L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. ....

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Axial Load Small Moment Large Moment Timber Timber and and Steel Steel Design Design Column Base Plate Column Base Plate . . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL ENGINEERING Visit www.tumcivil.com/DRMK/ for apps: weld Anchor bolts (a) (b) Concrete footing Column Column Base Base Plates Plates A 1 = = B x N A 2 = กก Transfer bearing to concrete footing B N A 1 A 2

Transcript of L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. ....

Page 1: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

� Axial Load

� Small Moment

� Large Moment

TimberTimber andand SteelSteel DesignDesign

Column Base PlateColumn Base Plate

������ ����..����..���� � ��������� ��������S U R A N A R E E INSTITUTE OF ENGINEERING

UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL ENGINEERING

Visit www.tumcivil.com/DRMK/ for apps:

weld

Anchor bolts

(a) (b)

Concrete

footing

ColumnColumn BaseBase PlatesPlates

A1 = ���������� �����ก�������

= B x N

A2 = ���������ก��������� �����ก

Transfer bearing to concrete footing

B

N

A1

A2

Page 2: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

��� A1 = A2,

��� A1 ���ก� � A2,

Allowable Bearing Pressure, Allowable Bearing Pressure, FFpp

A1 A2Fp = �� ����� ก�������!������ก���

f’ c = ก"��##$%�&�#����ก���

0.35p cF f ′=

2

1

0.35 0.7p c c

AF f f

A′ ′= ≤

Fp

A2/A101 2 3 4

0.35f’c

0.7f’c2

12

1

0.35 c

PA

A f

= ′

2

1 1

0.35 c

APf

A A′=

MinimumMinimum ThicknessThickness ofof ColumnColumn BaseBase PlatePlate

P

fp

t

B or N

1 cm

1 cm

bf

B

d N

m

0.95d

m

n n0.80bf

��$#� fp ����� �������� = P / ( B × N )

�*+��,��%-��������ก��� 1 /!.���� �&�*1�� 2$�!�� �3$�� ���� 0.80bf ��& 0.95d

2!�!��8$#$���� �&�*1��:2

2 2p

p

f nnM f n= = ��&

2

2 2p

p

f mmM f m= =

Page 3: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

1 cm

t2!$:�#������#$��� ��ก��� 1 /!.��� t ��

3 21/ (1)( ) /( / 2) / 6

12S I c t t t= = =

�� ����$#$!�� ��� �ก# M/S ��!�� �;! �ก*��� ����$#$����!��� Fb +&;$�� �

( )2 2

2 2

/ 2 3

/ 6p p

b

f m f mMF

S t t= = =

23 p

b

f mt

F=

�< ��$���ก#� ���ก�*1��,23 p

b

f nt

F=

AISC ก"���$�� ����$#$����!������� �� Fb

= 0.75Fy:

2 p

y

ft m

F= 2 p

y

ft n

F=��&

Critical Bending DimensionsCritical Bending Dimensions

B

N

bf

d

m

0.95d

m

n n0.80bf

b

B

b N

m

0.95b

m

n n0.95b D

B

N

m

0.80D

m

n n0.80D

Page 4: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

DesignDesign ofof ColumnColumn BaseBase PlatesPlates

1 cm

1 cm

bf

B

d N

m

0.95d

m

n n0.80bf ก��ก� �� �����ก+&%�&��#$����C$

�!���&�& N ��& B �:ก���ก+��"���� m = n

�D��&�< ����+&�ก*$�3���!��

1N A= + ∆

�!�� A1 = ���������� ������������ก��

∆ = 0.5(0.95d – 0.80bf)

�!���"���,���!��� N ;$����� ���!ก��� B �����ก��+&�"���,;$�+�ก B = A1/N

��������� 6-4 +ก� �� ���# �������"�$�������ก A36 �"���# ��� W300×94.0 (d

= 30 /!., bf= 30 /!.) ��&��"���#ก 160 �#� �����ก��ก��������# !����$ 2.5 × 2.5

�!�� = 210 กก.//!.2

����� ��������� ��!����$���กก� ������ก��� ������� A1 +&�<�� ����!�กก� ��

( )

22

21 ' 2

2

1 1 16075.8 cm

0.35 250 0.35 0.210c

PA

A f

= = =

21 '

1601,088 cm

0.7 0.7(0.210)c

PA

f= = = ������

��������������:

0.5(0.95 0.80 ) 0.5(0.95(30) 0.80(30)) 2.25 cmfd b∆ = − = − =

1 1088 2.25 35.2 cmN A= + ∆ = + = (� ! 35 $�.)

1 108831.1 cm

35

AB

N= = = (� ! 32 $�.)

