Metal Structures Lecture XII Joints - bolted and welded ...footbridge.pl/stud/z/se1/lec112.pdf ·...

Metal Structures

Lecture XII

Joints - bolted and welded(part I)

Contents

Joint beam-column → #t / 3

Examples of calculation → #t / 37

Column bases → #t / 78

Support on masonry wall → #t / 95

Examination issues → #t / 97

Bolted joint Welded joint

Column web in tension Column web in tension

Beam web in tension

Column flange in bending Column flange in bending

End-plate in bending

Column web in shear

Column web in transverse compression

Beam flange and web in compression

To be continued...

Joint beam-column

→ #11 / 90

Photo: Author

Bolted joint Welded joint

Column web in tension #t / 17 - 19 Column web in tension #t / 18 – 19

Beam web in tension

Column flange in bending #t / 20 - 27 Column flange in bending #t / 28

End-plate in bending

Column web in shear #t / 14 - 16

Column web in transverse compression #t / 6 - 13

Beam flange and web in compression #t / 5

There should be calculated resistances for each connection in joint („connection” = „row of

bolts” or „welds around tensed flange”). Equivalent resistance of connection is the smallest

value of resistance of sub-parts.

This means, for tensed connection „resistance of row of bolts” can be completely different

than resistance of shank of bolts (because, for example, resistance of web is smaller).

Fc, fb, Rd = Mc, Rd / (h - tfp)

Mc, Rd – resistance of beam

Beam flange and beam web in compression

The same rules for welded and bolted joints

EN 1993-1-8 (6.21)

Photo: Author

Fc, wc, Rd min (1 w kwc beff, c, wc twc fy, wc / gM0 ;

r w kwc beff, c, wc twc fy, wc / gM0 ) =

= min (1 ; r) w kwc beff, c, wc twc fy, wc / gM0

= resistance of stiffener

(→ lecture #14)

Column web in transverse compression

The same rules for welded and bolted joints

EN 1993-1-8 6.2.6.2

beff, c, wc – effecive with of column web in compression → #t / 7

r – reduction factor for plate buckling → #t / 9

kwc – reduction factor for longitudinal compression in column web→ #t / 10

w – reduction factor for interaction → #t / 11

gM0 = 1,0Photo: Author

beff, c, wc tfb + 2√2 ab + 5(tfc + s) tfb + 2√2 ap + 5(tfc + s) + sp 2ta + 0,6 ra + 5(tfc + s)

Geometrical parameters according to #t / 8 and #t / 9

EN 1993-1-8 6.2.6.2

Photo: Author

Photo: EN 1993-1-8 fig. 6.6

Column: sp s dwc

Welded I-beam min (tp + c ; 2tp) √2 ac hc - 2(tfc + √2 ac)

Hot rolled I-beam rc hc - 2(tfc + rc)

lp = 0,932 √ [ (beff, t, wc dwc fy, wc) / (E twc2) ]

_

lp r

≤ 0,72 1,0

> 0,72 (lp - 0,2) / (lp)2

_

_ _

EN 1993-1-8 6.2.6.2

scom, Ed / fy, wc kwc

≤ 0,7 1,0

> 0,7 1, 7 - scom, Ed / fy, wc

Max compression for plane part of web (ddwc):

[ s (Ned + MEd) ]dwc= scom, Ed

EN 1993-1-8 6.2.6.2

Photo: Author

b w

0,0 ≤ b ≤ 0,5 w = 1,0

0,5 ≤ b < 1,0 w = w1 + 2(1 - b) (1 - w1)

b = 1,0 w = w1

1,0 < b < 2,0 w = w1 + 2(1 - b) (w2 - w1)

b = 2,0 w = w2

w1 = 1 / √[1 + 1,3(beff, c, wc twc / Avc)2]

w2 = 1 / √[1 + 5,2(beff, c, wc twc / Avc)2]

Avc = Avc, column (≈ hw tw)

b - transformation parameter → #t / 12, 13

EN 1993-1-8 tab. 6.3

EN 1993-1-8 tab. 5.4

Type of joint configuration Action Value of b

Mb1, Ed b ≈ 1

Mb1, Ed = Mb2, Ed b = 0 *)

Mb1, Ed = Mb2, Ed > 0,0 b ≈ 1

Mb1, Ed = Mb2, Ed < 0,0 b ≈ 2

Mb1, Ed + Mb2, Ed = 0,0

*) in this cane the value of b is the exact value rater than an approximation

EN 1993-1-8 (5.4a), (5.4b):

b1 = min [ |1 – (Mj, b2, Ed / Mj, b1, Ed)| ; 2]

b2 = min [ |1 – (Mj, b1, Ed / Mj, b2, Ed)| ; 2]

Photo: EN 1993-1-8 tab. 5.4

V*wp, Rd = Vwp, Rd / b

Vwp, Rd = [(0,9 fy, wc Avc) / (gM0 √ 3)] + Vwp,add, Rd

b → #t / 12, 13

Vwp,add, Rd 0 min [ 4Mpl, fc, Rd / ds ; (2Mpl, fc, Rd + 2Mpl, st, Rd) / ds ]

