King Post Truss Joinery Analysis Case Study

Timber Frame Engineering Council Symposium Burlington, VT August 8, 2013

John Treybal, PE

1 6x12 Ridge 8x10 King Post 5x6 Strut

8x10 Rafter 6x12 Plate 8x12 Tie 8x8 Post

2 Truss Loading

340 plf

2000# 2000# 1000# Compression 1000#

Tension Compression Comp.

Compression Compression

Tension Basis of Design: 1000# • Douglas Fir #1, S4S, unseasoned 1000# • Loads are dead + snow, self•weight included • 24' span • 8:12 pitch • Rafters continuously laterally braced • Pinned connections

Comp. • No friction 3 Strut / Rafter Joint

13100#•in

980#

8260#

1140#

8x10 13100#•in

9140#

2300#

5x6

4 Strut / Rafter Joint

13100#•in

980#

8260#

1140# Failure Modes: 8x10 • Rafter Bearing on Strut

13100#•in • Bending and Compression in Rafter at 9140# Reduced Section

2120#

2300#

880# 5x6

5 Strut / Rafter Joint • Rafter Bearing on Strut (Check 1) 13100#•in 8x10 980#

8260# 1.5" typ.

1140#

8x10 5.6" 5x6 13100#•in 9140# = = 2120#

2300# = 2,120# = 1.5 " ∗ 5.6" ∗ 2 = 16.8 880# 5x6 .° = 1,020 = . = 625 = > ∴

6 Strut / Rafter Joint • Rafter Bearing on Strut (Check 2) 13100#•in 8x10 980#

8260#

1140#

8x10 5x6

0.75" 4.5" 13100#•in 9140# = = 2120#

2300# = 880# = 0.75" ∗ 4.5" = 3.38 Conservatively ignoring tenon

880# 5x6 bearing – some might argue for using half of it or more .° = 670 = . = 1,000 ∗ 1.15 = 1,150 = > ∴ 7 Strut / Rafter Joint • Bending and Compression in Rafter at Reduced Section Rafter Net Section Properties: 13100#•in = 58.1 980# = 71.5 8260# Side note: Is there an argumen

compression zone of rafter? 1140# Compression Only: 8x10 8,260# = = = 58.1

13100#•in = 1,000 ∗ 1.15 9140# = , > 142 ∴

2120#

2300# = , > 142 ∴ Bending and Axial Compression Interaction:

5x6 880# + = . < 1.0 ∴ ′ ′ 13,100# − = = = 183 71.5 = 1,200 ∗ 1.15 = 1,380 8 Strut / King Post Joint

5x6 8x10 2800# 2320#

5x6 2320#

8240#

8x12 110#

8240# 110#

9 Strut / King Post Joint

5x6 1930# 8x10 2800#

2320# 1290#

Failure Modes: 5x6 1930# 2320# • Strut Bearing on King Post 1290# • Shear Through King Post Relish

• King Post Tension at Reduced Section (not checked • top of king post joint will 8240# control due to lower cross•sectional area)

8x12 110# • Tie Tension at Reduced Section 8240# (not checked • heel joint will control) 110# • King Post/Tie Peg Shear (not checked• OK by inspection)

10 Strut / King Post Joint •

5x6 8x10 Strut Bearing on King Post (Check 1) 5x6 5x6 1.5" 1930# typ. 8x10 2800#

2320# 1290# 6.1"

1930# 5x6 8x12 2320# 1290#

= = = 1,930# 8250# = 1.5" ∗ 6.1" ∗ 2 = 18.3 8x12 .° = 914 110# = . = 625 8250#

110# = > ∴

11 Strut / King Post Joint •

5x6 8x10 Strut Bearing on King Post (Check 2) 5x6 5x6 1930# 8x10 2800#

2320# 1290#

0.75"

5x6 1930# 4.5" 8x12 2320# 1290#

= = = 1,290# 8250# = 0.75" ∗ 4.5" = 3.38 8x12 110# .° = 727 = . 8250# = 1,000 ∗ 1.15 = 1150 110# = > ∴

12 Strut / King Post Joint •

5x6 8x10 Shear Through King Post Relish 5x6 5x6 1930# 8x10 2800#

2320# 1290# 4.5" 0.75"

1930# 5x6 8x12 2320# 1290#

6" = = = 1,290# 8250# = 0.75" ∗ 2+4.5" ∗ 6" = 36 8x12 = 170 ∗ 1.15 110#

8250# = > ∴ 110#

13 Rafter / King Post Joint

2000#

630# 7180# 6x12 8x10

2000#

630#

8x10

7180# 6x12 2920# 8x10

14 Rafter / King Post Joint

2000# 350# 520# 630#

7180# 3980# 6x12 5970# 8x10 Failure Modes: 2000# 350# 630# • Ridge Beam Bearing on King Post

