Week 4 Challenge

1).Design of Foundation of Abutment  (as per IRC 6-2017 loads. optimize the design as per IRC: 112-2011):-

 

Here's a brief introduction to the design of abutment foundations:

An abutment foundation is a critical structural element used to support and distribute the loads from bridge abutments to the ground. Bridge abutments are the supporting structures at the ends of a bridge that connect the deck to the ground, providing stability and transferring the load of the bridge to the foundation. The design of abutment foundations is crucial to ensure the overall safety and long-term performance of the bridge.

These are the following step we have adopted to consider an abutment foundation design:-

1. Geotechnical Investigation:

   Before designing an abutment foundation, a comprehensive geotechnical investigation of the site is conducted. This investigation involves soil and rock testing to understand the subsurface conditions, including the soil type, bearing capacity, groundwater levels, and potential for settlement or lateral movement.

2. Foundation Types:

   Abutment foundations can be designed using various types, depending on the specific site conditions and bridge requirements. Common types of foundations include spread footings, pile foundations, drilled shafts (also known as caissons), and mat foundations. The choice of foundation type depends on factors such as soil conditions, bridge design, and the magnitude of loads to be supported.

3. Load Analysis:

   Engineers analyze the loads that will be transferred from the bridge deck to the abutment foundation. This includes the weight of the bridge structure itself, traffic loads, live loads, and any additional loads due to seismic events or other external forces.

4. Design Considerations:

   The design of the abutment foundation must consider several factors, including the bearing capacity of the soil, settlement limits, lateral stability, and resistance to overturning. It is crucial to ensure that the foundation can safely support the loads without excessive settlement or tilting.

5. Retaining Walls:

   In some cases, abutment foundations may also include retaining walls to support the approach embankments and prevent soil erosion. The design of these walls is also an essential part of the overall abutment foundation design.

6. Construction Materials:

   The materials used for abutment foundations typically include reinforced concrete, steel, and sometimes additional materials for specialized foundations like piles. The choice of materials depends on the specific design requirements and the local construction practices.

7. Drainage and Waterproofing:

   Adequate drainage and waterproofing measures are incorporated into the abutment foundation design to prevent the buildup of water pressure behind the abutment and to protect the foundation from potential water-related issues.

8. Construction and Quality Control:

   During construction, careful monitoring and quality control measures are implemented to ensure that the abutment foundation is built according to the design specifications. This includes conducting load tests on piles and verifying the foundation's performance before the bridge's superstructure is constructed.

Overall, the design of abutment foundations is a complex process that requires collaboration between geotechnical engineers, structural engineers, and bridge designers. By carefully considering the site conditions and applying engineering principles, a well-designed abutment foundation can provide a stable and durable support system for bridges, ensuring their safe and efficient functioning for many years.

General Arrangement Drawing :-

 

 

1.       Basic Design data: -
1.1.     Span and Cross Section Data
1.1.1.     C/C of expansion gap				=	14.40	m	(Sq.)
1.1.2.    C/C of Bearing				=	13.40	m	(Sq.)
1.1.3.    Distance of bearing to expansion gap				=	0.50	m	(Sq.)
1.1.4.    Carriage way width				=	9.00	m
1.1.5.    Total Width				=	12.00	m
1.1.6.    Footpath width (left Side) or Parapet				=	0.50	m
1.1.7.    Footpath width (right Side)				=	1.50	m
1.1.8.    Crash Barrier (Left Side)				=	0.50	m
1.1.9.    Crash barrier (Right Side)				=	0.50	m
1.1.10.  Handrail width (Left Side)				=	-	m
1.1.11.    Handrail (right Side)				=	-	m
1.1.12.  Skew Angle				=	-	o	00.00 radians
1.2.    Super-Structure Details:
1.2.1.    Depth of superstructure (Min)				=	1.60	m
1.2.2.   Depth of superstructure (Max)				=	1.60	m
1.2.3.   Depth of superstructure				=	0.88	m
1.2.4.  Thickness of wearing coat				=	0.065	m
1.2.5.   No of Girder				=	4.00	m
1.2.6.  Distance of FRL from bearing of least height				=	10.90	m
1.2.7.   Spacing between girder				=	3.00	m
1.2.8.  Cross-slope				=	2.5%	m
1.2.9.  Thickness of bearing				=	0.07	m
1.2.10. Thickness of pedestal				=	0.25	m
1.2.11.  Minimum Thickness of wedge				=	-	m
1.2.12. Thickness of bearing +pedestal				=	0.315	m
1.3.    Material Data:-
1.3.1.    Grade of Concrete			fck	=	M 35
1.3.2.   Design strength of Concrete			fcd	=	15.63	MPa	(Cl.6.4.2.8,IRC:112-2020,Page-38)
1.3.3.  Grade of steel			fyk	=	Fe 500
1.3.3.  Design strength of Steel			fyd	=	434.78
1.3.4.  Density of concrete				=	2.50	t/m3
1.3.5.  Density of wearing coat				=	2.20	t/m3
1.3.6.  Co-efficient of thermal expansion of concrete				=	1.20E-05	/oC	(Cl.215.4,IRC:6-2014)
1.3.7.   Shrinkage Strain				=	2.00E-04		(Cl.217.3,IRC:6-2014)
1.3.8.  Modulus of elasticity  of steel			Es	=	2.00E+05	MPa
1.3.9.  Modulus of elasticity  of Concrete			Es	=	3.20E+04	MPa
1.3.10.Mean Axial Tensile strength of concrete ftm			fctm	=	2.80	MPa
1.4.     Typical Levels:-
1.4.1.    Formation Level FRL				=	234.065	m
1.4.2.  Dirt wall Level				=	234.065	m
1.4.3.  Bearing Level				=	232.180	m
1.4.4.  Max.Abutment Cap level				=	231.850	m
1.4.5.  Stem top level				=		m
1.4.6.  Front Ground Level -GL				=	228.000	m
1.4.7.   Scour Level(MSL)				=	226.580	m
1.4.8.  Footing top level				=	225.250	m
1.4.9.  Minimum Founding Level required from scour calculations				=		m
1.4.10.      Founding level(Design) FL, considering and geo-tech. reqd.				=	224.250	m
1.4.11.  Height Flood Level, HFL				=	229.500	m
1.4.12.  Height from bearing top to deck top level(excl.WC)					1.820
1.5.    Soil Parameters:-
1.5.1.   Angle of shear resistance “				=	30	o
1.5.2.  Density of dry backfill “				=	2.00	t/m3
1.5.3.  Density of submerged backfill, “				=	1.00	t/m3
1.5.4.  Net Bearing Capacity				=	25.00	t/m2
1.5.5.  Gross Safe bearing capacity (LWL)				=	33.42	t/m2
1.5.6.  Gross Safe bearing capacity (HFL)				=	27.00	t/m2
1.5.7.   Live load surcharge				=	1.20	m
1.5.8.  Type of soil				=	Medium Soil
1.5.9.  Co-efficient of friction between the. (soil/rock & Concrete)				=	0.50
1.6.    Abutment Dimensions(square): -
1.6.1.    Length of abutment cap in L-L Directions at Top				=	1.64	m
1.6.2.  Length of abutment cap in L-L Directions at Bottom				=	1.00	m
1.6.3.  Width of abutment(sqr)				=	12.00	m
1.6.4.  Width of median wall				=	3.50	m
1.6.5.  Width of footings(sqr)				=	8.50	m
1.6.6.  Width of heel(sqr)				=	5.00	m
1.6.7.  Minimum footings thickness				=	0.30	m
1.6.8.  Heel thickness at root				=	1.00	m
1.6.9.  Toe thickness at root				=	1.00	m
1.6.10.Stem top thickness(straight)				=	1.00	m
1.6.11.  Stem bottom thickness(straight)				=	1.00	m
1.6.12. Dirt wall Thickness				=	0.30	m
1.6.13.Depth of Abutment Cap (Constant Portion)				=	0.30	m
1.6.14. Depth of Abutment Cap (Varying Portion)				=	0.30	m
1.6.15.Thickness of return wall (Avg)				=	0.50	m
1.6.16.No of return wall				=	1.00	m
1.6.17. Horizontal distance of CG of abutment shaft from vertical face				=	0.50	m
1.6.18.Provision of weep holes in abutment wall				=	Yes
1.6.19 Distance between bearing c/l and shaft c/l in L-L Dimension				=	-	m
1.6.20 Width of toe				=	2.50	m
			FRL	=	234.07
			Dirt-Wall Top	=	234.07		1.557
			BRG. Top Lvl	=	232.18
			Abt.Cap Top Lvl	=	231.85
			Abt.Shaft Top Lvl	=	231.25
			GL	=	228.00
			MSL	=	226.58
			FLT	=	225.25
			FL	=	224.25
			HFL	=	229.50
			Base Width	=	8.5
			Heel	=	5.0
			Toe	=	2.5
			Stem Btm Width	=	1.0
			Stem Top Width	=	1.0
			Edge Thickness	=	0.3
			Overall Height	=	1.0
			Abt. Shaft H	=	6.0
1.8 Load Data:-
·        Deal Load
o   Total Weight of Superstructure				=	210.00	t
o   Transverse eccentricity of DL from c/l of abutment				=	-	m
·        SILD (excluding of wearing course)
o   Self- weight of Crash Barrier				=	19.46	t/m
o   Self- weight of Railing/ Parapet(One Side)				=	16.20	t/m
o   Transverse eccentricity of crash barrier (with footpath case)				=	6.75	m
o   Transverse eccentricity of crash barrier (without footpath case)				=	4.75	m
o   Transverse eccentricity of Railing or Parapet				=	4.75	m
o   Total Weight of footpath/services				=	8.10	t
o   Transverse eccentricity of footpath/services				=	5.75	m
·        SILD (including of wearing course)					-
o   Load intensity due to wearing course				=	0.14	t/m2	Assume, W/C is 100mm thk.
o   Transverse eccentricity of wearing course (with footpath case)				=	-	m
o   Transverse eccentricity of wearing course (without footpath case)				=	-	m
·        FPLL:
o   Maximum intensity of footpath live load				=	500.00	kg/m2	Cl.206.1,IRC:6-2014
·        Live Load: - Cl 205, IRC:6-2014
o   Load % to be taken after reduction (in case of three Lane)				=	90%		Cl.205,IRC:6-2014
o   Fraction of live load remaining is seismic
o    1 Lane 70R -Wheeled				=	123.00	t	Refer LL calcualtion
o     CG				=	-	m
§  Load
o   1 Lane Class -A				=	68.14	t	Refer LL calcualtion
§  Load
o   Load % to be taken after reduction (in case of three Lane)				=	90%		Cl.205,IRC:6-2014
o   Fraction of live load remaining is seismic
1.9 Bearing Data:-
·        Type of bearing				=	Elastomeric
·        Elastomeric Bearing: -
o   Length (Along traffic dim.)			l	=	500.00	mm
o   Width (Perpendicular to traffic)			b	=	250.00	mm
o   Thickness of each elastomer			hi	=	10.00	mm
o   Number of internal elastomer layer			n	=	4	Nos
o   Thickness of Outer elastomer layer			he	=	5	mm
o   Thickness of steel plate			hs	=	3	mm
o   Overall thickness of bearing			ho	=	65.00	mm
o   Clear cover to steel plate (Vertical)			he	=	6.00	mm
o   No of Steel plates			n	=	5.00	Nos
o   Effective thickness of the elastomeric bearing			heff	=	50.00	mm
o   Shear modulus			G	=	1.00	Mpa
o   No of bearing over pier on support line			n	=	4	Nos
1.10 Clear Cover:-
·        Dirt wall				=	50.00	mm
·        Abutment Cap				=	50.00	mm
·        Abutment Stem				=	75.00	mm
·        Footing				=	75.00	mm
1.11 Seismic Data;-
·         Seismic Zone				=	III
·        Importance factor				=	1.20
·        Response Reduction factor				=	1.50		Cl219.8,IRC:6
·        Temperature Variation				=	47.50
				=
·        Condition of exposure				=	Moderate
·        Factor by which seismic force is increased for design of fnd.				=	1.35		Cl219.8,IRC:6
1.12 Sign Convention: -
·        Resisting moment (about toe)				=	Positive (+)
·        Overturning Moment (about toe)				=	Negative (-)
·        Horizontal Forces away from earth side				=	Positive (+)
·        Horizontal Forces towards earth side				=	Negative (-)
·        Downward force				=	Positive (+)
·        Upward Forces uplift				=	Negative (-)
·        In the transverse direction
o   Eccentricity towards footpath				=	Positive (+)
o   Eccentricity away from footpath				=	Negative (-)

 

