Steel Truss Bridge Design Example

1.0

Introduction This design note consists of 40m through trussed bridge.

The analysis of the structure has been done by a complete mathematical modelling using STAAD-Pro analysis software, while the design is done manually in line with the procedure & parameters laid down in the following standards: 1. 2. 3. 4. 5. 6.

IRC:6-2000 IRC:21-2000 IRC:22-1986 IRC:24-2001 IS:11384-1985 BS:5400-Part5:1979

2.0

Basic Design Data: Statical scheme

:

Main Girders

:

Cross Bracings

:

Top chord bracings

:

Simply supported N type trusses (2 sets) with concrete deck at the top acting compositely with the main longitudinals at locations of the joint of verticals & the top & bottom chord No bracing as the composite deck will serve the purpose At every panel, as crossed braces.

Bottom chord bracing : Span of Main girders (c/c of bearing)

:

40 m

Carriageway width

:

4.25 m

Crash barrier width

:

0.45 m

Total clear width of structure (span of cross girders)

:

5.15 m

Wearing coarse thickness

:

Cross fall on roadway

:

Minimum depth of slab

:

Live load

:

Density of concrete

:

2.5 t/m3

Density of wearing coarse

:

2.3 t/m3

Density of steel

:

7.85 t/m3

Grade of Concrete

:

M 20

Grade of Steel

:

Fe 540

Yeild Stress of Steel

:

390 MPa

Modulus of Elasticity of Steel

:

2.11E+05 MPa

Modulus of Elasticity of Conc.

:

Coefficient of thermal expansion Steel Concrete

: :

75 mm to be provided 100 mm for design purpose 2.5 % in both directions 200 mm 24 R

27500.00 MPa (as per IRC:21-2000 cl.303.1)

For class 25t tracked vehicle, impact factor (as per IRC:6-2000 cl.211.2 & figure 5)

0.000012 /°C 0.000012 /°C (as per IRC:22)

1.154

elling using STAAD-Pro ure & parameters laid

Design of Through Steel Bridge Effective Span 40.0m Calculation of Member properties Steel Members: Cross sectional area (A) (m2): C.g. distance from top (m): C.g. distance from left (m):

10

255

10 275

Bottom chord.(ND-1)

250

Ix-x (I about x-axis)

(m4):

Iy-y (I about y-axis)

(m4):

0.0101 0.1375 0.125 0.0001154585 0.000099524

Ix-y (torsional constant) (m4):

0.0001601964

Cross sectional area (A) (m2): C.g. distance from top (m): C.g. distance from left (m):

0.0101 0.1375 0.125

230

10

255

10 275

Bottom chord.(ND-2)

250


(m4):


(m4):

0.0001154585 0.000099524


0.0001601964


0.0101 0.1375 0.125

230

10

255

10 275

Bottom chord.(ND-3)

250

Ix-x (I about x-axis) (m4): Iy-y (I about y-axis) (m4):

0.0001154585 0.000099524


0.0001601964


0.0101 0.1375 0.125

230

10 FX 230

255

10 275

Top chord.ND-1

250

Ix-x (I about x-axis) (m4): Iy-y (I about y-axis) (m4):

0.0001154585 0.000099524


0.0001601964


10

255

10 275

Top chord.ND-2

250


(m4):


(m4):

0.0101 0.1375 0.125 0.0001154585 0.000099524


0.0001601964


0.0101 0.1375 0.125

230

10

255

10 275

Top chord.ND-3

250


(m4):


(m4):


0.0001154585 0.000099524 0.0001601964

230 8 Cross Sectional Area (m 2) C.g. distance from bottom (m) C.g. distance from left (m)

8 x

x

234

Vertical Member.

100 y

IX-X (m4)

0.00003198

IY-Y (m4)

0.00000134 0.00000007

Torsional Constant (m4)

y

8

100

0.0035 0.1250 0.0500

Zt (m3)

0.0003

Zb (m3)

0.0003

ZLeft (m3)

0.0000

ZRight (m3)

0.0000


8

234

8 250

Diagonal Member.

250


(m4):


(m4):

Ix-y (torsional constant) (m4): 234

0.0077 0.125 0.125 0.00007567 0.00007567 0.0001133799

Cross Sectional Area (m 2) C.g. distance from bottom (m) C.g. distance from left (m)

x

465.2

x

IX-X (m4)

y

17.4

150

X

X

Y 2-ISA50x50x6 Face to face with 20 mm gap in between 150 8 y

8 x

x

0.0003829 0.0000098


0.00000058

Zt (m3)

0.0015

Zb (m3)

0.0015

ZLeft (m3)

0.0001

ZRight (m3)

0.0001


(m4):

Iy-y (I about y-axis) (m4): Ix-y (tortional constant)

150

8

0.0001136 0.00000 0.03780 0.00000026

(m4):

0.00000256 0.00010 0.00000

zt (m3):

0.00001

zb (m3):

0.00000

Cross Sectional Area (m 2) C.g. distance from bottom (m) C.g. distance from left (m)

0.0043 0.1250 0.0750

IX-X (m4)

0.0000437

IY-Y (m4)

0.0000045 0.00000008


y

0.0096 0.2500 0.0750

IY-Y (m4)

Cross sectional area (A) (m2): (2-22 hole on each leg) C.g. distance from top (m):

Y

234

Top Main Transverse Member.

