Geometry

Circle
	The figure on the left shows a circle of radius r with centre O. The two radii shown here OA and OC intersect the circle at points A and B defining a minor Arc-ABC, wherein B is the mid-point of the arc. It also defines a major Arc at the same time, which is Arc-ADC. The minor Arc-ABC subtends an angle y at the centre. The major Arc-ADC subtends an angle (360-y) at the centre. (360 is the angle subtended by the whole circle at the centre).
The ratio of circumference to diameter of a circle is defined as π (Greek alphabet, pronounced ‘pi’) which has a numerical value of  π = 22/7 = 3.14 (approx.) Area = (πd2)/4 (where d is the diameter, diameter = twice radius) or          = πr2 where r is the radius Perimeter or Circumference = 2πr                                                      = πd The length of an Arc is directly proportional to the angle subtended by the Arc at the centre of the circle. The length of arc can be obtained by multiplying the ratio of the angle subtended by the arc to the total angle subtended by the circle with the perimeter of the circle.  Ratio of the angle subtended by the minor Arc-ABC to the total angle subtended by the circle = (y/360) Length of minor Arc-ABC = (y/360)*(2πr) Length of major Arc-ADC = (360-y/360)*(2πr)
Sector
	Area enclosed by an arc and its radii is called a sector. The blue colour indicates the area of a sector. Like the length of an arc, the area of a sector is also directly proportional to the ratio of the angle subtended by the arc to the total angle subtended by the circle. The area of a sector is obtained by multiplying this ration with the area of the circle which it is part of. If the angle subtended by the minor Arc-ABC is y, then
Ratio of the angle subtended by the minor Arc-ABC to the total angle subtended by the circle = (y/360) Area of the sector AOC= (y/360)*(πr2)
Segment
	The area enclosed by a chord and an arc is termed as a segment. In the figure on the left area shaded in blue is the segment formed by chord AC and Arc-ABC. A chord is a line segment joining any two points on a circle. The diameter is the largest chord a circle can have. In the figure on the left, ABC is the minor segment and ADC is the major segment.
If the radii OA and OC have a value r and the Arc-ABC subtends an angle y at the centre O, then the area of the segment ABC can be obtained from the relation given below:   Area of a segment = (r2/2)[{(π/180)*y}-Sin y]

Stairs and Ramps

Stair

Terminology & Components of a stair:

Flight: A continuous series of steps between one floor or landing. The number of risers on a flight of steps is often restricted to a minimum of 3 and a maximum of 12. In case of fire escape stairs it can be as high as 20 risers per flight. It varies with respect to the regulation of the statutory authority. 
Handrail: A wooden member  or a metal tube fixed to the sides of a stairway providing a handhold and support to the person using the stair.
Headroom: The clear vertical measurement taken from the nosing of a step to the bottom of the waist slab vertically above the point on the nosing. Depending on the regulation of the local statutory authority, it varies from 2000mm to 2400mm.
Nosing: The usually rounded edge of a stair tread that extends over the riser. 
Rise: The measurement of height of a stair. i.e. from the floor level (before the first step) to the last step. It is also used in place of 'riser'.
Riser: The vertical face of a stair step.
Raking Riser: The riser which inclines inward to permit more space on the tread.
Run: The horizontal distance between the first and last risers of a flight of steps.
Tread: The horizontal upper surface of a step in a stair on which the foot is placed.
Riser : Tread Ratio: The preferred ratio between the riser and tread of a stair step. It is specified by the formula mentioned below:

2R +T = 550mm to 700mm.

Recommended Riser & Tread Sizes for various functions
	Maximum Riser Height (mm)	Minimum Tread Depth (mm)
Internal Stair Residence	190	250
External Stair for Disabled	150	280
Internal Stair for Disabled	170	250
Institutional & Assembly	180	280
Assembly Building > 100 m2	180	250
It is good to provide a riser height of 150mm and tread width of 300mm wherever possible.

 

Stair Design Criteria – NFPA 101B
Standard Stair
Minimum clear width	1120mm or 910mm if total occupant load of all stories served by the stair is less than 50.
Maximum height of risers	178mm
Minimum height of risers	102mm
Minimum tread depth	279mm
Minimum headroom	2030mm
Maximum height between landings	3700mm
Exceptions	Industrial equipment access stair serving less than 20 people shall be permitted to have clear width of 559mm, min. tread depth of 254mm, max. riser height of 229mm, min. headroom of 2030mm and a max. height between landing of 3700mm.
	Stairs within dwelling units of a one and two family dwelling can have a max. riser height of 197mm and min. tread depth of 254mm.
Spiral Stairs
Spiral Stairs shall be permitted as a means of egress only when the occupant load is not more than five persons.	Clear width 660mm	660mm
	Max. height of riser	241mm
	Min. depth of tread	191mm at 305mm from the narrower edge.
	Min. headroom	1980mm
Occupancies permitting spiral stairs	Assembly	From lighting & access catwalks, gridirons, galleries
	Detention & Correctional	Access between staff locations
	Apartment Buildings	Within the dwelling
	Dwellings	Within the dwelling
Curved Stair
	Min. depth of tread	279mm at a point 305mm from the narrower end of tread
	Smallest radius	2 X width of stair