Load Calculation from super-structure
2	Load calculations from superstructure
2.1	Deal load of superstructure
	Total weight of super structure.				=	210.00	tonne
	Reaction.	Total Weight/2			=	105.00	tonne
	Total reaction on abutment		(210/2)		=	105.00	tonne
	Distance between bearing & Cl of Abutment shaft				=	-	m
	Longitudinal moment		(105*0)		=	-	t-m
	Transverse eccentricity of dead load from c/l of abutment				=	-	m
	Transverse moment.		(105*0)		=	-	t-m
2.2	SIDL(Crash barrier,railing,footpath)-Excluding Wearing Course
	Crash barrier Weight		Weight of C/B*Span*2		=	35.66	t
	Raling weigth				=	16.20	t
	Footpath/services weight				=	8.10	t
	Total reaction on abutment (SIDL excludinf W/c)			(59.96/2)	=	29.98	t
	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				=	6.75	m
	Transverse moment of C/B				=	240.67	t-m
	Transverse eccentricity of Railing				=	4.75	m
	Transverse moment of Railing				=	76.95	t-m
	Transverse eccentricity of  footpath/services				=	5.75	m
	Transverse moment of  footpath/services				=	46.58	t-m
	Total Transverse moment(SIDL Excl. W/C)				=	364.20	t-m
2.3	SIDL(Including Wearing Course
	Load Intensity due to wearing course			Weight of wc*span*cw	=	0.14	t/m2
	DL of Wearing Course				=	18.53	t
	Total reaction on abutment (SIDL excluding W/c)			(18.53/2)	=	9.27	t
	Longitudinal Moment( wearing Course)				=	-	t-m
	Transverse eccentricity of wearing Course				=	-	m
	Transverse moment( wearing Course)				=	-	t-m
2.4	Summary of loads from superstructure
	With Footpath Case
	At Bearing Level
	Load Item	P	ML	MT	HL	HT
		t	t-m	t-m	t-m	t-m
	Deal Load	105.00	0	0	0	0
	SIDL-Excluding W/C	29.98	0	0	0	0
	SIDL-including W/C	9.27	0	0	0	0
	At Abutment shaft bottom level
	Load Item	P	ML	MT	HL	HT
		t	t-m	t-m	t-m	t-m
	Deal Load	105.00	0	0	0	0
	SIDL-Excluding W/C	29.98	0	0	0	0
	SIDL-including W/C	9.27	0	0	0	0
	At Foundatiion bottom level
	Distance from centre of abutment to toe			toe width+shaft width/2	=	3.00	m
	ML		P*eccentricity		=
	Load Item	P	ML(about toe)	MT(about footing c/l	HL	HT
		t	t-m	t-m	t-m	t-m
	Deal Load	105.00	315.00	0	0	0	99.5x2.2 with respect to toe
	SIDL-Excluding W/C	29.98	89.93	0	0	0
	SIDL-including W/C	9.27	27.80	0	0	0
	Calcualtion of Active & Passive earth pressure co-efficients.
	Earth pressure co-efficient calcualtion			from Geo-technical report
		Degree	radians
	𝐴𝑙𝑝ℎ𝑎(𝛼)	90	1.57		alpha(   a  )	Inclination of  the wall with horizontal
	𝐵𝑒𝑡𝑎(𝛽)	0	0.00		Beta(b)	Angle of fill with horizontal
	𝐷𝑒𝑙𝑡𝑎(𝛿)	20	0.35		delta(d)	friction between wall and the soil
	𝑃ℎ𝑖(∅)	30	0.52		Phi(p)	Angle of internal friction of soil
	sin(𝛼+∅)	0.866025		sin(𝛼-∅)	0.866025		cos(𝛼+∅)	-0.5
	sin(𝛼)	1		sin(𝛼)	1		cos(𝛿-𝛼)	0.3420201
	sin(𝛼-𝛿)	0.939693		sin(𝛼+𝛿)	0.939693		cos(𝛼)	6.126E-17
							cos(𝛼-𝛽)	6.126E-17
	sin(∅+𝛿)	0.766044		sin(∅+𝛿)	0.766044
	sin(∅-𝛽)	0.5		sin(∅+𝛽)	0.5
	sin(𝛼-𝛽)	1		sin(𝛼+𝛽)	1
	By Coulombs formula
	Ka	0.290		Kp	3.447
	On  resolving into horizontal & vertical components
	Kah	ka*cos(𝛿)		Kph	kp*cos(𝛿)
	Kah	0.273		Kph	3.239
	Kav	ka*sin(𝛿)		Kpv	kp*sin(𝛿)
	Kav	0.099		Kpv	1.179

 

 

1 Lane-70R  Wheeled Loading:

 

Live load Reactions
	Ra	(123*(13.4-8.2762)/13.4)		=	47.03	t
	Rb	(123-47.03)		=	75.97	t
Total Load of 70R vehicle				=	100.00	t
Total Load of 70R vehicle according this span				=	100.00	t
Total Load (including Impact)			(100*1.23)	=	123.00	t
total length of 70R vehicle		3.96+1.52+2.13+1.37+3.05+1.37		=	13.4	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
Vertical reaction on abutment				=	75.97	t
Braking Force	(123* of 20%)			=	24.60	t
Change in reaction due to braking force			(24.6*(1.2+0.065+1.82)/13.4)	=	5.66	t
Max. Verical force on Abutment				=	81.63	t
Mini. Vertical force on abutment				=	70.30	t
longitudinal moment				=	-	t-m
Total Horozontal force at bearing level			Fh/2	=	12.30	t
Total Horozontal force (Longitudinal)			HL	=	12.30	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	=	237.14	t-m

 

 

 

1 lane Class - A  (Cl.204,IRC:6-2014):-

 

 

	Total Load of Class A vehicle		2.7*2+11.4*2+6.8*4		=	55.40	t
	(depending on the span, wheels can be reduced)
	Total Load of Class A vehicle according this span			(55.4-2.7*2-11.4)	=	38.60	t
	Total Load (including Impact)		(4.5/(6+13.3)+1)		=	47.6	t
	total length of Class A vehicle		1.1+3.2+1.2+4.3+3*3		=	18.80	m
	Actual length of Class A vehicle		4.3+3*3		=	13.30	m
	CG Calculation	(2.7*0+2.7*0+11.4*0+11.4*5.5+6.8*9.8+6.8*12.8+6.8*15.86.8*18.8)/38.6			=	6.20	m

 

 

 

Live load Reactions
	Ra	(47.59*(13.3-6.2)/13.3)		=	22.19	t
	Rb	(47.59-22.19)		=	25.40	t
Vertical reaction on abutment				=	25.40	t
Braking Force	(47.59* of 20%)			=	9.52	t
Change in reaction due to braking force			(9.52*(1.2+0.065+1.82)/13.3)	=	2.21	t
Max. Verical force on Abutment				=	27.61	t
Mini. Vertical force on abutment				=	23.20	t
longitudinal moment				=	-	t-m
Total Horozontal force at bearing level			Fh/2	=	4.76	t
Total Horozontal force (Longitudinal)			HL	=	4.76	t
Total Horozontal force (transverse)			HT	=	-	t

 

 

Transverse Eccentricity		(12/2-(0.15+0.5+2.3/2)		=	4.20	m
Transverse Moment				=	116.0	t-m

 

3	3 lane Class - A

Live load Reactions
	Ra	(3*22.19* of 90%)		=	59.91	t
	Rb	(3*25.4* of 90%)		=	68.59	t
Vertical reaction on abutment				=	68.59	t
Braking Force	(20% of 47.59+ 5% of 47.59%)*90%			=	10.71	t
Change in reaction due to braking force			(10.71*(1.2+0.065+1.82)/13.3)	=	2.50	t
Max. Verical force on Abutment				=	71.09	t
Mini. Vertical force on abutment				=	66.09	t
longitudinal moment				=	-	t-m
Total Horozontal force at bearing level			Fh/2	=	5.4	t
Total Horozontal force (Longitudinal)			HL	=	5.4	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				=	49.8	t-m

 

1 lane 70R +1 lane Class - A:-

Live load Reactions
	Ra	90% of (47.03+ 22.19)		=	62.30	t
	Rb	90% of (75.97+ 25.4)		=	91.23	t
Vertical reaction on abutment				=	91.23	t
Braking Force		(20% of 123+ 5% of 47.59%)*90%		=	24.28	t
Change in reaction due to braking force				=	6.1	t
(24.28*(1.2+0.065+1.82)/13.3)
Max. Verical force on Abutment				=	97.32	t
Mini. Vertical force on abutment				=	85.14	t
longitudinal moment				=	-	t-m
Total Horozontal force at bearing level			Fh/2	=	12.14	t
Total Horozontal force (Longitudinal)			HL	=	12.14	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	=	192.55	t-m
	(90% of (81.63*2.905+27.61*-0.84)

Summary
Load Cae		Pmax	Pmin	ML	MT	HL	HT
		t	t	t-m	t-m	t	t
1 lane 70R-W		81.63	70.30	0	237.14	12.30	0
1 lane Class-A		27.61	23.20	0	115.97	4.76	0
3 lane Class -A		71.09	66.09	0	49.76	5.4	0
1 lane 70R-W+1 lane Class A		97.32	85.14	0	192.55	12.14	0
LL1	Maximum Reaction Case			97.32	t
LL2	Maximum Moment Case			237.14	t-m
At Bearing level
Longitudinal moment at bearing level,ML=HL*(FRL-bearing level+1.2)
		Pmax	Pmin	ML	MT	HL	HT
		t	t	t-m	t-m	t	t
LL1- Maximum Reaction		97.32	85.14	37.45	192.55	12.14	-
LL2- Max. MT		81.63	70.30	37.95	237.14	12.30	-
At Abutment shaft bottom level
		Pmax	Pmin	ML	MT	HL	HT
		t	t	t-m	t-m	t	t
LL1- Maximum Reaction		97.32	85.14	121.59	192.55	12.14	0
LL2- Max. MT		81.63	70.30	123.18	237.14	12.30	0
At Foundation bottom level
Longitudinal moment atfoundation bottom level,ML due HL =ML at bearing level +HL*(bearing level- founding level)
Longitudinal moment at foundation bottom level,ML due P =Pmax* distance between toe & centre of bearing
	Pmax	Pmin	ML due to HL(about toe)	ML due to P(about toe)	MT (about footing)	HL	HT
	t	t	t-m	t-m	t-m	t	t
LL1- Maximum Reaction	97.32	85.14	-133.73	291.97	192.55	12.14	0
LL2- Max. MT	81.63	70.30	-135.48	244.89	237.14	12.30	0

 

Calculation of forces due to Earth Pressure
Provision of weep holes in abutment wall					=	Yes
No hydrostatic force needs to be applied					=	0

Horizontal force due to earth pressure on abutment acts in L-L direction
Width of abutment(skew)				b	=	12	m
Horizontal earth pressure co-efficient				Kah	=	0.273
Horizontal earth pressure co-efficient				Kav	=	0.099
Width of median wall(skew)				b	=	3.5	m
Horizontal earth pressure co-efficient				Kah	=	0.273
Horizontal earth pressure co-efficient				Kav	=	0.099
Earth Pressure@Foundation  bottom Level
Normal Case: LWL
H= Dirt wall top to Founding level					=	9.815
Horizontal force in long. L-L Dimension					=	315.16	t
Lever arm from abutment shaft bottom				0.42*H	=	4.12	t
Moment along L-L			ML		=	-1,299.20	t-m
Abutment Portion		:LWL
Vertical force					=	114.71	t
Lever arm from toe		Base  width of foundation			=	7.5	m
ML		Total Moment along L-L			=	860.33	t-m
Summary of forces at foundation  bottom level
Normal Case
	P	HL	ML due to HL(abouttoe	ML due to P(about toe)
	t	t	t-m	t-m
LWL	114.71	315.16	-1,299.20	860.33
HFL	94.50	266.20	942.88	708.50
Live load surcharge
Abutment shaft Bottom level
Normal Case: Abutment Portion
H					=	9.625	m
Horizontal force		Kah*y*1.2*H*b			=	77.3388	t
Lever arm		H/2-rectangualar shape			=	4.8125	m
ML					=	372.192975	t-m
Summary of forcesdue to live load surcharge at abutment shaft bottom level
Normal Case
			HL	ML due to HL(abouttoe
			t	t-m
		LWL	77.34	372.19
		HFL	77.34	372.19
Normal Case: Abutment Portion
LWL	to Foundation bottom
H	Dirtwall top level- founding level				=	9.815	m
Horizontal force		Kah*y*1.2*H*b			=	77.07	t
Lever arm		H/2-rectangualar shape			=	4.91	m
ML		Anti-clockwise			=	-378.20	t-m
HFL
Total Horizontal force in long Dimension					=	77.06500392
ML					=	-378.196507
Summary of forcesdue to live load surcharge at Foundation bottom level
Normal Case
			HL	ML due to HL(abouttoe
			t	t-m
		LWL	77.07	-378.20
		HFL	77.07	-378.20

 

Calculation of forces on Abutment and Foundation
Calculation of forces on Abutment and Foundation
Abutment Dimensions (square) as shown below:-

	Width of abutment					=	12.00	m
	Return wall in on			1 side		=
	horizontal distance of CG abutment shaft  from vertical face					=	0.5	m
	Normal case
	Component	Weight	Horizontal lever arm from bearing c/l		ML	Horizontal lever arm from toe		ML About toe
		t	m		t-m	m		t-m
	Dirt- wall bracket	4.05	0.953		3.86	3.970		16.08
	Dirt- wall	19.935	0.670		13.36	3.670		73.16
	Abutment Cap	26.64	0		0.00	3.000		79.92
	Abutment Shaft	180	0		0.00	3.000		540.00
	Total	230.625			17.22			709.160
	Hor. Eccentricity of weight of sub-structure from c/l of bearing					=	0.07	m
	Width of abutment shaft at HFL					=	1	m
	Volume of abutment shaft submerged in water					=	63.00	m3
	Bouyancy on abutment shaft					=	-63	t
	Longitudinal Movement due to bouyancy about toe					=	-189	t-m
	Summary of forces at abutment shaft bottom level
	Normal Case
	LWL
	Component	Pmax	Pmin	ML	MT	HL	HT
		t	t	t-m	t-m	t	t
	Weigth of sub-structure	230.625	230.625	17.22	0	0	0
	HFL
	Component	Pmax	Pmin	ML	MT	HL	HT
		t	t	t-m	t-m	t	t
	Weigth of sub-structure	230.625	230.625	17.22	0	0	0
	Bouyancy	-63	-63	-189
	Calcualtion of weight of foundation
	Rectangular Part
	Volume					=	30.60	m3
	Weight					=	76.50	t
	Trapezoidal Part
	Volume					=	39.9	m3
	Weight					=	99.75	t
	Total Volume of Foundation					=	70.50	m3
	Total weight of Foundation					=	176.25	t
						=
	Bouancy force on foundation					=	-70.50	t
	Lever arm from toe			Base width/2		=	4.25	m3
	Moment due to wt of foundation					=	749.06	t-m
	Moment due to buoyancy force on  foundation about toe				ML	=	-299.63	t-m
	Calculation  for Return wall
	Portion	Weight	Hor. Lever arm from toe in L-L dimension		ML about toe
		t	m		t-m
	a	51.6	6.16		317.7
	b	2.4	3.66		8.8
	c	0.06	3.71		0.2
	d	2.2	5.90		12.9
	Total	56.2			339.6
	Hor. Eccentricity of CG of return wall from toe in longitudinal dir.					=	6.04	m
	Hor. Eccentricity of CG of return wall from toe in tranverse dir.					=	5.75	m
	Total moment in transverse direction				MT	=	323.22	t-m
	Submerged height of return wall in HFL case upto foundation top level					=	0	m
	Submerged volume of return wall					=	0	m3
	longitudinal moment due to buoyancy force on return wall					=	0	t-m
	transverse moment due to buoyancy force about centre line of footing					=	0	t-m
						=
	Calculation of Backfill Weight
	width oof backfill in transverse direction(skew)				One side consider	=	11.50	m
	LWL
	Portion	Weight	Hor. Lever arm from toe in L-L dimension		ML about toe
		t	m		t-m
	a	948.85	6.16		5844.9
	b	44.16	3.66		161.6
	c	1.10	3.71		4.1
	d	38.64	6.83		264.0
	Total	1032.8			6274.7
	HFL
	Portion	Weight	Hor. Lever arm from toe in L-L dimension		ML about toe
		t	m		t-m
	a	689.34	5.26		3625.9
	b	15.64	2.86		44.7
	c	1.10	2.91		3.2
	d	19.32	5.90		114.0
	Total	725.4			3787.9
	Summary of forces at foundation bottom level
	Normal Case: LWL
	Components		Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	HL
			t	t	t-m	t-m	t-m	t
	Weigth of Sub-structure		230.63	230.63	-	709.16	-	-
	Weigth of foundation		176.25	176.25	-	749.06	-	-
	Weight of Return Wall		56.21	56.21	-	339.56	323.22	-
	Weight og Backfill		1,032.75	1,032.75	-	6,274.66	-	-