17.4

9.4

Top & Bottom Bracing Member.

Bottom Transverse chord.(ISMB 500)

150 y

Zt (m3)

0.0003

Zb (m3)

0.0003

ZLeft (m3)

0.0001

ZRight (m3)

0.0001

Design Of Bottom Transverse Member 0.925 m 6.412 kn

10.87 dead load 4.313 SIDL

6.412 kn

6 m DEAD LOAD ANALYSIS 1 I) ii) iii) iv) 2 I) ii) iii) iv)

Load calculation. Due to deck slab= =0.23182*2.5*1.875*10 Due to kerb & railing = =2.461*1.875+0.454*1.875 Due to future overlay= =0.1*1.875*2.3*10 Using ISMB550 as member= Moment calculation Moment due to dead load= =10.866563*6*6/8 Moment due to Railing & Kerb= =5.465*(6/2-0.925) Moment due to overlay butemen= =4.3125*6*6/8 Moment due to ISMB550 =1.037*6*6/8

10.8665625 5.465625 4.3125 1.037

kn/m kn kn/m kn/m

48.8995313 11.3411719 19.40625 4.6665

knm knm knm knm

LIVE LOAD ANALYSIS 64.04 kn

64.04 kn

520 A Reaction at A=Ra=

1560 B

6 m =64.04(2.98+5.06)/6

Moment at mid span=

85.8136 KNM 263.785883 knm

Load combination 1 Dead load + Deck Load= 2 SIDL+LL=

53.5660313 knm 294.533305 knm

Only steel member Z required=

357106.875 mm3 357.106875 cm3

Using ISMB 550 Zxx= Check for only steel member Calculated bending compression stress= Calculated bending tension stress= Check for composite section Stress at level1 Stress at level4

2359.8 cm3

22.70 Mpa 22.70 Mpa

Hence ok Hence ok

5.4889317 Mpa -96.334557 Mpa

Hence ok Hence ok

Calculation of section properties Modular ratio(m): Creep Factor(Kc):

10 0.5

Moduar ratio for permanent loadings(mp):

20

Moduar ratio for transient loadings(mt):

10

Sectional Properties of Top Chord: Member Profile: 0 200

3.0

Basic Property of ISMC 225: (refer IS:808-1989) Sectional Area (A): IXX : 2694.6 cm4 CYY : 2.3 cm

X

25.9 cm

2

IYY :

Thickness of Flange (Av.), tf =

187.2 cm4

0

12.4 mm

Thickness of Web, tw =

6.4 mm

For Steel Only Case: Area of Top Chord: (25.9*2*100-2*12.4*22-2*2*6.4*22)/10^6 = (Assuming 2-22 hole on the web & 1-22 hole on top flanges of the channels) C.g. Distance from top: Ix-x (I about x-axis) (m4):

2*(2694.6*1e+04)/1e+012 =

Iy-y (I about y-axis) (m4): 2*(187.2*10000+25.9*100*(2.3*10+80)^2)/1e+012 = For Composite (short term loading) Case: Area of Top Chord:

0.0041+(2575/10*200)/10^6 =

C.g. Distance from top: (0.0041*(0.2+0.1)+(2575*200/10*200/2)/1e+09)/0.0555712 =

m = mt

180

Ix-x (I about x-axis) (m4): 0.000054+0.0040712*(0.2+0.1-0.115)^2+ (2575*200^3/12+(2575*200*(200/20.115*1000)^2))/10/1e+012 = Iy-y (I about y-axis) (m4): 0.000059+((200*2575^3/12)/10)/1e+012 = m = mp

For Composite (long term loading) Case: Area of Top Chord: 0.00407+(2575*200+(6+0)/2*1)/(20*10^6) = C.g. Distance from top: (0.0041*(0.2+0.1)+(200*2575*100)/20/1e+09)/0.0298 = Ix-x (I about x-axis) (m4):

0.00005+0.0041*(0.2+0.1-0.12744)^2+((2575*200^3/12+2575*200*(127.44200/2)^2)/20)/1e+012 = Iy-y (I about y-axis) (m4): 0.000059+((200*2575^3/12)/20)/1e+012 = The other properties are calculated in line to above calculation & are tabulated as below: Value

Memb er

Profile

Item

Steel only

2575 Cross cestional area (A) (m2): 0.00407 (2-22 hole on web, 1-22 hole on flange) C.g. distance from top (m): 0.100

X

X 0

0

Top Chord

1 200

Y

Ix-x (I about x-axis) (m4): Iy-y (I about y-axis) (m4): Ix-y (tortional constant) (m4):

0.000054 0.000059 0.0001

6 Y 2-ISMC225 Back to back with 160 mm gap in between

zt (m3):

0.0005

zb (m ):

0.0002

3

Value

Memb er

Profile

Item

Steel only

Cross sectional area (A) (m2): 0.00407 (2-22 hole on web, 1-22 hole on flange) C.g. distance from top (m): 0.100

X

X

0


0.000054 0.000059 0.0001

0

Bottom Chord

Y

Y 2-ISMC225 Back to back with 160 mm gap in between

zt (m3):

0.0005

zb (m ):

0.0005

3

Cross cestional area (A) (m2): (2-22 hole on web) C.g. distance from top (m):

0.00511 0.100

Y Verticals

Ix-x (I about x-axis) (m4): X

X

Y 2-ISMC200 Face to face with 160 mm edge to edge dist.