Column web in shear

The same for welded and bolted joints

EN 1993-1-8 6.2.6.1

Mpl, fc, Rd , Mpl, st, Rd – resistances for flanges and stiffeners→ #t / 15

Photo: Author

Mpl, fc, Rd = 0,25 bc tfc2 fy, fc / gM0

Mpl, st, Rd = 0,50 bs ts2 fy, s / gM0

gM0 = 1,0

EN 1993-1-8 6.2.6.1

Photo: Author

Slenderness web: dwc / twc > 69e → supplementary web plates are needed (EN 1993-1-8 6.2.6.1)

Requirements for additional plates:

bs / ts ≤ 40e;

bs ≥ dwc

ts ≥ twc

fy, s = fy, wc

Influence on resistance: always there are

taken into consideration only one plate

(even if there are two supplementary plates)

Avc, new = Avc + bs twc

Photo: EN 1993-1-8 fig. 6.5

Column: Ft, wc, Rd = w beff, t, wc twc fy, wc / gM0

Beam: Ft, wb, Rd = w beff, t, wb twb fy, wb / gM0

beff, t, wc = leff, c → #11 / 84 - 86

beff, t, wb = leff, b → #11 / 84 - 86

w → #t / 11

gM0 = 1,0

Column web and beam web in tension

There are different rules for bolted and welded joints

EN 1993-1-8 6.2.6.3

Bolted joint:

beff, t, wc = tfb + 2√2 ab + 5(tfc + s)

w → #t / 11

s → #t / 9

gM0 = 1,0

Ft, wc, Rd w beff, t, wc twc fy, wc / gM0 ts ≥ tfb and Rweb ≥ Rs → ∞

Generally, this is min (resistance of welds between

stiffeners and column ; resistance of stiffeners for

tensile axial force)

Welded joint:

EN 1993-1-8 6.2.6.3

Photo: Author

Supplementary

web plate:

Full penetration butt welds

between web and

supplementary plate,

a ≥ ts

Filled welds between web and

supplementary plate,

a ≥ ts / √2

S235, S275, S355 S420, S460

tw, eff = One side 1,5 twc 1,4 twc 1,3 twc

Both sides 2,0 twc

The same rules for bolted and welded joints

Column web tension, supplementary web plates,

influence on resistance

EN 1993-1-8 6.2.6.3

Photo: EN 1993-1-8 fig. 6.5

Column flange and end plate in bending

There are different rules for bolted and welded joints

Bolted joint:

We must analyse three different mechanism of destruction,

according to prying actions phenomenon

S MA = 0

S MA = P x – (F / 2) (y + x) → P = (F / 2) (y + x) / x

(y + x) / x > 2 → P > F (!!!)

But, if plate and flange begin to deform...

Photo: Author

→ #11 / 78

Mode 1 – plate / flange destruction, no

bolt destruction

Mode 2 – plate / flange destruction and

bolts destruction

Mode 3 – bolts destruction, no plate

destruction

Generally, we must analyse three different mode of

destruction; 1st and 2nd with or without prying force and 3rd

without prying force.

Photo: Author

Lb ≤ Lb* → Prying forces

Lb > Lb* → No prying forces

Lb* = 8,8 m3 As / (Sleff tf

3)

tf – the thickness of the thinnest plate

m, Sleff → #11 / 83 ~ #11 / 86

When it can occur?

EN 1993-1-8 tab. 6.2

Photo: Author

→ #11 / 79

min (t1 ; t2) ≥ max (T1 ; T2)

T1 = 2,0 √ {c Ft,Rd / [fy (2c + d)]}

T2 = 1,67 d 3√ {fub / 1 000 [MPa]}

Tension connection – thickness of end plate (t1) and additional

plate for column flange (t1 = tflange + tplate)

Photo: Author → #11 / 31

There are two possibilities of flange reinforcement by additional plates:

Photo: Author

Prying forces No prying

forces:

FT, 1-2, Rd

Mode 1: FT, 1, Rd

= min (1.1 ; 1.2)

Method 1.1 Method 1.2

2 Mpl, 1, Rd / m4 Mpl, 1, Rd / m

(8n - 2ew) 4 Mpl, 1, Rd

/

[2mn - ew(m + n)]

(4 Mpl, 1, Rd + 2Mbp, Rd) / m

[(8n - 2ew) 4 Mpl, 1, Rd + 4n Mbp, Rd ]

/

[2mn - ew(m + n)]

Mode 2: FT, 2, Rd (2 Mpl, 2, Rd + n SFt, Rd) / (m + n)

Mode 3: FT, 3, Rd SFt, Rd

EN 1993-1-8 tab 6.2

Resistances

Photo: Author

n = min (emin ; 1,25m)

ew = dw / 4

dw = D or D1

SFt, Rd = S min (Ft, Rd ; Bp,Rd )

leff, 1 = min (leff, cp ; leff, nc)

