Egyptian steel lecture

7/30/2019 Egyptian steel lecture

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Chapter 14

Roadway Bridge


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contents

Roadway Bridge Floor

Side walks and Railings

Bridge Bracings

Design of lateral support at top chord of through

pony bridge

Cross Sections for wind Bracing End X-frame in deck bridges

Transmission of the braking forces the bearing


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Truss Bridges

A. Types of bridge trusses

B- Determination of forces in truss members

c. Proportioning of truss members

D- Box section for bridge trusses Top chords

Lacing bars, batten plates

Bottom chords

Diagonals

Verticals

Design of compression member

Design of Tension Members


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Design of Bolted Joint

Design of Battens and Diaphragms

Design of End Portals


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Roadway Bridge Floor

The floor of a Roadway Bridges consists of:

1. A wearing surface or Roadway Covering.

2. Sub floor transmitting the loads to the

stringers and X-girders.

The sub floor is similar to the solid floor of a

ballasted Railway Bridges. It may be timber, steel

floor or R.C. floor.

Back


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X.G

P

1-2 cm

5-6 cm

Timber floor (Type 1)

For bridges, generally two layers of flanks are provided.For calculating these flanks we assume that the maximum

wheel load is distributed over two flanks.


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Slab on X.G only

A

A

(1.2-1.5)m Rail way

(2.5-3.5) m

Sec A-A

X.G

(2.5-3.5) m

X.G X.G

Reinforced concrete floors (R.C. floor)

It may be supported by the main girders only, the X.G.

only or by stringers and X. girders. The span of the slab

may be 2.5 to 3.5 m, and thickness of slab to be 20 cm

nearly. The R.C. slab reinforcement, generally 12 bars

are used at least per one meter.


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Slab on M.G only

M.G

L.W.Br

U.W.Br

M.G

(2.5-3.5) m

M.G M.G


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Member to prevent

lateral buckling of web

Truss bracket

Kafre El-ziat Roadway Br.

Span of slab

Side walk stringer

M.G

Stringer

X.G (truss)

X.F


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M.G

Stringer

U.W.Br

X.F

L.W.Br

X.G


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X.G

5 cm Asphalt

X.G every 150 cm

Wearing surface

The wearing surface for roadway covering consists

of timber blocks, hard bricks, asphalt bricks, stone blocks,asphalt or concrete.

The choice of material depends on the traffic, the span of

bridge, the cost and climate


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The side walks are placed either inside or outside of themain girder. If they are arranged outside, they must be

supported on cantilever brackets situated in the plane of

the X.G. so that theve bending moment of the bracket is

transmitted to the X.G. The floor of these side walksshould be a precast R.C. slab (6cm) thick resting on the

side walk stringers. The wearing surface is a 2 cm layer of

asphalt. In through bridges the curb should be at least 50

cm inside the main girder

Back

Side walks and Railings


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Take strip 1 m and statical system as continuous beamsupported on side walk stringer (one way slab), take t = 8

cm and get As. The applied loads are considered 500

kg/m2 or one concentrated load 5 t.

Hand railings and brackets withstand the effect of a

transverse horizontal force of 150 kg/ m in cases of

Railway bridges, Roadway bridges, and foot bridges,

supposed acting at top level of hand rail. This horizontal is

transmitted from the hand rail to the main posts and from

their connections to the cantilever brackets.

Side walks parts

1. Slab


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X.G

Stringer

6

2

110 cm

3

4

5

1

2. Hand rail

Simple beam span distances between two brackets (take angle or

channel X. sec.).

1. Side walk stringer

Simple beam span distance between two brackets (take channel X.

sec.)


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4 Post

Cantilever beam (take 2-angle or 2-channel X. sec.).

yP=M

KgL501=P

OROR

OOR

150 Kg/mM=W.L /82 2


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5 Connections

Double shear bolts

yP=M

KgL501=P

21

1d

dM=F

F1

F2

F2

F1

M


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6 Bracket

Calculate M& N& Q at center of bracket.In case of beam loaded alone we must calculate Fl.t.b and

the check that the actual stress Fc is less than the

S.F

+

+

N.FB.M


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allowable stress Fp.b.

