Bolted Connection of an Angle Brace in Tension to a Gusset Plate

Example: Bolted connection of an angle brace in tension to a gusset plate (GB)

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SX034a-EN-GB

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Example: Bolted connection of an angle brace in tension to a gusset plate

Eurocode Ref Made by

Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

Localized resource for UK

Example: Bolted connection of an angle brace in tension to a gusset plate This worked example shows the procedure to check the bolted connection of an angle brace in tension to a gusset plate welded to a column web. Non preloaded bolts are used (Category A: bearing type). These types of connections are typical for cross bracings used both in facades and in roofs to withstand the actions of the horizontal wind load in the longitudinal axis of the single storey building. This is illustrated in SS048.

t n e m e e r g A e c n e c i L l e e t S s s e c c A e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . 0 d 1 e 0 v 2 r , e 0 s 1 e r r t s e h b g i m r e l v l o a N , t y h g a i d r s y e p n o d c s e i l W a i n r o t e d a e t m a i s e r h C T

In order to avoid eccentricities of the loads brought to the f oundation, the angle axis is aligned to meet the column vertical axis plane at the base plate and the gusset plate is placed as close as possible to the column major axis plane. Table 1.1

Modes of failure of the bracing connection

Mode of failure

Component Resistance

Bolts in shear

N Rd,1

Bolts in bearing (on the angle leg)

N Rd,2

Angle in tension

N Rd,3

Weld design

a

SS048


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SX034a-EN-GB

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Title


Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

Bracing Connection – Details

The Figure 1.1 shows the long leg of the 125x75 angle that is attached to the gusset plate.

UKA 125x75x12

125

UKC 305x305x118


Figure 1.1

Detail of the bolted connection: plan and section view

Common practice is to minimize the eccentricity between the bracing member and the column axis. The gusset plate is welded to the column web and to the base plate using double fillet welds (see Figure 1.1). Although there is some eccentricity in order to avoid the anchor bolt on the column axis, this is much better than having the bracing plane on the column flange axis. Main joint data

Configuration

Angle to gusset plate welded to a column web

Column

UKC 305 × 305 × 118, S275

Bracing

UKA 125 × 75 × 12, S275

Type of connection

Bracing connection using angle to a gusset plate and non-preloaded bolts Category A: Bearing type

Gusset plate

250 × 300 × 15, S275

Bolts

M20, grade 8.8

Welds

Gusset plate to column web: fillet weld, a = 4 mm (see section 4). Gusset plate to base plate: fillet weld, a = 4 mm (see section 4).


CALCULATION SHEET

Document Ref:

SX034a-EN-GB

Sheet

3

of

8


Title


Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

Column UKC 305 × 305 × 118, S275


BS4

Depth

hc

= 314.5 mm

Width

bc

= 307.4 mm

Thickness of the web

t w,c = 12 mm

Thickness of the flange

t f,c

= 18.7 mm

Fillet radius

r

= 15.2 mm

Area

Ac

= 150 cm

Second moment of area

I y

= 27672 cm

Depth between fillets

d c

= 246.7 mm

Yield strength

f y,c

= 275 N/mm

2

Ultimate tensile strength

f u,c

= 430 N/mm

2

Corus Advance

2 4

BS4

Angle UKA 125 × 75 × 12, S275

Depth

hac

= 125 mm

Corus Advance

Width

bac

= 75 mm

Thickness of the angle

t ac

= 12 mm

Root radius

r 1

= 11 mm

Toe radius

r 2

= 5.5 mm

Area

Aac

= 22.7 cm

Second moment of area

I y

= 354 cm

Yield strength

f y,ac

= 275 N/mm


f u,ac

= 430 N/mm2

2

4 2


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SX034a-EN-GB

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Eurocode Ref

Gusset plate 250

300

Made by

Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

15, S275

Depth

hp

= 300 mm

Width

bp

= 250 mm

Thickness

t p

= 15 mm

Yield strength

f y,p

= 275 N/mm

2


f u,p

= 430 N/mm

2

Number of bolt rows

n1

=3

Angle edge to first bolt row

el

= 50 mm

Pitch between bolt rows

pl

= 80 mm

Number of lines of bolts

n2

=1

Angle attached leg edge to bolt line

e2

= 80 mm

Total number of bolts ( n = n1 × n2 )