Iy-y (I about y-axis) (m4): Ix-y (tortional constant) (m4):

0.000036 0.000022 0.0001

zt (m3):

0.0004

zb (m3):

0.0004

Value

Memb er

Profile

Item


Diagonals

Y

X

X

Y 2-ISMC150 Face to face with 160 mm edge to edge dist.


0.00511 0.100 0.000036 0.000022 0.0001

zt (m3):

0.0004

zb (m ):

0.0004

3

Cross cestional area (A) (m2): (2-22 hole on web) C.g. distance from top (m): Bottom Bracing

Steel only

0.00057 0.004

Y Ix-x (I about x-axis) (m4): Iy-y (I about y-axis) (m4): X

X

Y ISMA 50x50x6

Ix-y (tortional constant) (m4):

0.0000001 0.0000001 0.0001

zt (m3):

0.000036

zb (m ):

0.000003

3

Value

Transversals at locations other than Xbracings

Transversals at cross bracing location

Memb er

Profile

Item


Steel only 0.00370 0.075

Y

X

X

Ix-x (I about x-axis) (m4): Iy-y (I about y-axis) (m4): Ix-y (tortional constant) (m4): zt (m3):

0.0002

zb (m ):

0.0002

3

Y 2-ISMC150 Back to back with 20 mm gap in between

0.000016 0.000006 0.0001


0.00169 0.075

Y Ix-x (I about x-axis) (m4): X

X

ISMB150

Y

Iy-y (I about y-axis) (m4): Ix-y (tortional constant) (m4):

0.000007 0.000001 0.0001

zt (m3):

0.0001

zb (m3):

0.0001

Value

Memb er

Profile

Item

Transvers Diagonals


Steel only 0.00140 0.075

Y

X

X

ISMC150

Y


0.000008 0.000001 0.0001

zt (m3):

0.0001

zb (m ):

0.0001

3

* mt = Properties of composite section using modular ratio as mt # mp = Properties of composite section using modular ratio as m p

2575 Y

X 0

180 0 Y 2-ISMC225

Back to back

0.0041 m2

0.1 m 0.000054 m4

0.000059 m4

0.0556 m2

0.115 m

0.000376 m4

0.028515 m4

0.0298 m2

0.127 m

0.000282 m4

0.014287 m4

e tabulated as below: Value mt

*

mp #

0.05557

0.02982

0.115

0.127

0.000376 0.000280 0.028515 0.014287 0.0001 0.0001 0.0033

0.0022

0.0008

0.0010

Value mt

*

mp #

Value mt

*

mp #

Value mt

*

mp #

Value mt

*

mp #

Calculation of Member properties Composite Members M20 25491.17 N/mm2 211000 N/mm2

Grade of Concrete = E of Concrete = E of Steel =

8.28 16.55

Modular Ratio for Short term loading = Modular Ratio for Long term loading = Member

Sectional Properties Short Term  = 8.28 (all in Steel units, except where specified otherwise)

Profile 200

1875 190 A

y

Level 1

B

x 8

x

19.3

515.6

11.2

Level 4

y 190

IX-X (m4)

0.0016

IY-Y (m4) Torsional Constant (m4)

0.0177 0.00001

Z1 (m3) (in concrete units)

0.0537


0.2961

Z3 (m3)

0.0358

Z4 (m3)

0.0031

ZA (m3) (in concrete units)

0.1562

ZA (m3)

0.0189

ZB (m3)

0.1862

ZC (m3)

0.1862

Cross Sectional Area (m2) C.g. distance from bottom (m) C.g. distance from left (m)

0.0455 0.4858 0.3788

IX-X (m4)

0.0015

IY-Y (m4) Torsional Constant (m4)

0.0045 0.00001


0.0437


0.1580

Z3 (m3)

0.0191

Z4 (m3)

0.0030

ZA1 (m3) (in concrete units)

0.0595

ZA3 (m3)

0.0072

ZB (m3)

0.0211

ZC (m3)

0.0211

ZD (m3)

0.0112

ZE (m3)

0.0112

19.3

937.5 y

Level 1

A

F

190

200

70

19.3

x 515.6

x

8

E

B

Level 2 & Level 3

C

11.2

D

Transverse Girders (Type 2)

0.0734 0.0131 0.5179 0.9375

& Level 3

C

Transverse Girders (ISMB 550)

Level 2

Cross Sectional Area (m2) Area steel only(m2) C.g. distance from bottom (m) C.g. distance from left (m)

Level 4

190

19.3 y

ZF3 (m3)

0.0119

ZF1 (m3) (in concrete units)

0.0987

Long Term  = 16.55 Cross Sectional Area (m2) Area steel only(m2) C.g. distance from bottom (m) C.g. distance from left (m)

0.0508 0.0131 0.3389 0.9375

IX-X (m4)

0.0015

IY-Y (m4)

0.0111 0.000002

Torsional Constant (m4) Z1 (m3) (in concrete units)

0.0585


0.1108

Z3 (m3)

0.0067

Z4 (m3)

0.0044

ZA (m3) (in concrete units)

0.1952

ZA (m3)

0.0118

ZB (m3)

0.1163

ZC (m3)

0.1163

Cross Sectional Area (m2) C.g. distance from bottom (m) C.g. distance from left (m)