For ST 37

If 100

If 100

2c 000065.040.1F

2

2c/

7500F cmt

= l/ i , where I for compression flange only.

for bracket l/ b 2 l/ b

assume unequal angle 80120

Bolts subjects to shear

21

1d

dM=F 2

221

2 dd2=d


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Bolts subjects to tension

A.Nt

IyM= 0.8 Ft

Nd1

d1

F1

F1

A

y


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Bridge Bracings

The bridge is provided with horizontal and

vertical bracings:-

1. The stringers are connected together bystringer bracing given before.

2. The chords of the main girders are jointed

together by an upper and lower horizontalbracing called wind bracings.


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These transmit to the bearings of the bridge;

a. The lateral forces due to wind.

b. The lateral shock 6t.

c. Centrifugal force.

3 - Special horizontal bracings for the braking forces.

4-Two vertical and transverse bracing called X-frames or

portals (in case of through) transmitting reaction of theupper lateral bracing to the bearings of bridge.

5- Some intermediate vertical transverse bracings called

intermediate X-frames or intermediate portals for therigidity of the structure.

It isnt necessary to find all these bracings in every bridge,

there existence depend upon the type of the bridge, the

span and the floor.


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I-The Deck Bridge

Deck Bridge.

U.W.Br

L.W.Br

End X Fram

The upper wind bracing transmits the wind

pressure WT on the train & WF on the floor & WG

on the wind ward side of the main girder.


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The lower wind bracing transmits the wind pressure

WG on the wind ward side of the main girder.

W = 100 kg/ m2 in case of loaded bridge

W = 200 kg/ m2 in case of unloaded bridge

* The wind pressure WT on the train produces in addition

to horizontal loading of the upper wind bracing.

a vertical loading, to the main girder.b

eW=V T


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M.G.G

W.F

W.T

L.W.Br

End X Fram

Dick

b

X.G

V e

3.5 m

U.W.Br

V=W .ebT


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In case of a truss bridge, only the exposed area of the

members is considered. This area is equivalent to 40 % of

the hole area of the surface of the truss. In all bridges with

an upper and a lower wind bracing, their shall be provided

End X Fram

L.W.Br

M.G

U.W.BrX.G

at each end a X-frame

to transmit to the

bearings,the

horizontal reactions of

the upper wind

bracing. The

horizontal reactions ofthe lower wind

bracing are

transmitted directly to

the bearings


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The end X-frames in deck bridges shall be of rigid

type. In all railways and in roadway deck bridges there

shall be intermediate transverse bracing at least at every

third panel point to increase the stiffness of the bridge.

These intermediate X-frames will release the end X-frame

from a part of the horizontal reaction of the upper wind

bracing. Yet it is recommended not to consider that release

unless the bridge as the space structure.


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ii-The Through Bridge

Through with upper bracing Bridge.

Portal Fram

U.W.Br

L.W.Br


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In through bridge two horizontal wind bracings should

be arranged if possible. In the plate girder through

bridges we cant arrange an upper wind bracing in the

bony truss Roadway Bridge we have only a lower wind

bracing which transmits all the wind loads to bearings.

The force WF on the floor will be considered to act on a

solid surface as the plate girder. The through RailwayBridge shown above is provided with two horizontal

wind bracings.


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W.F

W.G

Dick

3.5 m

U.W.Br

L.W.Br

Pony truss bracing

W.T

L.W.Br

2.5 m

W.G

W.F

W.T


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W.T

L.W.Br

3.5 m

Through

W.G

X.G

The upper wind bracing transmits the wind pressure

WG on the wind ward side of the main girder.

The lower wind bracing transmits the wind pressure (WG), WT on the train & WF on the floor & on the wind

ward side of the main girder.

At the connection ofeach X-G to the main

girder, stiffness

bracket shall be

arranged.

Back


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Design of lateral support at top

chord of through pony bridge C = force in flange = Af Ft

The U-frame formed by the two vertical stiffeners

and the horizontal stiff X-girder is acted upon by ahorizontal transverse force = C/100 at the centroidof compression flange as well as the wind pressurebetween two consequence X-girders. The

maximum stressed section is mn. The compressionstress at point n Fltb. If the stress isnt safe, weeither increase the thickness of the bracket plate oradd a stiffening angle.


