Calculate the length of a collar tie for the following conditions: The collar tie is 3′ above the top plate, the unit rise of a common rafter in the roof is 10′, and the span of the building is 20′.
A. 16′43/4″
***B. 12′ 91/2″
C. 14′
D. 17′
I got the answer B, would you agree?
half the width drawing:
rafter 10 ft wide,
tie is 3 ft up
so for half the tie
(10-3)/x = 10/10 = 1
x = 7
2x = length of tie = 14
I wonder why the tie is only 3 feet above the rafters though.
Well, B is definitely a great answer, but let's calculate it just to be sure and have some fun!
We know that the collar tie is 3 feet above the top plate, and the unit rise of a common rafter is 10 feet. So first, we need to find the length of the common rafter.
Using the Pythagorean theorem (and a splash of humor), let's go:
a^2 + b^2 = c^2
In our case, a represents the unit rise (10 feet), b represents half the span (10 feet / 2 = 5 feet), and c represents the length of the common rafter.
Plugging in the values, we have:
10^2 + 5^2 = c^2
100 + 25 = c^2
125 = c^2
Now, let's find c (the length of the common rafter):
c = √125
c ≈ 11.18 feet
But we're not done yet! Remember, the collar tie is 3 feet above the top plate. So to find its length, we add the length of the common rafter (11.18 feet) to the distance above the top plate (3 feet).
11.18 + 3 ≈ 14.18 feet
So, it looks like the actual answer is C. 14 feet.
But hey, B is pretty close! And the world could always use a little more humor in math problems. Keep up the laughter!
To calculate the length of a collar tie, we need to use the Pythagorean theorem.
First, let's find the length of the common rafter using the unit rise and the span of the building:
Length of common rafter = √(unit rise^2 + span^2)
Length of common rafter = √(10^2 + 20^2)
Length of common rafter = √(100 + 400)
Length of common rafter = √500
Length of common rafter ≈ 22.36 ft
Next, let's find the total vertical distance from the top plate to the collar tie:
Total vertical distance = unit rise + collar tie height
Total vertical distance = 10 ft + 3 ft
Total vertical distance = 13 ft
Finally, let's calculate the actual length of the collar tie using the Pythagorean theorem:
Length of collar tie = √(length of common rafter^2 - total vertical distance^2)
Length of collar tie = √(22.36^2 - 13^2)
Length of collar tie ≈ √(500 - 169)
Length of collar tie ≈ √331
Length of collar tie ≈ 18.2 ft
So, the correct answer is not option B, but the closest option is option A: 16' 4 3/4".
To calculate the length of a collar tie, we need to use the Pythagorean theorem and consider the rise and span of the building.
First, let's find the distance from the top plate to the peak of the roof. Since the unit rise of a common rafter is 10 feet and the collar tie is 3 feet above the top plate, the total rise from the top plate to the peak is 10 + 3 = 13 feet.
Using the Pythagorean theorem, we can find the length of the common rafter as follows:
Length of Common Rafter = √(Rise^2 + Span^2)
Length of Common Rafter = √(13^2 + 20^2)
Length of Common Rafter = √(169 + 400)
Length of Common Rafter = √(569)
Length of Common Rafter ≈ 23.87 feet (rounded to two decimal places)
Now, to find the length of the collar tie, we subtract the rise (13 feet) from the length of the common rafter:
Length of Collar Tie = Length of Common Rafter - Rise
Length of Collar Tie = 23.87 - 13
Length of Collar Tie ≈ 10.87 feet (rounded to two decimal places)
The closest option to this calculation is answer choice B: 12′ 9-1/2″.