n

=3

Tensile stress area

As

= 245 mm

Diameter of the shank

d

= 20 mm

Diameter of the holes

d o

= 22 mm

Diameter of the washer

d w

= 37 mm

Yield strength

f yb

= 640 N/mm

2


f ub

= 800 N/mm

2

Direction of load transfer (1)


Direction perpendicular to load transfer (2)

Bolts M20, 8.8

2

Partial safety factors

γM0

= 1.0

γM2

= 1.25 (for shear resistance of bolts)

Design axial tensile force applied by the angle brace to the gusset plate. N Ed

= 250 kN


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SX034a-EN-GB

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Title

Eurocode Ref

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Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

Bolts in shear

EN1993-1-8 Table 3.4.

N Rd,1 = nF v, Rd

= αv

Fv,Rd

f ub A

γ M,2

= 0.6 ×

800 × 245 1.25

× 10 −3 = 94.1 kN

= 3 × 94.1 = 282 kN

N Rd,1

2 Bolts in bearing (on the angle leg) Note: The angle leg thickness, 12mm, being less than that of the gusset plate, 15mm, and assuming an end distance of 50 mm or greater for the gusset plate, only the attached angle leg requires a design check for bearing. t n e m e e r g A e c n e c i L l e e t S s s e c c A e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . 0 d 1 e 0 v 2 r , e 0 s 1 e r r t s e h b g i m r e l v l o a N , t y h g a i d r s y e p n o d c s e i l W a i n r o t e d a e t m a i s e r h C T

N Rd,2

= nF b, Rd

F b, Rd

=

k 1α b f u, ac d t ac

γ M2

All bolts k 1

⎛ e = min⎜⎜ 2.8 × 2 − 1.7; d0 ⎝

2.8 ×

∴

k 1

e2 d0

− 1.7 = 2.8 ×

80 22

⎞

2.5 ⎟⎟

⎠

− 1.7 = 8.48

= min (8.48 ; 2.5) = 2.5

End bolt:

⎛ e α b = min⎜⎜ 1 ; ⎝ 3d 0 e1 3d 0 f ub f u,ac

= =

50 3 × 22 800 430

f ub f u,ac

⎞ ⎟ ⎠

; 1.0 ⎟

= 0.76

= 1.86

∴ α b = min(0.76; 1.86; 1.0 ) = 0.76 Fb, Rd, end bolt

=

2.5 × 0.76 × 430 × 20 × 12 1.25

× 10− 3 = 156.9 kN

EN1993-1-8 Table 3.4.


CALCULATION SHEET

SX034a-EN-GB

Document Ref:

Sheet

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Title


Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

Interior bolts:

⎛ p 1 α b = min ⎜⎜ 1 − ; ⎝ 3d 0 4 p1 3d 0 f ub f u,ac

1

80

4

3 × 22

− = =

800 430

f ub f u,ac

⎞ ⎟ ⎠

; 1.0 ⎟

1

− = 0.96 4

= 1.86

∴ α b = min(0.96; 1.86; 1.0) = 0.96 ∴ t n e m e e r g A e c n e c i L l e e t S s s e c c A e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . 0 d 1 e 0 v 2 r , e 0 s 1 e r r t s e h b g i m r e l v l o a N , t y h g a i d r s y e p n o d c s e i l W a i n r o t e d a e t m a i s e r h C T

Fb,Rd,interior bolt

=

2.5 × 0.96 × 430 × 20 × 12 1.25

×10 −3 = 198.1 kN

The bearing strength of the end bolt and of the interior bolt is greater than the bolt shear strength. The least value for the bearing strength of a bolt in the connection is adopted for all bolts.