 

 

Load combination( Limit  limited )
Overturning and sliding stability.
Ultimate limit state( For Verification of Equilibrium)
Basic Combination
Overturinig stability			Sliding Stability			Legends
LWL( Lower Water Level)		1	LWL( Lower Water Level)			O	Overturning
1.1	Maximum Reaction case		1.1	Maximum Reaction case		S	Sliding
1.2	Maximum Moment case		1.2	Maximum Moment case		U	Uplift
HFL( Height Flood Level)		2	HFL( Height Flood Level)			R	resisting
2.1	Maximum Reaction case		2.1	Maximum Reaction case		FOS	Factor of Safety
2.2	Maximum Moment case		2.2	Maximum Moment case		Fo	FOS for Overturnung
						Fs	FOS for Sliding
Oveturining Stability						ML	Moment along Longitudial
1	LWL
1.1	Maximum Reaction case
			Unfactored ML ( About toe)	Remarks	Partial safety factor	factored ML ( About toe)	factored  Overturing ML ( About toe)	factored Resistaing ML ( About toe)
			t-m			t-m	t-m	t-m
	DL-Sup		315.00	R	0.95	299.25	-	299.25
	SIDL(exclu.W/C)		89.93	R	0.95	85.44	-	85.44
	SIDL(W/C)		27.80	R	1.00	27.80	-	27.80
	LL1	Due to HL	-133.73	O	1.50	-200.60	-200.60	-
		Due to P	291.97	R	-	-	-	-
	EPLL1		0	O	1.15	-	-	-
	Shearing Rating		-43.1	O	1.00	-43.10	-43.10	-
	Earth Pressure	Due to HL	-1,299.20	O	1.50	-1,948.80	-1,948.80	-
		Due to P	860.33	R	-	-	-	-
	LL Surcharge	Due to HL	-378.20	O	1.20	-453.84	-453.84	-
	Weight of Sub-structure		709.16	R	0.95	673.70	-	673.70
	Weight of Foundation		749.06	R	0.95	711.61	-	711.61
	Return Wall Weight		339.56	R	0.95	322.58	-	322.58
	Backfill Weight		6,274.66	R	0.95	5,960.93	-	5,960.93
	Service Condiation		-1
	MO	-2,646.33	Overturning Moment
	MR	8,081.30	Resisting moment
	Fo	3.05	factor of safety
1.2	Maximum Moment case
			Unfactored ML ( About toe)	Remarks	Partial safety factor	factored ML ( About toe)	factored  Overturing ML ( About toe)	factored Resistaing ML ( About toe)
			t-m			t-m	t-m	t-m
	DL-Sup		315.00	R	0.95	299.3	-	299.25
	SIDL(exclu.W/C)		89.93	R	0.95	85.4	-	85.44
	SIDL(W/C)		27.80	R	1	27.8	-	27.80
	LL2	Due to HL	-135.48	O	1.5	-203.2	-203.23	-
		Due to P	244.89	R	0	0.0	-	-
	EPLL1		0	O	1.15	0.0	-	-
	Shearing Rating		-43.1	O	1	-43.1	-43.10	-
	Earth Pressure	Due to HL	-1,299.20	O	1.5	-1948.8	-1,948.80	-
		Due to P	860.33	R	0	0.0	-	-
	LL Surcharge	Due to HL	-378.20	O	1.2	-453.8	-453.84	-
	Weight of Sub-structure		709.16	R	0.95	673.7	-	673.70
	Weight of Foundation		749.06	R	0.95	711.6	-	711.61
	Return Wall Weight		339.56	R	0.95	322.6	-	322.58
	Backfill Weight		6,274.66	R	0.95	5960.9	-	5,960.93
	Service Condiation
	MO	-2,648.96	Overturning Moment
	MR	8,081.30	Resisting moment
	Fo	3.05	factor of safety
2	HFL
2.1	Maximum Reaction case
			Unfactored ML ( About toe)	Remarks	Partial safety factor	factored ML ( About toe)	factored  Overturing ML ( About toe)	factored Resistaing ML ( About toe)
			t-m			t-m	t-m	t-m
	DL-Sup		315.00	R	0.95	299.3	-	299.25
	SIDL(exclu.W/C)		89.93	R	0.95	85.4	-	85.44
	SIDL(W/C)		27.80	R	1	27.8	-	27.80
	LL1	Due to HL	-133.73	O	1.5	-200.6	-200.60	-
		Due to P	291.97	R	0	0.0	-	-
	EPLL1		0	O	1.15	0.0	-	-
	Shearing Rating		-43.1	O	1	-43.1	-43.10	-
	Earth Pressure	Due to HL	-1,299.20	O	1.5	-1948.8	-1,948.80	-
		Due to P	860.33	R	0	0.0	-	-
	LL Surcharge	Due to HL	-378.20	O	1.2	-453.8	-453.84	-
	Weight of Sub-structure		709.16	R	0.95	673.7	-	673.70
	Bouyancy on structure		-189	O	1	-189.0	-189.00	-
	Weight of Foundation		749.06	R	0.95	711.6	-	711.61
	Bouyancy on foundation		-299.63	O	1	-299.6	-299.63	-
	Return Wall Weight		339.56	R	0.95	322.6	-	322.58
	Bouyancy on return wall		0	O	1	0.0	-	-
	Backfill Weight		6,274.66	R	0.95	5960.9	-	5,960.93
	Service Condiation
	MO	-3134.9575	Overturning Moment
	MR	8081.30259	Resisting moment
	Fo	2.58	factor of safety
2.2	Maximum Moment case
			Unfactored ML ( About toe)	Remarks	Partial safety factor	factored ML ( About toe)	factored  Overturing ML ( About toe)	factored Resistaing ML ( About toe)
			t-m			t-m	t-m	t-m
	DL-Sup		315.00	R	0.95	299.3	-	299.25
	SIDL(exclu.W/C)		89.93	R	0.95	85.4	-	85.44
	SIDL(W/C)		27.80	R	1	27.8	-	27.80
	LL2	Due to HL	-135.48	O	1.5	-203.2	-203.23	-
		Due to P	244.89	R	0	0.0	-	-
	EPLL1		0	O	1.15	0.0	-	-
	Shearing Rating		-43.1	O	1	-43.1	-43.10	-
	Earth Pressure	Due to HL	-1,299.20	O	1.5	-1948.8	-1,948.80	-
		Due to P	860.33	R	0	0.0	-	-
	LL Surcharge	Due to HL	-378.20	O	1.2	-453.8	-453.84	-
	Weight of Sub-structure		709.16	R	0.95	673.7	-	673.70
	Bouyancy on structure		-189	O	1	-189.0	-189.00	-
	Weight of Foundation		749.06	R	0.95	711.6	-	711.61
	Bouyancy on foundation		-299.625	O	1	-299.6	-299.63	-
	Return Wall Weight		339.56	R	0.95	322.6	-	322.58
	Bouyancy on return wall		0	O	1	0.0	-	-
	Backfill Weight		6,274.66	R	0.95	5960.9	-	5,960.93
	Service Condiation
	MO	-3137.5869	Overturning Moment
	MR	8081.30259	Resisting moment
	Fo	2.58	factor of safety( overturning
	Sliding Stability
1	LWL
1.1	Maximum Reaction case
			Unfactored HL	Remarks	Partial safety factor	factored HL	Unfactored Pmin	Remarks	Partial safety factor	factored Pmin
			t			t	t			t
	DL-Sup		0	R	0.95	0.0	105.00	R	0.95	99.8
	SIDL(exclu.W/C)		0	R	0.95	0.0	29.98	R	0.95	28.5
	SIDL(W/C)		0	R	1	0.0	9.27	R	1	9.3
	LL1		12.14	S	1.5	18.2	85.1	R	0	0.0
	EPLL1		0	R	0	0.0	0	U	1.15	0.0
	Shearing Rating		4.8	S	1	4.8	0.0	U	1	0.0
	Earth Pressure		315.16	S	1.5	472.7	114.71	R	0	0.0
	LL Surcharge		77.07	S	1.2	92.5	0.0	U	1.2	0.0
	Weight of Sub-structure		0	R	0.95	0.0	230.625	R	0.95	219.1
	Weight of Foundation		0	R	0.95	0.0	176.25	R	0.95	167.4
	Return Wall Weight		0	R	0.95	0.0	56.2115	R	0.95	53.4
	Backfill Weight		0	R	0.95	0.0	1032.7506	R	0.95	981.1
				Service Condiation
					588.2
					1558.5
					0.50
				Fs	1.32
1.2	Maximum Moment case
			Unfactored HL	Remarks	Partial safety factor	factored HL	Unfactored Pmin	Remarks	Partial safety factor	factored Pmin
			t			t	t			t
	DL-Sup		0	R	0.95	0.0	105.00	R	0.95	99.8
	SIDL(exclu.W/C)		0	R	0.95	0.0	29.98	R	0.95	28.5
	SIDL(W/C)		0	R	1	0.0	9.27	R	1	9.3
	LL2		12.30	S	1.5	18.5	85.1	R	0	0.0
	EPLL1		0	R	0	0.0	0	U	1.15	0.0
	Shearing Rating		4.80	S	1	4.8	0.0	U	1	0.0
	Earth Pressure		315.16	S	1.5	472.7	114.71	R	0	0.0
	LL Surcharge		77.07	S	1.2	92.5	0.0	U	1.2	0.0
	Weight of Sub-structure		0	R	0.95	0.0	230.63	R	0.95	219.1
	Weight of Foundation		0	R	0.95	0.0	176.25	R	0.95	167.4
	Return Wall Weight		0	R	0.95	0.0	56.21	R	0.95	53.4
	Backfill Weight		0	R	0.95	0.0	1,032.75	R	0.95	981.1
				Service Condiation
					588.5
					1558.5
					0.50
				Fs	1.32
2	HFL
2.1	Maximum Reaction case
			Unfactored HL	Remarks	Partial safety factor	factored HL	Unfactored Pmin	Remarks	Partial safety factor	factored Pmin
			t			t	t			t
	DL-Sup		0	R	0.95	0.0	105.00	R	0.95	99.8
	SIDL(exclu.W/C)		0	R	0.95	0.0	29.98	R	0.95	28.5
	SIDL(W/C)		0	R	1	0.0	9.27	R	1	9.3
	LL1		12.14	S	1.5	18.2	85.1	R	0	0.0
	EPLL1		0	S	0	0.0	0	U	1.15	0.0
	Shearing Rating		4.8	S	1	4.8	0.0	U	1	0.0
	Earth Pressure		315.16	S	1.5	472.7	114.71	R	0	0.0
	LL Surcharge		97.32	R	1.2	116.8	0.0	U	1.2	0.0
	Weight of Sub-structure		0	R	0.95	0.0	230.625	R	0.95	219.1
	Bouyancy on structure		0	R	0	0.0	-63	U	1	176.3
	Weight of Foundation		0	R	0.95	0.0	176.25	R	0.95	53.4
	Bouyancy on foundation		0	R	0	0.0	-70.5	U	1	-63.0
	Return Wall Weight		0	R	0.95	0.0	56.2115	R	0.95	167.4
	Bouyancy on return wall		0	R	0	0.0	0	U	1	0.0
	Backfill Weight		0	R	0.95	0.0	1032.7506	R	0.95	981.1
				Service Condiation
					612.55
					1671.79
					0.50
				Fs	1.36
2	HFL
2.2	Maximum Moment case
			Unfactored HL	Remarks	Partial safety factor	factored HL	Unfactored Pmin	Remarks	Partial safety factor	factored Pmin
			t			t	t			t
	DL-Sup		0	R	0.95	0.0	105.00	R	0.95	99.8
	SIDL(exclu.W/C)		0	R	0.95	0.0	29.98	R	0.95	28.5
	SIDL(W/C)		0	R	1	0.0	9.27	R	1	9.3
	LL2		-	S	1.5	0.0	85.1	R	0	0.0
	EPLL1		0	S	0	0.0	0	U	1.15	0.0
	Shearing Rating		4.8	S	1	4.8	0.0	U	1	0.0
	Earth Pressure		266.20	S	1.5	399.3	114.71	R	0	0.0
	LL Surcharge		70.30	R	1.2	84.4	0.0	U	1.2	0.0
	Weight of Sub-structure		0	R	0.95	0.0	230.625	R	0.95	219.1
	Bouyancy on structure		0	R	0	0.0	99.75	U	1	99.8
	Weight of Foundation		0	R	0.95	0.0	176.25	R	0.95	167.4
	Bouyancy on foundation		0	R	0	0.0	-70.5	U	0	0.0
	Return Wall Weight		0	R	0.95	0.0	56.2115	R	0.95	53.4
	Bouyancy on return wall		0	R	0	0.0	0	U	1	0.0
	Backfill Weight		0	R	0.95	0.0	1032.7506	R	0.95	981.1
				Service Condiation
					488.47
					1658.29
					0.50
				Fs	1.70
	Summary	Normal
	FOS against Overturing	1
	FOS against Sliding	1
			Service Condition
			Foverturning	Check	Fsliding	Check
1	1.1		3.05	Ok	1.32	Ok
2	1.2		3.05	Ok	1.32	Ok
	2.1		2.58	Ok	1.36	Ok
	2.2		2.58	Ok	1.70	Ok
	Combination of Base Pressure( Open Foundation) Annex B,IRC 6:2014
	Following Limit states are considered
A	Ultimate Limit State(For Verification of Equilibrium)
A-1	Basic Combination
B	Ultimate Limit State(For Verification of structural strength)
B-1	Basic Combination
C	Serviceability Limit State(SLS)
C-1	Rare combination(For Checking stress limits)
C-2	Quasi-permanent combination(for checking crack width in RCC structure)
D	Combination for Design of Foundation
D-1	Combination -01
D-2	Combination -02
	Overturning & Sliding Stability
	Normal case
1	LWL
1.1	Maximum Reaction case
1.2	Maximum Moment case
2	HFL
2.1	Maximum Reaction case
2.2	Maximum Moment case
	Span present Condition
1	LWL
1.1	Maximum Reaction case
	Load Item	Unfactored
		Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
		t	t	t-m	t-m	t-m
	DL-Sup	105.00	105.00	-	315.00	-
	SIDL(exclu.W/C)	29.98	29.98	-	89.93	-
	SIDL(W/C)	9.27	9.27	-	27.80	-
	LL1	97.32	85.14	-133.73	291.97	192.55
	EPLL1	-	-	-	-	-
	Shearing Rating	-	-	-43.10	-	-
	Earth Pressure	315.16	315.16	-1,299.20	860.33	-
	LL Surcharge	-	-	-378.20	-	-
	Weight of Sub-structure	230.63	230.63	-	709.16	-
	Weight of Foundation	176.25	176.25	-	749.06	-
	Return Wall Weight	56.21	56.21	-	339.56	323.22
	Backfill Weight	1,032.75	1,032.75	-	6,274.66	-
	Total	2,052.57	2,040.39	-1,854.23	9,657.47	515.77
	Eccentricity of vertical load from c/l of footing				=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load from c/l of footing				=	0.455	m
	Longitudinal Moment about c/l of footing			ML	=	920.18	t-m
1.2	Maximum Moment case
	Load Item	Unfactored
		Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
		t	t	t-m	t-m	t-m
	DL-Sup	105.00	99.50	-	315.00	-
	SIDL(exclu.W/C)	29.98	13.30	-	89.93	-
	SIDL(W/C)	9.27	16.10	-	27.80	-
	LL2	81.63	70.30	-135.48	244.89	237.14
	EPLL1	-	-	-	-	-
	Shearing Rating	-	-	-43.10	-	-
	Earth Pressure	315.16	315.16	-1,299.20	1,033.16	-
	LL Surcharge	-	-	-378.20	-	-
	Weight of Sub-structure	230.63	230.63	-	709.16	-
	Weight of Foundation	176.25	176.25	-	749.06	-
	Return Wall Weight	56.21	56.21	-	339.56	323.22
	Backfill Weight	1,032.75	1,032.75	-	6,274.66	-
	Total	2,036.88	2,010.21	-1,855.98	9,783.23	560.36
	Eccentricity of vertical load from c/l of footing				=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing				=	0.553	m
	Longitudinal Moment about c/l of footing			ML	=	729.48	t-m
	Summary
	Service Condition
			Pmax	Pmin	ML	MT
			t	t	t-m	t-m
	1	1.1	2,052.57	2,040.39	920.18	515.77
		1.2	2,036.88	2,010.21	729.48	560.36
	2	2.1	1721	1713.1	321.7	488.3
		2.2	1701.4	1693.5	291.5	530.4
	Base Pressure for Design of Foundation
	Area of Base		=	8.5*12		A	=	102.00	m2
	Longinitudinal Section Modulus		=	12*8.5^2/6		ZL	=	144.50	m3
	Transverse Section Modulus		=	8.5*12^2/6		ZT	=	204.00	m3
	Combination of Base pressure for foundation
	Span Present Condition
		Forces/Moments				For Pmax				For Pmin
		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)	P/A+ML/Zl+MT/Zt	P/A+ML/Zl-MT/Zt	P/A-ML/Zl-MT/Zt	P/A-(ML/Zl+MT/Zt)
		t	t	t-m	t-m	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2
1	1.1	2,052.57	2,040.39	920.18	515.77	29.0	24.0	11.2	16.3	28.9	23.8	11.1	16.2
	1.2	2,036.88	2,010.21	729.48	560.36	27.8	22.3	12.2	17.7	27.5	22.0	11.9	17.4
2	2.1	1,721.00	1,713.10	321.70	488.30	21.5	16.7	12.3	17.0	21.4	16.6	12.2	17.0
	2.2	1,701.40	1,693.50	291.50	530.40	21.3	16.1	12.1	17.3	21.2	16.0	12.0	17.2
	LWL
	Normal
	Maximum Axial Force Condition						Maximum Axial Force Condition
	Maximum Base Pressure		=	29.0	t/m2		Maximum Base Pressure		=	29.0	t/m2
	Minimum Base Pressure		=	11.2	t/m2		Minimum Base Pressure		=	11.2	t/m2
	Maximum Base Pressure		=	29.0	t/m2	OK	<33.42	t/m2	Gross Pressure
	Minimum Base Pressure		=	11.2	t/m2	OK	>0	t/m2
	HFL
	Normal
	Maximum Axial Force Condition						Maximum Axial Force Condition
	Maximum Base Pressure		=	21.5	t/m2		Maximum Base Pressure		=	21.5	t/m2
	Minimum Base Pressure		=	12.0	t/m2		Minimum Base Pressure		=	12.0	t/m2
	Maximum Base Pressure		=	21.5	t/m2	OK
	Minimum Base Pressure		=	12.0	t/m2	OK
	Combination for Design of Foundation
	D-1 Combination-01(ULS)
1	LWL
1.1	Maximum Reaction case
1.2	Maximum Moment case
2	HFL
2.1	Maximum Reaction case