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The connection between the X-girder and bracket is

designed on the shearing force A that between X-girder

and the bracket and horizontal gusset of wind bracing on

force B. if the X-G is built up section the bracket

connection is designed as a web splice.


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m X.G

n

m

C.G

n

Cos =1/2002x1/200xC=1/100xC

hord1/100 C

C

C


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B

1/100 C

B

W.G

A

X.G (Rolled section)

A

X.G

Back


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Cross Sections for wind Bracing

The diagonal of wind bracing

The diagonal of wind bracing shall have

stiff section to prevent vibration and to helpin reducing the deflection of main girder

due to eccentric loading (space frame

treatment). The section should have a depthnot less than L/40. The recommended

sections are given in Fig.(5.).


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h < L/40

h


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The choice of the section depends more or less upon the

span of the diagonal, the two channel section is convenient

for too long spans executed in Banha and Samanoodbridges. The two channels are connected together by

latticing or batten plates.

in compression & in tension

Gusset for U.W.Br.

Lacing

End patten plat

h


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In case of one diagonal member only

Case of the warren system which designed on a force S;

forcencompressiofor85.0

forcenfor tensio85.0

=S

call

tall

all

FF

FF

FSin

Q


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Case of the N-system which designed on a force S;

forcenfor tensio85.0

=S

tall

all

FF

FSin

Q

C f th K t Rh bi A d M lti l hi h


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Multiple without vertical system

Rhombic system

K- system

Case of the K-system , Rhombic And Multiple which

designed on a force S;

Q


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allFSin

Q

2=S

If the bracing is made up of crossed diagonal and struts,the calculation is made under the assumption that the

tension diagonal are only acting. The struts here receive

compression force. If the multiple systems of wind bracing

a further reduction of 20 % in the allowable stresses givenbefore, shall be made to account for approximation of

solution that both systems (tension and compression

member) equally share the lateral loads. in case of one

angle in compression the allowable compression stressshall be reduced by 40% of Fc.


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Hence, the approximations in allowable stresses are;

ncompressioinonly)sectionsic(unsemmetractionangleonefor0.6stressesReduce

ancyindeterminforionapproximattodue0.80stressesReduce

effectspacetodue0.85stressesReduce

A&forcencompressiofor6.08.085.0

3

3AA&forcenfor tensio8.085.0

eff.

21

1

1eff

gressbpall

tall

AFF

AAAFF

Back


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End X-frame in deck bridges

The compression diagonal is assumed in acting and we design the

tension diagonal, also we assume that the X-frame is resting at amovable support at one end and the hinge support at other end.

.W.Br

U.W.Br + 6 t X.G

Ru+Rl+6 t

Back

T i i f h b ki f h b i


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Transmission of the braking forces the bearing

In Railway bridges especial bracing should be arranged to

transmit the longitudinal forces from the stringers to thepanel points of the main girder, hence; they are transmitted

through the main girder to the hinged bearings. Some times

a bracing is arranged at every panel point. But generally

two bracings at the quarter points of bridge are sufficient.The braking bracing system shown in sketch is statically

indeterminate but the loads are symmetric about

perpendicular axes to X-X. Therefore the diagonal Bn &

cn are zeros since they correspond to themselves. Also, theloads are antisymmetric about axes Y-Y and thus members

mb & mc & nb & nc are zeros, If special bracing of the

longitudinal forces isomitted, these forces are transmitted

from stingers to main girder by bending of the X girder


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from stingers to main girder by bending of the X-girder.

8

B/4

B/4

B/8

B/8B/8

B/8

x

y

b'

b c

c'

2

2 3

y

B/4

B/8

B/8

B/4

B/4

4

B/8

B/8

xX.G

B/8

B/8

X.G

65

7

7

B/8

B/8

B/4

B/8

B/8

M.G

My/Zy

9

Back


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Truss Bridges

b L/ 20, b h/ 3

Where, b = bridge width = distance between center lines

of two main girders

L = span of bridge

The depth of trusses shall be chosen in such away that the

elastic deflection due to L.L (without dynamic effect)

shouldnt exceed L/800 for Railway bridges and L/600

for Roadway bridges.

