King Post Truss Joinery AnalysisCase Study

Timber Frame Engineering Council Symposium Burlington, VTAugust 8, 2013

John Treybal, PE

1

8x12 Tie8x

10

King

Pos

t

8x10

Rafte

r5x6 Strut

6x12 Plate

6x12 Ridge

8x8

Post

2

2000#2000#

1000#1000#

1000#1000#

340 plf

Truss Loading

Basis of Design:­ Douglas Fir #1, S4S, unseasoned­ Loads are dead + snow, self­weight included­ 24' span­ 8:12 pitch­ Rafters continuously laterally braced­ Pinned connections­ No friction

Tension

Comp.

Com

pres

sion

Tens

ion

Com

pres

sion

Compression

Com

pres

sion

Com

p.

3

Strut / Rafter Joint

5x6

8x10

9140

#

1140#

1310

0#­in

8260

#

980#

13100#­in

2300#

4

Strut / Rafter Joint

5x6

8x10

9140

#

1140#

1310

0#­in

8260

#

980#

13100#­in

2300#

880#

2120#

Failure Modes:

­ Rafter Bearing on Strut

­ Bending and Compression in Rafter atReduced Section

5

�� = �� = P����� = 2,120#� = ?1.5" ∗ 5.6"D ∗ 2 = 16.8���

0�1

= 2��. 30��.4°89:;91 = 1,020=>�?@A�B��>C�D0�R:EF9G:1 = 625=>�

= ��S��K > P���� ∴ NO

1.5"typ.

Strut / Rafter Joint ­ Rafter Bearing on Strut (Check 1)

8x10

5x6

5x6

8x10

9140

#

1140#

1310

0#­in

8260

#

980#

13100#­in

2300#

880#

2120#

5.6"

6

Strut / Rafter Joint ­ Rafter Bearing on Strut (Check 2)

0.75"4.5"

8x10

5x6

5x6

8x10

9140

#

1140#

1310

0#­in

8260

#

980#

13100#­in

2300#

880#

2120#

�� = �� = ������ = 880#� = 0.75" ∗ 4.5" = 3.38���

Conservativelyignoringtenonbearing–somemightargueforusinghalfofitormore

-�.= /��. 0 -12.3°56786. = 670:;�<=>�?��;@�A

-�7BC6D7. = 1,000:;� ∗ 1.15 = 1,150:;�= �G���H > ����� ∴ KL

7

= N, NP��� > 142:;� ∴ LMBending and Axial Compression Interaction:

\ ��-�′^� + \ �̀-̀ ′^ = �. NP < 1.0 ∴ LM�̀ = b

Q = 13,100# − ��71.5��R = 183:;�

-̀. = 1,200:;� ∗ 1.15 = 1,380:;�

compressionzoneofrafter?Compression Only:

�� = �� = 8,260#

58.1��� = N[���-�. = 1,000:;� ∗ 1.15= N, NP��� > 142:;� ∴ LM

Strut / Rafter Joint ­ Bending andCompression in Rafter at Reduced Section

5x6

8x10

9140

#

1140#

1310

0#­in

8260

#

980#

13100#­in

2300#

880#

2120#

Rafter Net Section Properties:

� = 58.1���T = 71.5��USidenote:Isthereanargumen

8

Strut / King Post Joint

5x6

5x6

8x10

8x12

2320#

2320

#

2800

#

8240#

8240#

110#

110#

9

Strut / King Post Joint12

90#

5x6

5x6

8x10

8x12

2320#

1930#

2320

#

1290

#

1930#

2800

#

8240#

8240#

110#

110#

Failure Modes:

­ Strut Bearing on King Post

­ Shear Through King Post Relish

­ King Post Tension at Reduced Section (not checked ­ top of king post joint willcontrol due to lower cross­sectional area)

­ Tie Tension at Reduced Section (not checked ­ heel joint will control)

­ King Post/Tie Peg Shear (not checked­ OK by inspection)

10

1930#

�� = �� = P�S��� = 1,930#� = ?1.5" ∗ 6.1"D ∗ 2 = 18.3���

0�1 = 2��. 30UU.5°89:;91 = 914=>�?@A�B��>C�D0�Rhijklm891 = 625=>�

= ��S��K > P�S�� ∴ NO

Strut / King Post Joint ­ Strut Bearing on King Post (Check 1)

1290

#

6.1"

1.5"typ.