2.2	Maximum Moment case
1	LWL
1.1	Maximum Reaction case
		Partial Safety Factor	Unfactored					factored
			Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1.35	105.00	105.00	-	315.00	-	141.75	141.75	-	425.25	-
	SIDL(exclu.W/C)	1.35	29.98	29.98	-	89.93	-	40.47	40.47	-	121.41	-
	SIDL(W/C)	1.75	9.27	9.27	-	27.80	-	16.22	16.22	-	48.65	-
	LL1	1.30	97.32	85.14	-133.73	291.97	192.55	126.52	110.69	-173.85	379.57	250.32
	EPLL1	1.20	-	-	-	-	-	-	-	-	-	-
	Shearing Rating	0.90	-	-	-43.10	-	-	-	-	-38.79	-	-
	Earth Pressure	1.50	315.16	315.16	-1,299.20	860.33	-	472.75	472.75	-1,948.80	1,290.49	-
	LL Surcharge	1.20	-	-	-378.20	-	-	-	-	-453.84	-	-
	Weight of Sub-structure	1.35	230.63	230.63	-	709.16	-	311.34	311.34	-	957.37	-
	Weight of Foundation	1.35	176.25	176.25	-	749.06	-	237.94	237.94	-	1,011.23	-
	Return Wall Weight	1.35	56.21	56.21	-	339.56	339.40	75.89	75.89	-	458.40	458.19
	Backfill Weight	1.35	1,032.75	1,032.75	-	6,274.66	-	1,394.21	1,394.21	-	8,470.79	-
	Total							2817.1	2801.2	-2615.3	13163.2	708.5
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.423	m
	Longitudinal Moment about c/l of footing				ML		=	1,424.73	t-m
1.2	Maximum Moment case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1.35	105.00	105	0	315.00	0	141.8	141.8	0.0	425.3	0.0
	SIDL(exclu.W/C)	1.35	29.98	29.977632	0	89.93	0	40.5	40.5	0.0	121.4	0.0
	SIDL(W/C)	1.75	9.27	9.2664	0	27.80	0	16.2	16.2	0.0	48.6	0.0
	LL2	1.5	81.63	70.30	-135.48	244.89	237.14	122.4	105.5	-203.2	367.3	355.7
	EPLL2	1.2	0	0	0	0.0	0	0.0	0.0	0.0	0.0	0.0
	Shearing Rating	0.9	0	0	-43.1	0.0	0.0	0.0	0.0	-38.8	0.0	0.0
	Earth Pressure	1.5	315.16	315.16	-1,299.20	860.33	0.0	472.7	472.7	-1948.8	1290.5	0.0
	LL Surcharge	1.2	0	0	-453.5	0.0	0.0	0.0	0.0	-544.2	0.0	0.0
	Weight of Sub-structure	1.35	230.63	230.625	0	709.16	0	311.3	311.3	0.0	957.4	0.0
	Weight of Foundation	1.35	176.25	176.25	0	749.06	0	237.9	237.9	0.0	1011.2	0.0
	Return Wall Weight	1.35	56.21	56.2115	0	339.56	323.22	75.9	75.9	0.0	458.4	436.3
	Backfill Weight	1.35	1,032.75	1032.7506	0	6,274.66	0	1394.2	1394.2	0.0	8470.8	0.0
	Total							2813.0	2796.0	-2735.0	13150.9	792.1
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.425	m
	Longitudinal Moment about c/l of footing				ML		=	1,539.37	t-m
2	HFL
2.1	Maximum Reaction case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1.35	99.5	99.5	0	218.9	0	134.3	134.3	0.0	295.5	0.0
	SIDL(exclu.W/C)	1.35	13.3	13.3	0	29.3	0	18.0	18.0	0.0	39.5	0.0
	SIDL(W/C)	1.75	16.1	16.1	0	25.4	0	28.2	28.2	0.0	62.0	0.0
	LL1	1.5	85.4	77.5	-115.6	187.9	148.9	128.1	116.3	-173.5	281.8	223.4
	EPLL1	1.2	0	0	0	0.0	0	0.0	0.0	0.0	0.0	0.0
	Shearing Rating	0.9	0	0	-43.1	0.0	0.0	0.0	0.0	-38.8	0.0	0.0
	Earth Pressure	1.5	94.5	94.5	-1686.4	1033.2	0.0	141.8	141.8	-1618.2	1062.9	0.0
	LL Surcharge	1.2	0	0	-453.5	0.0	0.0	0.0	0.0	-544.3	0.0	0.0
	Weight of Sub-structure	1.35	262.1	262.1	0	577.9	0	353.8	353.8	0.0	780.2	0.0
	Buoyancy on sub.str	1	-89.1	-89.1	0	-195.9		-89.1	-89.1	0.0	-195.9	0.0
	Weight of Foundation	1.35	156.8	156.8	0	587.8	0	211.6	211.6	0.0	793.5	0.0
	Buoyancy on Foundation	1	-62.7	-62.7		-235.1	0	-62.7	-62.7		-235.1
	Return Wall Weight	1.35	59	59	0	304.6	339.4	79.7	79.7	0.0	411.2	458.2
	Buoyancy on return wall	1	0	0	0	0	0	0.0	0.0	0	0	0
	Backfill Weight	1.35	1086.1	1086.1	0	5604.1	0	1466.2	1466.2	0.0	7566.5	0.0
	Total							2409.8	2398.0	-2374.8	10862.1	681.6
	Eccentricity of vertical load fron c/l of footing						=	0.8	m
	Longitudinal Moment about c/l of footing				ML		=	551.00	t-m
2.2	Maximum Moment case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1.35	99.5	99.5	0	218.9	0	134.3	134.3	0.0	295.5	0.0
	SIDL(exclu.W/C)	1.35	13.3	13.3	0	29.3	0	18.0	18.0	0.0	39.5	0.0
	SIDL(W/C)	1.75	16.1	16.1	0	25.4	0	28.2	28.2	0.0	62.0	0.0
	LL1	1.5	65.8	57.8	-116	144.7	191.0	98.7	86.7	-173.5	217.0	286.5
	EPLL1	1.2	0	0	0	0.0	0	0.0	0.0	0.0	0.0	0.0
	Shearing Rating	0.9	0	0	-43.1	0.0	0.0	0.0	0.0	-38.8	0.0	0.0
	Earth Pressure	1.5	94.5	94.5	-1686.4	1033.2	0.0	141.8	141.8	-1618.2	1062.9	0.0
	LL Surcharge	1.2	0	0	-453.5	0.0	0.0	0.0	0.0	-544.3	0.0	0.0
	Weight of Sub-structure	1.35	262.1	262.1	0	577.9	0	353.8	353.8	0.0	780.2	0.0
	Buoyancy on sub.str	1	-89.1	-89.1	0	-195.9		-89.1	-89.1	0.0	-195.9	0.0
	Weight of Foundation	1.35	156.8	156.8	0	587.8	0	211.6	211.6	0.0	793.5	0.0
	Buoyancy on Foundation	1	-62.7	-62.7		-235.1	0	-62.7	-62.7		-235.1
	Return Wall Weight	1.35	59	59	0	304.6	339.4	79.7	79.7	0.0	411.2	458.2
	Buoyancy on return wall	1	0	0	0	0	0	0.0	0.0	0	0	0
	Backfill Weight	1.35	1086.1	1086.1	0	5604.1	0	1466.2	1466.2	0.0	7566.5	0.0
	Total							2380.4	2368.4	-2374.8	10797.3	744.7
	Eccentricity of vertical load fron c/l of footing						=	0.8	m
	Longitudinal Moment about c/l of footing				ML		=	505.80	t-m
	Summary
	Service Condition		Pmax	Pmin	ML	MT
			t	t	t-m	t-m
	1	1.1	2,817.08	2,801.25	1,424.73	708.51
		1.2	2,813.01	2,796.02	1,539.37	792.05
	2	2.1	2,409.83	2,397.98	551.00	681.60
		2.2	2,380.43	2,368.43	505.80	744.70
	Combination for design of Foundation
	D-2 Combination-02(SLS)
1	LWL
1.1	Maximum Reaction case
1.2	Maximum Moment case
2	HFL
2.1	Maximum Reaction case
2.2	Maximum Moment case
1	LWL
1.1	Maximum Reaction case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1	105.00	105.00	-	315.00	-	105.00	105.00	-	315.00	-
	SIDL(exclu.W/C)	1	29.98	29.98	-	89.93	-	29.98	29.98	-	89.93	-
	SIDL(W/C)	1	9.27	9.27	-	27.80	-	9.27	9.27	-	27.80	-
	LL1	1.3	97.32	85.14	-133.73	291.97	192.55	126.52	110.69	-173.85	379.57	250.32
	EPLL1	1	-	-	-	-	-	-	-	-	-	-
	Shearing Rating	0.8	-	-	-43.10	-	-	-	-	-34.48	-	-
	Earth Pressure	1.3	315.16	315.16	-1,299.20	860.33	-	409.71	409.71	-1,688.96	1,118.42	-
	LL Surcharge	1	-	-	372.19	-	-	-	-	372.19	-	-
	Weight of Sub-structure	1	230.63	230.63	-	709.16	-	230.63	230.63	-	709.16	-
	Weight of Foundation	1	176.25	176.25	-	749.06	-	176.25	176.25	-	749.06	-
	Return Wall Weight	1	56.21	56.21	-	339.56	339.40	56.21	56.21	-	339.56	339.40
	Backfill Weight	1	1,032.75	1,032.75	-	6,274.66	-	1,032.75	1,032.75	-	6,274.66	-
	Total							2176.3	2160.5	-1525.1	10003.2	589.7
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.346	m
	Longitudinal Moment about c/l of footing				ML		=	771.28	t-m
1.2	Maximum Moment case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1	105.00	105.00	-	315.00	-	105.00	105.00	-	315.00	-
	SIDL(exclu.W/C)	1	29.98	29.98	-	89.93	-	29.98	29.98	-	89.93	-
	SIDL(W/C)	1	9.27	9.27	-	27.80	-	9.27	9.27	-	27.80	-
	LL2	1.3	81.63	70.30	-135.48	244.89	237.14	106.12	91.40	-176.13	318.36	308.28
	EPLL2	1	-	-	-	-	-	-	-	-	-	-
	Shearing Rating	0.8	-	-	-43.10	-	-	-	-	-34.48	-	-
	Earth Pressure	1.3	315.16	315.16	-1,299.20	860.33	-	409.71	409.71	-1,688.96	1,118.42	-
	LL Surcharge	1	-	-	372.19	-	-	-	-	372.19	-	-
	Weight of Sub-structure	1	230.63	230.63	-	709.16	-	230.63	230.63	-	709.16	-
	Weight of Foundation	1	176.25	176.25	-	749.06	-	176.25	176.25	-	749.06	-
	Return Wall Weight	1	56.21	56.21	-	339.56	339.40	56.21	56.21	-	339.56	339.40
	Backfill Weight	1	1,032.75	1,032.75	-	6,274.66	-	1,032.75	1,032.75	-	6,274.66	-
	Total							2155.9	2141.2	-1527.4	9942.0	647.7
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.361	m
	Longitudinal Moment about c/l of footing				ML		=	748.06	t-m
2	HFL
2.1	Maximum Reaction case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1	105.00	105	0	218.9	0	105.0	105.0	0.0	218.9	0.0
	SIDL(exclu.W/C)	1	29.98	29.977632	0	29.3	0	30.0	30.0	0.0	29.3	0.0
	SIDL(W/C)	1	9.27	9.2664	0	25.4	0	9.3	9.3	0.0	25.4	0.0
	LL1	1.3	97.32	77.5	-115.6	187.9	148.9	126.5	100.8	-150.3	244.3	193.6
	EPLL1	1	0	0	0	0.0	0	0.0	0.0	0.0	0.0	0.0
	Shearing Rating	0.8	0	0	-43.1	0.0	0.0	0.0	0.0	-34.5	0.0	0.0
	Earth Pressure	1.3	315.16	315.16	-1,299.20	860.33	-	409.7	409.7	-1689.0	1118.4	0.0
	LL Surcharge	1	0	0	-453.5	0.0	0.0	0.0	0.0	-453.5	0.0	0.0
	Weight of Sub-structure	1	230.63	230.625	0	709.2	0	230.6	230.6	0.0	709.2	0.0
	Buoyancy on sub.str	1	-63	-63	0	-189.0		-63.0	-63.0	0.0	-189.0	0.0
	Weight of Foundation	1	176.25	176.25	0	749.1	0	156.8	156.8	0.0	749.1	0.0
	Buoyancy on Foundation	1	-70.5	-70.5		-235.1	0	-70.5	-70.5	0.0	-235.1	0.0
	Return Wall Weight	1	56.21	56.2115	0	339.6	339.4	56.2	56.2	0.0	339.6	339.4
	Buoyancy on return wall	1	0	0	0	0	0	0.0	0.0	0.0	0.0	0.0
	Backfill Weight	1	1,032.75	1032.7506	0	6274.7	0	1032.8	1032.8	0.0	6274.7	0.0
	Total							2023.4	1997.6	-2327.2	9284.6	533.0
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.339	m
	Longitudinal Moment about c/l of footing				ML		=	1,641.89	t-m
	HFL Case
2.2	Maximum Moment case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1	105.00	105	0	218.9	0	105.0	105.0	0.0	218.9	0.0
	SIDL(exclu.W/C)	1	29.98	29.977632	0	29.3	0	30.0	30.0	0.0	29.3	0.0
	SIDL(W/C)	1	9.27	9.2664	0	25.4	0	9.3	9.3	0.0	25.4	0.0
	LL2	1.3	81.63	70.30	-135.48	244.89	237.14	85.4	75.2	-176.1	318.4	308.3
	EPLL1	1	0	0	0	0.0	0	0.0	0.0	0.0	0.0	0.0
	Shearing Rating	0.8	0	0	-43.1	0.0	0.0	0.0	0.0	-34.5	0.0	0.0
	Earth Pressure	1.3	315.16	315.16	-1,299.20	860.33	-	409.7	409.7	-1689.0	1118.4	0.0
	LL Surcharge	1	0	0	-453.5	0.0	0.0	0.0	0.0	-453.5	0.0	0.0
	Weight of Sub-structure	1	230.63	230.625	0	709.2	0	230.6	230.6	0.0	709.2	0.0
	Buoyancy on sub.str	1	-63	-63	0	-189.0		-63.0	-63.0	0.0	-189.0	0.0
	Weight of Foundation	1	176.25	176.25	0	749.1	0	156.8	156.8	0.0	749.1	0.0
	Buoyancy on Foundation	1	-70.5	-70.5		-235.1	0	-70.5	-70.5	0.0	-235.1	0.0
	Return Wall Weight	1	56.21	56.2115	0	339.6	339.4	56.2	56.2	0.0	339.6	339.4
	Buoyancy on return wall	1	0	0	0	0	0	0.0	0.0	0.0	0.0	0.0
	Backfill Weight	1	1,032.75	1032.7506	0	6274.7	0	1032.8	1032.8	0.0	6274.7	0.0
	Total							1982.2	1972.0	-2353.1	9358.7	647.7
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.471	m
	Longitudinal Moment about c/l of footing				ML		=	1,418.88	t-m	-2353+934.0750211663
	Summary Comb-1
	Service Condition		Pmax	Pmin	ML	MT
			t	t	t-m	t-m
	LWL	1.1	2,817.08	2,801.25	1,424.73	708.51
		1.2	2,813.01	2,796.02	1,539.37	792.05
	HFL	2.1	2,023.37	1,997.59	1,641.89	532.97
		2.2	1,982.24	1,972.04	1,418.88	647.68
	Base Pressure for Design of Foundation
	Area of Base		A	=	102.00	m2	Corner-01	p1	=	P/A+ML/Zl+MT/Zt		++
	Longinitudinal Section Modulus		ZL	=	144.50	m3	Corner-02	p2	=	P/A+(ML/Zl-MT/Zt)		+-
	Transverse Section Modulus		ZT	=	204.00	m3	Corner-03	p3	=	P/A-ML/Zl-MT/Zt		-,-
							Corner-04	p4	=	P/A-ML/Zl+MT/Zt		-,+
	Combination of Base pressure for foundation_ Ultimate Limit state (ULS)
	D-1 Combination-01
	Service Condition
		Forces/Moments				For Pmax				For Pmin
		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)	P/A+ML/Zl+MT/Zt	P/A+ML/Zl-MT/Zt	P/A-ML/Zl-MT/Zt	P/A-(ML/Zl+MT/Zt)
		t	t	t-m	t-m	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2
1	1.1	2,817.08	2,801.25	1,424.73	708.51	41.0	34.0	14.3	21.2	40.8	33.8	14.1	21.1
	1.2	2,813.01	2,796.02	1,539.37	792.05	42.1	34.3	13.0	20.8	41.9	34.2	12.9	20.6
2	2.1	2,409.83	2,397.98	551.00	681.60	30.8	24.1	16.5	23.2	30.7	24.0	16.4	23.0
	2.2	2,380.43	2,368.43	505.80	744.70	30.5	23.2	16.2	23.5	30.4	23.1	16.1	23.4
	Combination-01
	Critical Case for Design
	Ultimate Limit state (ULS)
	Maximum pressure at toe corresponding pressure at heel						Manimum pressure at heel corresponding pressure at toe
	Corner1,2	Toe End
	Corner 3,4	Heel End
	LWL			HFL			LWL			HFL
	Corner	Gross Pressure		Corner	Gross Pressure		Corner	Gross Pressure		Corner	Gross Pressure
		t/m2			t/m2			t/m2			t/m2
	1	42.1		1	30.8		1	40.8		1	30.4
	2	34.3		2	24.1		2	33.8		2	23.1
	3	14.3		3	16.5		3	12.9		3	16.1
	4	21.2		4	23.5		4	20.6		4	23.0
	Combination of Base pressure for foundation
	D-2 Combination-02
	Summary Comb 2 Serviceability  Limit state (SLS)
	Service Condition		Pmax	Pmin	ML	MT
			t	t	t-m	t-m
	LWL	1.1	2,176.32	2,160.48	771.28	589.72
		1.2	2,155.92	2,141.19	748.06	647.68
	Service Condition
		Forces/Moments				For Pmax				For Pmin
		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)	P/A+ML/Zl+MT/Zt	P/A+ML/Zl-MT/Zt	P/A-ML/Zl-MT/Zt	P/A-(ML/Zl+MT/Zt)
		t	t	t-m	t-m	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2
1	1.1	2,176.32	2,160.48	771.28	589.72	29.6	23.8	13.1	18.9	29.4	23.6	13.0	18.7
	1.2	2,155.92	2,141.19	748.06	647.68	29.5	23.1	12.8	19.1	29.3	23.0	12.6	19.0
2	2.1	2,023.37	1,997.59	1,641.89	532.97	33.8	28.6	5.9	11.1	33.6	28.3	5.6	10.8
	2.2	1,982.24	1,972.04	1,418.88	647.68	32.4	26.1	6.4	12.8	32.3	26.0	6.3	12.7
	Combination-02
	Serviceability  Limit state (SLS)
	Maximum pressure at toe corresponding pressure at heel						Manimum pressure at heel corresponding pressure at toe
	LWL			HFL			LWL			HFL
	Corner	Gross Pressure		Corner	Gross Pressure		Corner	Gross Pressure		Corner	Gross Pressure
		t/m2			t/m2			t/m2			t/m2
	1	29.6		1	33.8		1	29.3		1	32.3
	2	23.8		2	28.6		2	23.0		2	26.0
	3	13.1		3	6.4		3	12.6		3	5.6
	4	19.1		4	12.8		4	18.7		4	10.83