Back


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b > L/20 , b


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Either both chords are straight and parallel or only one

of them. In a through bridge the upper chord may

polygonal, in a deck bridge the lower chord may be

polygonal. Curved chord should not be used in bridge

trusses on a account of the additional bending stresses.The loads are transmitted to the panel point of the truss

by a system of stringers and cross girder. No load except

the own weight of the truss members should act between

the panel point.

A. Types of bridge trusses

1 Trusses with horizontal chords


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They suitable for span up to 60 m. the joints are

simpler than in trusses with polygonal chords. The depthis h L/ 8 for Railway Bridge, or h L/ 10 for RoadwayBridge. For continuous and cantilever trusses the depth

may be taken h L/ 10 for Railway bridges, h L/ 12 for

Roadway bridges. Some times a greater depth is used toallow an upper wind bracing. The arrangement of web

members may be N-system or warren system. The warren

system trusses require generally less material than the N-

shaped trusses, since the vertical members have smallerforces, the number of joints and changes of cross section

in warren system are also less. Shop work for warren

trusses will be cheaper.

1.Trusses with horizontal chords


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N shaped

Warrren

h

h

N through

N through


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They are used for spans up to 60 m. the economical depth

at middle is h = L/7. The web system is either N-shapedor warren. The economical inclination of the diagonal to

horizontal = = 40 - 60. A polygonal chord trusseslighter than a truss with horizontal chords since the forces

in the diagonals are smaller. On the other hand the shop

work is more complicated which means a higher cost.

2-Trusses with polygonal chords

(0.5-0.7)h

= 40-60N or Warren

h=1/7 L


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3-Trusses with subdivided panels (e), with

Rhombic diagonal (f) and K-system

These kinds are economical for span over 80 m. The panellength is reduced in all this system and thus the cost of the

floor is less, but the increased number of joint increase the

cost of shop work. A truss with Rhombic diagonal has a

good appearance; a truss with subdivided panels has big

secondary stresses. K-system trusses have the smaller

secondary stress.


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Rhombic system

e- Subdived system

K- system

4 T ith lti l b t


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4- Trusses with multiple web system

These were used in past where the tension diagonals

consist of flat bars. Now they are again used for maingirders, but type h with crossed diagonals is frequently

used for wind bracing. For approximate calculation, the

common assumption is that the truss may be divided up

into two or more component trusses with the same chordsbut with different web system. The loads also are divided

and placed upon this component trusses. Then the stress in

a web member is determined as its stress calculated in the

truss of which it is a part. The chords are a part of allcomponent trusses, hence the stresses in a chord member is

obtained by adding it partial stress from each component

truss.


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= +

5- Trusses with 3 chords

The arch truss with a tie (k) and the truss reinforced by a

hinged arch (Pow string truss) are supported on a hingedbearing at one end and a movable bearing at the other.

They are therefore externally static determinant but

internally they are static indeterminate. These trusses

have good appearance but they more expansive than

trusses with two chords.


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Row String

Arch with atie

Back

b D t i ti f f i t b


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b- Determination of forces in truss members

We determine the forces in the truss members on the

assumption that the member are connected by hinges, so thatloads applied at the panel point produce only axial forces in

the truss member. The secondary stress which are the

bending stress induced by the rigidity in connection, are

generally neglected. In our specification it is required tocalculate the secondary stress in the following cases:

1- For trusses with subdivided panels.

2-For member whose width in the plane of the truss ismore than 1/10 of its length.

3-For loads acting between the panel point.Back


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c. Proportioning of truss members

For the chord member we can use either sections with one

web plate (T section) or sections with two web plates(Box section). T-sections are used only for small bridge.

Box sections have grates moment of inertia about axis y-y

and are better used for the connection of gusset plate. The

sections of all chords and web member should be

symmetrical about axis y-y in the plane of the truss.

Diagonals and verticals are usually symmetrical about axis

x-x also. The required area of the chords change at every

panel point of the truss and in choosing the different cross

section we must try to get simpler connection and splices

at the panel point. Back

y y


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x

y

x

Chord membersxx

y

D- Box section for bridge trusses

Top chords

The minimum section consists of a horizontal plate and 2

channels or a horizontal plate, 2 vertical plates and four

angles.