EN1993-1-8 §3.7(1)

∴ N Rd,2 = 3 ×156.9 = 471 kN

3 Angle in tension N Rd,3

=

2.5d 0

= 2.5 × 22 = 55 mm

5d 0

EN1993-1-8 §3.10.3

β 3 Anet f u γ M2

= 5 × 22 = 110 mm

2.5d 0

< p1 < 5d 0

β 3 can be determined by linear interpolation:

∴ β3 = 0.59 Anet

∴

= A − t ac d 0 = 2270 − 12 × 22 = 2006 mm2

N Rd,3

=

0.59 × 2006 × 430 1.25

×10 −3 = 407 kN


Document Ref:

CALCULATION SHEET

Title

SX034a-EN-GB

Sheet

7

of

8



Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

4 Weld design The weld is designed as follows: The gusset plate is welded to the column web and to the base plate using double fillet welds. The procedure to determine the throat thickness of the double fillet welds is the same for the gusset plate/column web connection and for the gusset plate/base plate connection. The following calculations show the design of the weld between the gusset plate and the base plate. It is possible to provide full strength double fillet welds following simplified recommendations, see SN017, however that approach is too conservative for this example. t n e m e e r g A e c n e c i L l e e t S s s e c c A e h t f o s n o i t i d n o c d n a s m r e t e h t o t t c e j b u s s i t n e m u c o d s i h t f o e s U . 0 d 1 e 0 v 2 r , e 0 s 1 e r r t s e h b g i m r e l v l o a N , t y h g a i d r s y e p n o d c s e i l W a i n r o t e d a e t m a i s e r h C T

SN017

The recommended procedure to follow is to propose a size of the weld throat and to check whether it complies with the requirement of resistance: Here, propose a = 4 mm Design resistance for the double weld, according to the simplified method is: N Rd, w,hor F w, Rd

f vw,d

=

= 2 F w,Rdl

= f vw,d a f u

3

βw γ M2

=

430

3

0.85 × 1.25

= 233.7 N/mm2

∴ Fw,Rd = 233.7 × 4 = 934.8 N/mm ∴

N Rd,w,hor

= 2 × 934.8 × 250 × 10 −3 = 467 kN

It supports the horizontal component of the force acting in the bracing, which is: N Ed, hor

= N Ed sin 40 = 250 × sin 40 = 161 kN

Therefore the horizontal weld is OK. Similar approach applies to the vertical weld (the gusset plate is welded to the column web).

EN1993-1-8 §4.5.3.3

o E

g

x

a

m

p

N i

CALCULATION SHEET

y

a o d c

Document Ref:

:

B

SX034a-EN-GB

o

l

t

8

Sheet

of

Laurent Narboux

Date

Dec 2006

Checked by

Abdul Malik

Date

Jan 2007

The following table summarizes the resistance values for the critical modes of failure. The governing value for the joint (i.e. the minimum value) is shown in bold type. Summary of the resistance values in the bolted bracing

Mode of failure

s

n i

d

e l

W a

i

n r

o e

t

d a

e m

t

a s

e i

r h

C T

8

Made by

5 Summary

Table 5.1 connection

d


s

e

e

Eurocode Ref

,

p

e

Title

r

y

l

Component resistance

Bolts in shear

N Rd,1

282 kN

Bolts in bearing on the angle leg

N Rd,2

471 kN

Angle in tension

N Rd,3

407 kN

Some modes of failure are not checked. For example, the gusset plate in bearing and in tension is not checked because its thickness is greater than that of the angle, and therefore the angle cleat would fail before the plate.

c


Example: Bolted connection of an angle brace in tension to a gusset plate SX034a-EN-GB

Quality Record RESOURCE TITLE


Reference

SX034a-EN-GB

LOCALISED RESOURCE DOCUMENT


Name

Company

Date

Created by

Laurent Narboux

SCI

Dec 2006

Technical content checked by

Abdul Malik

SCI

Jan 2007

Editorial content checked by

D C Iles

SCI

19/2/07

Bolted Connection of an Angle Brace in Tension to a Gusset Plate

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