8.2 t	HT Wind	=	4.1 t
-	ML due to HL	=	22.9 t-m	ML due to HL	=	11.4 t-m
-	ML due to P wind	=	. t-m	ML due to P wind	=	. t-m
-	MT due to HT	=	91.5 t-m	MT due to HT	=	45.7 t-m
-
-
-	Calculation of Wind forces on Sub-structure
-	<!-- [if gte vml 1]> Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap <![endif]--><!-- [if !vml]--><!--[endif]--> Pier Cap
-
-
-
-
-
-
-	Area of Rectangular part		A1			=	0.55	m2
-	Area of Trapezoidal Part		A2			=	0.725	m2
-	Total Area		A=(A1+A2)				1.275	m2
-
-						=
-	CG of Rectangular part					=	0.1250	m
-	CG of Trapezoidal Part						0.2069	m
-
-	Moment of rectangular area					=	0.06875	m3
-	Moment of Trapezoidal  area					=	0.17586207	m3
-	CG of the section fom top					=	0.22978364	m
-						=
-						=
-	Average height of exposed surface from GL to Pier cap top Level					=	3.73521636
-	hourly mean Wind Speed			Vz	=	42.1	m/s	from code
-	Hourly mean Wind pressure			Pz	=	1064.5	N/m2	from code
-	Exposed  solid area			A	=	1.275	m2
-	Gust Factor			G	=	2
-	Drag Co-efficeint			CD	=	1.2
-
-	Width of Cap(Skew)			b	=	2.2	m
-	Length of Cap(Skew)			t	=	10.1	m
-				t/b	=	4.59
-				Height/Breadth	=	0.34
-	Force intransverse Direction			FT	=	Pz*A1*G*CD
-					=	3,257.37	N
-				FT	=	0.33	t
-				acting at RL	=	227.913	m
-	Total Wind forces at bearing level from pier cap
-		HL Wind	=	`-FT sin𝜃	=	-	t
-		HT Wind	=	FT cos𝜃	=	1.0	t
-		ML			`	-	t
-		MT			=	10.88	t-m
-
-	Calculation of Wind forces on Pier Shaft
-	Pier Shaft		<!-- [if gte vml 1]> Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap Bitmap <![endif]--><!-- [if !vml]--><!--[endif]-->
-
-
-
-
-
-
-
-
-
-	Average height of exposed surface from GL
-					=	9.131	m
-	hourly mean Wind Speed			Vz
-	Hourly mean Wind pressure			Pz	=	42.1	m/s
-	Exposed Solid area LWL Case			A1	=	1064.5	N/m2
-	Gust factor			G	=	6.39	m2
-	Height/breadth				=	2.00
-	Drag Co-effient			CD	=	13.04
-				t/b	=	1.20
-	Force intransverse Direction			FT	=	13.14
-					=	Pz*A1*G*CD
-				FT	=	16,329.515	N
-				acting at RL	=	1.63	t
-	Forces at footing bottom level due to wind forces on pier shaft				=	228.74	m
-		HL Wind	=	`-FT sin𝜃
-		HT Wind	=	FT cos𝜃	=	-	t
-		ML			=	6.1	t
-		MT			=	-	t
-					=	76.14	t-m
-	Summary of Forces due to Wind on super-structure+Sub-structure
-	Both Span present
-	At Pier bottom level
-	Pmax	Pmin	ML	MT	HL	HT
-	t	t	t-m	t-m	t	t
-	25.48	-25.48	22.87	91.49	2.04	8.17
-
-	At Footing bottom level
-	Pmax	Pmin	ML	MT	HL	HT
-	t	t	t-m	t-m	t	t
-	25.48	-25.48	24.92	99.66	2.04	8.17
-
-	Single Span present
-	At Pier bottom level
-	Pmax	Pmin	ML	MT	HL	HT
-	t	t	t-m	t-m	t	t
-	12.74	-12.74	11.44	45.75	1.02	4.09
-
-	At Footing bottom level
-	Pmax	Pmin	ML	MT	HL	HT
-	t	t	t-m	t-m	t	t
-	12.74	-12.74	12.46	49.83	1.02	4.09

Load Combination:

Load Combiantion LSM Annexure B,IRC :6-220
	Following Load Combiantions are considered
A	Ultimate Limit State( for Verification of structural Strength )
A-1	Basic Combination
A-2	Seismic Combination
B	Serviceability Limit State
B-1	Rare combination( For checking stress limit)
B-2	Quasi-Peermanent Combination(For Checkong crack width in RCC structure)
C	Combiantion Base Pressure & design of Foundation
C-1	Combiantion-1
C-2	Combiantion-2
C-3	Combiantion-3
-	Load Combiantion- Base Pressure Check
-	Combination for base Pressure
-	Normal Case
-	Both Span present
-	LWL without Scour			Unfactored forces
-	Load Item			Pmax	Pmin	ML	MT	HL	HT
-				t	t	t-m	t-m	t	t
-	DL(Superstructure)			199.00	199.00	-	-	-	-
-	SIDL (Excluding w/c)			26.33	26.33	-	-	-	-
-	SIDL(Including w/c)			20.92	20.92	-	-	-	-
-	LL1-Max. reaction case			150.97	150.97	224.27	200.04	9.70	0.00
-	Substructure Weight			199.42	199.42	-	-	-	-
-	Weight of soil on footing			761.10	761.10	-	-	-	-
-	Weight of Foooting			105.05	-	-	-	-	-
-	Wind Load			25.48	-25.48	22.87	91.49	2.04	8.17
-	Total for unfortored loads			1,488.27	1,332.26	247.14	291.53	11.74	8.17
-
-	LL2-max. Longitudinal Moment Case			Unfactored forces
-	Load Item			Pmax	Pmin	ML	MT	HL	HT
-				t	t	t-m	t-m	t	t
-	DL(Superstructure)			199.00	199.00	-	-	-	-
-	SIDL (Excluding w/c)			26.33	26.33	-	-	-	-
-	SIDL(Including w/c)			20.92	20.92	-	-	-	-
-	LL2-max. Longitudinal Moment Case			162.84	162.84	165.64	113.99	4.83	-
-	Substructure Weight			199.42	199.42	-	-	-	-
-	Weight of soil on footing			761.10	761.10	-	-	-	-
-	Weight of Foooting			105.05	-	-	-	-	-
-	Wind Load			25.48	-25.48	22.87	91.49	2.04	8.17
-	Total for unfortored loads			1,500.14	1,344.13	188.52	205.48	6.87	8.17
-
-	LL3-max.  Transverse Moment Case			Unfactored forces
-	Load Item			Pmax	Pmin	ML	MT	HL	HT
-				t	t	t-m	t-m	t	t
-	DL(Superstructure)			199.00	199.00	-	-	-	-
-	SIDL (Excluding w/c)			26.33	26.33	-	-	-	-
-	SIDL(Including w/c)			20.92	20.92	-	-	-	-
-	LL3-max.  Transverse Moment Case			116.82	116.82	62.73	81.78	3.49	-
-	Substructure Weight			199.42	199.42	-	-	-	-
-	Weight of soil on footing			761.10	761.10	-	-	-	-
-	Weight of Foooting			105.05	-	-	-	-	-
-	Wind Load			25.48	-25.48	22.87	91.49	2.04	8.17
-	Total for unfortored loads			1,454.12	1,298.11	85.60	173.27	5.54	8.17
-
-	One Span dislodged Condition
-	Load Item			Unfactored forces
-				Pmax	Pmin	ML	MT	HL	HT
-				t	t	t-m	t-m	t	t
-	DL(Superstructure)			199.00	199.00	-	-	-	-
-	SIDL (Excluding w/c)			26.33	26.33	-	-	-	-
-	SIDL(Including w/c)			20.92	20.92	-	-	-	-
-	Substructure Weight			199.42	199.42	-	-	-	-
-	Weight of soil on footing			761.10	761.10	-	-	-	-
-	Weight of Foooting			105.05	-	-	-	-	-
-	Wind Load			25.48	-25.48	22.87	91.49	2.04	8.17
-	Total for unfortored loads			1,337.30	1,181.29	22.87	91.49	2.04	8.17
-
-
-
-
-	Summary of Load case for normal case
-	LWL Case without Scour
-	Both Span present
-	Load case			Pmax	Pmin	ML	MT	HL	HT
-				t	t	t-m	t-m	t	t
-	N1			1,488.27	1,332.26	247.14	291.53	11.74	8.17
-	N2			1,500.14	1,344.13	188.52	205.48	6.87	8.17
-	N3			1,454.12	1,298.11	85.60	173.27	5.54	8.17
-
-	One  Span dislodged condition
-	Load case			Pmax	Pmin	ML	MT	HL	HT
-				t	t	t-m	t-m	t	t
-	N4			1,337.30	1,181.29	22.87	91.49	2.04	8.17
-
-
-	Base Pressure Check
-	Area of Footing				A	=	61.1	m2
-	Section Modulus in Trans. Direction				Zt	=	95.72	m3
-	Section Modulus in Longi.. Direction				Zl	=	66.19	m3
-
-	Load Case No	Pmax	Pmin	ML	MT	P/A+ML/Zl+MT/Zt	P/A+ML/Zl-MT/Zt	P/A-ML/Zl-MT/Zt	P/A-(ML/Zl+MT/Zt)	Check
-	N1	1,488.27	1,332.26	247.14	291.53	31.14	25.05	17.58	23.67	Ok
-	N2	1,500.14	1,344.13	188.52	205.48	29.55	25.25	19.56	23.85	Ok
-	N3	1,454.12	1,298.11	85.60	173.27	26.90	23.28	20.70	24.32	Ok
-	N4	1,337.30	1,181.29	22.87	91.49	23.19	21.28	20.59	22.50	Ok