Depth of top chord h = (1/121/15) of the panels length Width a = (0.751.25) h

10

L


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min

a a

max(3/4 - 5/4)h

h

To avoid local buckling, the minimum thickness of web

and cover plates should be as follows;The unsupported width of a plate measured between

adjacent lines of rivets or welds connection the plate to

other parts of the section should not exceed:

t thi k f i l l t f 2 l t


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t = thickness of a single plate or of 2 or more plate

provided that this plates are adequately tacked together.

YFtb 64

(3/4 - 5/4)hmax

t

max

b

b

t

(3/4 - 5/4)h

b


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(3/4 - 5/4)hmax

t

d1

t

b

yFtd 301

Only excess over this width should not be included in the

effective sectional area in computing direct compressivestresses. The center of gravity axis x-x for the different

section should not change too much. In drawing the truss

we use an average value y = (y1 + y2 + y3 + ....)/ n.

It i d ti t l t th h l


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It is good practice to use a cover plate over the whole

length of the top chord even if the end members have

excessive cross section.

y1

x2

y

x

y

y

y3

y

y

xx x

y

y

x

Back

Lacing bars batten plates


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Lacing bars, batten plates

The two plates of the compression members shall be

connected together by diaphragms and the open side of thebox section shall be provided with batten plate close to the

gusset plate and with intermediate batten plates or lacing

bars to avoid lateral buckling of their component parts.

The slenderness ratio of each component part betweenconsequent connections of lacing bars or batten plates shall

be not more than 50 (and 2/3 l/i of the whole section).


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View A

Lz

batten pl.

y

yz

z

A

Bottom chords


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Bottom chords

The depth of the bottom chord is equal to that of the top

chords h = (1/12 1/15) of the panels length, or slightlymore (2 4 cm). No horizontal plate is provided at the

bottom of the section to avoid water packets. In

continuous and cantilever bridges where some bottom

chord members are in compression, horizontal plate maybe used and it must be provide with drainage holes (4 5

cm) . The two component parts of tension member shallbe connected together by diaphragms and batten plates

similar to these of the compression members, but theirthickness may be taken 25 % lighter (t2 lmember/ 15).


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bottom with cover plate (holes)

hh

Diagonals

For appearance the width of the diagonal should not be

more than that of the top chord and should decrease from

the end to the middle of the bridge. The compression

diagonal at end of the warren truss has a section similar to

that of the top chord.Back

Verticals


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Verticals

In trusses with a N-shape web system, the vertical have

similar sections as diagonals. In warren trusses the verticalmay consist of a web plate + 4 flange plates or an I-beam

(B.F.I.B).

For diagonal or vertical tension member;

t2 lmember/ 15 ( D & V )

t2 (lmember)/ 30 Railway bridges ( D & V & C )

t2 (lmember)/ 35 Roadway bridges ( D & V& C )

t2 (lmember)/ 10 (C )

D Diagonal & V Vertical & C Chord


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< 10 mm

2tt

2t2

2t

Back

Design of compression member


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The slenderness ratio l/ i of compression member of main

girder shall not exceed 90 for Railway bridges and 110 for

Roadway bridges.

E. Effective buckling lengths

Table 4.5

Table (4.5)


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Out of planeIn planeMember

Compression chord

Unbraced

Compressio

n chord

Effectively

braced

0.75 span

(Clause 4.3.2.2

or equation 4.2 if

using U-frames)

0.85 l0.85 lChords

1.20 l0.85 l0.70 lDiagonals- Singletriangulated

web system

l0.75 l0.85 l/2- Multiple


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/Intersected

web

rectangular

systemadequately

connected

- K-system

1.50 l1.20 l0.90 l

1.20 l0.85 l0.70 lVerticalmembers

- Single

triangulated

web system- K-

intersected

web system

(0.9+0.3Ns/

Nl)l

(0.75+0.25N

s/Nl)Ll0.35

Effective buckling lengths


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1.2

0.85

0.7

1.2

0.85

0.85

x

x

x

y

y

y

x

y

0.7

0.85

x x

y

y

Lb out-plan

(No- bracing)