 

Moment of Resistane of rectangular concrete section (as per IRC:112-2011)

 

Properties of Concrete

Grade of Concrete

From IRC 112,Table 6.5

=

M 35

Characteristic Strength of Concrete

fck

=

35

Mpa=N/mm2

Design compressive Strength of Concrete

fcd

=

15.63

Mpa

fcd

α*fck/𝛾𝑚

Tensile Strength of Concrete

fctm

=

2.80

Mpa

Table 6.5

Momulus of Elasticity of Concrete

Ecm

=

3.20E+04

Mpa

Partial Materials Safety Factor for Concrete

𝛾𝑚

=

1.5

Ultimate Compressive strain in the concrete

=

0.0035

Constant

α

=

0.67

Properties of Steel

Grade of Steel

=

Fe 500

Characteristic Strength of Steel

fyk

=

500

Mpa=N/mm2

Momulus of Elasticity of Steel

Es

=

2.00E+05

Mpa

Refer Cl.6.2.2 & 6.3.5,IRC:112-2011

Partial Materials Safety Factor for Steel

𝛾s

𝛾s

=

1.15

Ultimate Compressive strain in the Steel

=

2.17E-03

=

fyk/Es*𝛾s

Design Yield Strength

fyd

=

434.78

Mpa

fyd

=

fyk/𝛾s

ULS

Grade of Concrete

fck

=

M 35

N/mm2

As per Clause6.4.2.8,IRC:112-2020,Page No-39

fcd

=

15.63

N/mm2

𝛼

=

0.67

for basic & Seismic combination

𝛾𝑠

=

1.5

Grade of Concrete

fy

=

500

N/mm2

Ys

=

1.15

fyd

=

434.78

Refer Fig. 6.2 of IRC 112-2011

For Steel reinforcement, simplified bilinear diagram is used

Minimum strain in steel reinforcement

=

0.87fy/Es+0.002

Modulus of Elasticity of steel

Es

=

2.00E+05

Mpa

Compressive force

Cu

=

0.36*fck*b*xulim

=

17/21*fcd*b*xu,lim

=

0.80952*fcd*b*xu,lim

CG of compression block from top fibre

=

0.42Xu,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)