Basic  Comb for Design Foundation:

Design of  Flexure:-

Properties of Concrete
Grade of Concrete		From IRC 112,Table 6.5			=	35.00
Characteristic Strength of Concrete				fck	=	35.00	Mpa=N/mm2
Design compressive Strength of Concrete				fcd	=	15.63	Mpa
Tensile Strength of Concrete				fctm	=	2.80	Mpa
Momulus of Elasticity of Concrete				<!-- [if gte vml 1]> Bitmap <![endif]--><!-- [if !vml]--><!--[endif]--> Ecm	=	32,000.00	Mpa
Partial Materials Safety Factor for Concrete				𝛾𝑚	=	1.50
Ultimate Compressive strain in the concrete			<!-- [if gte vml 1]> Bitmap <![endif]--><!-- [if !vml]--> <!--[endif]--><!-- [if !mso & vml]><![endif]-->		=	0.00
Constant				α	=	0.67

Properties of Steel
Grade of Steel					=	500.00
Characteristic Strength of Steel				fyk	=	500.00	Mpa=N/mm2
Momulus of Elasticity of Steel				Es	=	2,00,000.00	Mpa
Partial Materials Safety Factor for Steel			<!-- [if gte vml 1]> Bitmap Bitmap <![endif]--><!-- [if !vml]--> <!--[endif]--> 𝛾s	𝛾s	=	1.15
Ultimate Compressive strain in the Steel					=	0.00
Design Yield Strength				fyd	=	434.78	Mpa

Compressive force
Cu					=	0.36*fck*b*xulim
					=	17/21*fcd*b*xu,lim
					=	0.80952*fcd*b*xu,lim
Tensile force
Tu					=	.87*fy*Ast
So, Limiting Resistance is equal to limiting moment
Rlim			=	Mu,lim/bd2	=	0.36*fck*Xu,lim/d(1-.429Xu,lim/d)
					=	5.78
For Fe500, Xu,lim/d					=	0.62
Design Moment,Mu					=	15.45
Overall Depth                 D					=	1,000.00
Equivalent width of rectangular section					=	1,425.00
d required					=	137.00
d provided					=	925.00
Moment of Resistance,                          R					=	0.13
Ast,required					=	385.76
Limiting Percentage of steel reinforcement for balanced  Section
(𝑝𝑡,𝑙𝑖𝑚)					=	38,576.01
Ast,required	per meter width				=	270.71
Minimum Ast,required		per meter width			=	1,551.20
Governing Ast,required		per meter in central bandwitch			=	1,551.20
Provide of Reinforcement in remaining width					=
Dia. Of Bar	16 mm	+	mm		At Bottom
Spacing c/c	125 mm	+	125 mm
Ast,provided					=	1,608.50
Percentage of Steel provided					=	0.00
Max. Ast per meter width				Ast,max	=	23,125.00

Reinforcement details :-

2. The difference between "free" and "fixed" piers in the context of foundation construction.

Explain the concepts and how they can impact foundation sizing:-

• <!-- [if !supportLists]-->Free Piers:

A free pier is a support column or pier that is not restrained laterally. In other words, it can move or sway horizontally (Longitudinal & Transverse Direction). Free piers are typically allowed to move independently due to factors like temperature changes, soil settlement, and other dynamic forces. They are usually used in situations where some degree of movement is expected and acceptable without compromising the stability or integrity of the structure.

• Fixed Piers:

A fixed pier, on the other hand, is a support column that is restrained laterally, preventing horizontal movement (Longitudinal & Transverse Direction). These piers are often used when there is a need to limit movement, such as in structures where even small horizontal shifts could lead to issues. Fixed piers are designed to resist lateral forces, and they provide a higher level of stability compared to free piers. The fixing of the pier's lateral movement can be achieved through various means, such as using foundation beams, tie beams, braces, or other structural elements.

Impact on Foundation Sizing:

The choice between free and fixed piers can have an impact on the design and sizing of the foundation. Here's how:

• Free Piers:

Since free piers are allowed to move, the foundation can be designed to accommodate some degree of settlement or lateral movement(Longitudinal & Transverse Direction). This might allow for a slightly simpler and more flexible foundation design, as it doesn't need to resist the same level of lateral forces.

• Fixed Piers:

Fixed piers require a more robust foundation design to resist lateral forces (Longitudinal & Transverse Direction) and prevent all those movement. The foundation needs to be designed to handle these additional loads and restraints, which might involve more complex calculations and potentially larger foundation elements.

• Conclusion:

In summary, the choice between free and fixed piers depends on the specific requirements and constraints of the project. Factors such as the level of lateral movement allowed, the structural stability needed, and the soil conditions at the construction site will influence the decision. The impact on foundation sizing will primarily be seen in the design and reinforcement of the foundation elements to accommodate the chosen type of pier.