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).
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|
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)
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|
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]
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archipaedia
Thursday, February 9, 2012
Geometry
Monday, February 6, 2012
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:
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
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||
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.
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|
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
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Min. depth of tread
|
191mm at 305mm from the narrower edge.
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|
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
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|
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
|
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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.
Labels:
architecture,
grade,
handrail,
headroom,
interior design,
nfpa,
nfpa 101b,
pitch,
ramp,
riser,
slope,
stair,
staircases,
tread
Saturday, February 4, 2012
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)
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|
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
|
-
|
-
|
Labels:
architecture,
auditoriums,
cinema,
concert halls,
factory,
interior design,
office,
plumbing requirements,
restaurants,
sanitary requirements,
shop,
urinals,
wash basins,
water closets
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