Sleff, 1 = min (Sleff, cp ; Sleff, nc)

leff, 2 = leff, nc

Sleff, 2 = Sleff, nc

Bolt-row considered individually As part of a group of bolt-rows

Mpl, 1, Rd 0,25 leff, 1 tf2 fy / gM0 0,25 Sleff, 1 tf

2 fy / gM0

Mpl, 2, Rd 0,25 leff, 2 tf2 fy / gM0 0,25 Sleff, 2 tf

2 fy / gM0

Mbp, Rd 0,25 leff, 1 tbp2 fy, bp / gM0 0,25 Sleff, 1 tbp

2 fy, bp / gM0

EN 1993-1-8 tab 6.2 Photo: Author

Welded joint

beff, t, fc = twc + 2s + 7 k tf

k = min [ (tf / tp)(fy, f / fy, p) ; 1,0 ]

Ft, wc, Rd beff, b, fc tfc fy, fc / gM0 ts ≥ tfb and Rweb ≥ Rs → ∞

Generally, this is min (resistance of welds between

stiffeners and column ; resistance of stiffeners for

tensile axial force)

EN 1993-1-8 4.10 Photo: Author

Resistance of joint:

Generally:

Resistance of joint = S (equivalent resistance of connection ∙ arm action)

equivalent resistance of connection = the lowest value for resistance from each parts of

joint

Parts, which we must analyse:

Photo: Author

One connection (bolt), one

equivalent resistance

One connection

(welds), one

equivalent resistance

Three connections (bolts),

three equivalent

resistances

Three connections (bolts), three

equivalent resistances

Arm of action

Photo: Author

No bolts in joint – rotation of beam around

bottom part of compressed zone. Theoretical

axis of rotation: centre of gravity of

compressed beam’s flange.

Arm of action:

Photo: Author

1. We should take into consideration no more than three rows of bolt in tensed part

of joint (the furthest from compressed flange of beam).

2. Although it, we should applied rows through whole high of beam for category E.

3. There should be no more than one row of bolts over top flange of beam.

4. One row of bolt = 2 bolts.

Photo: Author

There are four main types of bolted joint for beam-column joint:

Photo: steelconstruction.info

Photo: uwyo.edu

Photo: lusas.comPhoto: gic-edu.com

Full depth end plate ↔ extended end plate → different formulas for leff (→ #11 / 84 - 86);

Stiffened depth end plate → application of additional vertical stiffener is recommended

(greated resistance and stiffness of joint);

Haunched beam → greated resistance and stiffness of joint (→ #t / 76);

Photo: Author

leff

leff

leff

There is possible, that effective areas from two

row of bolts would be common. In this situation

we must analysed group of bolts, not separate

bolts. But, on the other hand, if there is any

horizontal plate (flange, stiffeners) between

rows of bolts, these rows are completely

separated. In this case we not taken into

consideration group, only separated bolts.

First (the higher) row of bolt is always analysed

as separated row only.

EN 1993-1-8 p.6.2.7.2 (9)

If for any row of bolts its equivalent resistance is greater than 1,9 resistance of bolt for

axial force, equivalent resistances lower rows of bolt must be reduced by linear way.

Photo: Author

F3, red = F1 z3 / z1

F3, red = F2 z3 / z2

Examples of calculation Photo: Author

Only bending moment and shear force

1. Beam-column, extended end plate + vertical stiffener, no

horizontal stiffeners on column (#t / 38 – 50);

2. Beam-column, welded joint (#t / 51 – 52);

3. Beam-beam, extended end plate + vertical stiffener (#t / 53 – 62);

4. Beam-column, flange cleats, no horizontal stiffeners on column

(#t / 63 – 66);

5. Column-column, no stiffeners (#t / 67 - 68);

Example 1

Example 2

Example 3

Example 4

Example 5

1st row of bolts:

Beam flange and beam web in compression (BFC) → #t / 5

Column web in transverse compression (CWC) → #t / 6

Column web in shear (CWS) → #t / 14

Column web in tension, 1st row (CWT1) → #t / 17

The highest row - we analyse only bolt-row considered individually (i) (→ #11 / 85). We

must analyse circular (c) and non-circular (nc) patterns (→ #11 / 82):

CWT1-i-c, CWT1-i-nc

Beam web in tension 1st row (BWT1) → #t / 17

There is no web, but stiffener will be treated as web. The highest row - we analyse only bolt-

row considered individually (i) (→ #11 / 85). We must analyse circular (c) and non-circular (nc)

patterns (→ #11 / 82):

BWT1-i-c, BWT1-i-nc

Example 1

Photo: Author

1st row of bolts continuation:

Column flange in bending 1st row (CFB1) → #t / 20:

The highers row - we analyse only bolt-row considered individually (i) (→ #11 / 85). We

must analyse circular (c) and non-circular (nc) patterns (→ #11 / 82). We must analyse three

different mechanism of flange destruction (1, 2, 3) (→ #t / 26):

CFB1-i-c-1, CFB1-i-c-2, CFB1-i-c-3,

CFB1-i-nc-1, CFB1-i-nc-2, CFB1-i-nc-3

End-plate in bending 1st row (EB1) → #t / 20:

The highest row - we analyse only bolt-row considered individually (i) (→ #11 / 84). We


different mechanism of plate destruction (1, 2, 3) (→ #t / 26):

EB1-i-c-1, EB1-i-c-2, EB1-i-c-3,

EB1-i-nc-1, EB1-i-nc-2, EB1-i-nc-3


Resistance for first bolt-row – the smallest value among 19:

1BR = min ( BFC ; CWC ; CWS ; CWT1-i-c ; CWT1-i-nc ; BWT1-i-c ; BWT1-i-nc ;

CFB1-i-c-1 ; CFB1-i-c-2 ; CFB1-i-c-3 ; CFB1-i-nc-1 ; CFB1-i-nc-2 ; CFB1-i-nc-3 ;

EB1-i-c-1 ; EB1-i-c-2 ; EB1-i-c-3 ; EB1-i-nc-1 ; EB1-i-nc-2 ; EB1-i-nc-3 )

2nd row of bolts:

Beam flange and beam web in compression (BFC) → the same as for 1st row

Column web in transverse compression (CWC) → the same as for 1st row

Column web in shear (CWS) → the same as for 1st row

Column web in tension, 2nd row (CWT2) → #t / 17

No horizontal stiffeners on column web - we analyse bolt-row considered individually (i)

and as part of a group of 1st and 2nd bolt-rows (12g) (→ #11 / 85). We must analyse circular (c)

and non-circular (nc) patterns (→ #11 / 82):

CWT2-i-c, CWT2-i-nc

CWT2-12g-c, CWT2-12g-nc

Beam web in tension 2nd row (BWT2) → #t / 17

There is beam flange between 1st and 2nd row, these rows are separated each other. We

analyse only bolt-row considered individually (i) (→ #11 / 84). We must analyse circular (c) and

non-circular (nc) patterns (→ #11 / 82):

BWT2-i-c, BWT2-i-nc

2nd row of bolts continuation:

Column flange in bending 2nd row (CFB2) → #t / 20:


and as part of a group of 1st and 2nd bolt-rows (12g) (→ #11 / 85). We must analyse circular (c)

and non-circular (nc) patterns (→ #11 / 82). We must analyse three different mechanism of flange

destruction (1, 2, 3) (→ #t / 26):



CFB2-12g-c-1, CFB2-12g -c-2, CFB2-12g -c-3,

CFB2-12g -nc-1, CFB2-12g -nc-2, CFB2-12g -nc-3


End-plate in bending 2nd row (EB2) → #t / 20:



non-circular (nc) patterns (→ #11 / 82). We must analyse three different mechanism of plate

destruction (1, 2, 3) (→ #t / 26):

EB2-i-c-1, EB2-i-c-2, EB2-i-c-3,



Resistance for second bolt-row – the smallest value among 27:

2BR = min [ BFC ; CWC ; CWS ; CWT2-i-c ; CWT2-i-nc ;

( CWT2-12g-c – 1RB ) ; ( CWT2-12g-nc – 1RB ) ; BWT2-i-c ; BWT2-i-nc ;


( CFB2-12g-c-1- 1RB) ; ( CFB2-12g -c-2 – 1RB) ; ( CFB2-12g -c-3 – 1RB) ;

( CFB2-12g -nc-1 – 1RB) ; ( CFB2-12g -nc-2 – 1RB) ; ( CFB2-12g -nc-3 – 1 RB) ;

EB2-i-c-1 ; EB2-i-c-2 ; EB2-i-c-3 ; EB2-i-nc-1 ; EB2-i-nc-2 ; EB2-i-nc-3 ]

3rd row of bolts:


Column web in transverse compression (CWC) → the same as for 1st row

Column web in shear (CWS) → the same as for 1st row

Column web in tension, 3rd row (CWT3) → #t / 17


and as part of a group of 2nd and 3rd bolt-rows (23g) and as part of a group of 1st, 2nd and 3rd bolt-

rows (123g) (→ #11 / 85). We must analyse circular (c) and non-circular (nc) patterns (→ #11 /

82):

CWT3-i-c, CWT3-i-nc



3rd row of bolts continuation:

Beam web in tension 3rd row (BWT3) → #t / 17

There is beam flange between 1st and 2nd row, these rows are separated each other. There is

no separating element for 2nd and 3rd row. We analyse only bolt-row considered individually (i)

and as part of a group of 2nd and 3rd bolt-rows (23g) (→ #11 / 84). We must analyse circular (c)


BWT3-i-c, BWT3-i-nc

BWT3-23g-c, BWT3-23g-nc


Column flange in bending 3rd row (CFB3) → #t / 20:


and as part of a group of 2nd and 3rd bolt-rows (23g) and as part of a group of 1st, 2nd and 3rd bolt-

rows (123g) (→ #11 / 85). We must analyse circular (c) and non-circular (nc) patterns (→ #11 /

82). We must analyse three different mechanism of flange destruction (1, 2, 3) (→ #t / 26):



CFB3-23g-c-1, CFB3-23g-c-2, CFB3-23g-c-3,

CFB3-23g-nc-1, CFB3-23g-nc-2, CFB3-23g-nc-3

CFB3-123g-c-1, CFB3-123g-c-2, CFB3-123g-c-3,

CFB3-123g-nc-1, CFB3-123g-nc-2, CFB3-123g-nc-3


End-plate in bending 3rd row (EB3) → #t / 20:




and non-circular (nc) patterns (→ #11 / 82). We must analyse three different mechanism of plate

destruction (1, 2, 3) (→ #t / 26):

