IS800-2007 Plate Girder.ppt

Mr.Naveen Choudhary,GEC,Ajmer
1
PLATE GIRDERS
Built-up sections with deep thin webs
susceptible to buckling in shear

2
Types of Plate Girders
• Unstiffened Plate Girder
• Transversely Stiffened Plate Girder
• Transversely and Longitudinally Stiffened Plate Girder
web plate flange plates
ITS
BS
LS

3
SHEAR RESISTANCE OF
STIFFENED GIRDER
Shear resistance of a web
• Pre-buckling behaviour (Stage 1)
– Requirements of equilibrium in an element inside a
square web plate subject to a shear stress result in
generation of complementary shear stresses
– This results in element being subjected to principal
compression along one diagonal and tension along
the other

4
Shear resistance of a web - 1
A
q
q
45o
B
D
C
q
E
q
Unbuckled Shear panel

Mr.Naveen Choudhary,GEC,Ajmer 5
Shear buckling of a plate
BUCKLING OF WEB PLATES IN SHEAR
cr

– As the applied loading is incrementally enhanced,
plate will buckle along direction of compressive
diagonal - corresponding shear stress in plate
is“critical shear stress”
– Critical shear stress in such a case is given by
– Boundary conditions assumed to be simply
supported
2
d
t
2
1
12
E
2
s
k
cr
q 










 




• shear buckling coefficient (ks) given by
panels
wide
for
e
i
d
c
where
c
d
ks .
.
,
1
4
35
.
5
2









stiffeners
transverse
spaced
closely
with
webs
for
e
i
d
c
where
c
d
ks .
.
,
1
4
35
.
5
2









c
d

• Post buckled behaviour (Stage 2)
– Compression diagonal is unable to resist any
more loading beyond elastic critical stress
– Any further increase in shear load is supported
by a tensile membrane field, anchored to top
and bottom flanges and adjacent stiffener
members on either side of web
– Total state of stress in web plate may be
obtained by superimposing post-buckled
membrane tensile stresses upon critical shear
stress

Post buckled behaviour - 1
Anchoring of Tension Field

Tension field action

• Collapse behaviour (Stage 3)
– When load is further increased, tensile
membrane stress continues to exert an
increasing pull on flanges
– Eventually resultant stress obtained by
combining the buckling stress and membrane
stress reaches yield value for web - can be
determined by Von-Mises yield criterion

Collapse behaviour - 1
Collapse of the panel
Tensile membrane stress at yield

Three phases of tension field action
Pre-buckling post-buckling collapse

14
ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS
Transverse stiffeners play important role
by increasing web buckling stress
by supporting tension field after web buckling
by preventing tendency of flanges to get pulled
towards each other
Stiffeners should possess sufficient rigidity
to ensure that they remain straight, while
restricting buckling to individual web panels

15
ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS - 1
Force imposed on transverse stiffeners by tension field

16
GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS
 Generally located in compression zones of girder
 Main function - to increase buckling resistance of
web
 When it is subject predominantly to shear would
develop a collapse mechanism, provided
stiffeners remained rigid up to failure
 Once one of sub panels has buckled, post
buckling tension field develops over whole depth
of web panel and influence of stiffeners may be
neglected

GENERAL BEHAVIOUR OF
LONGITUDINALLY STIFFENED GIRDERS – 1
Longitudinal and Transverse stiffeners

8.4 Shear
The factored design shear force, V, in a beam due to
external actions shall satisfy
V  Vd
Vd = design strength calculated as , Vd = Vn / γm0
8.4.1 The nominal plastic shear resistance under pure
shear is given by: Vn = Vp
Av = shear area
Cont…
3
yw
v
p
f
A
V 

8.4.2 Resistance to Shear Buckling
for an unstiffened web
for a stiffened web
a) Simple Post-Critical Method
The nominal shear strength is
Vn = Vcr Vcr = d twb
b = shear stress corresponding to buckling,
b) Tension Field Method
The nominal shear strength is
V n = V tf

67

w
t
d
y
f
/
250


v
k



8.4.2.2 Shear Buckling Design Methods
a) Simple Post-Critical Method -The nominal shear strength is
Vn = Vcr Vcr = d twb
b = shear stress corresponding to buckling, determined as follows:
a) When w < 0.8
b) When 0.8 < w < 1.25
c) When w 1.25
b =0.9 fyw/(3w
2)
Cont…
3
/
yw
b f


 
  
3
/
8
.
0
625
.
0
1 yw
w
b f


 

0.8 1.25 w
b

λw = non -dimensional web slenderness ratio for shear buckling stress,
given by
The elastic critical shear stress of the web, cr is given by:
kv = 5.35 when transverse stiffeners are provided only at supports
= 4.0 +5.35 /(c/d)2 for c/d < 1.0
= 5.35+4.0 /(c/d)2 for c/d  1.0
Cont…
)
3
( ,e
cr
yw
w f 
 