0.0333 0.4513 0.3332

IX-X (m4)

0.0013

IY-Y (m4)

0.0032 0.000002

Torsional Constant (m4) Z1 (m3) (in concrete units)

0.0697


0.1955

Z3 (m3)

0.0118

Z4 (m3)

0.0029

ZA1 (m3) (in concrete units)

0.0793

ZA3 (m3)

0.0048

ZB (m3)

0.0192

ZC (m3)

0.0192

ZD (m3)

0.0090

ZE (m3)

0.0090

ZF3 (m3)

0.0097

ZF1 (m3) (in concrete units)

0.1605

3.0

Calculation of section properties Modular ratio(m): Creep Factor(Kc):

10 0.5

Moduar ratio for permanent loadings(mp):

20

Moduar ratio for transient loadings(mt):

10 Value

Memb er

Profile

Item

Steel only

2575 Cross cestional area (A) (m2): 0.00858 (2-22 hole on web, 2-22 hole on flange) 0.059 C.g. distance from top (m):

X

Top Chord

1 200

Y

X

Y 1/2-ISMB500 Top Fl. Width = Top Fl. thickness = Web Thickness = with 260 plate on top

180 mm 17 mm 10.2 mm x 20 thk

Bottom Chord

Y

0.000048 0.000038 0.0001

zt (m3):

0.0008

zb (m3):

0.0002

Cross sectional area (A) (m2): 0.00893 (2-22 hole on web, 2-22 hole on flange) C.g. distance from top (m): 0.248

X

X

Y 1/2-ISMB600 Top Fl. Width =


210 mm

Top Fl. thickness = 21 mm 12.0 mm Web Thickness = with 210 x 16 thk plate on bottom


0.000081 0.000028 0.0001

zt (m3):

0.0003

zb (m3):

0.0012

Value

Memb er

Profile

Item


Steel only 0.00395 0.100

Verticals

Y

X

X

Y 200NB (Heavy) Tube

Diagonals

X

Y 2-ISA130x130x15 Face to face with 20 mm gap in between

0.000022 0.000022 0.0001

zt (m3):

0.0002

zb (m3):

0.0002

Cross sectional area (A) (m2): (2-22 hole on each leg) C.g. distance from top (m):

Y

X



0.00434 0.038 0.000011 0.000022 0.0001

zt (m3):

0.0003

zb (m3):

0.0001

Value

Memb er

Profile

Item

Steel only

Bottom Bracing


0.004

Y

X

X

Y ISMA 50x50x6

Transversals at cross bracing location

0.00044


1.29E-07 1.29E-07 0.0001

zt (m3):

0.000036

zb (m3):

0.000003

Cross cestional area (A) C.g. distance from top

(m2):

(m):

0.00101 0.033

Y

X

X

Y 65NB (Heavy) Tube


0.000001 0.000001 0.0001

zt (m3):

2.00E-05

zb (m ):

2.00E-05

3

Value

Transvers Diagonals

Transversals at locations other than Xbracings

Memb er

Profile

Item


Steel only 0.00101 0.033

Y

X

X

Y 65NB (Heavy) Tube


0.000001 0.000001 0.0001

zt (m3):

2.00E-05

zb (m3):

2.00E-05


0.00136 0.003

Y

X

X

Y ISA 100x100x8


0.0000015 0.0000015 0.0001

zt (m3):

0.000526

zb (m3):

0.000015

* mt = Properties of composite section using modular ratio as mt # mp = Properties of composite section using modular ratio as mp

erties

Value mt

*

mp #

0.06008

0.03433

0.123

0.140

0.000405 0.028494 0.0001

0.000296 0.014266 0.0001

0.0033

0.0021

0.0012

0.0009

Value mt

*

mp #

Value mt

*

mp #

Value mt

*

mp #

4.0

Load Calculation

4.1

Selfweight of truss

Selfweight of the truss is inserted in the analysis through the use of "SELFWEIGHT" command of STAAD. However, the total load is increased by 7% to take care of the gussets, joints & variation in member weights due to rolling margin, which otherwise is not accounted for. 4.2

Dead Load due to deck The deck is proposed to be cast after erection of the trusses and all bracings in place. The weight of the deck concrete thus will be carried by the two truss only. Running thickness of the deck:

200 mm

Additional thickness at the center for cross slope at deck:

53.125 mm

Integral Wearing Coarse :

12 mm

So, average (weighted) thickness of deck:

231.82 mm

So, Weight of the deck on the truss in running portion: 231.82*/2000**10 = 14.92 kN/m load on each transverse girder due to deck slab= =2.5*231.82*2.5*10/1000 14.49 kN/m

Superimposed Dead Load a. Due to kerb 425

225

4.3

0.5*(0.45+0.425)*0.225**10 =

2.461 kN/m

450 b. Due to Railing 1. 1200 LONG ISMC 150 @ 1000c/c 2. 4 Nos 65NB (Medium) Pipe

1.2*16.4*10/1000 = 4*6.42*10/1000 = Total

0.197 kN/m 0.257 kN/m 0.454 kN/m

c. Due to Future Overlay of Bituminous Wearing Coarse =2.50*2.3*0.1*10 Net Load :

5.750+0.454+2.461 =

5.75 kN/m 8.665 kN/m

Page 31 of 63

4.4

Live Load Since the other type of loads in 24R category are lesser in total weight & they are spread out over larger spaces also, we are considering 24R Tracked Vehicle only for live load actions, as this shall produce the most severe actions. Live will be generated and applied for one lane Class 24R vehicle within the STAAD analysis on the top chord only. Impact factor: (refer IRC:6-2000 cl.211.2 and figure 5.)