EB3-i-c-1, EB3-i-c-2, EB3-i-c-3,


EB3-23g-c-1, EB3-23g-c-2, EB3-23g-c-3,

EB3-23g-nc-1, EB3-23g-nc-2, EB3-23g-nc-3


Resistance for third bolt-row – the smallest value among 43:

3BR = min [ BFC ; CWC ; CWS ; CWT3-i-c ; CWT3-i-nc ; ( CWT3-23g-c – 2RB ) ;

( CWT3-23g-nc – 2RB ) ; ( CWT3-123g-c – 1RB – 2RB ) ; ( CWT3-123g-nc – 1RB – 2RB ) ;

BWT3-i-c ; BWT3-i-nc ; ( BWT3-23g-c – 2RB ) ; ( BWT3-23g-nc – 2RB) ;


( CFB3-23g-c-1 – 2RB ) ; ( CFB3-23g-c-2 – 2RB ) ; ( CFB3-23g-c-3 – 2RB ) ;

( CFB3-23g-nc-1 – 2BR ) ; ( CFB3-23g-nc-2 – 2RB ) ; ( CFB3-23g-nc-3 – 2RB ) ;

( CFB3-123g-c-1 – 1RB – 2RB ) ; ( CFB3-123g-c-2 – 1RB – 2RB ) ;

( CFB3-123g-c-3 – 1RB – 2RB ) ; ( CFB3-123g-nc-1 – 1RB – 2RB ) ;

( CFB3-123g-nc-2 – 1RB – 2RB ) ; ( CFB3-123g-nc-3 – 1RB – 2RB ) ;

EB3-i-c-1 ; EB3-i-c-2 ; EB3-i-c-3 ; EB3-i-nc-1 ; EB3-i-nc-2 ; EB3-i-nc-3 ;

( EB3-23g-c-1 – 2RB ) ; ( EB3-23g-c-2 – 2RB ) ; ( EB3-23g-c-3 – 2RB ) ;

( EB3-23g-nc-1 – 2RB ) ; ( EB3-23g-nc-2 – 2RB ) ; ( EB3-23g-nc-3 – 3RB )]

Mj, Rd = 1RB ∙ z1 + 2RB ∙ z2 + 3RB ∙ z3

Mj, Ed / Mj, Rd ≤ 1,0

Shear force – acts on bolts in compressed part of joint

In addition, welds between beam and end plate must be calculated according to #9 / example 3


Welded joint - there are no bolts




Column web in tension (CWT) → #t / 17

Column flange in bending (CFB) → #t / 20

Example 2

Photo: Author

R = min (BFC ; CWC ; CWS ; CWT ; CFB )

Mj, Rd = R ∙ z

Mj, Ed / Mj, Rd ≤ 1,0

In addition, welds must be calculated according to #9 / example 3


Beam-beam joint - there is no column

1st row of bolts:


Beam web in tension 1st row (BWT1) → #t / 17

There is no web, but these stiffeners will be treated as web. The „highest” row - we analyse

only bolt-row considered individually (i) (→ #11 / 84). We must analyse circular (c) and non-

circular (nc) patterns (→ #11 / 82):

BWT1-i-c, BWT1-i-nc

Example 3

Photo: Author


End-plate in bending 1st row (EB1) → #t / 20:

The „highest” row - we analyse only bolt-row considered individually (i) (→ #11 / 84). We


different mechanism of plate destruction (1, 2, 3) (→ #t / 26):

EB1-i-c-1, EB1-i-c-2, EB1-i-c-3,



Resistance for first bolt-row:

1BR = min ( BFC ; BWT1-i-c ; BWT1-i-nc ;

EB1-i-c-1 ; EB1-i-c-2 ; EB1-i-c-3 ; EB1-i-nc-1 ; EB1-i-nc-2 ; EB1-i-nc-3 )

2nd row of bolts:


Beam web in tension 2nd row (BWT2) → #t / 17



non-circular (nc) patterns (→ #11 / 82):

BWT2-i-c, BWT2-i-nc


End-plate in bending 2nd row (EB2) → #t / 20:



non-circular (nc) patterns (→ #11 / 82). We must analyse three different mechanism of plate

destruction (1, 2, 3) (→ #t / 26):

EB2-i-c-1, EB2-i-c-2, EB2-i-c-3,



Resistance for second bolt-row:

2BR = min [ BFC ; BWT2-i-c ; BWT2-i-nc ;

EB2-i-c-1 ; EB2-i-c-2 ; EB2-i-c-3 ; EB2-i-nc-1 ; EB2-i-nc-2 ; EB2-i-nc-3 ]

3rd row of bolts:


Beam web in tension 3rd row (BWT3) → #t / 17





BWT3-i-c, BWT3-i-nc

BWT3-23g-c, BWT3-23g-nc


End-plate in bending 3rd row (EB3) → #t / 20:




and non-circular (nc) patterns (→ #11 / 82). We must analyse three different mechanism of plate

destruction (1, 2, 3) (→ #t / 26):

