metal structures lecture xiv joints - bolted and welded...
TRANSCRIPT
Metal Structures
Lecture XIV
Joints - bolted and welded(part II)
Contents
Interactions → #t / 3
Truss nodes → #t / 7
Splice joints of hollow sections → #t / 47
Stiffeners → #t / 57
L section; additional rules → #t / 83
I-beam, welded joints; additional rules → #t / 84
Pins; additional rules → #t / 86
Column head → #t / 88
Examination issues → #t / 95
Joints
Small parts of members, where are contact between two or
more members. There are many specific phenomenons on
there short part of beams, columns, etc. Calculation
according to level of cross-section and level of element.
Example from Ist design project: bearing resistance and
punching resistance (effects of contact between bolts and
plates and memebers), slip resistance and block tearing
(effect of contact between plates and members).
Photo: Author
Interactions
→ #3 / 69
Joints - more examples:
• vertical stiffeners;
• support on masonry structures;
• contact with concrete base;
• rigid connection beam-column;
• and many many others;Photo: Author
→ #3 / 70
• Trusses nodes are welded joints. There are contact between part of nodes. Way of
calculations is presented on lecture #14;
• Stiffeners can be used for different reasons (support of slender web, joint with
secondary beam, reinforcement of column-beam joint, reinforcement of beam in
place of support on wall or on column). General rules for calculations are presented
on lecture #14;
• Column head is welded joint and part could be bolted joint. Way of calculations
for both parts is presented on lecture #14;
Intercaction / contact element-element, bolted, pinned and welded joints
(continuation)
Photo: EN 1993-1-8 fig 7.3, 7.4 Photo: Author
→ #11 / 36
• Additional rules for welded joint between L section and plate are presented on
lecture #14;
• Additional rules for welded joint between two I-beam are presented on lecture
#14;
• Additional rules for pin ended members and contact bearing stresses for pins are
presented on lecture #14;
• Bolted joint for R&CHS are presented on lecture #14.
Intercaction / contact element-element, bolted, pinned and welded joints
(continuation)
→ #11 / 37
Truss nodes
For steel memebers used as a part of truss, requirements for resistance and stability
must be satisfied (→ #13). But, additionally, many requirements for local behaviour of
joints must be satisfied. For joints, different types of local instability and local
concentration of stresses are very important. These local phenomenons make, that
many types of cross-sections are banned for truss.
PN B 03200 EN 1993
Elements Each types of cross-sections are accepted
Joints No additional requirements Additional requirements → many
types of cross-sections are not
accepted
Cross-sections of truss members
→ #13 / 11
Modern types of cross-sections
(EN)
Old types of cross-sections (PN-B)
Chords
Web
members
Photo: Author
→ #13 / 12
Additional requirements for truss nodes
(EN 1993-1-8 7.1):
Chords → ✓ I ;
Web members → ✓ ;
Deformation ends of element are not accepted;
fy (✓) ≤ 460 MPa;
fy (✓) > 355 MPa → fy, design = 0,9 fy;
t (✓) ≥ 2,5 mm;
tchord (✓) ≤ 25 mm;
Compressed chords and web memebers → Ist or IInd class of cross-section;
bi ≥ 30o;
Distances between web members (eccentricitire) must be respected (→ #t / 11 - 14);
Shape of joints must be respected (EN 1993-1-8 fig. 7.1), (→ #t / 15 - 16);
(Length of member) / (depth of member) > 6 (EN 1993-1-8 5.1.5.(3));
Photo: tatasteelconstruction.com
Photo: Author
D
Permissible:
g ≥ t1 + t2
Permissible:
q / p ≥ 0,25
Not permissible:
g < t1 + t2
or
q / p < 0,25
t1t2
g
p
q
EN 1993-1-8 7.1Photo: Author
Additionally
d1 ≤ d2
and
fy,1 t1 ≤ fy,2 t2
EN 1993-1-8 7.1
Photo: Author
Results:
e
e
There is possible, that we must trace other
axis of member to satisfy requiremen for
g ≥ t1 + t2 or q / p ≥ 0,25
It makes eccentricities. Eccentricities make
non-zero values of bending moment.