Lb out-plan

(with upper bracing)

Ns/N

Ns/N

2.5 EI a

bracing

4

1.5

1.2

1.0

0.75

x

x

x

x

0.7

0.9

0.85

y

y Lb in plan

Unbraced compression chords


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Unbraced compression chords

a- For simply supported truss, with laterally

unsupported compression chords and with no cross-framesbut with each end of the truss adequately restrained

(Figure 4.1), the effective bucking length (kL), shall be

taken equal to 0.75 of the truss span, (clause 4.3.2.2).

b- For a bridge truss where the compression chord is

laterally restrained by U-frames composed of the cross

girders and verticals of the trusses, the effective buckling

length of the compression chord (Lb) is:

aa..I.E2.50=L 4 yb


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y

y

2dI1

1d

2

B

I

E = the Youngs modulus = 2100 t/cm2

Iy = the moment of inertia of the chord member about the Y-Y axis.

a = the distance between U-frames (cm) = S

23 *dd B


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2

2

1

1

EI*2

*d

EI*3

d=

B

d1 = the distance from the centroid of the compression

chord nearest face of the cross girder of the U-frame = dw

Hx.G.

d2 = the distance from the centroid of the compressionchord to the centroidal axis of the cross girder of the U-

frame = dwHx.G./2

I1 = the second moment of area of the vertical memberforming the arm of the U-frame about the axis of bending.

I th d t f f X G b t th i f


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I2 = the second moment of area of X-G about the axis of

bending = IX

B = the distance between centers of consecutive MainGirders connected by the U-frame

Back

Design of Tension Members


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Tension members shall always be of rigid construction

and their slenderness ratio l/ i shall not exceed 160 for

Railway bridges and 180 for Roadway bridges. Theeffective net section area shall be taken for all tension

members. This area shall be the least that can be

determined from any plane or planes cutting each

component plate or sections to its axis,

g

diagonally or following zig-zag line through adjacent


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diagonally or following zig zag line through adjacent

rivet holes. In each case all holes of line to meet with

shall be deducted from the gross sectional area where any

portion of the sectional area is measured for a diagonalplane adding (S2/ 4g) for each gauge space. The minimum

sectional area should not be less than that obtained by

assuming all the holes to be in one perpendicular plane.

Back

Design of Bolted Joints


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80

Design of Bolted Joints

Connection of web member to gusset plate and splices of

chord member shall have a strength equal to themaximum strength of the connected members. The bolts

shall be arranged symmetrical about the center line of the

member. The connection to either direct or part of it is

indirectly connected by:-

1- Splice plates or lug angles.

2- If breaking is along section S-S bolts (1 single + 2

double + 3 double) shear, must carry the load.

3- The strength of the splice plate should be enough to

carry a force corresponding to bolts (4 + 5) single shear.


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81

40 % more

20 % more

Lug angleLug angle

20 % more

10 % more

UnsymmetricalSymmetrical


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82

gusst pl.

gusst pl.

Splice pl.

S

S

Sec S-S

Connections for members


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83

Connections for members

The connection shall be designed for a capacity based on

the maximum of:-

1- The average between the actual force and the

maximum strength of the member of not less than 0.75 the

maximum strength of the member.2 The bolts between the chord and the gusset plate must

correspond to the algebric sum of the horizontal

components of the strength of the diagonals S1

, S2

L = S1Cos + S2Cos S2S1

3 The number of bolts should correspond to the


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84

3. The number of bolts should correspond to the

effective strength of the two diagonal, i.e., the number of

= (number of bolts in member 1 + number of bolts inmember 2)Cos .

Example


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85

I.L.S1

S1 S2

S3 S4

I.L.S1

/tan

1/tan

196 t

70 t

126 t

94 t

L=750

In a lower chord panel, if the maximum force in chords

and diagonals are as given, design suitable cross section,

connections and splices.