EB3-i-c-1, EB3-i-c-2, EB3-i-c-3,


EB3-23g-c-1, EB3-23g-c-2, EB3-23g-c-3,

EB3-23g-nc-1, EB3-23g-nc-2, EB3-23g-nc-3


Resistance for third bolt-row:

3BR = min [ BFC ; BWT3-i-c ; BWT3-i-nc ; ( BWT3-23g-c – 2RB ) ; ( BWT3-23g-nc – 2RB) ;

EB3-i-c-1 ; EB3-i-c-2 ; EB3-i-c-3 ; EB3-i-nc-1 ; EB3-i-nc-2 ; EB3-i-nc-3 ;

( EB3-23g-c-1 – 2RB ) ; ( EB3-23g-c-2 – 2RB ) ; ( EB3-23g-c-3 – 2RB ) ;

( EB3-23g-nc-1 – 2RB ) ; ( EB3-23g-nc-2 – 2RB ) ; ( EB3-23g-nc-3 – 3RB )]

Mj, Rd = 1RB ∙ z1 + 2RB ∙ z2 + 3RB ∙ z3

Mj, Ed / Mj, Rd ≤ 1,0


In addition, welds must be calculated according to #9 / example 3


Flange cleat - there is olny one row of bolts:




Column flange in bending (CFB) → #t / 20:

Only one row - we analyse only bolt-row considered individually (i) (→ #11 / 85). We must

analyse circular (c) and non-circular (nc) patterns (→ #11 / 82). We must analyse three different

mechanism of flange destruction (1, 2, 3) (→ #t / 26):

CFB-i-c-1, CFB-i-c-2, CFB-i-c-3,

CFB-i-nc-1, CFB-i-nc-2, CFB-i-nc-3

Example 4

Photo: Author

Flange cleat in bending (FC):

Only one row - we analyse only bolt-row considered individually (i) (→ #11 / 87). We must

analyse circular (c) and non-circular (nc) patterns (→ #11 / 82). We must analyse three different

mechanism of destruction (1, 2, 3) (→ #t / 26):

FC-i-c-1, FC-i-c-2, FC-i-c-3,

FC-i-nc-1, FC-i-nc-2, FC-i-nc-3

Column web in tension (CWT) → #t / 17

Only one row - we analyse bolt-row considered individually (i) (→ #11 / 85). We must

analyse circular (c) and non-circular (nc) patterns (→ #11 / 82):

CWT-i-c, CWT-i-nc

Resistance for bolt-row:

BR = min ( BFC ; CWC ; CWS ; CFB-i-c-1, CFB-i-c-2, CFB-i-c-3 ;

CFB-i-nc-1 ; CFB-i-nc-2 ; CFB-i-nc-3 ; FC-i-c-1, FC-i-c-2 ; FC-i-c-3 ;

FC-i-nc-1 ; FC-i-nc-2 ; FC-i-nc-3 ; CWT-i-c ; CWT-i-nc )

Mj, Rd = 1RB ∙ z

Mj, Ed / Mj, Rd ≤ 1,0



Photo: Author

Way of calculations depends on shape of stresses in joint.

Relatively small bending moment to compressive axial force →

compression only → bolts calculated only for shear force.

Relatively big bending moment to compressive axial force →

compression and tension → classical tension joint → bolts

calculated for tensile force and shear force.

Example 5

Photo: Author

Column-column – there is no beam

Photo: Author

Cross-sectional forces are applied to joint of column in the same manner as to beam in

classical tension joint.

Because of this, during calculation of column joint,

sould be calculated resistance of:

• compressive flange;

• tensile part of web;

• local bending for end plate;

Formulas are the same as for parts of beam in classical

tension joint.

For different values of forces in flanges, we analysed different calculation model.

More information will be presented on lecture #11 and 12.

Axial force (NEd, c or NEd, t) can be neglected when NEd ≤ 0,05 NRd of beam

EN 1993-1-8 p.6.2.3

Photo: Author

→ #10 / 80

There is few inconsequences in Eurocode.

According to EN 1993-1-8 6.2.7.1 (2), we can calculate joints, only when axial force in

beam NEd ≤ 0,05 NRd of beam. If this requirement is not satisfied, we can't calculate

resistances according to formulas, presented in this lecure - but there is no information

in Eurocode, which formulas we can use.

There is information in EN 1993-1-8 6.2.7.1 (2), that if NEd > 0,05 NRd then we

calculate resistance of joint according to formula:

Mj, Ed / Mj, Rd + Nj, Ed / Nj, Rd ≤ 1,0

But there is no clear, what means Nj, Rd and if Mj, Rd is calculated according the same

way as for cause NEd ≤ 0,05 NRd.

Assumptions for case NEd > 0,05 NRd:

First possibility of calculation:

Mj, Rd is calculated according the same formulas as for NEd ≤ 0,05 NRd;

Nj, Rd depends on direction of force:

for compressive force, Nj, Rd = min (column web in compression, beam flange in

compression, column web in shear);

for tensile force, Nj, Rd = [minfirst row of bolt (column web in tension, beam web in

tension, column flange in bending, end plate in bending) + minsecond row of bolt (...) + ... +

minlast row of bolt (...), column web in shear]

Second possibility of calculation:

Resistances of both parts (top and bottom) are calculated separately (as for only tensed and

only compressed part).