Page 5: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

��������(����ก���ก��:

2160(1000)143 kg/cm

(32)(35)p

Pf

B N= = =

×

�����*������� m �+, n :

0.95 35 0.95(30)3.25 cm

2 2

N dm

− −= = =

0.80 32 0.80(30)4.00 cm

2 2fB b

n− −

= = =

����+�ก�� ��;! �� ��C!��ก����#��!$

2' 22

1

2500.35 0.35(210) 549 kg/cm

(32)(35)P c

AF f

A= = =

' 20.7 147 kg/cmP cF f= = ������

fp

< Fp

OK

�����*����/���������������:

1432 2(4.0) 1.9 cm

2,500p

y

ft n

F= = = (� ! 2 $�.)

� !����0/+1ก PL 2 ×××× 32 ×××× 35 $�. �

www.tumcivil.com/DRMK/

Base Plate 1 : Axial Load

Page 6: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

Moment Resisting Column BaseMoment Resisting Column Base

MomentMoment--Resisting Column BasesResisting Column Bases

PM

ColumnFilletWeld

NutWasher

Anchor bolt

PM

Column

Angle welded orbolted to columnin shop

Anchor bolt

PM

Anchor bolt

Weld

2.5 cm

Page 7: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

Bearing PressureBearing Pressure

B

d

N

bf

fp,min

fp,max

P

M

Pressure from axial load: fpa = P / A

Pressure from moment: fpb = M / S

where A = B x N and S = B x N2 / 6

0NB

M6NB

Pf

2min,p ≥−=

p2max,p FNB

M6NB

Pf ≤+=

Small Moment without Uplift (Full Plate Bearing)

fp1

fp2

n

Base Plate Design

1 2

2 21 2

1 2 12 3 2 3

3 6

p p

p p

n nM f n f n

f n f n

= +

= +

Moments at critical sections:

��������� �����������ก���� 1 ��. � t ���

32

1(1)( )

12/ 2 6

tI tS

C t= = =

�� ��� AISC ก!��"� Fb = 0.75Fy

P

fp

M

n

bf

B

d N

m

m

n n0.80bf

0.95d

n/3 n/3

2 21 2Another direction, 3 6

p pf m f mM = +

2

6b

M MF

S t= =

2

6 6 80.75 y

b y

M M MF t

F Ft= → = =

Page 8: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

�������������ก���� 50 x 80 "�.(�����กก����������$)

&������'() 14-6 ��ก�##������" �$�� ��%���$� &$'�(������#$�� W350x159 �)(��*+!��ก �����ก 150 � ��,��$� &��� 15 �-$� � ".�$�/ก A36 ��, F

b=

0.75(2,500) = 1,875 กก./��.2 ��ก�* ����ก�*��� = 210 กก./��.2 ��, Fp

= 0.35(210) = 73.5 กก./��.2

� *('+� W350x159 (d = 35.6 ��., tw = 14 ��., bf = 35.2 ��., tf = 22 ��.)

�,5,$5�+��6�5& e = M /P = 15(100)/150 = 10 ��.

�����'7&�5��8�5"9:ก$�� '5�5��;��"��5��".��� 1/3 ก���������$�/ก

2pNB

M6NB

Pf ±=

2

53

8050

10156805010150

×

××±

××

=

13.285.37 ±=

=2

2

kg/cm 9.37

kg/cm 63.65 < Fb = 73.5 kg/cm2 OK

> 0 OK

9.37

65.63

80 cm

33.4 cm23.3 cm23.3 cm

49.27

�����������ก 7.5 x 50 x 80 "�.

����������������ก'()&��ก��

8 8(16,237)7.21 cm

2,500y

Mt

F= = =

�����&-�����.����/)�:

2 249.27(23.3) 65.63(23.23)16,237 kg-cm

6 3+ =

Page 9: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

Max Moment without UpliftMax Moment without Uplift

0

fp,max

P

M

N

P

e

N/3

0NB

M6NB

Pf

2min,p =−=

6NP

M ==eP

6N

e =

Criteria for full plate bearing:6N

e6N

≤≤−

Load P within middle third of plate length N

−′=+

3

NN

2

BNFMNP ppp

T

2

BNFPT pp=+

Large Moment with UpliftLarge Moment with Uplift

B

dN

bf

TFp

P

M

bedge

N’Np

NT

2N

e6N

≤≤Eccentricity limit:

[ ΣFy = 0 ]

[ ΣMT = 0 ]

where T = Tensile force in anchor rod

NT = Distance between anchor rodand column center

Np = Bearing Length ( < N )

N’ = Distance between anchor rodand plate edge

Page 10: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

−′=+

3

NN

2

BNFMNP ppp

T[ ΣMT = 0 ]From

Solve quadratic function to determine the bearing length Np :

where f’ = Fp B N’ / 2

3/BF

)MNP()6/BF(4ffN

p

Tp2

p

+−′±′=

Tensile force in anchor rod: P2

BNFT pp −=

&������'() 14-7 %!� ���5���%*( 14-6 �+!���5".�$�� W350x159 �$�=� ��#+!��ก P = 50

� ��,��$� &��� M = 10 �-$� � ����ก�* �*���$%�����$�/ก f’c = 240 ksc

� *('+� W350x159 (d = 35.6 ��., tw = 14 ��., bf = 35.2 ��., tf = 22 ��.)