Member S1 = + 94 t


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86

1

2 [ No 24

Bolts M22, = 24

Anet = 2(42.32.40.95 - 22.41.3) = 67.56 cm2

Fact = 94/ 67.56 = 1.39 t/ cm2

< 1.6 t/ cm2

Maximum force = 67.561.60 = 108.10 t

Rleast = Rs. sh

qb = 0.25 Fub For bolts of grade ( 8.8),

Rs. sh = qbAsn = 0.258.03.03 1 = 6.06 t(n = No. of shear planes)

Bolts connecting diagonal to gusset = (Maximum force/


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87

g g g (

Rleast) 1.15

= (108.1/ 6.06)1.15 = 20.52 boltsUse 24 bolt M22

Member S2

= - 70 t

2 [ No 22 & Bolts M22, = 24

Agross = 2(37.40) = 74.80 cm2

y = ly/ iy = (0.85750/ 11) 1.20 = 69

(1.20 due to lacing bars)

x

= lx/ i

x= (0.70750/ 8.5) 1.20 = 61

x

y

y

x

max = 69 Fp.b = 1.600.000085 (l/ i)2 = 1.119 t/ cm2


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88

Fact = 70/ 74.80 = 0.94 t/ cm2 < 1.119 t/ cm2

Maximum force = 74.801.119 = 83.70 tRleast = Rs. sh

qb = 0.25 Fub For bolts of grade ( 8.8),

Rs. sh = qbAsn = 0.258.03.03 1 = 6.06 t(n = No. of shear planes)

Bolts connecting diagonal to gusset = (Maximum force/

Rleast) 1.15

= (83.7/ 6.06)1.15 = 15.88 bolts

Use 16 bolt M22

Member S3 = + 126 t


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89

y

y

x

2 [ No 30 & Bolts M22, = 24

Anet=2(58.8022.41.00 - 22.41.6) = 92.64 cm2

Fact = 126/ 92.64 = 1.36 t/ cm

2 < 1.6 t/ cm2

Member S4 = + 196 t


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90

y

y

x

2 [ No 30 + 2 PL 24012 & Bolts M22, = 24

Anet for 2[

= 2(58.8022.41.00 - 22.41.6) = 92.64 cm2

Anet for 2PL = 2(2422.4) 1.2 = 46.08 cm2

Anet for 2[+2PL = 92.64 + 46.08 =

138.72 cm2

Fact = 196/ 138.72 = 1.413 t/ cm2

< 1.6 t/ cm2

Force to be transmitted from gusset plate to bottom chord


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91

= Fmax

Fmax

= (S1

+ S2)Cos = (67.561.6 + 74.801.119) 1/2

= 135.62 t

Bolts connecting diagonal to gusset = (135.62/ 6.06)1.15= 25.74 bolts

Use 28 bolt M22

The bolts in the framing angle are not counted as they used

to transmit the reaction of the cross girder.

Splice of chord


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92

Splices of tension or compression chord shall be

designed on the maximum strength of the member. For

straight chord the splice shall be outside the gussetplate. For broken chord the splice will be within the

gusset plate.

Member S3

2 [ No 30 & Bolts M22, = 24

Net area of flange = (1023) 1.60 = 12.30 cm2

Net area of splice plate = (1023) 1.60 = 12.30 cm2

Number of single shear field bolts =

(12.301.6/ 6.06) 1.15 = 3.25 bolts

Net area of web = (3021.60) 1.00 = 22.20 cm2


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93

Use 2 splice plates = 300.80 + 240.80

Net area of 2 splice plates = (30 22.3) 0.80 + (24 -22.30) 0.8 = 35.80 cm2

Rleast = RD. sh or Rb

Rb = Fb d min t

Fb = Fub

= 0.60 for end distance (S1.5d), (Table 6.2)

Fb = 0.60 8.00 = 4.80 t/ cm2

yRb = 4.80 2.20 1.00 = 10.56


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94

Splice pl.

x

y

y

x

b

t

qb = 0.25 FubFor bolts of grade ( 8.8),

Rs. sh = qbAsn =

0.258.03.03 2 = 12.12 t

Rb = 10.56 t


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95

Number of double shear field bolts = (22.201.6/ 10.56)1.15 = 3.87 bolts

Use 4 bolt M22

The splices in the chords are placed in the side of the:-

1. Smaller cross section except in cases where the erectionis done by the cantilever method.

2. Gusset plate; in a polygonal chord in order to avoid the

bending of plates, angles and channels the splice plate isplaced at the brake of the chord on the gusset plates.

