For a roof of 3/12 pitch or having a pitch of “3 in 12” slope; the rafter length is 15.46 feet that is around 4.712 meters. It has a span of 30 feet. The rafter length will increase with the increase in span and it will decrease with the decrease in span for varying pitches.
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3/12 pitched roof
A pitched roof is one of the most common roofs used for the construction of houses. The concept of a pitched roof has not been introduced today. It has been in use for many decades. This type of roof is mostly used for hilly areas and for regions which face very severe climatic conditions.
The pitched roofs are inclined roofs with some angle so that it helps in providing an adequate drainage of water and also found suitable for snowfall areas.
The design of pitched roof is of more importance because if we do not design a roof according to our location of region and climatic conditions it will cause damage in terms of life and money.
There are some important terms which are necessary to understand for designing the pitched roofs. Here in this article, we will discuss all the terms and know about the procedure of finding the pitch and length of sloping members.
In pitched roofs Span is a horizontal distance between inner faces of walls of a building
A ridge board is horizontal member of timber which is provided at the apex of pitched roof
It is a vertical distance between the wall plate and top of ridge.
Pitch is an inclination of sides of roof to the horizontal plane.
A Rafter is a member which is inclined at some angle and laid from ridge to the eaves.
The rafter is a very important member of a pitched roof. The rafter is connected with ridge board at the top and projected beyond the walls.
The rafter takes a load of all the roof covering so the selection of rafter and its length should be accurate so that it can safely transfer the load of roof covering to the walls and then walls transfers the load to a ground.
The timber is used as a sloping rafter. The timber should be of good quality so that it can take the load of roof and transfer it safely.
Length of 3 in 12 sloping Rafter
In pitched roof there is a ridge at the middle of span with slope on both sides in opposite direction. This type of roof is constructed by providing sloping rafter from ridge board to eaves in both the sides of ridge. Here we have to determine the length of rafter for roof pitch of 3 in 12.
Here 3 in 12 mean that rafter will rise 3 units for 12 horizontal units. For example, if we have a 20 ft span of house then ridge board will be provided at 10ft horizontal distance and vertical height will be according to the slope of roof.
if recommended slope is 3 in 12 than it means that for every 1 ft horizontal distance a rise of 3 inch will be provided or we can also say that a total of 30 inch rise of rafter will be provided for 10 ft horizontal distance exactly at the middle of span
The pitch of roof is very easy to calculate. It can be calculated by the simple mathematical trigonometric calculation. The concept is simple which is rise/run method. Here rise is representing the vertical distance between wall plate from center of span to a ridge board at the top and run is representing the horizontal distance from wall plate to center of span.
Pitch of roof = Rise/Run
Pitch of roof = 1/4
After deciding the pitch of roof, we can easily calculate the length of rafter. The length of rafter is calculated by Pythagoras theorem. We already know the pitch of roof now we will multiply the pitch of roof by half of span to calculate the rise of rafter. After knowing the rise and run value we can use Pythagoras theorem it will giver the length of sloping portion which is a length of rafter.
For example, if we have a 30 ft span of house then ridge board will be provided at 15ft horizontal distance and vertical height will be according to the pitch of roof .if recommended slope is 3 in 12 or 1/4 then it means that for every 1 ft horizontal distance a rise of 3 inch will be provided or we can also say that a total of 45 inch rise of rafter will be provided for 15 ft horizontal distance exactly at the middle of span.
Run of slope =15 ft
Rise of slope= pitch × run value
Rise of slope = (1/4 × 15ft)
Rise of slope = 3.75ft
Now apply Pythagoras theorem
c^2 = a^2 + b^2 Length of rafter = √(a^2+b^2 ) Length of rafter = √(〖3.75^〗^2+〖15〗^2 ) Length of rafter = 15.46 ft
The pitch of roof is an important factor which depends upon the many conditions such as climate of region. The pitch of roof can be calculated by rise/ run method. The pitch or slope of roof is further used to calculate the sloping member such as rafter.
A rafter is sloping member provided with suitable spacings and it is provided to take the load of roof covering and then transfer it to walls. The length of rafter is calculated by Pythagoras theorem. The length of rafter for a 30ft span of house and for pitch of 3 in 12 is 15.46 ft. For a 30 ft span of a house a rafter of 15.46 ft will be provided on both the sides of ridge with suitable spacing.