Shear force acts on bolts in compressed part only.

Photo: Author

There is no axial force in bolts, only

shear force acts on bolts.

Photo: Author


Resistances of both parts (top and bottom) are calculated separately (as for only compressed

part).

There are axial force shear force act on

bolts. For this case:

FEd, top / FRd, top ≤ 1,0 ; FEd, bottom / FRd, bottom ≤ 1,0

Fv, Ed, top / Fv, Rd, top + Ft, Ed, top / (1,4 Ft, Rd, top) ≤ 1,0

Fv, Ed, bottom / Fv, Rd, bottom + Ft, Ed, bottom / (1,4 Ft, Rd, bottom) ≤ 1,0

Photo: Author


Resistances of both parts (top and bottom) are calculated separately (as for only tensed part,

but both parts can have different resistance because of different number of bolts).

There is possible, that for different combinations of loads we have different situations for

cross-sectional forces for one joint.

Photo: Author

Haunched beam - way to increase arms of action → increase resistance Mj, Rd

Photo: Author

Requirement:

b ≤ 45o

EN 1993-1-8 p.6.2.6.7

There are transverse compression of beam web (F1) and compression of haunched flange (F2):

F = MEd / h

F1 = F tg b

F2 = F / cos b

Calculations of resistance are the same as for transverse compression of web and compression

of flange.

Column bases

General assumptions → #t / 79 - 82

Hinge support → #t / 83 - 88

Rigid support → #t / 89 - 94

Photo: Author

Photo: diy.stackexchange.com

Photo: osha.gov

General assumptions

1. Concrete (fcd) decides about

resistance of base: it is the weakest

element, which can be destroyed as

first. Resistance of base depends on

effective area of contact between

steel and concrete.

2. Effective area is the area of the cross-section of the column and

in its immediate vicinity. This is the result of imperfections of base

plate (not completely flat) and linearisation of stress under base

plate.

Photo: Author

Photo: Author

3. Range of immediate vicinity is proportional to the thickness of base plate.

tp

tf

c(tp)

tf + 2 c(tp)

Ac0 = Ac0 (I-beam, c)

c = tp √ [ fy / (3 fjd gM0 ) ]

fjd = bj FRdu / Ac0

bj = 2/3

Ac0 - area of efective contact between steel and concrete

1992-1-1 p.6.7:

FRdu = min [ Ac0 fcd √(Ac1 / Ac0) ; 3 Ac0 fcd ]

NEd / FRdu ≤ 1,0

Centres of gravity for Ac1 and Ac0 must be at one vertical line;

Ac1 and Ac0 have the same proportion;

Ac1 - maximum possible area

For more than one force Fi, Aic1 and Ai

c0 should not overlap

EN 1993-1-8 p.6.2.5

Photo: EN 1992-1-1 fig 6.29

Correctly Incorrectly - centres of gravity not at one vertical line

Photo: Author

Incorrectly - no similar shape

(d1 / b1) ≠ (d2 / b2)

Incorrectly - d2 / d1 > 3 ; b2 / b1 > 3

Incorrectly - no maximum possible area

(Correctly)

Incorrectly - overlap

(Correctly)

Photo: Author

Hinge support

There are two ways of calculations:

• if we know nothing about dimension of concrete

base (rough method);

• if we know everything about dimension of concrete

base (accurate method);Photo: Author

Photo: EN 1993-1-8 fig. 6.19

EN 1993-1-8 6.2.8.2.(1) –effective area under flanges and web of

column is taken into consideration.

It is inconsequence in Eurocode: bottom area for part 2 has different

proportion than top area, or there is overlapping 2-1 and 2-3.

Rough method:

EN 1992-1-1 → fcd

Assumption: √(Ac1 / Ac0) = 1,5

FRdu = 1,5 Ac0 fcd

fjd = bj FRdu / Ac0 = bj 1,5 Ac0 fcd / Ac0 = (2/3) 1,5 (Ac0 / Ac0 ) fcd = fcd

tp = c / √ [ fy / (3 fjd gM0 ) ]

Theoretically: Ac0 under flanges only;

Practically: Ac0 under total cross-section of

column.

c and NRd according to table:

"Konstrukcje stalowe, przykłady obliczeń według PN-EN 1993-1, część II, stropy i

pomosty", praca zbiorowa pod redakcją A. Kozłowskiego, Oficyna Wydawnicza

Politechniki Rzeszowskiej, Rzeszów 2009.

Accurate method:

EN 1992-1-1 → fcd

Ac0 = b1 d1

Ac1 = b2 d2 (according to dimensions of concrete base)

Ist iteration:

FRdu = √(Ac1 / Ac0) Ac0 fcd

fjd = bj FRdu / Ac0 = bj 1,5 Ac0 fcd / Ac0 = √(Ac1 / Ac0) bj fcd

cI = tp √ [ fy / (3 fjd gM0 ) ]

AIc0 = AI

c0 (I-beam, cI)

AIc1 = bI

2 dI2 (according to dimensions of concrete base and I-beam)

IInd iteration:

fjd = √(AIc1 / AI

c0) bj fcd

cII = tp √ [ fy / (3 fjd gM0 ) ]

AIIc0 = AII

c0 (I-beam, cII)

AIIc1 = bII

2 dII2 (according to dimensions of concrete base and I-beam)

IIIrd iteration:

fjd = √(AIIc1 / AII

c0) bj fcd

cIII = tp √ [ fy / (3 fjd gM0 ) ]

AIIIc0 = AIII

c0 (I-beam, cIII)

AIIIc1 = bIII

2 dIII2 (according to dimensions of concrete base and I-beam)

IVth iteration:

...