=

5.86

For Fe500, Xu,lim/d

=

0.633

Calculation of Reinforcement

Tensile reinforcment caan be calculated from the follwing formalu

pt/100=Ast/bd=.973fcd/fyd[1-sqrt(1-2.005*Mulim/fcd)

Where

R=Mu/bd2

pt,lim

=

Where

Rlim=Mu,lim/bd2

=

1.81957562

 

 

Design of Heel and Toe Slab (LWL Case)

 

 

Case:01	Max.Pressure at toe and corresponding pressure at heel
Case:02	Max.Pressure at heel and corresponding pressure at toe
	Corner1,2	Toe End
	Corner 3,4	Heel End
1	Max.Pressure at toe(Corner -1) and corresponding pressure at heel @Ultimate Limit state (ULS)
	Corner	Gross Pressure
		t/m2
	1	42.1
	2	34.3
	3	14.3
	4	21.2
	Ultimate Limit state (ULS) combo-1
Using interpolation of triangles, the pressure at face to the support & at "d" distance from the support is determined
	Heel End		21.23/2+14.29/2			=	17.76	t/m2
	A-A		17.76+5/8.5*(38.23-17.76)			=	29.80	t/m2
Gross	Toe End		34.35/2+42.11/2			=	38.23	t/m2
	B-B		17.76+(8.5-2.5)/8.5*(38.23-17.76)			=	32.21	t/m2
	at deff from A-A		29.8-0.9125/5*(29.8-17.76)			=	26.07	t/m2
	at deff from B-B		38.23-0.9125/2.5*(38.23-32.21)			=	36.03	t/m2
	Heel End		17.76-((9.82-0.3)*2-0.3*2.5)*1.35			=	-6.92	t/m2
	A-A		29.8-((9.82-1)*2-1*2.5)*1.35			=	9.38	t/m2
Net	Toe End		38.23-((226.58-224.25)*2+0.3*2.5)*1.35			=	30.93	t/m2
	B-B		32.21-(1*2.5)*1.35			=	28.84	t/m2
	at deff from A-A		26.07-((9.82-0.872)*2-0.872*2.5)*1.35			=	4.84	t/m2
	at deff from B-B		36.03-(0.745*2.5)*1.35			=	33.52	t/m2
	Overall  depth	at A-A	((1-0.3)*(5-0.9125)/5)+0.3			=	0.872	mm
	Overall  depth	at B-B	((1-0.3)*(2.5-0.9125)/2.5)+0.3			=	0.745	mm

 

 

2	Min.Pressure at heel(Corner -3) and corresponding pressure at toe@Ultimate Limit state (ULS)
	Corner	Gross Pressure		Corner1,2	Toe End
		t/m2		Corner 3,4	Heel End
	1	40.8
	2	33.8
	3	12.9
	4	20.6
	Ultimate Limit state (ULS) combo-1
	Using interpolation of triangles, the pressure at face to the support & at "d" distance from the support is determined
	Heel End		(20.64+12.88)/2			=	16.76	t/m2
	A-A		16.76+5/8.5*(37.32-16.76)			=	28.86	t/m2
Gross	Toe End		(33.85+40.8)/2			=	37.32	t/m2
	B-B		16.76+(8.5-2.5)/8.5*(37.32-16.76)			=	31.27	t/m2
	at deff from A-A		28.86-0.9125/5*(28.86-16.76)			=	25.10	t/m2
	at deff from B-B		37.32-0.9125/2.5*(37.32-31.27)			=	35.12	t/m2
	Heel End		16.76-((9.82-0.3)*2-0.3*2.5)*1.35			=	-7.92	t/m2
	A-A		28.86-((9.82-1)*2-1*2.5)*1.35			=	8.43	t/m2
Net	Toe End		37.32-((226.58-224.25)*2+0.3*2.5)*1.35			=	30.02	t/m2
	B-B		31.27-(1*2.5)*1.35			=	27.90	t/m2
	at deff from A-A		25.1-((9.82-0.872)*2-0.872*2.5)*1.35			=	3.90	t/m2
	at deff from B-B		35.12-(0.745*2.5)*1.35			=	32.60	t/m2
	Overall  depth	at A-A	((1-0.3)*(5-0.9125)/5)+0.3			=	0.872	mm
	Overall  depth	at B-B	((1-0.3)*(2.5-0.9125)/2.5)+0.3			=	0.745	mm
	Effective depth provided		At top		dprovided				=
		Section
	Pressure(t/m2)	Heel End	A-A	Toe End	B-B	at deff from A-A	at deff from B-B
	Gross Pressure (Case 1)	17.8	29.8	38.2	32.2	26.1	36.0
	Gross Pressure (Case 2)	16.8	28.9	37.3	31.3	25.1	35.1
	NetPressure (Case 1)	-6.9	9.4	30.9	28.8	4.8	33.5
	Net Pressure (Case 2)	-7.9	8.4	30.0	27.9	3.9	32.6

 

 

Design of Heel Slab
Design for Flexure
Critical section is at face of wall
Overall depth of Section					=	1000	mm
Design moment per m width
((-6.92*5^2)/2+((0.5(9.38-(-6.92))*5^2))/3				Mu	=	-18.59	t-m	178	mm
((-7.92*5^2)/2+((0.5(8.43-(-7.92))*5^2))/3				Mu	=	-30.87	t-m	230	mm
				Rlim	=	5.86	Mpa	1 Mpa=1N/m2
Effective depth required				dreqd	=	Sqrt(Mu/Rlim*b)
					=	178	mm
Effective depth provided		At top		dprovided	=	912.5	mm	>	178	OK
		At top		dprovided	=	912.5	mm	>	230	OK
				R	=	Mu/bd2
					=	0.22
Ast,required				Ast	=
Ast,required
				Ast	=	472.02	mm2
Minimum,Ast required per m width		(max. of 0.26fctm/fyk*bt*d and 0.0013bt*d)			=	1,186.25	mm2
Governing,Ast required per m width			1,530.24	1186.25	=	1,186.25	mm2
Provide	25 mm  Dia.	Bars	@	200 mm c/c	at top
	25 mm  Dia.	Bars	@	200 mm c/c
Ast,provide					=	4,908.74	mm2	Ok
So				Ru	=	Mu/bd2
				Ru	=	0.371
Ast,required					=	787.58	mm2
Minimum,Ast required per m width		(max. of 0.26fctm/fck*bt*d and 0.0013bt*d)			=	787.58	mm2
Governing,Ast required per m width			1,530.24	1186.25	=	787.58	mm2
Provide	25 mm  Dia.	Bars	@	200 mm c/c	Bottom
	25 mm  Dia.	Bars	@	200 mm c/c
Ast,provided					=	4,908.74	mm2	Ok
Design of One way Shear
Critical section is at deff distance from the face of abutment wall
Overall depth of section					=	0.872	mm
Design shear force per m width				Vu	=	11.93	t
Tensile reinforcement				Ast	=	4,908.74	mm2
Width of beam				bw	=	1000	mm
Effective depth				d	=	784.75	mm
Area of Concrete				Ac	=	7.79E+05	mm2
Axial force due to prestress				NEd	=	0	Kn	Cl.10.2.3,IRC 112-2011
	K=			k	=	1.50	Ok	Cl.10.3.2,IRC:112-2011
		=			=	0.34	n/mm2
Concrete Compressive stress at centroidal axis due to axial loading or prestressing		=	NEd/Ac<0.2fcd		=	0	Ok
	pl	=	Asl/bw*d<=0.02		=	0.00626	Ok	Cl.10.3.2,IRC:112-2011
Shear Capacity of section without Shear reinforcement(Cl10.3.2,IRC:112-2011,Page no-88)
						>=
Design Shear Resistance(VRd.c)		=	[0.12K(80plfcd)^0.33+0.15*𝜕cp]*bw*d>=(Vmin+0.15*𝜕cp)bw*d
	VRd.c	=	0.365	t	>=	0.266	t	Ok

 

 

 

Design of Toe Slab
Design for Flexure
Critical section is at face of wall
Overall depth of Section					=	1000	mm
Design moment per m width
(35.01*1.7^2)/2+(0.5*(32.63-35.01)*1.7^2)/3				Mu	=	94.47	t-m
(34.11*1.7^2)/2+(0.5*(35.08-34.11)*1.7^2)/3				Mu	=	91.60	t-m
			Design	Mu	=	94.47	t-m	49.76x10^7	N-mm
				Rlim	=	5.86	Mpa	1 Mpa=1 N/mm2
Effective depth required				dreqd	=	Sqrt(Mu/Rlim*b)
					=	402	mm
Effective depth provided				dprovided	=	912.5	mm	Ok
				R	=	Mu/bd2
					=	1.13
Ast,required				Ast	=	0.973fcd/fyd[1-sqrt(1-2.055Rlim/fcd)bd
Ast,required				Ast	=	2,476.66	mm2	Not Satisfied
Minimum,Ast required per m width		(max. of 0.26fctm/fyk*bt*d and 0.0013bt*d)			=	1186.25	mm2
Governing,Ast required per m width			1,530.24	1186.25	=	2,476.66	mm2
Provide	25 mm  Dia.	Bars	@	200 mm c/c	at bottom
	25 mm  Dia.	Bars	@	200 mm c/c
Ast,provide					=	4,908.74	mm2
Design of One way Shear
Critical section is at deff distance from the face of abutment wall
Overall depth of section					=	0.745	mm
Design shear force per m width				Vu	=	8.60	t
Tensile reinforcement				Ast	=	4,908.74	mm2
Width of beam				bw	=	1000	mm
Effective depth				d	=	657.00	mm
Area of Concrete				Ac	=	6.57E+05	mm2
Axial force				NEd	=	0	Kn	No axial force act here		Cl.10.2.3,IRC 112-2011
	K=			k	=	1.55	<=	2	Ok	Cl.10.3.2,IRC:112-2011
	Vmin	=	0.031k^3/2fck^1/2		=	0.35	n/mm2
Concrete Compressive stress at centroidal axis due to axial loading or prestressing		=	NEd/Ac<0.2fcd		=	0.00E+00	t/mm2	ok	<.2fcd=3.1267
	pl	=	Asl/bw*d<=0.02		=	0.00747	<=0.02	Ok	Cl.10.3.2,IRC:112-2011
Shear Capacity of section with out shear reinforcement(Cl10.3.2,IRC:112-2011,Page no-88)
						>=
	VRd.c	=	[0.12K(80plfcd)^0.33+0.15*𝜕cp]*bw*d>=(Vmin+0.15*𝜕cp)bw*d
		=	0.334	t	>=	0.233	t	Ok
Distribution Reinforcment
Secondary reinforcment required per meter					=	495.33	mm2
20% of main reinforcement, Cl.16.6.1,IRC 112-2011
Provide	12 mm  Dia.	Bars	@	200 mm c/c
Ast,provided					=	565.49	mm2
							Ok

 

	Serviceability Limit State(SLS) Combination-02
1	Max.Pressure at toe(Corner -1) and corresponding pressure at heel
	Corner	Gross Pressure
		t/m2
	1	29.6
	2	23.8
	3	13.1
	4	19.1
	Heel End		(23.78+29.56)/2			=	16.12	t/m2
	A-A		16.12+5/8.5*(26.67-16.12)			=	22.33	t/m2
Gross	Toe End		(23.78+29.56)/2			=	26.67	t/m2
	B-B		16.12+(8.5-2.5)/8.5*(26.67-16.12)			=	23.57	t/m2
	at deff from A-A		22.33-0.9125/5*(22.33-16.12)			=	21.20	t/m2
	at deff from B-B		26.67-0.9125/2.5*(26.67-23.57)			=	25.54	t/m2
	Heel End		16.12-((9.82-0.3)*2-0.3*2.5)*1.35			=	-8.56	t/m2
	A-A		22.33-((9.82-1)*2-1*2.5)*1.35			=	1.90	t/m2
Net	Toe End		26.67-((226.58-224.25)*2+0.3*2.5)*1.35			=	19.37	t/m2
	B-B		23.57-(1*2.5)*1.35			=	20.20	t/m2
	at deff from A-A		21.2-((9.82-0.872)*2-0.872*2.5)*1.35			=	-0.01	t/m2
	at deff from B-B		25.54-(0.745*2.5)*1.35			=	23.44	t/m2
	Overall  depth	at A-A	((1-0.3)*(5-0.9125)/5)+0.3			=	0.872	mm
	Overall  depth	at B-B	((1-0.3)*(2.5-0.9125)/2.5)+0.3			=	0.745	mm
2	Min.Pressure at heel(Corner -3) and corresponding pressure at toe
	Corner	Gross Pressure
		t/m2
	1	29.3
	2	23.0
	3	12.6
	4	18.7
	Heel End		(22.99+29.34)/2			=	15.69	t/m2
	A-A		15.69+5/8.5*(26.17-15.69)			=	21.85	t/m2
Gross	Toe End		(22.99+29.34)/2			=	26.17	t/m2
	B-B		15.69+(8.5-2.5)/8.5*(26.17-15.69)			=	23.09	t/m2
	at deff from A-A		21.85-0.9125/5*(21.85-15.69)			=	20.73	t/m2
	at deff from B-B		26.17-0.9125/2.5*(26.17-23.09)			=	25.04	t/m2
	Heel End		15.69-((9.82-0.3)*2-0.3*2.5)*1.35			=	-8.99	t/m2
	A-A		21.85-((9.82-1)*2-1*2.5)*1.35			=	1.43	t/m2
Net	Toe End		26.17-((226.58-224.25)*2+0.3*2.5)*1.35			=	18.87	t/m2
	B-B		23.09-(1*2.5)*1.35			=	19.71	t/m2
	at deff from A-A		20.73-((9.82-0.872)*2-0.872*2.5)*1.35			=	-0.51	t/m2
	at deff from B-B		25.04-(0.745*2.5)*1.35			=	22.94	t/m2
	Overall  depth	at A-A	((1-0.3)*(5-0.9125)/5)+0.3			=	0.872	mm
	Overall  depth	at B-B	((1-0.3)*(2.5-0.9125)/2.5)+0.3			=	0.745	mm
		Section
	Pressure(t/m2)	Heel End	A-A	Toe End	B-B	at deff from A-A	at deff from B-B
	Gross Pressure (Case 1)	16.1	22.3	26.7	23.6	21.2	25.5
	Gross Pressure (Case 2)	15.7	21.9	26.2	23.1	20.7	25.0
	NetPressure (Case 1)	-8.6	1.9	19.4	20.2	0.0	23.4
	Net Pressure (Case 2)	-9.0	1.4	18.9	19.7	-0.5	22.9
	Modular Ratio				m	=	6.25E+00
	Permissible stress in concrete			0.48*fck		=	16.8	Mpa
	Permissible stress in Steel			0.8*fyk		=	400	Mpa
	Neutral Axis Depth					=	[(-m*Ast)+sqrt[m*Ast)^2+2*1000*Ast*m*d]/1000
						=	207.92
	Stress in Concrete					=	[(-Mu)x10^7]/(((1000/3)*NA^3+m*Ast*(d-NA)^2))/NA
						=	7.23	Mpa
	Stress in Concrete					=	[(-Mu)x10^7]/(((1000/3)*NA^3+m*Ast*(d-NA)^2))/(d-NA)*m
						=	153.12	Mpa
side	Face	Moment	deff	Ast.provided	Neutral Axis Depth	Stress in Concrete	Stress in Steel	Check
		t-m	mm	mm2/m	mm	Mpa	Mpa
Heel	Top	-63.38	912.5	4,908.74	207.92	7.23	153.12	ok
	Bottom	-68.97	912.5	4,908.74	207.92	7.23	153.12	ok
Toe	Bottom	61.39	912.5	4,908.74	207.92	7.23	153.12	ok