Photo: Author
Photo: EN 1993-1-8 fig. 5.3
Acceptable limits for
eccentricities:
-0,55 a0 ≤ e ≤ +0,25 a0
a0 = h0 or d0
EN 1993-1-8 (5.1a), (5.1b)
Types of permissible joints
Photo: EN 1993-1-8 fig. 7.1
For each type of joint, many additional requirements must be fulfilled. These requirements are
presented in few tables in EN 1993-1-8; symbols are explained in EN 1993-1-8 1.5.(4), (5), (6).
Joint Table Comments
Chord Web members
CHS CHS 7.1 -
RHS CHS, RHS 7.8, 7.9 -
I-beam CHS, RHS 7.20 -
C-section CHS, RHS 7.21 C-section for chord is acceptet, but in this situation local
bending moments must be taken into consideration (this
means, this structure is not ideal truss).
Geneally, requirements presentes in tables, are as follow:
min ≤ (depth of HS) / (thickness of its wall) ≤ max
There are three groups of requirements for nodes of truss (EN 1993-1-8 5.1.5):
Acceptable values of eccentricities (→ #t / 14);
Loads applied according to ideal truss (→ #13 / 3);
General and additional requirements, permissible shapes of joints (→ #t / 10, 15, 16).
Consequences of satisfied or not satisfied (partial satisfied) are various, in dependence of group
of requirements. It must be taken into consideration in calculation model of truss. There are
three basis models of calculation:
1. Ideal truss 2. Continous chords 3. Frame
(hinge joints) (hinge/rigid joints) (rigid joints)
Photo: Author
Additionally, there are three possibilities for ideal truss in case of local bending moments:
1a. No bending moments 1b. Bending moments act on
chord only
1c. Bending moments act on
joint and chord
Ideal truss: axial forces only
for elements and joints.
Axial forces only for most
part of elements; axial forces
and bending moments for part
of chords; axial forces for
joints.
Axial forces only for most
part of elements; axial forces
and bending moments for part
of chords; axial forces and
bending moments for joints.
Model 2: axial forces only for web members; axial forces and bending moments for chords;
axial forces and bending moments for joints.
Model 3: axial forces and bending moments for each members and joints.
Photo: Author
Models of calculations for various values of eccentricities:
Member Eccentricities
0 Inside
acceptable
limits (#t / 14)
Outside
acceptable limits
(#t / 14)
Compression
chord
1a 1b 1c
Tension chord 1a 1b = 1a 1c = 1a
Brace
member
1a 1b = 1a 1c = 1a
Joint 1a 1b = 1a 1c
No difference between
1b or 1c and 1a (ideal
truss) for this part of
structure
In case of continous loads (for example: truss purlin), or applied out of nodes – model 2.
In case of not satisfied general, requirements or permissible shapes of joints – model 3.
Algorithm
Photo: Author
→ #3 / 84
There are many ways of local destrucion for truss nodes. According to EN 1993-1-8,
there are 6 modes of failure, presented on fig. 7.3, 7.4.
Photo: eqclearinghouse.org
Photo: scielo.br
Photo: offshoremechanics.asmedigitalcollection.asme.org
Sections 1. Chord face failure
F M
CHS - CHS
RHS - RHS
C/R HS - I / H - -
Photo: EN 1993-1-8 fig 7.3, 7.4
Sections 2. Chord wall / web failure
F M
CHS - CHS
RHS - RHS
C/R HS - I / H
Photo: EN 1993-1-8 fig 7.3, 7.4
Sections 3. Chord shear failure
F M
CHS - CHS
RHS - RHS
C/R HS - I / H
Photo: EN 1993-1-8 fig 7.3, 7.4
Sections 4. Punching shear
F M
CHS - CHS
RHS - RHS
C/R HS - I / H - -
Photo: EN 1993-1-8 fig 7.3, 7.4
Sections 5. Brace failure
F M
CHS - CHS
RHS - RHS
C/R HS - I / H
Photo: EN 1993-1-8 fig 7.3, 7.4
Sections 6. Local buckling
F M
CHS - CHS
RHS - RHS
C/R HS - I / H
Photo: EN 1993-1-8 fig 7.3, 7.4
For various shapes of nodes and various cross-sections of members (CHS, RHS, I-beam),
various modes of failure are the most dangerous. Resistance of node is defined in
dependence of the most dangerous modes.