B

dN

bf

bedge

���$���ก������$�/ก;�ก���$��#�ก�,5,��#���5)�

N > d + 2 x 8 = 35.6 + 16 = 51.6 cm

B > bf + 2 x 8 = 35.2 + 16 = 51.2 cm

������$�/ก N = 52 cm, B = 52 cm

�,5,$5�+��6�5& e = M/P = 10x100/50 = 20 cm

N/6 = 8.67 cm < e = 20 < N/2 = 26 cm

∴∴∴∴ �����&-��ก��'+�����ก ����1��.���1�

Page 11: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

TFp

P

M

N’Np

NT

2 ���3��������4ก'��:

f’ = Fp B N’ / 2

= 84 x 52 x 48 / 2

= 104832 kg

Np = 24.0 cm

Fp = 0.35 x 240 = 84 kg/cm2

3/BF

)MNP()6/BF(4ffN

p

Tp2

p

+−′±′=

2 ���3����1��.���1�:

T = 84 x 24.0 x 52 / 2 – 50x103

= 2416 kg

Trod = T/2 = 1208 kg

2 ���3���������������ก:

�,5,5�( m = (N – 0.95d)/2

= (52 – 0.95x35.6)/2

m = 9.1 cm

Tfp = 84 ksc

P

M

24.0

m = 9.1 cm

fpm

fpm = 84 x (24.0 – 9.1) / 24.0 = 52.2 ksc

P2

BNFT pp −=

Page 12: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

cm 1.32500

30398t =

×=

31.984

61.92.52

M22

pl×

=

84

m = 9.1 cm

52.2

�����&-�������������ก:

�����������ก PL 3.1 x 52 x 52 "�.

= 3039 kg-cm

Alternative Shorter MethodAlternative Shorter Method

B

dN

bf

TFp

P

M

bedge

N’Np

NT

2

BNFRPT pp==+[ ΣFy = 0 ]

�=7*�5������5"ก���!��>����5���#ก%���5���? ="�6�5&@��������" ��� ��ก�#9:ก��#������

Np/3

R

where T = Tensile force in anchor rod

NT = Distance between anchor rodand column center

Np = Bearing Length ( < N )

N’ = Distance between anchor rodand plate edge

R = Resultant force from bearing pressure

[ ΣMT = 0 ]

−′=+

3

NNRMPN p

T

Page 13: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

&������'() 14-7 %!� ���5���%*( 14-6 �+!���5".�$�� W350x159 �$�=� ��#+!��ก P = 50

� ��,��$� &��� M = 10 �-$� � ����ก�* �*���$%�����$�/ก f’c = 240 ksc

� *('+� W350x159 (d = 35.6 ��., tw = 14 ��., bf = 35.2 ��., tf = 22 ��.)

B

dN

bf

bedge

������$�/ก N = 52 cm, B = 52 cm

N/6 = 8.67 cm < e = 20 < N/2 = 26 cm

����5���#ก%� Np = 3 (52 – 35.6 + 2.2) / 2

= 27.9 cm

T = 84 x 27.9 x 52 / 2 – 50x103 = 10934 kg

Trod = T/2 = 5467 kg

2 ���3����1��.���1�: P2

BNFT pp −=

2 ���3���������������ก:

�,5,5�( m = (N – 0.95d)/2

= (52 – 0.95x35.6)/2

m = 9.1 cm

Tfp = 84 ksc

P

M

27.9

m = 9.1 cm

fpmfpm = 84 (27.9 – 9.1) / 27.9

= 56.6 ksc

84

m = 9.1 cm

56.6

�����&-�������������ก:

�����������ก PL 3.2 x 52 x 52 "�.

= 3100 kg-cm

31.984

61.96.56

M22

pl×

=

cm 2.32500

31008t =

×=

Page 14: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

BiBi--Axial Bending Base PlateAxial Bending Base Plate

B

dN

bf

Small moment: e < N/6 ?

My

Mx

fp,minfp,max

0NB

M6

BN

M6

BNP

f2

x2y

min,p ≥−−=

p2x

2y

max,p FNB

M6

BN

M6

BNP

f ≤++=

B

dN

bf

fp,max

fpm

Ix = NB3/12, Iy = BN3/12

x

fx

y

ypm

)2/b80.0(M)2/d95.0(M

BNP

fΙΙ

++=x

fpm fp,max

x

3

xf

6

xfM

2max,p

2pm

pl +=

yFM8

t =

Page 15: L16 Base Plate · Axial Load Small Moment Large Moment Timber and Steel Design Column Base Plate. . S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL

BiBi--Axial Bending Base PlateAxial Bending Base Plate

Large moment :

B

dN

bf

My

MxB

dN

bf

M