4.5

1.154

Seismic Load

6. Calculation of Actions Due To Seismic Load 6.01 Arunachal Pradesh Section is in Seismic Zone

V

Type of Soil

Ah

Medium Soil

=

Horizontal Seismic Coefficient (Z/2)*(Sa/g)/(R/I)

=

0.18

=

Vertical Seismic Coefficient

=

0.09

Z

=

Zone factor

=

0.36

I

=

Importance factor

=

1

R

=

Response reduction factor

=

2.5

Sa/g

=

Average response acceleration coefficient (depending upon fundamental time period T)

=

2.5

T

=

Fundamental Time Period 2.0*sqrt(D/1000F)

=

0.33

sec

F

=

Horizontal Force in KN required to be applied at the centre of the superstructure for 1mm deflection at the top of pier/abutment (6EI/L3)

=

68.7

t



=

Deflection at the top of Pier/abutment

=

1

I

=

Moment of Inertia of the Pier/Abutment (()*d4/64)

=

0.785

m4

d

=

Diameter of the Pier/Abutment

=

2.0

m

G

=

Grade of Concrete for Pier/Abutment

=

M20

E

=

Modulus of Elasticity of Concrete 5700*sqrt(fck) as per IRC:18,2000 Cl:10.2

=

25491.17 Mpa

=

3.15E+06 t/m^2

Av

mm

Page 32 of 63

L

=

Height of the Pier/Abutment above Fixity Level

=

6.000

m

D

=

Appropriate Dead Load of the Superstructure and Live Load

=

1884.69

t

TOTAL LOAD ON SUPERSTRUCTURE Top Chord : Bottom Chord : Verticals : Diagonals : Vertical Short Member : Vertical Short Diagonal Member : Transversals (Bottom): Transversals (Top): Top Bracings : Total Steel Work: Add 7% for gussets & Connections : Gross Weight :

63.428 63.428 29.436 99.993 13.082 39.997 112.956 18.109 1.466 441.895

kN kN kN kN kN kN kN kN kN kN

30.933

kN

472.828

kN

Deck Slab : kerb, railing : Wearing course overlay :

Refer sectional area of corresponding member given in Property Calculation page

0.23182***40*10 = 477.556 kN (2.461+0.4536)*40 *2= 233.163 kN 11.2786726358056*40 = 451.14691 kN

Total Weight of the Structure Including SIDL: Total Weight of the Structure Excluding SIDL:

472.83+477.56 =

1634.694 kN 950.384 kN

Page 33 of 63

Live load arrangement on deck during earthquake: 3660

3660

25t

25t

30 40000 Maximum live load on the deck = So, Live load on the bridge for seismic case:

2*25 =

50 t 0.5*50*10 =

250 KN

0.18*(1,634.69+250) =

339.24 kN

339.24/32 = 10.60/2 =

10.60 kN 5.30 kN

So, net horizontal seismic force:

So, seismic force on interior nodes: and that on end nodes:

(Since the main contributor to this load is the concrete deck slab, so the force will be imposed on the mathematical model on the bottom chord nodes only)

Page 34 of 63

Wind Load (according to IRC:6-2000): Note:-Assuming height of formation level from river bed =20.m Wind load on the structure : Minimum bed level= Formation level=

20.00m

Hieght of formation level from river bed : Depth of Slab : Depth of bottom Girder :

200 mm 350 mm

Depth of top Girder : Depth of vertical member: Depth of diagonal member:

350 mm 100 mm 300 mm

136.00 kM/H 139.6 kM/H

Wind Speed at deck level : Wind Speed at a height of 23.00from bed level : Wind Speed at a height of 26.0m from bed level :

143 kM/H

So, Wind force on the deck =

0.065 t/m

& Wind force on top girder:

0.048 t/m

Wind Force Height from river bed 20.00m 0.042 t/m (on 23.00m 0.013 t/m (on 23.00m 0.041 t/m (on 26.00m 0.048 t/m (on 26.00m 0.014 t/m (on 26.00m 0.041 t/m (on Wind load on exposed moving load (as per cl.212.4 of IRC:6-2000) : = =

300 kg/linear meter 0.3 t/linear meter

Pressure at that level: Pressure at that level: Pressure at that level:

0 20

119 126.5 136.6

the bottom chord) vertical member) diagonal member) the top chord member) vertical member) diagonal member)

As wind speed is more than 130km/hr no live load considered for wind load analysis.

As per cl.212.6 of IRC:6-1966 minimum wind load on structure :

450

kg/linear meter

Page 35 of 63

7.2863

Page 36 of 63

Page 37 of 63

Page 38 of 63

Page 39 of 63

kg/m2 kg/m2 kg/m2

Page 40 of 63

5.0

Design of truss members

CL SYMM.