  2
2
2
/
1
12 w
v
cr
t
d
E
k






b) Tension Field Method - the nominal shear resistance, Vn, should be
Vn=Vtf
 Vnp
fv = yield strength of the tension field obtained from
 =1.5 b sin 2
 = inclination of the tension field
The width of the tension field, wtf, is given by:
wtf = d cos – (c-sc-st) sin 
  

 



5
.
0
2
2
2
3 b
yw
v f
f






 
c
d
1
tan
c
t
f
M
s
w
y
fr










5
.
0
sin
2

 
 
 
2
0
2
/
/
1
25
.
0 m
yf
f
f
f
yf
f
f
fr f
t
b
N
f
t
b
M 


 

 sin
9
.
0 v
w
tf
b
w
tf f
t
w
t
d
V 

sc
st
c
wtf

8.6 Design of Beams and Plate Girders with Solid Webs
8.6.1 Minimum Web Thickness
8.6.1.1 Serviceability Requirement
a) when transverse stiffeners are not provided
(web connection by flanges along both longitudinal edges)
(web connection by flanges along one longitudinal edge only)
b) when transverse stiffeners only are provided;
i) when c  d
ii) when 0.74 d < c < d
iii) when c < 0.74 d
Cont…

180

w
t
d

90

w
t
d
w
w
t
d

200

w
w
t
c

200

w
w
t
d

270


c) when transverse and longitudinal stiffeners are provided at one
level only
(0.1 d from compression flange)
i) when c > d
ii) when 0.74 d < c < d
iii) when c < 0.74 d
d) when a second longitudinal stiffener (located at neutral axis is
provided )
Cont…
w
w
t
d

250

w
w
t
c

250

w
w
t
d

340

w
w
t
d

400


Design Procedure
Initial Sizing
1) Taking L/d as 15, calculate min. d and provide suitably
2) Afreqrd. = BM/ (fy/mo)d ; using bf = 0.3d select flange plate
Also calculate Nf = axial force in the flange
3) Check that flange criteria gives a plastic section
b = (bf – tw)/2 and b/ tf < 7.9
4) Web thickness for serviceability 67 < d/ tw < 200
choose such that tw > d/200
5) Check for flange buckling into web
Assuming c >1.5d , d/ tw < 3452

Design Procedure
6) Check for shear capacity of web
V < Vd = Vn/ mo; Vn = A (fyw /3) or Vcr
7) Check for calculating resistance to shear buckling
d/ tw > 67 (kv/5.35) use kv for c/d > 1
8) Simple post-critical method
Vcr = d tw b where b = (w) and w = (cr )
9) If V < Vcr/ mo then safe else tension field calculation
reqrd.
10) Vn = Vtf = (fv and ); also calculate Mfv = (Nf )
If V < Vn/ mo safe ! else revise design

Design Procedure
• 8.7 Stiffener design
– a) Intermediate Transverse Web Stiffener  To improve
the buckling strength of slender web due to shear.
– b) Load Carrying Stiffener  To prevent local buckling
of the web due to concentrated loading.
– c) Bearing Stiffener  To prevent local crushing of the
web due to concentrated loading .
– d) Torsion Stiffener  To provide torsional restraint to
beams and girders at supports.
– e) Diagonal Stiffener To provide local reinforcement to
a web under shear and bearing.
– f) Tension Stiffener  To transmit tensile forces applied
to a web through a flange.

Design Procedure
11) End panel design – check as a beam between flanges
Rtf = Hq/2
Av = c t and Vtf = Av (fy /3) > Rtf
12) Mtf = Hqd/10
MR = tc3/12*fyd / (c/2) > Mtf
13) Intermediate Transverse Stiffener Design
i) decide to provide stiffener on one side or both sides
ii) choose tq > tw ; outstand bs < 14tq also < b
14) check for minimum stiffness Cl.8.7.2.4 p91
for c = 1.5d, c > 2 d giving
I prov. = (bs-tw/2)3 tq/12 > 0.75dtw
3
)
/
1
(
.
25
.
1 dp
cr
dp
q V
V
V
H 
 Rtf
c
bs
tq

Design Procedure
15) Check for Buckling Cl.8.7.2.5 p91
Stiffener force, Fq = V - Vcr/mo  Fqd
Buckling Resist. Pq with 20tw on either side Cl.8.7.1.5 p90
Calculate Ixx and A, rxx = (Ixx/A)
Leff = 0.7d,  = Leff/rxx, Find fc
Pq = fc A > Fq
16) Connection to web Cl.8.7.2.6 p92
shear = tw2 / 8bs kN/mm choose appropriate weld size
19) Check for Intermediate Stiffener under Load Cl.8.7.2.5 p91
1




ys
s
xd
x
qd
x
q
M
M
F
F
F
F
F
bs
tq

IS800-2007 Plate Girder.ppt

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IS800-2007 Plate Girder.ppt