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Topic 10 – Calculate Hip Roofs Using Metric Measurements

Unit of Run and Line Length

As hip rafters run at 45° to the exterior walls, we need to use a unit of run which accounts for the extra distance that must be covered. The unit run can be found using the same methods as with imperial measurements:

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U n i t R u n H of i p equals the square root of open paren u n i t r u n c o m m o n close paren squared plus open paren u n i t r u n c o m m o n close paren squared

U n i t R u n H of i p equals the square root of 1000 squared plus 1000 squared equals 1414 m m

When calculating the unit line length, this value must be used. For example, below we will find the hip ULL for a 400/1000 roof:

H of i p U L L equals the square root of 1414 squared plus 400 squared equals the square root of 2159396 equals 1469.5 times 1470

We will use the above ULL to find the line length of a hip rafter and tail for the following roof. Remember, when using ULL, the amount of units of run used is the same as the common rafters, which is 1 for every meter of run.

– Building 9200 x 15000 (4.6 units of run)
– 400/1000 slope
– 600 mm overhang
L i n e L e n g of t h H of i p R a. f of t e r equals 4.6 open paren u n i t s o f r u n close paren times 1470 equals 6762 m m
L i n e L e n g of t h o f H of i p R a. f of t e r T a. i l equals 0.6 times 1470 m m equals 882 m m

Ridge Boards and Deductions

The additions in length for the ridge board are the same as in imperial:

– Single cheek cut = add ½ the 90° thickness of the ridge board and ½ the 45° thickness of the hip rafter on each end
  1. For 38 mm stock, this would be 19 mm and 27 mm, respectively for a total of 92 mm added to the ridge board
– Double Cheek Cut = add ½ the 90° thickness of the common rafters on each end
  1. For 38 mm stock, this is 19 mm for a total of 38 mm added to the ridge board

The same deductions are made as imperial roofs:

– Top of Hip Rafter
  1. Single Cheek Cut – deduct half the 45° thickness of the ridge board
  2. Double Cheek Cut – deduct half the 45° thickness of the common rafter
– Bottom of Rafter
  1. Deduct the full 45° thickness of the fascia

All of these deductions are measured at right angles to the plumb cut

Line Length of the Hip Jacks

The same processes are used as in imperial hip jacks.

– The units of run are equal to the distance from the exterior corner in meters
– The unit line length is the same as the common rafters (remember 1000 unit run for hip jacks as they are essentially shortened commons)

We will calculate the line length of a hip jack which is 3.6 m from the corner in a 400/1000 roof:

U L L equals the square root of 400 squared plus 1000 squared equals 1077 m m

L i n e L e n g of t h o f H of i p J a. c k equals 3.6 times 1077 m m equals 3877 m m

 

We can also find common difference by multiplying the spacing (in meters) by the ULL. We will use the ULL of a 400/1000 roof with 400 mm spacing:

C o m m o n D i f of f of e r e n c e H of i p J a. c k s equals 0.4 times 1077 equals 431 m m

The deductions for hip jacks is ½ the 45° thickness of the hip rafter at the top and the full 90° thickness of the fascia at the bottom.

Review Questions

  1. Fill in the following Table:

SI Slope

Span

Run

Number of Units of Run

Unit of Rise

Unit of Line Length

Line length of Hip Rafter

Overhang Projection

Line Length of Overhang

A

1:2.5

10000

600

B

1:3.33

7200

600

C

1:1.67

8500

300

D

1:2

4800

300

E

1:1.43

2600

400

F

1:1.33

2840

400

G

1:4

9750

600

H

1:1.25

4330

600

I

1:1

7780

400

Answer:

SI Slope Span Run Number of Units of Run Unit of Rise Unit of Line Length Line length of Hip Rafter Overhang Projection Line Length of Overhang
A 1:2.5 10000 5000 5 400 1470 7350 600 882
B 1:3.33 7200 3600 3.6 300 1446 5206 600 868
C 1:1.67 8500 4250 4.25 600 1536 6528 300 461
D 1:2 9600 4800 4.8 500 1500 7200 300 450
E 1:1.43 5200 2600 2.6 700 1578 4103 400 631
F 1:1.33 2840 1420 1.42 300 1446 2053 400 578
G 1:4 9750 4875 4.875 250 1436 7000 600 862
H 1:1.25 8660 4330 4.33 800 1625 7036 600 975
I 1:1 7780 3890 3.89 1000 1732 6737 400 693

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Carpentry Refresher Program Manual Copyright © by Saskatchewan Indian Institute of Technologies-Trades and Industrial is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.