ND 103

5.1

ND 102

Recapitulation of member forces

(From STAAD Output)

(Sign Convention: +ve : Compression, Sagging Moment, -ve : Tension, Hogging Moment)

(Values corresponding to live load case are inclusive of impact factor) a. Top Chord Axial

Shear

Moment Midspan Support (kN-m) (kN-m)

ND 103

ND 102

ND 101

(kN) (kN) Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Seismic Vertical Wind load Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Seismic Vertical Wind load Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Seismic Vertical Wind load Legend: 'ND' represents a segment, comprising of a "top chord", a "bottom chord", a "diagonal" and a "vertical member". The vertical member to the left of panel is a part of the segment under consideration.

ND 103

ND 102

ND 101

b. Bottom Chord

Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Seismic Vertical Wind load Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Seismic Vertical Wind load Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Seismic Vertical

Axial

Shear

(kN)

(kN)

Moment Midspan Support (kN-m) (kN-m)

ND 101

ND 103 Wind load

c. Long Verticals Axial Forces in (kN) ND 101 ND 102 ND 103 Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Load Seismic Vertical Wind load d. Long Diagonals Axial Forces in (kN) ND 101 ND 102 ND 103 Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Shrinkage Load Seismic Horizontal Load Seismic Vertical Wind load e. Short Verticals Axial Forces in (kN) ND 101 ND 102 ND 103 Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Shrinkage Load Seismic Horizontal Load Seismic Vertical Wind load e. Short Diagonals Axial Forces in (kN) ND 101 ND 102 ND 103 Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Shrinkage Load Seismic Horizontal Load Seismic Vertical Wind load f. Transvarsals (at top) Axial Forces in (kN) ND 101 ND 102 ND 103 Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Load Seismic Vertical Wind load

h. Top Bracings Axial Forces in (kN) ND 101 ND 102 ND 103 Selfweight of Truss Deadweight of deck slab Superimposed deadload Live load Seismic Horizontal Load Seismic Vertical Wind load

5.2

Calculation of Allowable Stresses a. Top Chord. Permissible axial compressive stress in concrete:

5.0 MPa (From IRC:21-2000 cl.303.1)

Permissible flexural compressive stress in concrete:

6.67 MPa (From IRC:21-2000 cl.303.1)

Permissible axial tensile stress in concrete:

0.53 MPa (From IRC:21-2000 cl.303.3)

Permissible stresses in steel lxx = lyy =

Effective length of member: Radii of gyration :

Maximum slenderness ratio:

5625= 5625=

5625 mm 5625 mm

rxx =

106.92 mm

ryy =

99.27 mm

=

5625/99.3 =

56.67

Allowable stress in axial compression :

175.34 MPa

Allowable stress for axial tension :

234.00 MPa

Flexural compressive stress: (in steel)

Since the top flange of the beam will be supported by the concrete deck throughout its length, so the allowable compressive stress shall be same as allowable tensile stress.

Allowable stress in bending tension:

241.80 MPa

Allowable stress for equivalent stress for combined actions:

358.80 MPa

Allowable average shear stress: Allowable maximum shear stress:

148.20 MPa 167.70 MPa

b. Bottom Chord. Effective length of member:

lxx = lyy =

1875 mm 1875 mm

Radii of gyration :

rxx = ryy =

106.92 mm 99.27 mm

Maximum slenderness ratio :

=

18.89


234.00 MPa


234.00 MPa


241.80 MPa


358.80 MPa


148.20 MPa 167.70 MPa

c. Verticals Effective length of member: Radii of gyration :

lxx =

6000 mm

rxx =

95.97 mm

ryy = Maximum slenderness ratio :

6000 mm

lyy =

=


19.67 mm 305.04 18.00 MPa


234.00 MPa

Allowable stress in bending compression:

241.80 MPa


241.80 MPa


358.80 MPa


148.20 MPa 167.70 MPa

d. Diagonals Effective length of member: Radii of gyration : Maximum slenderness ratio :

lxx =

4110.0 mm

lyy =

4110.0 mm

rxx = ryy =

98.85 mm 98.85 mm

=

41.58


206.84 MPa


234.00 MPa


241.80 MPa


358.80 MPa


148.20 MPa 167.70 MPa

e Main Transversal at top Permissible stresses in steel Effective length of member:

lxx = lyy =

6000 mm 6000 mm

Radii of gyration :

rxx = ryy =

32.49 mm 101.13 mm

=

184.66

Maximum slenderness ratio : Allowable stress in axial compression : Allowable stress for axial tension :

32.60 MPa 234.00 MPa

f Bottom Transvarsals Permissible stresses in steel Effective length of member:

lxx = lyy =

6000 mm

Radii of gyration :

rxx =

199.80 mm

ryy =

31.99 mm

Maximum slenderness ratio :

=


6000 mm

187.53 31.74 MPa

Allowable stress for axial tension : Allowable stress for bending compression tension :

234.00 MPa 257.40 MPa

I. Top Bracing Member. Permissible stresses in steel Effective length of member:

Radii of gyration :

Maximum slenderness ratio : Allowable stress in axial compression : Allowable stress for axial tension :

lxx =

4110 mm

lyy =

4110 mm

rxx = ryy =

150.07 mm

=

47.66 mm

86.24 31.74 MPa 234.00 MPa

Note:-All the allowable stresses will be increased by 25% incase of wind load is considered and 40% when seismic load is considered.