Nodes are loaded by axial forces (Ni, Ed) from web members, first of all. In many cases, local
bending moments must be taken into consideration. For flat truss we analysed only bending
moments in plane (ip) of truss (Mip, i, Ed). Additionally, for multi-chords truss, bending
moments out of plane (op) of truss (Mop, i, Ed) must be taken into consideration.
There are different formulas for resistance of truss nodes (Ni, Rd, Mip, i, Rd, Mop, i, Rd) for
different shapes of nodes and different modes of failue. These formulas are presented on EN
1993-1-8, tab. 7.2-7.7, 7.10-7.19, 7.21, 7.22, 7.24. Way of check of resistance depends on
type of cross-sections of members (CHS, RHS, I-beam).
Web memebers
- chord
Chapter Tables General formula Comment
CHS - CHS 7.4 7.2, 7.3, 7.4,
7.5, 7.6, 7.7
Ni, Ed / Ni, Rd +
(Mip, i, Ed / Mip, i, Rd)2 +
Mop, i, Ed / Mop, i, Rd ≤ 1,0
Gusset plates are
possible
Tab. 7.4 - I/H is not a
chord
C/R HS - RHS 7.5 7.10, 7.11,
7.12, 7.13,
7.14, 7.15,
7.16, 7.17,
7.18, 7.19,
Ni, Ed / Ni, Rd +
Mip, i, Ed / Mip, i, Rd +
Mop, i, Ed / Mop, i, Rd ≤ 1,0
Gusset plates are
possible
C/R HS - I / H 7.6 7.21, 7.22 Ni, Ed / Ni, Rd +
Mip, i, Ed / Mip, i, Rd ≤ 1,0
I / H chord is not
recommended for
multi-chords trusses
C/R HS - C 7.7 7.24 Different formulas Secondary moments
should be taken into
account
Modern truss: for joints must be calculated:
Stiffness (lecture # 20, #21)
Resistance of connecting elements (welds / bolts; lecture #9, #11)
Resistance of joint (lecture #t)
Old type truss (designed „under rule” of old Polish Standard) - only connecting
elements were calculated; gusset plates were drawed; stifeness of nodes were not
calculated.
Old type:
Axes must intersect in one point;
Ends of members must be as close as possible each other (10-15 mm place for welds);
Photo: Author
There must be marked length of connecting elements (length of weld / space for bolts) along
members;
Outline of gusset plate = ends of connecting elements;
Photo: Author
Reflex angles are not accepted.
Photo: Author
Old type and modern trusses cam be designed with gusset plates or without gusset plates
Photo: Konstrukcje stalowe, K. Rykaluk,
Dolnośląskie Wydawnictwo Edukacyjne
Wrocław 2001
Photo: Konstrukcje stalowe, K. Rykaluk,
Dolnośląskie Wydawnictwo Edukacyjne
Wrocław 2001
There is need additional flat surface ("mounting table") for support of purlins when
we use CHS
Photo: Konstrukcje stalowe, K. Rykaluk,
Dolnośląskie Wydawnictwo Edukacyjne
Wrocław 2001
Deformations: elongation (tensile force) and abridgement (compressive force):
Transmission of forces form chords to supports and zero force members:
Photo: Author
→ #13 / 87
Members with big value of forces
should goes to nodes as close as
posible.
Photo: Author
Example: web members CHS,
chords HEB
Photo: Author
Example: web members CHS,
chords CHS
Support of truss
There are two most important types of supports:
Steel columns;
(concrete columns – rare case)
Steel columns;
Concrete columns;
Masonry walls
Photo: Author
Joints truss - steel column
Photo: Author Photo: vijaylaxmiengineering.in
Photo: aleo.com
Way of calculation → #t / 46
Joints truss - steel column
Photo: Author
Photo: wasatchsteel.blogspot.com
Photo: fireengineering.com
Joints truss - concrete / masonry structure
Photo: Author
Photo: tboake.com
Photo: structuremag.org Way of calculation → #12 / 78, #12 / 95
There is big horizontal reaction for symmetrical support. Because of this reaction, truss will
behave as for unsymmetrical supports after short time of exploatation (deformations of
columns, local destruction of masonry or concrete structure around anchor bolts).