3.Gusset shall be proportion to withstand the effective forces

in the web member

The thickness of the gusset is determined from the critical


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96

section abcd. This section should be at least 15 20 %

stronger than the diagonal it self generally all gusset are

made of the same thickness. The thickness of gusset plateshall be at least 12 mm in Railway bridges and 10 mm in

Roadway bridges.


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97

2 Pl. 240x12

2 NO.300

12M22(8.8)

14M22(8.8)

Bolts for framingonly.

2 NO.240

4M22(8.8)

4M22(8.8)

a

Gusset pl.for L.W.Br.

d

b c

2 NO.220

8M22(8.8)


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98


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99

4- At the chord panel point the cover plate should be


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100

connected to a gusset plate by special connection angle to

make the center of gravity of the rivet group between gusset

plate and top chord nearer to the center of gravity of the topchord.

A

S

S


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101

n

A

A

A

nn

Sec A-A

S

Sec A-A

S

3

221

4

3 223

1

3

3

S

2

1

4

2

1

S

Back

Design of Battens and Diaphragms


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102

The two parts of the box section must be connected

together in such away that they act ass one unit. Forcompression member stronger details are necessary than

for ten member.

Diaphragms

Diaphragms are transverse plates or channel connected to

the two webs of the box section by angles. They are

necessary to assume the rectangular shop of the box

section. For the chords wee have at least one diaphragmbetween the two panel points. In the diagonals, we arrange

at least one diaphragm near each end.

Batten plate


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103

One the open sides of the box section we have batten plates

as close to the gusset plate as possible one intermediate

batten plate or lacing bars to avoid lateral buckling of the

unsupported flange for the calculation of the lattice bars of

a compression member we assume a transverse force = 2 %

of the longitudinal force in the member. If there is acontinuous plate at the upper side of the box section,

latticing will be in the lower side only and transverse force

will be according to cross section of the lower side only. In

tension member a lattice system and batten plates 25 %lighter is used.

A


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104

Sec A-AA

S S

Sec S-S

B


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105

B

B D

D

B

Battening of compression member

The number of batten is such that we get at least 3 bays

batten shall be of plates, channels, I-section bolted or

welded to resist the following forces:-

The member as a whole can be considered as avierandeen girder or we can assume hinges at mid

distances and change it to statically determine system.

Shear in batten plate = Qd/ a

Bending moment in batten = Qd/ 2


106/110

106Q.d/a

Q.d/2

M=Q.d/2

Q.d/4

Q/2

F1

F1

Q.d/a

Q/2

d/2

d/2

Q/2

t

a

Q/2

Q/2

Q/2

Q.d/a


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107

batten pl.

d

Design of End Portals

End transverse bracing are called portals. The portals areplaced either in the vertical plan of the end post (1), in

the plan of the first vertical (2), or in the inclined plan of

the end diagonal (3). In case (2) the first panel of the

lower wind bracing is affected by the reactiontransmitted by the end portals. The arrangement of end

portal in case (2) is stiffer than in case (3). The portal

must not interfere the clearance line.

Back

The shop of the portal depends on the depth and on the

l li Th l ll i


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108

1 3

2

W1

clearance line. The portals are generally static

indeterminate closed frames in which the post over subject

to bending stresses.

Approximate calculation of portals


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109

The point of inflection of the post are situated according

to the relative stiffness of the cross girders, post, and the

upper strut at height between 1/31/2 of the force height

h. We can replace the point of inflection by two hinges

at C and C each of them transmits W1. Then the portal

can be calculated as static determine frame. If the portalis in the plan of inclined end diagonal, the points of

inflection C, C should net be more than h/ 3 from A and

A.

W1 W1


110/110

W1.d/2

W1.d/2+W1.e

W1.h/b

W1.d/2

W1 f/2

h

X.G

h'

b

h'

W1.d/2

W1.h/b

W1 f/2

W1

W1/2

W1

h

d

e

W1.h/b

X.G

W1/2

b

W1/2

W1/2

W1.h/b

f

W1

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Egyptian steel lecture

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