 

	Crack Width Check
	Combination for Design of Foundation
	Combination 3(SLS Qausi permanent Combination)
1	LWL
1.1	Maximum Reaction Case
1.2	Maximum Moment Case
1	LWL
1.1	Maximum Reaction Case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1	105.00	105.00	-	315.00	-	105.00	105.00	-	315.00	-
	SIDL(exclu.W/C)	1	29.98	29.98	-	89.93	-	29.98	29.98	-	89.93	-
	SIDL(W/C)	1.2	9.27	9.27	-	27.80	-	11.12	11.12	-	33.36	-
	LL1	0	97.32	85.14	-133.73	291.97	192.55	-	-	-	-	-
	EPLL1	0	-	-	-	-	-	-	-	-	-	-
	Shearing Rating	0	-	-	-43.10	-	-	-	-	-	-	-
	Earth Pressure	1	315.16	315.16	-1,299.20	860.33	-	315.16	315.16	-1,299.20	860.33	-
	LL Surcharge	0	-	-	372.19	-	-	-	-	-	-	-
	Weight of Sub-structure	1	230.63	230.63	-	709.16	-	230.63	230.63	-	709.16	-
	Weight of Foundation	1	176.25	176.25	-	749.06	-	176.25	176.25	-	749.06	-
	Return Wall Weight	1	56.21	56.21	-	339.56	339.40	56.21	56.21	-	339.56	339.40
	Backfill Weight	1	1,032.75	1,032.75	-	6,274.66	-	1,032.75	1,032.75	-	6,274.66	-
	Total							1957.1	1957.1	-1299.2	9371.1	339.4
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.538	m
	Longitudinal Moment about c/l of footing				ML		=	245.81	t-m
1.2	Maximum Moment Case
			Unfactored					factored
		Partial Safety Factor	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT	Pmax	Pmin	ML due to HL about toe	ML due to P about toe	MT
			t	t	t-m	t-m	t-m	t	t	t-m	t-m	t-m
	DL-Sup	1	105.00	105	0	218.9	0	105.0	105.0	0.0	218.9	0.0
	SIDL(exclu.W/C)	1	29.98	29.977632	0	29.3	0	30.0	30.0	0.0	29.3	0.0
	SIDL(W/C)	1.2	9.27	9.2664	0	25.4	0	11.1	11.1	0.0	30.5	0.0
	LL1	0	81.63	70.30	-135.48	244.89	237.14	0.0	0.0	0.0	0.0	0.0
	EPLL1	0	0	0	0	0.0	0	0.0	0.0	0.0	0.0	0.0
	Shearing Rating	0	0	0	-43.1	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	Earth Pressure	1	114.71	114.71023	-1686.4	1033.2	0.0	114.7	114.7	-1686.4	1033.2	0.0
	LL Surcharge	0	0	0	-453.5	0.0	0.0	0.0	0.0	0.0	0.0	0.0
	Weight of Sub-structure	1	230.63	230.625	0	577.9	0	230.6	230.6	0.0	577.9	0.0
	Weight of Foundation	1	176.25	176.25	0	587.8	0	176.3	176.3	0.0	587.8	0.0
	Return Wall Weight	1	56.21	56.2115	0	304.6	339.4	56.2	56.2	0.0	304.6	339.4
	Backfill Weight	1	1,032.75	1032.7506	0	5604.1	0	1032.8	1032.8	0.0	5604.1	0.0
	Total							1756.6	1756.6	-1686.4	8386.2	339.4
	Eccentricity of vertical load from c/l of footing						=	(ML due to P/Load P)-(width of footing/2)
	Eccentricity of vertical load fron c/l of footing						=	0.524	m
	Longitudinal Moment about c/l of footing				ML		=	765.90	t-m
	Summary
	Service Condition-Qausi Parmanent Case
			Pmax	Pmin	ML	MT
			t	t	t-m	t-m
	Maximum Reaction Case		1957.1	1957.1	245.81	339.4
	Maximum Moment Case		1756.6	1756.6	765.90	339.4
	Area of Base		A	12*8.5	=	102.00	m2	Corner-01	p1	=	P/A+ML/Zl+MT/Zt
	Longinitudinal Section Modulus		ZL	12*8.5^2/6	=	144.50	m3	Corner-02	p2	=	P/A+(ML/Zl-MT/Zt)
	Transverse Section Modulus		ZT	8.5*12^2/6	=	204.00	m3	Corner-03	p3	=	P/A-ML/Zl-MT/Zt
								Corner-04	p4	=	P/A-ML/Zl+MT/Zt

 

	Combination of Base pressure for foundation
	D-1 Combination-01
	Service Condition
		Forces/Moments				For Pmax				For Pmin
		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)	P/A+ML/Zl+MT/Zt	P/A+ML/Zl-MT/Zt	P/A-ML/Zl-MT/Zt	P/A-(ML/Zl+MT/Zt)
		t	t	t-m	t-m	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2	t/m2
Maximum Reaction Case		1,957.10	1,957.10	245.81	339.40	22.55	19.22	15.82	19.15	22.55	19.22	15.82	19.15
Maximum Moment Case		1,756.64	1,756.64	765.90	339.40	24.19	20.86	10.26	13.59	24.19	20.86	10.26	13.59

 

Corner 1,4	Toe End
Corner 2,3	Heel end
Serviceability Limit state (SLS) combo-3
Max.Pressure at toe and corresponding pressure at heel					Min.Pressure at heel and corresponding pressure at toe
Corner	Gross Pressure				Corner	Gross Pressure
	t/m2					t/m2
1	24.2				1	29.3
2	20.9				2	23.0
3	15.8				3	12.6
4	19.1				4	18.7
Using interpolation of triangles, the pressure at face to the support & at "d" distance from the support is determined
Heel End		(15.82+20.86)/2			=	17.5	t/m2
A-A		17.49+5/8.5*(22.52-17.49)			=	20.4	t/m2
Toe End		(15.82+20.86)/2			=	22.5	t/m2
B-B		17.49+(8.5-2.5)/8.5*(22.52-17.49)			=	21.0	t/m2
at deff from A-A		20.45-0.9125/5*(20.45-17.49)			=	19.5	t/m2
at deff from B-B		22.52-0.9125/2.5*(22.52-21.04)			=	22.0	t/m2
Heel End		17.49-((9.82-0.3)*2-0.3*2.5)*1.35			=	-7.2	t/m2
A-A		20.45-((9.82-1)*2-1*2.5)*1.35			=	0.0	t/m2
Toe End		22.52-((226.58-224.25)*2+0.3*2.5)*1.35			=	15.2	t/m2
B-B		21.04-(1*2.5)*1.35			=	17.7	t/m2
at deff from A-A		19.53-((9.82-0.872)*2-0.872*2.5)*1.35			=	-1.7	t/m2
at deff from B-B		21.98-(0.745*2.5)*1.35			=	19.5	t/m2
Overall  depth	at A-A	((1-0.3)*(5-0.9125)/5)+0.3			=	0.872	mm
Overall  depth	at B-B	((1-0.3)*(2.5-0.9125)/2.5)+0.3			=	0.745	mm

 

Crack-Width Check as Per IRC 112
Condition of Exposure						=	Moderate
Size of Footing						=	7.50m	x	12.00m
Refer Previous Design data Calculations for the below Data
Heel Slab
Overall depth of Section						=	1000	mm
Effective depth Provided					dprovided	=	912.5	mm	ok
Provided	25 mm  Dia.	Bars	@	200 mm c/c		=	200	mm c/c	+
	25 mm  Dia.	Bars	@	200 mm c/c		=	200	mm c/c
Ast,provided						=	4,908.74	mm2	at Top
						=
Toe Slab
Overall depth of Section						=	1000	mm
Effective depth Provided					dprovided	=	912.5	mm	ok
Provided	25 mm  Dia.	Bars	@	200 mm c/c		=	200	mm c/c	+
	25 mm  Dia.	Bars	@	200 mm c/c		=	200	mm c/c
Ast,provided						=	4,908.74	mm2	at Bottom
Min.Pressure at heel and corresponding pressure at toe
Corner	Gross Pressure
	t/m2
1	23.6
2	19.8
3	20.9
4	17.1
Heel End		(19.8+23.6)/2			=	19.00	t/m2
A-A		19+5/8.5*(21.7-19)			=	20.59	t/m2
Toe End		(19.8+23.6)/2			=	21.70	t/m2
B-B		19+(8.5-2.5)/8.5*(21.7-19)			=	20.91	t/m2
at deff from A-A		20.59-0.9125/5*(20.59-19)			=	20.30	t/m2
at deff from B-B		21.7-0.9125/2.5*(21.7-20.91)			=	21.41	t/m2
Heel End		19-((9.82-0.3)*2-0.3*2.5)*1.35			=	-5.68	t/m2
A-A		20.59-((9.82-1)*2-1*2.5)*1.35			=	0.16	t/m2
Toe End		21.7-((226.58-224.25)*2+0.3*2.5)*1.35			=	14.40	t/m2
B-B		20.91-(1*2.5)*1.35			=	17.53	t/m2
at deff from A-A		20.3-((9.82-0.872)*2-0.872*2.5)*1.35			=	-0.94	t/m2
at deff from B-B		21.41-(0.745*2.5)*1.35			=	19.30	t/m2
Overall  depth	at A-A	((1-0.3)*(5-0.9125)/5)+0.3			=	0.872	mm
Overall  depth	at B-B	((1-0.3)*(2.5-0.9125)/2.5)+0.3			=	0.745	mm
	Section
Pressure(t/m2)	Heel End	A-A	Toe End	B-B	at deff from A-A	at deff from B-B
Gross Pressure (Case 1)	19.0	20.6	21.7	20.9	20.3	21.4
Gross Pressure (Case 2)	19.0	20.6	21.7	20.9	20.3	21.4
NetPressure (Case 1)	-5.7	0.2	14.4	17.5	-0.9	19.3
Net Pressure (Case 2)	-5.7	0.2	14.4	17.5	-0.9	19.3

 

Modular Ratio					Es/Ecm	=	6.25			m =Es/Ecm	Es
Spacing of Steel provided						=	100	mm			Ecm
Grade of Concrete					fck	=	M 35	Mpa	(Refer from table No.6.5,IRC:112-2011)
Tensile Strength of Concrete					fctm	=	2.80	Mpa
Characteristic strength of Concrete					fck	=	35	Mpa
Grade of Steel						=	Fe 500
Characteristic strength of Steel					fyk	=	500	Mpa
Modulus of Elasticity of Concrete					Ecm	=	32000	Mpa
Modulus of Elasticity of Steel					Es	=	200000	Mpa
Depth					h	=	1000	mm
Width considered					b	=	1000	mm
Cover					c	=	75	mm
Face	Moment	Moment/m width	deff	Ast.provided	Neutral Axis Depth	Check
	t-m	t-m	mm	mm2/m	mm
Top	-46.64	-3.89	912.5	4,908.74	207.92	ok
Bottom	-46.64	-3.89	912.5	4,908.74	207.92	ok
Bottom	48.25	4.02	912.5	4,908.74	207.92	ok
Moment	(-7.85*4.8^2)/2+((0.5*(-1.9-(-7.85))*4.8^2))/3				=	-67.968	t-m
					=	207.92	mm
Moment per m width		-67.968/12				-5.66	t-m
side	Face	Sr,max	MI of Cracked Section	Stress in Concrete	Stress in Steel		Crack Width (Wk)	Check
		mm	mm4	Mpa	Mpa		mm
Heel	Top	444.39	1.82E+10	0.64	13.58	0.00004	0.018	Ok
	Bottom	444.39	1.82E+10	0.64	13.58	0.00004	0.018	Ok
Toe	Bottom	444.39	1.82E+10	0.64	13.58	0.00002	0.009	Ok
Calcualtion of Pp,eff
		Where	Ac,eff  is the effective area of concrete in tension surrounding the reinforcement, of depth he,eff where he,eff is lesser of
			2.5*(h-d);(h-x)/2;h/2		( refer Fig.12.2)
			h	Overall depth			As	4,908.74
			d	effective depth			2.5*(h-d)	218.75
			x	Neutral axis depth from top			(h-x)/2	264.03
							h/2	500
						=	0.02244

 

=	437.5	444.39	Nearly Close	^3
=	437.5	1,029.70

 