Calculation as for symmetrical supports means, that forces taken under consideration in
design project are completely different than real forces in structure: for bottom chord real are
much more bigger than theoretical. This means big probability destruction of bottom chord
and collapse total structure.
Better way is to model the truss with unsymmetrical supports - this is closer its real
behaviour.
Photo: Author→ #13 / 85
There are special design way for diversity pinned and roller supports for massive
structures or structures with big loads (bridges).
Photo: web.mit.edu
Photo: web.mit.edu
Photo: .tatasteelconstruction.com
Photo: .texasescapes.com
Photo: . fbcdn-photos-g-a.akamaihd.net
Photo: wikipedia
Because of susceptibility of column /
wall, and / or anchor bolts, there are
spring supports for horizontal direction
and rotation in real truss.
One roller and one pinned support is
good approximation and idealisation
for this situation.
Changing the static scheme due to the
susceptibility of structural elements is common
in the analysis of steel structures. For example,
difference between pinned and rigid column
base is only number and position of anchor
bolts.
Photo: Author
Photo: j-p.com.ua
Photo: 1.bp.blogspot.com
Splice joints of hollow sections
Photo: Author
Because of transport loading gauge, long structre should be divided into transport
members. There is good idea, that max length of membes (L 1 or L2) should not be greated
than 12,00 m. Members are connected each other by splice joints on construction site.
For I-beam chords, there can be adopted shear joint (→ Des #1).
Photo: gsi-eng.eu
Photo: encrypted-tbn0.gstatic.com
Photo: zs4-sanok.pl
For hollow sections, there is used tension joint.
The problem is, that in EN 1993-1-8 tension joint is presented for I-beams only. The
same in old Polish Standard PN B 03200.
Generalisations of both methods are presented on literature.
Generalisation of Literature Comments Page
PN B 03200 J. Bródka, M. Broniewicz,
Konstrukcje stalowe z rur,
Arkady 2001
Separated procedures for CHS and
RHS;
No clear influence of longitudinal
stiffeners for resistance;
Similar methods, only few small
differeces;
#t / 50 –
52
EN 1993-1-8 Access Steel SN044a-EU
Design models for splices
in structural hollow,
Internet edition
#t / 53 -
56
PN B 03200, CHS
tptpri
re
rp
r0
e1 e2
p2
re = ri + t
r0 = re + e2
rp = r0 + e1
rp = 2 r0 - ri
tp = max (t1 ; t2)
t1 = √[(2 NEd / (fyp k)]
k = [k1 + √(k22 - k1
2)] / (2 k1)
k1 = ln (r0 / ri)
k2 = k1 + 2
NEdNEd
t2 = 1,2 √[(c SRt) / (fyp beff)]
beff = min (2pm ; 4m + 1,25 e)
m = r0 - ri
e = min (rp - r0 ; 1,25m)
c = m - 0,5d
SRt = As min (0,65fub ; 0,85fyb)
Photo: Author
n = max (n1 ; n2)
n1 = NEd k3 / SRt
n2 = NEd / SRt
k3 = 1 - 1 / k + 1 / (k k4)
k4 = ln (rp / r0)
Additionally, welds should be calculated according to Lec #9 example 4.
Requirements satisfy → no additionaly condition for NEd / NRd
PN B 03200, RHS
Photo: Author
NEd NEd
tp tp
A B C
p2 p2e1 e1
e2 e2 e2
e3 e3e3
For cases A and B:
• M16, M20 or M24 are recommended;
• tp ≥ d (case A, n = 4)
• tp ≥ d + 3 mm (case B, n = 8)
• NRd = 0,8 n SRt
• SRt → #t / 50
Additionally, welds should be calculated according
to Lec #9 example 4.
NEd / NRd ≤ 1,0
√{K NEd / [n (1+d)]} ≤ tp ≤ √(K NEd / n)
d = 1 - d / p2
K = 4000 bred / (fyp p2)
bred = e2 + tRHS - d / 2
NRd = tp2 (1 + d a) n / K
a1 = [(K SRt / tp2) - 1] (e3 + 0,5 d) / [d (e3 + e2 + tRHS)]
e1 = 0,5 p2
e3 ≤ 1,25 e2
PN B 03200, RHS
Photo: Author
NEd NEd
tp tp
A B C
p2 p2e1 e1
e2 e2 e2
e3 e3 e3
For case C:
Neff = NEd {1 + bred d a2 / [a3 (1 + d a2 )]} / n
a2 = [K NEd / (n tp2) -1 ] / d
a3 = e3 + d / 2
SRt → #t / 50NEd / NRd ≤ 1,0
Neff / SRt ≤ 1,0
Additionally, welds should be calculated according
to Lec #9 example 4.