7.0 Check for truss during construction stage During construction, it is assumed that the 40% of the deck shall be supported by the top chord of the truss & the rest by proper & adequet arrangement of propping from the top transversals & bottom chord. Additionaly, construction stage loading of 150kg/m2 is also considered. Modified forces in the members: Top Chord: Axial 0.0

Moment 0.0

Shear 0.0

Weight of the green concrete

0.0

0.0

0.0

=(2.6/2.5)*corresponding values of member forces for deck loading =(1.5/2.5)*corresponding values

Construction Stage Loading

0.0

0.0

0.0

of member forces for deck loading

Selfweight

Other members will not be checked as they are already safe with much higher loads & without any change in properties. Allowable stresses in top chord: Effective length of member: Radii of gyration :

rxx = ryy =

Maximum slenderness ratio:

lxx = lyy =

2500 2500

(0.000/0.009)^0.5*1000 = (0.00004/0.009)^0.5*1000 =

74.41 66.24

=

37.74


213.39 MPa


234.00 MPa

Calculation of allowable stress in bending compression: c1 = 58.9 mm c2 = 191.1 mm D= 250 mm T= 17.2 mm l= 2125 mm ry = 66.2 mm k1 = 1.0 k2 = = 0.005

-1

Y= = 26.5*10^5/(2125/66.2)^2 = 2575 X = = 2575*sqrt(1+(2125/20)*((2125*17.2)/(66.2*250))^2) = 58642 fcb = = 1*(58642-1*2575)*(59/191) = 17264 Allowable stress in bending compression:

164.00


241.80


148.20 167.70

Actual Stresses: Axial:

(0.0+0.0+0.0)/(0.0086*1000) =

0.00

Flexural Tension : Flexural Comp. :

(0.00+0.00+0.00)/(-0.0002*1000) = (0.00+0.00+0.00)/(0.0008*1000) =

0.00 0.00

Shear:

(0.00+0.00+0.00)/(0.00858496*1000) =

0.00

Net Stresses:

(max) (min)

0.00 0.00

All stresses are within the allowable limit.

0.00+0.00 = 0.00+0.00 = Hence, OK.

be supported by the top f propping from the top

.5)*corresponding values ber forces for deck

.5)*corresponding values ber forces for deck

much higher loads &

mm mm mm mm

MPa 6.2*250))^2) = MPa MPa MPa MPa MPa MPa

MPa MPa MPa MPa MPa MPa

DESIGN OF CONNECTION Dia of bolt= Bolt capacity Singel shear= Double shear= 1) BOTTOM CHORD Area of bottom chord= Maximum force carried by the member= No of bolts required= Provide= Dia of bolt= Bolt capacity Singel shear= Double shear= 2) TOP CHOTD Area of top chord= Maximum force carried by the top chord= No of bolts required= Provide= Dia of bolt= Bolt capacity Singel shear= Double shear= 3) VERTICAL MEMBER Area of vertical member= Maximum force carried by the vertical member= No of bolts required= Provide= Dia of bolt= Bolt capacity Singel shear= Double shear= 4) VERTICAL DIAGONAL MEMBER Area of vertical diagonal member= Maximum force carried by the diagonal member= No of bolts required= Provide=

20 3.4 6.8 0.0101 244.218 36.2 32 20 3.4 6.8 0.0101 177 26 28 20 3.4 6.8 0.003472 81.2448 12 10 20 3.4 6.8 0.007744 160 24 22

Dia of bolt= Bolt capacity Singel shear= Double shear= 5) TOP MAIN TRANSVERSE MEMBER. Area of transverse member= Maximum force carried by the transverse member= No of bolts required= Provide= Dia of bolt= Bolt capacity Singel shear= Double shear= 6) BOTTOM TRANSVERSE MEMBER. Area of transverse member= Maximum force carried by the transverse member= No of bolts required= Provide= Dia of bolt= Bolt capacity Singel shear= Double shear= 7) TOP BRACING MEMBER. Area of transverse member= Maximum force carried by the transverse member= No of bolts required= Provide=

20 3.4 6.8 0.00427 14 2 4 20 3.4 6.8 0.00959288 91.13236 13 14 20 3.4 6.8 0.0001136 2.65824 0.3938 4

mm ton ton m2 ton nos nos mm ton ton m2 ton nos nos mm ton ton m2 ton nos nos mm ton ton m2 ton nos nos

mm ton ton m2 ton nos nos mm ton ton m2 ton nos nos mm ton ton m2 ton nos nos

7.0

Design of end cross girder for jack-up condition

It is assumed that the superstructure will be needed to be lifted off the bearing for bear replacement. The jacks shall be placed below the transverse member at the end. For this purpo the location of these jacks alongwith their capacity shall have to be engraved on the locat proposed.

1) Reaction on each each bearing=

409

KN

centre line. 409

kn

6 m

409 kn

0.45 A

B 5.1 m

Design of end cross girder. a) b) c) d)

Reaction on each bearing. Support moment= Maximium mid span moment= Maximum shear force=

409 184 184 409

Zxx required for the section=

kn knm knm kn

760559 mm3

Using ISMB 550 as end cross girder. Zxx of the girder=

2359800 mm3

Now maximum bending tensional stress= Now maximum compression stress=

78 mpa 78 mpa

Hence provide ISMB 500 as end cross girder. Dia of bolt= Bolt capacity Singel shear= Double shear=

20 mm 3.4 ton 6.8 ton

Maximum shear force of the member= No of bolts required Provide 8nos bolt.