	K1	=	0.8
	K2	=	0.5
	C	=	75
	We will be adopted Sr,max is 444.39 mm for checking.
	MI of Cracked section		((207.92)^3/3*1000)+((6.25*4909*(912.5-207.92)^2))				=	1.82E+10

 

Kt	=	0.5
	=	-0.0002878
	=	0.00004074
	=	0.00004074	Take Maximum Value of-0.00029,0.00004

 

		=	0.018	mm
	Wmax	=	0.3	mm	From table 12.1,IRC:112-2011
			Hence Ok

As per Code:-

 

Design of Concrete
Input Data
Nature of Bending			(Hogging)
Width of Plate				B	=	1000	mm
Depth of Plate/Top Slab				h	=	900	mm
Clear cover to reinforcement on earth face				CT	=	75	mm
No of Reinforcement Layers provided				B	=	2	No
Diameter of Tension Steel			1st Layer	d1	=	32	mm @200c/c
			1st Layer	d2	=	0	mm @200c/c
Diameter of Tension Steel			2nd Layer	d3	=	0	mm @200c/c
			2nd Layer	d4	=	0	mm @200c/c
Diameter of Tension Steel			3rd Layer	d5	=	0	mm @200c/c
			3rd Layer	d6	=	0	mm @200c/c
Effective Depth				d	=	799	mm
Diameter of Shear Reinforcement					=	10
Characteristic compressive strength of concrete.				fck	=	40	N/mm2
Characteristic yield a strength of the steel.				fyk	=	500	N/mm2
Design yield the strength of main reinforcement.				fyd	=	435	N/mm2
Characteristic yield the strength of stirrups				fywk	=	500	N/mm2
Mean value of axial tensile strength of concrete.				fctm	=	.259*fck^2/3	N/mm2
As per IRC: 112 -2011 Annexture-2				fctm		3.03	N/mm2
Bending moment as per ULS combination.				Mu	=	1000	KN-m
Effective depth as per provided.				deff.provided	=	799	mm
				b	=	1000	mm
Ast provided.		Pi()/4*32^2*5*1		Ast,provided	=	4,021	mm2	0.5%	<2.5%
Minimum reinforcement as per IRC 112,Cl.16.6 .1 .1.				So, Section is under-Reinforced
				Ast ,min	=	0.26*fctm*bt*d/fyk & 0.0013bt*d whichover is greater-
				Ast ,min	=	1,258
				Ast ,min	=	1,039
		0.16%	<0.5%	Ast ,min	=	1,258	Max.Value
				Ast,provided		4,021	OK
Limiting depth of neutral axis as per IRC 112 ,Table no-4.2
				Xu,lim/d	=	0.46	Depth ratio.
Calculate the neutral axis from top fibre.  As per below formula				Xu/d	=	0.152	Depth ratio.
				Xu/d<Xu,lim/d	=	0.152	Under-Reinforced
After that we will calculate the Ultimate bending moment.
Mu=	"0.87*fy*d*(1-0.42*Xu/d)			Mu	=	1,308	KN-m
						Hence it is safe
		ecu3=0.0035
	Ultimate tensile strength in the steel
Check for  stresses and crack width.
Properties of middle Wall
Width of middle wall.				Bs	=	1000	mm
Thickness of middle wall				Ts	=	900	mm
Diameter of tensile reinforcement outer layer.				d1	=	32	mm
CGOP section from inner face			900/2	Yinner	=	450	mm
CG of section from outer face.			900/3	Youter	=	450	mm
Area of steel provided.				Ast,prov	=	4,021	mm
Effective depth			900-cover	deff	=	799	mm
Modulus of elasticity of steel.				Es	=	2.00E+05	N/mm2
Modulus of elasticity of concrete.				Ecm	=	3.30E+04	N/mm2
Long term modular ratio.			IRC 21- 2000. Cl.No.A 1.	m	=	12.1	Es/0.5*Ecm
Properties of gross section.			Values	Unit
Cross area.			9.00E+05	mm2		1000*900	b*D
Gross moment of inertia.			6.08E+10	mm4		(1000*900^3)/12	(b*D3)/12

 

Properties of uncrackked transformed section
YiT	=	((b*D*D/2)+(m-1)*(Ast*d))/((9B*d)+(m-1)*Ast)
	=	467
YbT	=	D-YtT	900-467
	=	433
YsT	=	d-YtT	799-467
	=	332
IT	=	(b*D3/12+b*D*(D/2-YiT)2)+((m-1)*Ast*(d-YsT)2)
	=	6.59E+10

 

Properties of uncrackked transformed section				Values	Unit
YiT				467	mm
CG of  uncracked section from tension face, YbT				433	mm
CG of uncracked section from tension steel,YsT				332	mm
Uncracked moment of inertia,  IT				6.59E+10	mm4

 

Properties of cracked section :
B*Y2outCr/2=m*Ast*(d-YoutCr)
1000/2*Y2outCr=12.12*4021*(799-YoutCr)
500a2+48742a-4E+07=0
a	=	238
YoutCr	=	238
Properties of crackked transformed section				Values	Unit
YoutCr				238	mm
CG of  uncracked section from inner face, YinnCr				662	mm
CG of uncracked section from tension steel,YsCr				561	mm
Uncracked moment of inertia,  Icr				1.98E+10	mm4

Stresses under Rare Combination
Calculation of Stresses for Middle Wall
Bending Moment( rare combination)				Mrare	=	700	kNm	IRC6-2017
Compressive Stress in concrete at outer face,				fcc	=	(M/I)*Yout.Cr
			Safe for fcc	fcc	=	8.41	N/mm2	Mcr	=
Tensile Stress in concrete at Steel level				fct,steel	=	(M/I)*Ys.Cr			=
				fct,steel	=	19.79	N/mm2	Mrare	>
Tensile Stress in  Steel				fst	=	m*(M/I)*Yscr		So, Section is Cracked
			Safe for fst	fst	=	239.87	N/mm2	We will take all values in cracked section
Permissible compressive  Stress in Concrete					=	0.48fck
					=	19.2	N/mm2	IRC:112-2011, Cl No.12.2.1
Permissible Tensile Stress in Steel					=	0.8fy or 300
					=	400	N/mm2	IRC:112-2011, Cl No.12.2.2
					=	300	N/mm2	400>300
Calcualtion of Crack width for Middle wall
Bending Moment ( Quasi-Permanent combination)				Mquasi	=	550	kNm
Permissible compressive  Stress in Concrete				fcc	=	0.36*fck		IRC:112-2011, Cl No.12.2.2
				fcc	=	14.4	N/mm2
Cracking Moment of the section				Mcr	=	Igr(MOI Uncracked)*fctm/Yb(CG of Uncracked)
				Mcr	=	461	kNm	Cracked Section
When Mcr is less than Mquasi			So, Section is Cracked		=
Calculate the Crack width
Compressive Stress in concrete at outer face,				fcc	=	(M/I)*Yout.Cr
					=	6.61	N/mm2
Tensile Stress in concrete at Steel level				fct,steel	=	(M/I)*Ys.Cr
					=	15.55	N/mm2	Cracked Section
Section is Cracked,fst>fct,steel
Distance of Neutral Axis from outer face for cracked section					=	deff/(1+fct.steel*m/fcc)
					=	27.06	mm
Calculation the Crack width
Wheere
	Wk	=
	Sr,max	=	Maximum Crack Spacing
	Sr,max	=
	c	=	50	Clear Cover to longitudinal reinforcement
	K1	=	0.8	for deformed bars
	K2	=	0.5	for bending
	𝜌𝑝,𝑒𝑓𝑓	=
	∅	=	32	Diameter of bar
	esm	=	Mean strain in the reinforcement.
	ecm	=	Mean strain in the concrete between cracks
Now
		=
	𝜎𝑠𝑐	=	Stress in the tension reinforcementin crack section
	𝛼𝑒	=	Moduler Ratio	Es/Ecm
	𝜌𝑝,𝑒𝑓𝑓	=
	As	=	Area of Steel
	Ac,eff	=	Effeective area of concrete in tension surrounding the reinforcement=bw*hc,eff

 

	hc,eff	=	hc,eff is the lesser of
	2.5*(h-d)	=	252.5	mm		(900-799)*2.5
	(h-x)/3	=	291.0	mm		(900-27.06)/3
	h/2	=	450	mm		900/2
	hc,eff	=	252.50	mm
	Ac,eff	=	252500	mm2
	𝜌𝑝,𝑒𝑓𝑓	=	0.01593
	Kt	=	0.5	factor dependent on duration of load
	𝜎𝑠𝑐	=	188	N/mm2
	fct,eff	=	3.03	N/mm2	fctm	Mean value of axial tensile strength of concrete.
	𝛼𝑒	=	12.1	m=Es/Ecm
		=	0.000375
	Sr,max	=	512	mm
		=	0.192	mm	<	0.3	IRC:112-2011, Table No-12.1

 

Check for Shear
Design shear force				VEd	=	737	kN
For uniform cross section				Vccd	=	0
For uniform cross section				Vtd	=	0
			VRds	VNS	=	737
Minimum allowable shear force( for maximum shear force take  𝜃 =21.80)
				IRC:112-2011,Cl.no.10.3.3.2,Eq10.8
𝛼cw	=	1	Co-efficient taking account of the state of the stress in the compression chord
Z	=	0.9d	Liver arm	For RCC Structure
V1	=	0.52	0.6*(1-40/310)	Strength reduction factor for concrete cracked in shear
				IRC:112-2011,,Eq10.6
𝜃	=	21.8	2.50	Design value of compression strength
fcd	=	𝛼cc*fck/ym		IRC:112-2011,Cl.No.10.3.1)
𝛼cc	=	0.67		Refer IRC:112-2011,Page No-87)
Ym	=	1.5		(Partial Factor of Concrete for ULS)
fcd	=	17.87	N/mm2
	=
VRd,max	=	2,303.65	kN
Allowable shear force without reduction factor
VEd	<=	0.5*bw*d*v*fcd		(IRC:112-2011,Cl.No.10.3.2,Eq.10.5)
Wheere
v	=	Strength reduction factor=0.6*[1-(fck/310)]
bw	=	1000	mm
v	=	0.52	N/mm2
VEd	=	3,730.04	kN	Section is Safe
Allowable shear force without shear reeinforcement
VRdc	=			(IRC:112-2011,Cl.No.10.3.2(2))
VRd.c min	=
Vmin	=
	=	Concrete compessive stress at the Centroidal axis  due to axial loading or prestressing
	=	Reinforccement ratio for longitudinal reinforcement,
				K	=	1.50	Which is less than <=2
					=	0.005	Which is less than <=0.02
					=	0	Axial force is nil
				Vmin	=	0.360
				VRd.c min	=	287.88	kN
				VRdc	=	359.91	kN
						Shear reinforcement is required
Design of Shear Reinforcement:
	𝜃
The value of  "^ " is determined by equating Vrd,s to VNS
Vrd,s	=	The design value of shear force, which can be sustained by yielding shear reinforcement.
Vrd,s	=
Where
Asw	=	The cross section area of the shear reinforcement
s	=	Spacing
fywd	=	The design yield strength of the shear reinforcement
Shear reinforcement due to combine shear and Torsion.
Provide	5L	10 mm	Dia. Stirrups	spacing	s=	200	mm
				𝜃	=	21.8	o
Asw	=	392.70	mm2	z	=	0.9d	mm
z	=	719.1	mm
Vrd,s	=	1,764.94	kN
Reinforcement ratio for Shear Reinforcement.					=	0.002
Check for minimum shear reinforcement
Minimum shear reinforcement ratio					=	0.072*sqrt(fck)/fyk
					=	0.0009	Safe

 

 

 

 

 

 

 

 

 

 

 

 

 

3).Shallow foundations( Stability, Designing & Construction) in Fly-Over & River Bridge:-

Shallow foundations are commonly used in both flyovers and river bridges to support the structures and transmit loads to the underlying soil. However, there are some differences in terms of stability, designing, and construction for these two types of structures due to their varying environmental conditions and load requirements.

1. Stability:

1.1.Flyover:

Flyovers are elevated roads or structures that span over existing roadways or intersections. They typically have a relatively uniform and stable soil profile since they are constructed above ground level. The stability concerns for flyovers primarily involve ensuring that the foundation can withstand the vertical loads from the structure itself, along with the dynamic loads from the passing vehicles.

1.1.River Bridge:

River bridges are structures that span across water bodies like rivers or streams. The soil conditions near riverbanks can be more challenging, as they may have different layers of soils, sediment, and waterlogged areas. The stability of a river bridge foundation needs to consider factors like scour (erosion of soil around bridge piers due to water flow) and potential lateral forces from water currents.

2. Designing:

2.1.Flyover:

The design of shallow foundations for flyovers typically involves conducting a thorough geotechnical investigation to determine the soil properties and bearing capacity. The load-bearing capacity of the foundation should be sufficient to support the weight of the flyover and the live loads from traffic. Typically, reinforced concrete footings or pile caps are used for flyover foundations.

2.1.River Bridge:

Designing shallow foundations for river bridges requires more complex considerations. The geotechnical investigation becomes crucial, not only for determining bearing capacity but also for assessing scour potential. In some cases, foundations might need to be designed with special features, such as scour protection, to prevent erosion around the bridge piers. Bridge foundations may also need to accommodate horizontal forces caused by water flow.

3. Construction:

3.1.Flyover:

Flyover construction typically involves building columns and spans above the ground level. The shallow foundations are constructed by excavating the soil to the required depth, compacting it, and pouring reinforced concrete into the excavated area. The columns are then built on top of these footings.

3.2.River Bridge:

Construction of a river bridge involves more challenging conditions. The foundation construction may require working in or near water, which can be complicated and may necessitate the use of cofferdams or specialized construction techniques. Scour protection measures must be installed during or after the construction of the foundation to safeguard against erosion.

 Conclusion:-

In summary, while both flyovers and river bridges use shallow foundations, the key differences lie in the stability considerations, designing for longer spans and water loads, and the challenges of construction near or in water bodies. Each type of structure requires careful engineering and planning to ensure the stability and longevity of the bridge or flyover.