Design of cross section connection EBS and IS design

1. Sanjivani Rural Education Society's
Sanjivani College of Engineering, Kopargaon 423603.
-Department of Civil Engineering-
By
Mr. Sudhir B. Gayake (Assistant Professor)
Mail Id- gayakesudhircivil@sanjivani.org.in
Prof. Sudhir B. Gayake, SCOE Kopargaon

2. Prof. Sudhir B. Gayake, SCOE Kopargaon
Que- Design a welded plate girder for following data. Use intermediate transverse
stiffners. Span=24m, Wu=159kN/m, Max BM=11448kNm, Max SF=1908kN, Steel
grade=fe410.
Given data-
span=l=24000mm,
w=159kN/m,
Mu=11448kNm
Vu=1908kN
fy=250MPa, fu=410MPa,
Solution-
Step 1) Depth of Web plate-
ØIf stiffners are to be avoided the value of (d/tw)=k= 67 to 100;
Ø If only end bearing stiffners are to be provided then, value of (d/tw)=k= 100 to 200;
ØIf intermediate stiffners are to be provided the value of (d/tw)=k= 200 to 270 .
adopting K=(d/tw)= 220 as IS, EBS ad end block is to be designed.

3. Prof. Sudhir B. Gayake, SCOE Kopargaon
d= 3√ (MuXk/fy)= 3√ (11448X106X220/250)= 2159.75= 2160mm
as we have assumed the k=(d/tw)=220
tw=(2160/220)=9.81 mm=12mm
Provided web plate of size 2160mmX12mm
Area of flanges required= [AfXfyXd/γm0]=Mu
Af= [(11448X106 X1.10)/(250X2160]
= 23320mm2
for flanges to be in plastic or semi-compact assume bf= (0.3 to 0.4 times of d adopted)
= 0.3X2160= 648mm= 650mm
as Af= bfXtf
tf=23320/650= 35.87mm= 38mm
Provided flange plate of size 650mmX38mm

4. Prof. Sudhir B. Gayake, SCOE Kopargaon
38
2160
38
650
2236
12
Classification of cross section-
(bf/2)/(tf)= (650/2)/(38)= 8.55< 9.4 ε...............Flange is plastic
(d/tw)= (2160/12)= 180 > 67ε ..........................Web is slender
therefore the section is plastic and βb=1.0
( intentionally web kept in slender class for economy)
Ap= 2(650X38)+(2160X12)= 75320 mm2
Moment of inertia -
Izz= [Ig+Ah2]
= 2[((650X383)/(12))+(650X38)X(1099)2]+[(12X21603)/(12)]
= 6.97X1010 mm4
Iyy= 2[(38X6503/12]+[(2160X123/12)]=1.7396X109 mm4
yb=yt= 2236/2= 1118mm
Zez= Izz/Yb= 62.34X106 mm3
Zpz= ZezXShape factor= 71.07X106 mm3
Design bending strength of section-
Md= βbXZpzXfy/γm0 = 16152.62kN-m > Mu= 11448kN-m

5. Prof. Sudhir B. Gayake, SCOE Kopargaon
Shear Capacity of Web- (Cl.No. 8.4.2.2 Pg.No. 59 )
The nominal shear strength of web(Vn) with or without stiffners may be
computed using one of the following method;
1) Simple post critical method,
adopting Simple post critical method-
tcr,e= elstic critical share stress=
[(KvXπ2XE)/(12(1-μ2)(d/tw)2)]
As per Cl.No. 8.7.2.4, Pg.No. 66 assume (c/d)=1.40
Kv= 5.35+4/(c/d)2 if (c/d)>1.0
Kv= 5.35+4/(1.4)2 = 7.39
tcr,e=[(7.39Xπ2X2X105)/(12(1-0.32)(2160/12)2)]
= 41.22 MPa
λw= √(fyw/√3Xtcr,e )
= 1.8710 > 1.2
τb= [(fyw)/(√3Xλw2)]
= 41.23 MPa
Vn=Vcr= AvXτb= 2160X12X41.23= 1068.68 kN< 1908kN
use IS to improve the buckling strength of web.
38
2160X12
38
650
2236
(c/d)=1.4
c=1.4X2160= 3024mm
No. of panels= 24000/3024
= 7.93= 8nos.
C=24000/8= 3000mm
revised (c/d)= 1.38 < 1.40.......ok

6. Prof. Sudhir B. Gayake, SCOE Kopargaon
Design of end panel (Cl.No. 8.5 Pg.No. 60)
Shear capacity of end panel-
Hq= 1.25Vp[1-(Vcr/Vp)]0.5
Vp= (dXtXfy/√3)= (2160X12X250/√3)= 3741.22kN
Vcr= 1068.68kN
Hq= 1.25X3741.22[1-(1068.68/3741.22)]0.5 = 3952.56kN+
Resulting longitudnal shear=Rtf= (Hq/2)= 1976.28kN
Vd= (AvXfyw/√3Xγm0)= 3401.11 kN > Rtf...........end panel is safe to carry reaction.
Moment capacity of end panel-
Mtf= (HqXd/10)= (3952.56X1000X2160/10)= 853.75kNm
Design bending strength of end panel= Mq= (IXfy/yXγm0)
I=(twXc3/12)= (12X30003/12)= 27000X106 mm4 , y=(3000/2)=1500mm,
Mq=(27000X106X250/1500X1.10)= 4090.90 kNm > Mtf=853.75kNm
P7P6P5P4P3P2P1 P8

7. Prof. Sudhir B. Gayake, SCOE Kopargaon
Design of IS-As per Cl.No. 8.7.2.4, Pg.No. 66
(c/d)=1.38 < √2
adopting thickness of stiffner as tw=12mm;
Is= (1.5d3tw3/c2)
= (1.5X21603X123/30002)= 2.90X106 mm4
Maximum outstand possible= (650-12)/2=
319mm ,
Minimum outstand required= 14tq= 168mm ,
Maximum outstand not greater than= 20tq=
280mm .
adopt outstand= 240mm ,
use IS of size= 240X12mm alternate pattern
Ixx= (Ig+Ah2)=
[(12X2403/12)+(240X12X1262 )]+[12X4803/12)]=
170X106 mm4 > Is=2.90X106 ...........safe for MI
required.
240X12
20XtqX2
B
B
A
A
PLAN
SECTION B-BSECTION A-A

8. Prof. Sudhir B. Gayake, SCOE Kopargaon
Design of EBS-
use EBS of size= 280X12mm on both sides of web
Aeff= [2X280X12+2X20X12X12]
= 12480 mm2
Izz=
2[(12X2803/12)+(280X12)X(146)2]
+[480X123/12]
= 187.21X106 mm4
r=(√I/A)= 122.50
KL/r= (0.7X2160/122.50)= 12.34
For buckling class c refer table 9(c) . fcd= 226.29MPa
Pd= 12480X226.29= 2824kN
Max Vu = 1908kN <Pd for EBS ......safe.
Connection of IS and EBS with web of girder(Cl.No.8.7.2.6 Pg.No.
67)
Shear carried by stiffners= (tw2/5bs)= (122/5X240)= 0.10kN/mm
adopt s=5mm , t=0.7X5= 3.5mm
280
12
2X20tq
design strength of fillet weld=fwd=
=(1X3.5X410/√3X1.25)
= 0.662kN/mm > 0.10kN/mm.....safe