Ramp

Acceptable Gradients of Ramp for various functions
Function	Slope Ratio	Slope Percentage	Remarks
Pedestrian walking	1:20	5%
Cyclist	1:20	5%
Vehicular ramp	1:20	5%	For parking cars on sloped parking floors.
Wheelchair ramp	1:15	6.7%	For up to a length of 10m
Wheelchair ramp	1:12	8.3%	For up to a length of 5m
Vehicular ramp	1:10	10%	For vehicular access to high or low surfaces
Vehicular ramp	1:8.3	12%	Absolute max. for vehicles w/o snow tyres
Slopped pavements	1:8.3	12%	Not more than 1mlong
Vehicular ramp	1:6.7	15%	Absolute max. for multi-storeyed car parks

The maximum slope for a vehicular ramp should be 15%. For slopes over 10%, a transition at least 2400mm long should be provided at each end of the ramp at one half the slope of the ramp itself.

Straight ramps, with on-way traffic shall have a minimum acceptable width of 3600mm; and for straight ramps, with two-way traffic, where opposing traffic flows are not separated; a recommended minimum width of 6700mm shall be provided. Where a barrier is used between lanes to separate traffic flows, each lane should be at least 3600mm wide.

Helical ramps should have a minimum inner radius of 9750mm. A radius of 10600mm to 11300mm radius is most desirable. The width of a helical ramp shall be between 4300mm to 5500mm.

Design Criteria For Helical Ramp With Two Lanes Side By Side
Item	Dimension	Remarks
Radius of inside face of outer curb of inner lane	9750mm
Radius of inside face of outer face of outer lane	13715mm
Width of inside lane between curbs	3600mm
Width of outside lanes between curbs	3350mm
Width of border curb	300mm
Width of median curb	600mm
Maximum super-elevation on ramp turns	1:10	of ramp width

Super-elevation is the inclination of the driveway toward the center of the curve.

Sanitary Requirements for Buildings

A minimum of two WCs should be provided in public buildings, so that one may act as a reserve if the other fails. Washbasins are generally provided in equal numbers to WCs with one for every five urinals.

The requirement for sanitary facilities such as WC, Wash basin and Urinal for various building types are provided below:

Building Type: OFFICES & SHOPS (when no urinals are provided)
No. of persons	No. of WCs and Basins
Up to 15	1
16-30	2
31-50	3
51-75	4
76-100	5
Over 100	1 extra for each additional 25

Building Type: OFFICES & SHOPS (when urinals are provided)
No. of persons	No. of WCs and Basins
Up to 20	1
21-45	2
46-75	3
76-100	4
Over 100	1 extra for each additional 25

Building Type: Factories
No. of persons	No. of WCs and Basins
For every 25	1
	No. of Washbasins
For every 20	1 (for clean processes)
For every 10	1 (for dirty processes)
For every 5	1 (for injurious processes)
	No specific requirement for urinals; may follow the relationship mentioned above i.e. five urinals for every WC.

Building Type: Restaurants
Male		Female
No. of persons	No. of WCs and Basins	No. of persons	No. of WCs and Basins
Up to 400	1 per 100	Up to 200	2 per 100
Over 400	1 extra for each additional 250 or part thereof	Over 200	1 extra for each additional 100 or part thereof
No. of persons	No. of Urinals	No. of persons	No. of Urinals
For every 25	1	-	-
No. of persons	No. of Wash Basins	No. of persons	No. of Wash Basins
-	1 per WC or 1 per 5 Urinals	-	1 per 2 WCs

Building Type: Concert Halls, Theatres & other Auditoriums
Male		Female
No. of persons	No. of WCs and Basins	No. of persons	No. of WCs and Basins
Up to 250	1	Up to 50	2
Over 250	1 extra for each additional 500 or part thereof	Over 50-100	1 extra for each additional 40 or part thereof
No. of persons	No. of Urinals	No. of persons	No. of Urinals
Up to 100	2	-	-
Over 100	1 extra for each additional 80 or part thereof	-	-

Building Type: Cinemas
Male		Female
No. of persons	No. of WCs and Basins	No. of persons	No. of WCs and Basins
Up to 250	1	Up to 75	2
Over 250	1 extra for each additional 500 or part thereof	Over 76-100	3
		Over 100	1 extra for each additional 80 or part thereof
No. of persons	No. of Urinals	No. of persons	No. of Urinals
Up to 200	2	-	-
Over 200	1 extra for each additional 100 or part thereof	-	-