520# • King Post Bearing on Rafters

8x10 • Shear Through King Post Relish 7180# 6x12

3980# 5970# • King Post Tension at Reduced Section

2920# • Rafter Compression over Effective Area at Connection 8x10

15 Rafter / King Post Joint • = = Ridge Beam Bearing on King Post = 2,000#

2000# 350# = 1.25" − 0.25" shrinkage ∗ 5.5" − 1.5" 520# 630#

7180# 3980# = 4.00 6x12 5970# 8x10 = 625 = . = 1,000 ∗ 1.15 = 1,150 2000# 350# = > ∴ 630#

520# 1.25"

8x10 2" TYP. 7180# 1.5" 6x12

3980# 5970# 2920# 8x10

16 Rafter / King Post Joint • = = King Post Bearing on Rafters (Check 1) = 5,970#+350# = 6,320# 2000# 350# = 6.75" ∗ 2.75" ∗ 2 = 37.1 520# 630# 7180# 3980# = 625 = . 6x12 .° = 914 5970# 8x10 = > ∴ 6.75" 2000# 350# 630# 2.75" typ. 520#

8x10

7180# 6x12

3980# 5970# 2920# 8x10

17 Rafter / King Post Joint • = = King Post Bearing on Rafters (Check 2) = 2,920# + 2,000# + 2,000# = 6,920# 2000# 350# = 1" * 7.5"2 = 15 1" 520# 630# 7180# 3980# = 1,000 ∗ 1.15 = 1,150 = . 6x12 .° = 727 = > ∴ 5970# 8x10

2000# 350# 630# 520#

8x10

7180# 6x12

3980# 5970# 2920# 8x10

18 Conservatively neglecting rafter tenons Rafter / King Post Joint • Shear Through King Post Relish = = 2000# 350# = 2,920# + 2,000# + 2,000# = 6,920# = 4.6" ∗ 7.5" ∗ 2 = 69.0 520# 630#

7180# 3980# = 170 ∗ 1.15 6x12 4.6" = > ∴ 5970# 8x10

2000# 350# 630# 520#

8x10

7180# 6x12

3980# 5970# 2920# 8x10

19 Rafter / King Post Joint • King Post Tension at Reduced Section HOUSING 2000# 350# PEG SPLINE PEG TENONS 520# 630# = 19.0 HOUSING HOUSING

7180# 3980# PEG PEG 6x12 SPLINE HOUSING 5970# 8x10 King Post Cross Section 2000# 350# 630# = = 520# = 2,920# + 2,000# + 2,000# = 6,920# 8x10 = 19.0 7180# 6x12 = 825 ∗ 1.15

3980# 5970# = > ∴

2920# 8x10

20 Rafter / King Post Joint • = = Rafter Compression Over Effective Area at Connection = 7,180# 2000# = 6.1" * 7.5" = 45.8 = 1,000 ∗ 1.15 630# 7180# = , > ∴ 6x12 8x10 6.1" 2000#

630#

8x10

7180# 6x12 2920# 8x10

21 Heel Joint

1000# (plate not shown)

8x10 870# 10480#

1000#

6x12

160# 8240#

8x12 8690# 8x8 22 Heel Joint

1000# (plate not shown)

480#

8720# 720# 8x10 870# 10480# Failure Modes: 5810# 1000# • Plate Bearing on Post

• Rafter Bearing on Tie

• Shear Through Tie Relish

6x12 • Tie Tension at Reduced Section

160# 8240# • Tie Bearing on Post 8x12 8690# 8x8 23 Heel Joint • = = Plate Bearing on Post = 1,000# 1000# (plate not shown) = 1" − 0.25" shrinkage ∗ 5.5" = 4.13 480# = 625

720# = . 8720# = 1,000 ∗ 1.15 = 1,150 8x10 870# 10480# = > ∴ 5810# 1000#

6x12

1"

160# 8240#

8x12 8690# 8x8 24 Heel Joint • = = Rafter Bearing on Tie 1000# (plate not shown) = 10,480# = 2.4" ∗ 2.75" ∗ 2 = 13.2 480# .° = 875 ℎ = . = 1,000 ∗ 1.15 = 1,150 8720# 720# 8x10 870# = > ∴ 10480# 5810# 1000#

2.4"

2.75" TYP. 2" 6x12

160# 8240#

8x12 8690# 8x8 25 Heel Joint • = = Shear Through Tie Relish 1000# (plate not shown) = 8,720# = 79.8 = 170 ∗ 1.15 480# = > ∴

8720# 720# 8x10 870# 10480# 5810# 1000#

6x12

160# 8240#

8x12 8690# 8x8 26 Heel Joint • = = Tie Tension at Reduced Section 1000# (plate not shown) = 8,720# = 9.5" * 7.5" = 71.3 = 675 ∗ 1.15 480# = > ∴

8720# 720# 8x10 870# 10480# 5810# 1000# 9.5"

6x12

160# 8240#

8x12 8690# 8x8 27 Heel Joint • = = Tie Bearing on Post 1000# (plate not shown) = 5,810#+720#+160# = 6,690# = 30.3 480# = 625 = . = 1,000 ∗ 1.15 = 1,150 8720# 720# 8x10 870# = > ∴ 10480# 5810# 1000#

6x12 1.75" typ. 1"

160# 8240# typ. 8x12 8690# 8x8 28 Thank You

Questions? Comments?