Case Study King Post Truss Joinery Analysis...King Post Truss Joinery Analysis Case Study Timber...

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?