EN 1993-1-8, CHS
tptpri
re
rp
r0
e1 e2
p2
2,2 d0 ≤ p2 ≤ min (14 tp ; 200 mm)
d0 = d + 2 mm (d ≤ 24 mm)
d0 = d + 3 mm (d > 24 mm)
1,2 d0 ≤ e2 ≤ 1,5 - 2,0 d
1,2 d0 ≤ e1
NEdNEd
Photo: Author
Additionally, welds should be calculated according to Lec #9 example 4.
NRd = min (NRd1 ; NRd2)
NRd1 = tp2 fyp p k / (2 gM0)
k → #t / 50
NRd2 = n Ft, Rd / k3
k3 = 1 - 1 / k + 1 / (k k5)
k5 = ln (reff / r0)
reff = re + e2 + eeff
eeff = min (e2 ; 1,25 e1)NEd / NRd ≤ 1,0
EN 1993-1-8, RHS
Photo: Author
NEd NEd
tp tp
A B C
p2 p2e1 e1
e2 e2 e2
e3 e3e3
Cases A and B are not recommended. SHS are accepted in case C.
12 mm ≤ tp ≤ 26 mm
4 ≤ n ≤ 2 + 2 hRHS / p2
d0 = d + 2 mm (d ≤ 24 mm)
d0 = d + 3 mm (d > 24 mm)
1,2 d0 ≤ e2 ≤ 1,5 - 2,0 d
1,2 d0 ≤ e1
2,2 d0 ≤ p2 ≤ min (5,0 d ; 14 tp ; 200 mm)
EN 1993-1-8, RHS
Photo: Author
NEd NEd
tp tp
A B C
p2 p2e1 e1
e2 e2 e2
e3 e3 e3
For case C:
EN 1993-1-8, RHS
Photo: Author
NEd NEd
tp tp
A B C
p2 p2e1 e1
e2 e2 e2
e3 e3 e3
For case C, continuation:
√{K NEd / [n (1+d)]} ≤ tp ≤ √(K NEd / n)
K → #t / 52
NRd = min (n Ft, Rd ; n Bp,Rd ; N1, Rd)
Ft, Rd → #10
Bp,Rd → #11
Additionally, welds should be calculated
according to Lec #9 example 4.
N1, Rd = tp2 (1 + d a1) n / (K gM2)
a1 → #t / 52
NEd / NRd ≤ 1,0
Stiffeners
• Support for transverse beams
(connection between primary and
secondary beams);
• Support for slender web
(prevention of web local
instability);
• Support for slender flange
(prevention of flange local
instability);
• Increasing of web resistance
under shear forces.
Photo: Author
Support for transverse beams (connection between primary and secondary beams)
Photo: Author
Support for slender web (prevention of web local instability);
Support for slender flange (prevention of flange local instability)
Probability of instability for compressed flange and / or compressed part of web is much lower
for little sub-panels than for one big panel.
Photo: Author
Increasing of web resistance under shear forces.
Photo: Author
Photo: Author
1. No end post
2. Non-rigid end post
3. Rigid end post
4. Transverse stiffener
5. Intermediate support
stiffener
6. Longitudinal stiffener
7. Column transverse
stiffener
8. Diagonal stiffener
Location of stiffeners
Photo: Author
Vertical (2, 3, 4, 5): over
supports, in connections
between primary and
secondary beam and
under big transversal
loads;
Transversal (7): on axes
of flanges;
Longitudinal (6): h / hc=
1/3 - 1/2;
Diagonal: on joints beam-
columns.