5x6 5x68x10

8x125x6

5x6

8x10

8x12

2320#

2320

#

1290

#

1930#

2800

#

8250#

8250#

110#

110#

11

�� = �� = de���� = 1,290#� = 0.75" ∗ 4.5" = 3.38���

0�1

= 2��. 3 0g4.U°89:;91 = 727=>�?@A�B��>C�D0�hijklm891 = 1,000=>� ∗ 1.15 = 1150=>�

= J�J��K > de��� ∴ NO

Strut / King Post Joint ­ Strut Bearing on King Post (Check 2)

1290

#

0.75"

4.5"

5x6 5x68x10

8x125x6

5x6

8x10

8x12

2320#

1930#

2320

#

1290

#

1930#

2800

#

8250#

8250#

110#

110#

12

Strut / King Post Joint ­ Shear Through King Post Relish

0.75" 4.5"

6"

8x12

5x68x10

5x612

90# 2320#

1930#

2320

#

1290

#

1930#

2800

#

8250#

8250#

110#

110#

�p = q� = d���q = 1,290#� = ?0.75" ∗ 2+4.5"D ∗ 6" = 36���

0p1 = 170=>� ∗ 1.15= Qr��� > d���∴ OP

5x6

5x6

8x10

8x12

13

Rafter / King Post Joint

8x10

2000#

2000#

2920

#6x12

6x12

8x10

7180

#

630#

8x10

7180#

630#

14

Rafter / King Post Joint

8x10

2000#

2000#

2920

#6x12

6x12

8x10

7180

#

630#

5970#

3980

#

520#

350#

8x10

7180#

630#

520#

350#

5970#

3980

#

Failure Modes:

­ Ridge Beam Bearing on King Post

­ King Post Bearing on Rafters

­ Shear Through King Post Relish

­ King Post Tension at Reduced Section

­ Rafter Compression over Effective Areaat Connection

15

�� = �� = S����� = 2,000#� = ?1.25" − 0.25"shrinkageD

∗ ?5.5" − 1.5"D= 4.00���

0�1

= 2��. 3 0�R:irkG1 = 625=>�0�hijklm891 = 1,000=>� ∗ 1.15 = 1,150=>�

= ��S��K > S���� ∴ NO

Rafter / King Post Joint ­ Ridge Beam Bearing on King Post

8x10

2000#

2000#

2920

#

1.5"

1.25"

6x12

6x12

8x10

7180

#

630#

5970#

3980

#

520#

350#

8x10

7180#

630#

520#

350#

5970#

3980

#2"

TYP.

16

�� = �� = PJ���� = 5,970# + 350# = 6,320#� = ?6.75" ∗ 2.75"D ∗ 2 = 37.1���

0�1= 2��. 3 0�Rhijklm891 = 625=>�

0UU.5°:EF9G:1 = 914=>�?@A�B��>C�D= ��S��K > PJ��� ∴ NO

Rafter / King Post Joint ­ King Post Bearing on Rafters (Check 1)

8x10

8x10

6x12

6x12

2000#

2000#

7180

#

630#

7180#

630#

2.75"typ.

8x10

2920

#

6.75

"

5970#

3980

#

520#

350#

520#

350#

5970#

3980

#

17

�� = �� = [�P��� = 2,920# + 2,000# + 2,000# = 6,920#� = ?1"*7.5"D2=15���

0�1

= 2��. 30�hijklm891 = 1,000=>� ∗ 1.15 = 1,150=>�0g4.U°:EF9G:1 = 727=>�?@A�B��>C�D

= J�J��K > [�P�� ∴ NO

Rafter / King Post Joint ­ King Post Bearing on Rafters (Check 2)

6x12

6x12

2000#

2000#

1"

8x10

2920

#

8x10

7180

#

630#

5970#

3980

#

520#

350#

8x10

7180#

630#

520#

350#

5970#

3980

#

18

Conservatively neglecting rafter tenons

�n = o� = P����o = 2,920# + 2,000# + 2,000# = 6,920#� = ?4.6" ∗ 7.5"D ∗ 2 = 69.0���

0n1 = 170=>� ∗ 1.15= Pp��� > P����∴ NO

Rafter / King Post Joint ­ Shear Through King Post Relish

6x12

6x12

2000#

2000#4.

