1. PLATE GIRDERS Built-up sections with deep thin webs
susceptible to buckling in shear
Dr S R Satish Kumar, IIT Madras

2. Dr S R Satish Kumar, IIT Madras
Types of Plate Girders
Unstiffened Plate Girder
Transversely Stiffened Plate Girder
Transversely and Longitudinally Stiffened Plate Girder
web plate
flange plates
ITS BS LS
Dr S R Satish Kumar, IIT Madras

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
Dr S R Satish Kumar, IIT Madras

4. Shear resistance of a web - 1q
45o B D C E
Unbuckled Shear panel
Dr S R Satish Kumar, IIT Madras

5. BUCKLING OF WEB PLATES IN SHEAR
cr
Shear buckling of a plate
Dr S R Satish Kumar, IIT Madras

6. Shear resistance of a web - 2
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
Dr S R Satish Kumar, IIT Madras

7. Shear resistance of a web - 3
shear buckling coefficient (ks) given by c d
Dr S R Satish Kumar, IIT Madras

8. 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
Dr S R Satish Kumar, IIT Madras

9. Anchoring of Tension Field
Post buckled behaviour - 1
Anchoring of Tension Field
Dr S R Satish Kumar, IIT Madras

10. Dr S R Satish Kumar, IIT Madras
Tension field action
Dr S R Satish Kumar, IIT Madras

11. 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
Dr S R Satish Kumar, IIT Madras

12. Tensile membrane stress at yield
Collapse behaviour - 1
Collapse of the panel
Tensile membrane stress at yield
Dr S R Satish Kumar, IIT Madras

13. Three phases of tension field action
Pre-buckling post-buckling collapse
Dr S R Satish Kumar, IIT Madras

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 14
Dr S R Satish Kumar, IIT Madras

15. ULTIMATE BEHAVIOUR OF TRANSVERSE WEB STIFFENERS - 1
Force imposed on transverse stiffeners by tension field 15
Dr S R Satish Kumar, IIT Madras

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  16
Dr S R Satish Kumar, IIT Madras

17. GENERAL BEHAVIOUR OF LONGITUDINALLY STIFFENED GIRDERS – 1
Longitudinal and Transverse stiffeners
Dr S R Satish Kumar, IIT Madras

18. IS 800: 2007
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…
Dr S R Satish Kumar, IIT Madras

19. IS 800: 2007 8.4.2 Resistance to Shear Buckling for an unstiffened web
for a stiffened web
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
V n = V tf
Dr S R Satish Kumar, IIT Madras

20. 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w2)
Cont…
0.8
1.25 w b
Dr S R Satish Kumar, IIT Madras

21. IS 800: 2007
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
= /(c/d) for c/d < 1.0
= /(c/d)2 for c/d  1.0
Cont…
Dr S R Satish Kumar, IIT Madras

22. IS 800: 2007
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  sc st c
wtf
Dr S R Satish Kumar, IIT Madras

23. (web connection by flanges along one longitudinal edge only)
IS 800: 2007
8.6 Design of Beams and Plate Girders with Solid Webs
8.6.1 Minimum Web Thickness
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;
when c  d
ii) when 0.74 d < c < d
iii) when c < 0.74 d
Cont…
Dr S R Satish Kumar, IIT Madras

24. (0.1 d from compression flange) i) when c > d
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…
Dr S R Satish Kumar, IIT Madras

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

26. Design Procedure Check for shear capacity of web
V < Vd = Vn/ mo; Vn = A (fyw /3) or Vcr
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
Dr S R Satish Kumar, IIT Madras

27. IS 800: 2007 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.
Dr S R Satish Kumar, IIT Madras

28. Design Procedure Rtf c bs tq
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 p91
for c = 1.5d, c > 2 d giving
I prov. = (bs-tw/2)3 tq/12 > 0.75dtw3
Rtf c bs tq
Dr S R Satish Kumar, IIT Madras

29. Design Procedure bs tq 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 p90
Calculate Ixx and A, rxx = (Ixx/A)
Leff = 0.7d,  = Leff/rxx, Find fc
Pq = fc A > Fq
16) Connection to web Cl p92
shear = tw2 / 8bs kN/mm choose appropriate weld size
19) Check for Intermediate Stiffener under Load Cl p91 bs tq
Dr S R Satish Kumar, IIT Madras