h
h
hc
hc
compression
compressiontension
tension
Geometry of stiffeners:
a
hw
bs
ts
tw
Photo: Author
Conditions:
Independent of the load Load-dependent
Conditions: Stiffeners: Stiffeners: Conditions:
Thickness of adjacent
elements
(#t / 65)
2, 3, 4, 5, 7 2, 4, 5, 7 Contact stress
(#t / 70)
Class of the cross-section
(#t / 66)
2, 3, 4, 5, 6,
7, 8
2, 4, 5, 7 Axial compression
(#t / 71 - 77)
Prevent torsional buckling of
stiffener (#t / 67)
2, 4, 5, 7 6 Cross-sectional resistance
(#t / 78)
Rigid supports for web panel
(#t / 68)
2, 4, 5, 7 8 Diagonal stiffener
(#t / 79 - 81)
Rigid end post
(#t / 69)
3 2, 3, 4, 5, 6,
7, 8
Welds
(#t / 82)
Thickness of adjacent elements:
ts ≥ thickness of secondary beam web
or
ts ≥ thickness of beam flange
Photo: Author
Photo: Author
Class of the cross-section:
There is no special requirements in EN 1993, but each formula for stiffeners is
as for cross-section of no-VIth class of cross-section. Because of this stiffeners
should have Ist, IInd or IIIrd class of cross-section.
bs / ts ≤ 14 e
Prevent torsional buckling of stiffener
EN 1993-1-5 (9.3)
JT / Jp ≥ 5,3 fy / E
JT = bs ts3 / 3
Jp = bs3 ts / 3 + bs ts
3 / 12
Rigid supports for web panel
EN 1993-1-5 9.3.3 (9.6)
a / hw ≥ √2 → Jst ≥ 1,50 hw3 tw
3 / a2
a / hw < √2 → Jst ≥ 0,75 hw tw3
Jst = 2 [ bs3 ts / 12 + bs ts (bs + tw)2 / 4 ]
Rigid end post
EN 1993-1-5 9.3.1 (3)
EN 1993-1-5 fig. 9.6
Two couples of stiffeners: 2 As ; Ws, x
e ≥ 0,1 hw
As ≥ 4 hw tw2 / e (two couples of plates)
Ws, x ≥ 4 hw tw2 (hot rolled I-beam as end post)
Contact stresses
EN 1993-1-5 9.4 (2)
Fs, Ed / (2 cs ts fy) ≤ 1,0
cs
bs
Photo: Author
Stiffeners are treated as bar, compressed by axial force Ns, Ed;
We analyse flexural buckling about x-x axis;
We take into consideration cross-section of stiffeners and cooperating
part of web (┼ cross-section);
Axial compression
EN 1993-1-5 9.2.1
EN 1993-1-5 9.4 (2)
Axial force Ns, Ed contains imperfections
of stiffeners;
Additionally we must analyse
imperfections of web - represented by
additional load q;
We must analyse interaction between
axial force Ns, Ed, buckling about x-x and
bending moment Ms, Ed (q).Photo: Author
Photo: lmsteelfab.com
Ns, Ed = max (Fs, Ed + DNst ; V*Ed + DNst ; DNst )
Fs, Ed - transverse force, acts on stiffeners (from secondary beam, from supports...);
there is possible that Fs, Ed = 0 (for stiffeners used as support for slender web or flange only
→ #t / 73 );
DNst = sm b2 / p2 - from imperfections of stiffeners (b = hw for analysis of stiffeners);
V*Ed = max [VEd - fyw hw tw / (lw gM1 √3) ; 0] - part of shear force over web
resistance of shearing;
VEd - shear force at the distance 0,5 hw from the edge of the panel with the largest
shear force;
gM1 = 1,0;
lw → #t / 74;
sm → #t /75;
_
_
Ns, Ed = DNst (for stiffeners used as support for
slender web or flange only)
Ns, Ed > DNst
Requirements from #t / 71 may be assumed to
be satisfied provided when:
Jst ≥ (1 + 300 w0 u / b) (sm b4) / (E p4)
Jst = 2 [ bs3 ts / 12 + bs ts (bs + tw)2 / 4 ]
Total procedure of calculations is necessary (#t
/ 71 - #t / 77):
q = p sm (w0 + wel) / 4
sm → #t /75;
w0, u, wel → #t / 76;
b = hw
EN 1993-1-5 A.3
a = a / hw
a < 1,0
kt kzts + 4,00 + 5,34 / a2 kzts + 5,35 + 4,00 / a2
a ≥ 1,0
kzts = max { [2,1 3√ (Jst / hw)] / tw ; [9 hw2 4√ (Jst / (hw t3
w))] / a2 }
Jst - about axis z for longitudinal stiffeners;
If no longitudinal stiffeners, kzts = 0
Slenderness factor for web resistance:
Photo: Author
lw = hw / (86,4 tw e) lw = hw / (37,4 tw e √kt )
_ _
sm = (scr, c / scr, p) (1 / a1 + 1 / a2) Neq- axial / b
scr, c = p2 E tw2 / [ 12 (1 - n2) a2 ] ≈ 190 000 (tw / a)2 [MPa]
scr, p = ks (28,4 e)2 fy (tw / b)2 ≈ 190 000 ks (tw / b)2 [MPa]
a = (a1 + a2) / 2 (usually a = a1 = a2)
b = hw
ks - for web,
according to EN
1993-1-5 tab. 4.1
Neq- axial → #t / 76;
w0 = s / 300
s = min (a1 ; a2 ; b)
wel = b / 300
u = max [ 1,0 ; p2 E emax gM1 / (fy 300 b) ]
emax = bs / 2
b = hw
Neq- axial = max (NEd, 1 ; smax A / 2 )
smax is analised when MEd or MEd + NEd,1 is
applied to beam.