6"

8x10

2920

#

8x10

7180

#

630#

5970#

3980

#

520#

350#

8x10

7180#

630#

520#

350#

5970#

3980

#

19

Rafter / King Post Joint ­ King Post Tension at Reduced Section

6x12

6x12

2000#

2000#

HOU

SIN

G

HOU

SIN

G

TENONS

HOUSING

HOUSING

PEG

PEG

PEG

PEG

SPLIN

ESP

LINE

King Post Cross Section

� = 19.0���

8x10

2920

#

8x10

7180

#

630#

5970#

3980

#

520#

350#

8x10

7180#

630#

520#

350#

5970#

3980

#

�9 = v

� = d�[��v = 2,920# + 2,000# + 2,000# = 6,920#� = 19.0���

091 = 825=>� ∗ 1.15= r[r�� > d�[��∴ OP

20

Rafter / King Post Joint ­ Rafter Compression Over EffectiveArea at Connection

8x10

2000#

2000#

2920

#

6.1"

6x12

6x12

8x10

7180

#

630#

8x10

7180#

630#

�� = �� = QSJ��� = 7,180#� = 6.1"*7.5"=45.8���

0�1 = 1,000=>� ∗ 1.15= Q, QS��� > QSJ�� ∴ OP

21

Heel Joint

1000#

10480#

870#

8690

#

1000# (plate not shown)

8x8

6x12

8x10

8240#

160#

8x12

22

Heel Joint

1000#

10480#

870#

8690

#8720#

5810

#

480#72

0#

1000# (plate not shown)

8x8

6x12

8x10

8240#

160#

8x12

Failure Modes:

­ Plate Bearing on Post

­ Rafter Bearing on Tie

­ Shear Through Tie Relish

­ Tie Tension at Reduced Section

­ Tie Bearing on Post

23

�� = �� = �[��� � = 1,000#� = <1" − 0.25"shrinkageA ∗ <5.5"A

= 4.13���-�.= /��. 0 -�OluB6D. = 625:;�

-�lm56. = 1,000:;� ∗ 1.15 = 1,150:;�= ��P��H > �[��� ∴ KL

Heel Joint ­ Plate Bearing on Post

1000#

10480#

870#

8690

#8720#

5810

#

480#72

0#

1000# (plate not shown)

8x8

6x12

8x10

8240#

160#

8x12

1"

24

�� = �� = Gpd�� � = 10,480#� = <2.4" ∗ 2.75"A ∗ 2 = 13.2���

-�.= /��. 0 -RR.2°6iD. = 875:;�<ℎ>�?��;@�A

-�7BC6D7. = 1,000:;� ∗ 1.15 = 1,150:;�= eGP��H > Gpd�� ∴ KL

1000#

10480#

870#

8690

#8720#

5810

#

480#72

0#

1000# (plate not shown)

8x8

6x12

8x10

Heel Joint ­ Rafter Bearing on Tie

2.4"

8240#

160#

8x12

2"

2.75"TYP.

25

1000#

10480#

870#

8690

#8720#

5810

#

480#72

0#

1000# (plate not shown)

8x8

6x12

8x10

Heel Joint ­ Shear Through Tie Relish

8240#

160#

8x12

�p = q� = N�r��q = 8,720#� = 79.8���

-p. = 170:;� ∗ 1.15= Nr��� > N�r��∴ LM

26

�6 = t� = M����t = 8,720#� = 9.5"*7.5" = 71.3���

-6. = 675:;� ∗ 1.15= GG��� > M����∴ KL

1000#

10480#

870#

8690

#8720#

5810

#

480#72

0#

1000# (plate not shown)

8x8

6x12

8x10

Heel Joint ­ Tie Tension at Reduced Section

8240#

160#

8x12

9.5"

27

�� = �� = ��M�� � = 5,810# + 720# + 160# = 6,690#� = 30.3���

-�.= /��. 0 -�O6iD. = 625:;�

-�lm56. = 1,000:;� ∗ 1.15 = 1,150:;�= ��P��H > ��M�� ∴ KL

1000#

10480#

870#

8690

#8720#

5810

#

480#72

0#

1000# (plate not shown)

8x8

6x12

8x10

Heel Joint ­ Tie Bearing on Post

8240#

160#

8x12

1"typ.

1.75"typ.

28

Thank You

Questions?Comments?