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# = = P 2120# 2300# = 2,120# = ?1.5 " 5.6" D 2 = 16.8 1 0 1 880# 5x6 0.47 89:;9 = 1,020 => ?@AB>C D = 2. 3 1 0R :EF9G: = 625 => = S K L P M NO 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 Conser ati ely ignoring tenon 880# 5x6 bearing ( some might argue for using half of it or more . - . -12.34 56786 = 970 :; <=>?;@ A = /. 0 . - 7BC6D7 = 1,000 :; 1.15 = 1,150 :; = G H I J KL 7 Strut / Rafter Joint • Bending and Compression in Rafter at Reduced Section Rafter Net Section Properties: 13100#•in = 58.1 980# U T = 71.5 8260# Side no e: Is here an arg.men compression zone of rafter? 1140# Compression Only: 8x10 8,290# = = = N[ 58.1 13100#•in . - = 1,000 :; 1.15 9140# = N, NP I 142 :; K LM 2120# 2300# = N, NP I 142 :; K LM Bending and Axial Compression Interaction: 5x6 ` 880# \ ^ _\ ^ = .NP a 1.0 K LM -] -`] b 13,100# c ` = = = 183 :; Q 71.5 R . -` = 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# = = PS = 1,f30# 8250# = ?1.5" 6.1"D 2 = 18.3 1 8x12 1 0UU.57 89:;9 = f14 => ?@AB>C D 110# 0 = 2. 3 1 0R hijk lm89 = 625 => 8250# K 110# = S L PS M NO 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# = = de = 1,2f0# 8250# = 0.75" 4.5" = 3.38 1 8x12 0 110# 1 0g4.U7 89:;9 = 727 => ?@AB>C D = 2. 3 1 8250# 0 hijk lm89 = 1,000 => 1.15 = 1150 => 110# = JJ K L de M NO 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" q p = = d q = 1,2f0# 8250# = ?0.75" 2_4.5"D 6" = 36 1 8x12 0p = 170 => 1.15 110# 8250# = Qr L d N OP 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 • = = S Ridge Beam Bearing on King Post = 2,000# 2000# 350# = ?1.25" c 0.25" shrinkage D ?5.5" c 1.5"D 520# 630# 7180# 3980# = 4.00 1 6x12 0 1 5970# 8x10 0R :irkG = 625 => = 2. 3 1 0 hijk lm89 = 1,000 => 1.15 = 1,150 => 2000# K 350# = S L S M NO 630# 520# 1.25" 8x10 2" TYP. 7180# 1.5" 6x12 3980# 5970# 2920# 8x10 16 Rafter / King Post Joint • = = PJ King Post Bearing on Rafters (Check 1) = 5,f70#_350# = 6,320# 2000# 350# = ?6.75" 2.75"D 2 = 37.1 1 0 520# 630# 1 7180# 3980# 0R hijk lm89 = 625 => = 2. 3 1 6x12 0UU.57 :EF9G: = f14 => ?@AB>CD 5970# 8x10 = S K L PJ M NO 6.75" 2000# 350# 630# 2.75" typ. 520# 8x10 7180# 6x12 3980# 5970# 2920# 8x10 17 Rafter / King Post Joint • = = [P King Post Bearing on Rafters (Check 2) = 2,f20# _ 2,000# _ 2,000# = 6,f20# 2000# 350# = ?1" s 7.5"D2 = 15 1 1" 0 520# 630# 1 hijk lm89 7180# 3980# 0 = 1,000 => 1.15 = 1,150 => = 2. 3 1 6x12 0g4.U7 :EF9G: = 727 => ?@AB>CD = JJ K L [P M NO 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 o n = = P 2000# 350# o = 2,f20# _ 2,000# _ 2,000# = 6,f20# = ?4.6" 7.5"D 2 = 6f.0 520# 630# 7180# 3980# 1 0n = 170 => 1.15 6x12 4.6" = Pp L P M NO 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# v 9 = = d[ 520# v = 2,f20# _ 2,000# _ 2,000# = 6,f20# 8x10 = 1f.0 7180# 6x12 1 09 = 825 => 1.15 3980# 5970# = r[r L d[ N OP 2920# 8x10 20 Rafter / King Post Joint • = = QSJ Rafter Compression Over Effective Area at Connection = 7,180# 2000# = 6.1" s 7.5" = 45.8 1 0 = 1,000 => 1.15 630# 7180# = Q, QS L QSJ N OP 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" c 0.25" shrinkage A <5.5"A = 4.13 . - 480# . -O luB6D = 925 :; 720# = /. 0 . 8720# - lm56 = 1,000 :; 1.15 = 1,150 :; 8x10 870# 10480# = P H I [ J KL 5810# 1000# 6x12 1" 160# 8240# 8x12 8690# 8x8 24 Heel Joint • = = Gpd Rafter Bearing on Tie 1000# (plate not shown) = 10,480# = <2.4" 2.75"A 2 = 13.2 . - . 480# -RR.24 6iD = 875 :; <v>?;@A = /. 0 . - 7BC6D7 = 1,000 :; 1.15 = 1,150 :; 8720# 720# H 8x10 870# = eGP I Gpd J KL 10480# 5810# 1000# 2.4" 2.75" TYP. 2" 6x12 160# 8240# 8x12 8690# 8x8 25 q Heel Joint • p = = Nr Shear Through Tie Relish 1000# (plate not shown) q = 8,720# = 7f.8 . -p = 170 :; 1.15 480# = Nr I Nr K LM 8720# 720# 8x10 870# 10480# 5810# 1000# 6x12 160# 8240# 8x12 8690# 8x8 26 t Heel Joint • 6 = = M Tie Tension at Reduced Section 1000# (plate not shown) t = 8,720# = f.5" s 7.5" = 71.3 . -6 = 975 :; 1.15 480# = GG I M J KL 8720# 720# 8x10 870# 10480# 5810# 1000# 9.5" 6x12 160# 8240# 8x12 8690# 8x8 27 Heel Joint • = = M Tie Bearing on Post 1000# (plate not shown) = 5,810#_720#_190# = 9,9f0# = 30.3 . - . 480# -O 6iD = 925 :; = /. 0 . - lm56 = 1,000 :; 1.15 = 1,150 :; 8720# 720# H 8x10 870# = P I M J KL 10480# 5810# 1000# 6x12 1.75" typ. 1" 160# 8240# typ. 8x12 8690# 8x8 28 Thank You Questions? 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