Photo: Author
Ms, Ed = q hw2 / 8
cx = cx (c, ┼, lcr) (according to lecture #5)
lcr = 0,75 hw
NRd = A┼ fy / gM0
MRd = W┼, x, el fy / gM0
Ns, Rd / (cx NRd) + Ms, Ed / MRd ≤ 1,0 - D0, x
Class of cross-section ┼ 1 or 2 3 or 4
D0, x 0,1 + 0,2 [ (W┼, x, pl / W┼, x, el) - 1] 0,1
tw
ts 15 e tw15 e tw
EN 1993-1-1 NA.20
Photo: Author
Cross-sectional resistance (longitudinal stifeners)
EN 1993-1-5 9.3.4
There are two possibilities of calculations:
1.
Longitudinal stiffeners are
treated as a part of cross-section;
their geometry is added to
geometry of beam;
2.
NEd, eq = scomp, max Acomp / 2
NRd = 2 bh-s th-s fy
NEd,eq / NRd ≤ 1,0
Photo: Author
Diagonal stiffeners
Photo: fgg.uni-lj.si
Photo: Author
Possibility of increasing resistance and stiffness of column web in shear;
Rarely use, first of all in exterior columns of frames;
No information in Eurocode;
No clear guidance in the literature;
Photo: microstran.com.au
MEd
MEd
hIc
hIb
a
F1F1
F1
F2
F2
F2
F3
F1 = MEd / hIc
F2 = MEd / hIb
F3 = √ (F12 + F2
2)
Diagonal stiffener
under tension
Photo: Author
MEd
hIb
hIc
a
F1F1
F1
F3
F2
F2F2
Diagonal stiffener
under compression
(more often used)
According to supposition in literature, if diagonal stiffness and its welds have
enough resistant to bear tension F3:
resistance of column web in shear Vwp, Rd → ∞ (→ #12);
stiffness of column web in shear k2 → ∞ (→ #21, #22);
Photo: microstran.com.au
Photo: skcthailand.com
Photo: chodor-projekt.net
Welds
Vertical and transversal stiffeners:
Lecture #9 example 1, FV = max (Fs, Ed ; V*Ed ; 0) → #t / 72;
Longitudinal stiffeners:
Lecture #9 example 6a, s1, t1 according to max values on analysed member;
Diagolnal stiffeners:
Lecture #9 example 2, Fy = F3 → #t / 80;
Resistance of L section, connected by one leg:
NRd = Aeff fy / γM1
L - section; additional rules
Photo: Author
Recommendation:
b1 ≈ b – 30 mm
b2 ≈ b + 30 mm
t1 = t2 b2 / b1
For distribution of cross-section forces:
t = (t1 + t2) / 2
b = (b1 + b2) / 2
Afp = t b
Jfp = 2 [b t3 / 12 + b t (h / 2)2]
For this project is possible to take the same geometry of flange plates and web plates as for bolted connection.