Rigid support

There are two ways of calculations:

• if we know nothing about dimension of

concrete base (rough method);

• if we know everything about dimension

of concrete base (accurate method);

Photo: Author

Photo: EN 1993-1-8 fig. 6.19

EN 1993-1-8 6.2.8.3.(1) – only effective area under flanges of

column is taken into consideration.

Resistance of concret is for both method of calculations the same as for hinge support.

For calculation of resistance rigid support, we need to know:

• resistance of concrete (#t / 79);

• resistance of column web in tension (as beam web in tension, #t / 17);

• resistance of base plate in bending (as end plate in bending, #t / 20);

• resistance of column flange in compression (as beam flange in compression, #t / 5);

Photo: EN 1993-1-8 fig. 6.18

Author

FT, l, Rd

FT, l, Rd

FC, l, Rd

FC, l, Rd

FC, r, Rd

FC, r, RdFT, r, Rd

FT, r, Rd

NEd < 0 MEd > 0 NEd > 0 MEd > 0

NEd < 0 MEd < 0 NEd < 0 MEd > 0

FT, l, Rd = min (column web in tension, left ; base plate in bending, left)

FT, r, Rd = min (column web in tension, right ; base plate in bending, right)

FC, l, Rd = min (concrete in compression, left ; column flange in compression, left)

FC, r, Rd = min (concrete in compression, right ; column flange in compression, right)

Resistance of column web in tension must be

taken into consideration only when bolts are

located between flanges.

Photo: Author

EN 1993-1-8 tab. 6.7, first part

Loading Lever arms Resistance Mj, Rd

Left-T, Right-C, exampe:

MEd > 0 ; NEd < 0 z = zT, l + zC, r

e = MEd / Ned

NEd > 0 e > zT, l NEd ≤ 0 e ≤ -zC, r

min [ z FT, l, Rd / (1 + zC, r / e) ; - z FC, r, Rd / (-1 + zT, l / e)]

Left-T, Right-T, exampe:

MEd > 0 ; NEd > 0 z = zT, l + zT, r

e = MEd / NEd

NEd > 0 0 < e < zT, l NEd > 0 -zT, r < e ≤ 0

min [ z FT, l, Rd / (1 + zT, r / e)

z FT, r, Rd / (-1 + zT, l / e)]

min [ z FT, l, Rd / (1 + zT, r / e)

z FT, l, Rd / (-1 + zT, l / e)]

EN 1993-1-8 tab. 6.7, second part

Loading Lever arms Resistance Mj, Rd

Left-C, Right-T, exampe:

MEd < 0 ; NEd < 0 z = zC, l + zT, r

e = MEd / Ned

NEd > 0 e ≤ -zT, r NEd ≤ 0 e > zC, l

min [ -z FC, l, Rd / (1 + zT, r / e) ; z FT, r, Rd / (-1 + zC, l / e)]

Left-C, Right-C, exampe:

MEd > 0 ; NEd < 0 z = zC, l + zC, r

e = MEd / NEd

NEd ≤ 0 0 < e < zC, l NEd ≤ 0 -zC, r < e ≤ 0

min [ -z FC, l, Rd / (1 + zC, r / e)

-z FC, r, Rd / (-1 + zC, l / e)]

min [ -z FC, l, Rd / (1 + zC, r / e)

-z FC, r, Rd / (-1 + zC, l / e)]

NEdc / NRdc ≤ 1,0

NRdc = b Ab fd

b = min { 1,25 + a1 / (2 hc) ; 1,5 ; max [(1 + 0,3 a1 / hc) ∙ (1,5 - 1,1 Ab / Aef) ; 0 ] }

Aef = lefm t

Support on masonry wall

EN 1996-1-1 p.6.1.3

Photo: EN 1996-1-1 fig 6.2

Masonry (fd) decides about

resistance of support: it is

the weakest element, which

can be destroyed as first.

If resistance of support is too small, we use

additional horizontal plate. It is wider than width of

flange, its thickness is equal or bigger than thickness

of flange. We must use vertical stiffeners too.

Photo: Author

Resistance of bolted connection A, B, C, D, E

Redistribution of loads (MEd., NEd., VEd.) in shear joint

Redistribution of loads (MEd., NEd., VEd.) in tension joint

Parts of tension joint important for resistance

Resistance of joint beam-column, algorithm of calculations

Resistance of column base, algorithm of calculations

Examination issues

Base - fundament

Flange cleat - nakładka z kątownika

End-plate - blacha czołowa

Base plate - blacha stopowa

Double-side joint - węzeł dwustronny

Metal Structures Lecture XII Joints - bolted and welded ...footbridge.pl/stud/z/se1/lec112.pdf ·...

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