409 kn 41 ton 6.05 nos

e bearing for bearing end. For this purpose aved on the location

8.0

Connection Design a. Splicing of 300x300x12 box used as top chord. C/s Area:

101 cm2

Reduction for holes:

28*2.2*12 =

Net Area:

73.92 cm2

138.24-73.92 =

27.08 cm2

Allowable stress in compression in the BOX:

175.34 MPa

So, total maximum load that the section can take : 64.32*100*137.45/1000 =

474.8095 kN

Assuming the BOLT shall all be site installed. So, the allowable stresses for bolts are (as per IRC:24-2001): in shear: in bearing:

0.33*250 = 0.67*250 =

82.5 MPa 167.5 MPa

So, bolt resistance in double shear = 2*82.5*/4*222/1000 = 62.72 kN & in bearing =167.5*12*22/1000 = 44.22 kN So, bolt value: No. of bolts required:

44.22 kN 474.809451207655/44.22 =

10.7 Nos. 20 Nos.

say

Thickness of the cover plate required = 6432/(1200-26*2.2) = 8.00mm on both side. So, provide 12mm thick cover plate on both side.. b. Splicing of 300x300x12 box used as bottom chord. C/s Area:

101 cm2

Reduction for holes:

32*2.2*12 =

Net Area:

84.48 cm2

138.24-84.48 =

16.52 cm2

Allowable stress in tension in the BOX:

234.00 MPa

So, total maximum load that the section can take : 53.76*100*150/1000 =

386.568 kN

Assuming the BOLT shall all be site installed. So, the allowable stresses for bolts are (as per IRC:24-2001): in shear: in bearing:

0.33*250 = 0.67*250 =

82.5 MPa 167.5 MPa

So, bolt resistance in double shear = 2*82.5*/4*222/1000 = 62.72 kN & in bearing =167.5*12*22/1000 = 44.22 kN So, bolt value: No. of bolts required:

44.22 kN 386.568/44.22 = say

8.7 Nos. 20 Nos.

The arrangement of bolts (using 4 bolts in one row) in the joint Thickness of the cover plate required =5376/(1200-32*22) = 8mm.plate on both side. So, provide 10mm thick cover plate on both side..

Axial compression (Table 11.1 of IRC:24-2001) Fy = 250 340 400

Bending compression (Table 8.2 of IRC:24-2001) fy 250 340 fcb

l = l/r 10

150

204

239

20

13

13

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

148 145 139 132 122 112 101 90 80 72 64 57 51 45 41 37 33 30 28 25 23 21 20 18

201 194 183 168 152 135 118 103 90 79 69 61 54 48 43 38 34 31 28 26 24 22 20 18

235 225 210 190 168 147 127 109 94 82 71 62 55 49 43 39 35 31 28 26 24 22 20 19

30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 420 440 460 480 500 520 540 560 580 600

19 25 31 36 41 46 51 55 60 64 67 71 74 78 81 84 87 89 92 94 96 99 101 103 104 106 108 110 111 113 114 115 117 118 119 120 121 122 124 126 128 130 131 133 134 135 136 137

19 26 31 37 43 48 54 59 64 68 73 77 81 85 89 93 97 100 103 106 110 113 115 118 121 123 126 128 130 133 135 137 139 141 143 144 146 148 151 154 157 159 162 164 166 168 170 172

620 640 660 680 700 720 740 760 780 800 850 900 950 1000 1050 1100 1150 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000 3500 4000 4500 5000 5500 6000

138 139 140 141 142 143 143 144 145 145 147 148 149 150 151 152 152 153 154 155 156 157 157 158 158 159 160 160 161 161 161 162 163 163 163 163 164

174 175 177 178 180 181 182 184 185 186 188 191 193 195 196 198 199 200 203 205 206 208 209 210 211 212 213 215 216 216 217 218 219 220 221 221 222

ression (Table 8.2 of IRC:24-2001)



1

0.9

0.8

0.7

0.6

k1

1

1

1

0.9

0.8

11473613 0.5 0.4

22947226 0 -0.2

0.5

190 225 210

168 210 190

175.34 213.39 206.84

239

235

235.44

400 13 19 26 32 38 44 49 55 60 65 70 75 80 84 89 93 97 102 105 109 112 116 119 122 126 129 132 135 137 140 143 145 148 150 152 155 157 159 161 165 169 172 175 178 181 184 187 189 192



k2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0.5 0.4 0.3 0.2 0.1 0 -0.2 -0.4 -0.6 -0.8 -1

Axial stress: (top chord) 50 60 30 40 40 50 Axial stress: (bottom chord) 10 20 Axial stress: (tension tie)

Bending compression (tension tie): 6000 0 164 6000 0 164 Axial compression (truss): 250 0 18 Bending compression (truss): 6000 0 222 Axial compression (bracing): 10 20 204 180 190 34 180 190 34 60 70 152 Bending compression (bracing): Bending compression (truss): 6000 0 222

0 -1790.2719 0 -143.87455 0

-81.07

0 86.065404 201 31 31 135

201.51 32.60 31.74 142.46

0 -1249.0755

194 196 198 200 202 204 205 207 208 210 213 216 219 222 224 226 228 230 233 236 238 240 242 243 245 246 248 250 251 252 253 255 257 258 259 259 260

0.5

0.4

0.3

0.2

0.1

0

0.7

0.6

0.5

0.4

0.3

0.2

Steel Truss Bridge Design Example

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