Photo: Author
I-beam, welded joints; additional rules
→ Des #1 / 62
min 10 mm
min 30o
min 10 mm
min 30o
h ≥ 25 mm; h ≥ 3 t r ≥ 25 mm; r ≥ 3 t
t t
h r r
t
Photo: Author
→ #8 / 17
Geometrical requirements for pin ended members
EN 1993-1-8 tab 3.9
Pins
FEdd0
a
c
When thickness t is given:
a ≥ [FEd gM0 / (2 t fy)] + 2 d0 / 3
c ≥ [FEd gM0 / (2 t fy)] + d0 / 3
FEd
d02,5 d0
0,75 d0
1,6 d0
0,3 d0
1,3 d0
When geometry is given:
t ≥ 0,7 √ [FEd gM0 / fy]
d0 ≤ 2,5 t
Photo: Author
sh, Ed / fh, Rd ≤ 1,0
sh, Ed = 0,591 √ [E FEd, ser (d0 - d) / (d2 t)]
fh, Rd = 2,5 fy / gM6, ser
Contact bearing stress for pins
EN 1993-1-8 3.13.2
Jb / Jc ≥ 20 20 > Jb / Jc ≥ 10 10 > Jb / Jc
No rocker Flat rocker Round rocker
Cap plate bending
Cap plate - column welds
Rocker - beam compression
Rocker - cap plate welds
Rocker - cap plate
compression
Cap plate - bending
Cap plate - column welds
Cap plate - column
compression
Rocker - beam compression
Rocker - cap plate welds
Rocker - cap plate
compression
Cap plate bending
Cap plate - column welds
Cap plate - column
compression
Column head
Hinge support for bean on columnPhoto: Author
Rocker-beam compression
EN 1337-6
Structural bearings; rocker bearings
Beam (round rocker):
(NEd / bf) /[23 r fu2 / (E γ
M)] ≤ 1,0 γ
M= 1,0
or (flat rocker):
(NEd / bf) / [fy (2 tf + bf) / γM] ≤ 1,0 γ
M= 1,1
Rocker: (round and flat)
(NEd / bf ) / [fy (2 tr + bf) / γM ] ≤ 1,0 γ
M= 1,1
tf
tr
r
b
L bf
L ≈ bf ≈ hchc
Photo: Author
Alternatively, according to PN B 03200:
Contact flat - flat element:
NEd / Acontact ≤ 1,25 fy
Contact round - flat element:
0,42 √ [ E NEd / (bf r) ] ≤ 3,6 fy
Rocker-cap plate compression
NEd / ( L b fy ) ≤ 1,0
Rocker - narrow thick member; stress between
rocker and cap plate has nearly constant value
s s
Photo: Author
Welds between cap plate
and column
Lecture #9, example #3
Welds between roocker and
cap plate
Photo: Author
Cap plate bending
With rocker:
tcp ≥ min { tf ; √[ (3 NEd l12) / (a b fy) ] - tr }
Without rocker:
tcp ≥ min {tf ; √[ (3 NEd l2) / (a b1 fy) ]}
tcp
tcptcp
Calculated as short
cantilever
Photo: Author
Cap plate-column compression
Cap plate - wide thin member; stress between cap plate and column has non-linear
character; we assume big constant value in central part and zero at ends of flange. Constant
value of stress exists in distance from end of column.
NEd / Aeff ≤ fy
2 tcp + b
2 tcp + b
b
tcp
s
s
s
sPhoto: Author
Calculation of resistance for truss nodes
Modes of failure for truss nodes
The role and placement of horizontal and vertical stiffeners
Calculation of vertical stiffeners
Calculation of columns heads
Examination issues
Whether-in-plane - obciążenie przęsłowe w prętach kratownicy
Out-of-plane - obciążenie prostopadłe do płaszczyzny kratownicy
Closely spaced build-up members - pręt wielogałęziowy
Chord size failure - zniszczenie przystykowe pasa
Chord size wall / web failure - zniszczenie boków / środnika pasa
Chord shear failure - ścięcie pasa
Punching shear - przebicie
Brace failure - zniszczenie elementu skratowania
Local buckling - wyboczenie miejscowe
Gussed plate - blacha węzłowa
Splice joint - styk montażowy
Head - głowica
Stiffener - żebro
Contact strength - docisk
Rocker - płytka centrująca
Cap plate - płyta głowicy