Design of Plate Girders

UNIT 7 DESIGN OF PLATE GIRDERS Structure Introduction Objectives

Elements of Plate Girder Types of Plate Girder 7.3.1 7.3.2

Riveted Plate Girder Welded Plate Girder

Design Assumptions Design of Flange Splice 7.5.1

7.5.2

Splice of Flange Angles Splice of Flange Plates

Design of Web Splice 7.6.1

Rational Splice

7.6.2 7.6.3

Moment Splice Shear Splice

Stiffeners 7.7.1 7.7.2

Intermediate Web Stiffener Bearing Stiffener

Design Problems Summary Answers to SAQs

7.1 INTRODUCTION The plate girders are essentially built-up beams to carry heavier loads over large spans. They are deep structural members subjected to transverse loads. The plate girders consist of plates and angles riveted together. Plates and angles form an I-Section. They are used in building constructions and also in bridges. When the span and load combination is such that the rolled steel beams become insufficient to furnish the requirement and built-up beam becomes uneconomical, then plate-girders are used. The built-up beams are used where overall depth is limited. In the built-up beams a rolled section was strengthened by riveting or welding additional plates to its flanges. In a plate girder the web is a solid plate and hence the plate girders are also called as "Solid web girders". As such the use of beams, built-up beams and plate girders is a step by step approach for the increase in loads and the spans. The object of the design is to achieve overall economy, which involves the cost of fabrication in addition to the cost of material. The cost of fabrication is more for built-up beams as compared to beams, and it is still higher for plate girders as compared to both. Attempt is made to provide deep sections for economy as regards materials and cost of fabrication. The plate girders are economically used for spans upto about 30 m in building construction. The depth of plate girder may range upto 5 m or more, 1.5 m to 2.5 m depths are very common.

Objectives After studying this unit, you should be able to describe the elements of a plate girder, distinguish between riveted and welded plate girders, design flange splice,

Members in Flexure & Column Bases

e

design and differentiate among the various types of web splices, understand the function of stiffeners. and

e

design intermediate (vertical & horizontal) and bearing stiffeners.

7.2 ELEMENTS OF PLATE GIRDER A plate girder essentially consists of a vertical plate termed as web plate to which angles are connected at top and bottom to form top flange angles and bottom flange angles. The horizontal plates connected with the flange angles are known as flange plates or cover plates. The web and flange plates are thin, and hence likely to buckle under compression. In order to avoid buckling of web due to shear, and bending, and buckling of web at points of concentrated loads, the web has to be stiffened by intermediate stiffeners, horizontal stiffeners and bearing stiffeners.

Flange. plates

1 Flange angles

Depth over angles

, End stiffener

Flange cover plates.

,Load

I

Flange splice

Figure 7.1: Elements of Plate Girder

Transverse or Vertical Stiffener - Stiffeners provided perpendicular to the length of the girder to guard against buckling of web.

Longitudinal or Horizontal Stiffener - Stiffeners provided along the length of the girder to prevent buckling of web of the girder.

Bearing Stiffeners - Stiffeners provided just under the load. Web Splice - Plates used to joint the two web plates together. Flange Splice - Plates used to joint two flange plates together.

7.3 TYPES OF PLATE GIRDER Mainly there are two types of plate girders. They are:

1)

Riveted plate girder,

2)

Welded plate girder.

Flange plates

Bearing stiffener

Figure 7.2(a): Riveted Plate Girder

Figure 7.2(b): Welded Plate Girdcr

Design of Hate Girders


7.3.1 Riveted Plate Girder The shear intensity across the depth of the girder varies, as more than 90% shear is taken by the web. The maximum stresses obtained should be multiplied by the ratio of gross flange area to net flange area to get the actual stresses. The gross cross-section shall comprise of flange plates plus flange angles and the web area between flange angles. The net cross- sectional area shall be the gross area minus the rivet holes on tension side and on compression side deduction shall be made for all open holes. Figure 7.2(a) shows the simplest type of riveted plate girder, in which each flange consists of a pair of angles connected to solid web plate. For larger moments, the flange area can be increased by riveting additional plates called cover plates. In a simple beam, the maximum bending moment generally occurs near the mid-span and it goes on decreasing towards the supports. The cover plates can be curtailed as the moment decreases.

Riveting of Flange Plate to Flange Angles The horizontal shear per 1 cm is given by where,

F = vertical shear force,

-1

-x A y

[F

A L = moment of area above the section about N.A., and I = moment of inertia, If R is the strength of the rivet in single shear or bearing

R Spacing of rivets = F -xAy .I For plate girders, the shear stress is taken uniform over the whole depth of girder of web, therefore, the horizontal shear at the junction of flange plate and flanges F per 1 cm will be - where F is vertical shear and D is the depth over angles in cm.

D

R Spacing of rivets = F/D where, R is the strength of one rivet in single shear or bearing.

Riveting in Flange Angles to Web The rivets will have to be designed for horizontal shear and vertical loads directly applied to the flange expecting where bearing stiffeners are provided to transfer such direct loads to the web. The rivets will be in double shear. The minimum of the strength in double shear and bearing should be taken for design purposes. If F,, is the horizontal shear per 1 cm length and v is the vertical load per 1 cm length, the resultant shear per 1 cm r =

R If R is the strength of 1 rivet spacing of rivets = -

r

Horizontal shear per cm

Now

A y =A

Design of Plate Girden

D

x -;; (approx.)

I

and

I

If the shear intensity is taken uniform on the web

I

1

I

Web Stiffeners: The web of the plate girder is so thin that there is always tendency for diagonal buckling and vertical buckling. Therefore, stiffeners are provided. In'riveted plate girders, angle sections are used as stiffeners. Curtailment of Plates As the bending moment decreases towards the supports, some of the flange plates may be curtailed. There is not much difference in the effective depth after curtailment and will nearly equal to 'D', the depth over angles.

M-Mn /

F

Figure 7.3(a)

i) b

\

Curtailment of Plates for Girder Carrying Uniformly Distributed Load Moment of resistance varies as effective flange - area i.e. area of flange A, 'plus 118 area of web (=A+ -) d Let L,,be the theoretical length of the plate which is to be curtailed.

a = net area of plate to be curtailed plus the net area of plates above this as taken in full section. A l = total effective flange area. B.M. diagram will be a parabola.

M = U ,


ii)

Accurate Method of Curtailment In this method, the moment or resistance of the section after removing the plate is calculated and the point at which the B.M. will be equal to this moment of resistance, will be the theoretical point at which the plate may be cut-off.

Figure 7.3(b)

For U.D.L. the B.M. diagram will be a parabola(see Figure 7.3(b)). If M is the maximum B.M. and M, is the moment of resistance of the section after removing the plate and L, is the length of plate

Self weight of plate girder (riveted). For riveted plate girder, total self weight may be determined from the formula

w1

- kg.

380

Depth Over Angles For riveted plate girder, depth over angles may be approximately determined from the formula

D will be in crn, if M is in kg-cm and f is in kg/cm2

7.3.2 Welded Plate Girder A welded plate girder is more efficient section as the whole area is effective in resisting loads. The flange plate is welded directly to the web and no flange angles

are used. The flange plate is welded directly to the web and no flange angles are used. The box girders may also be fabricated by using two or more webs. It is uneconomical to use a number of thin cover plates as flanges one thick plate may be used as a flange and where it is desired to decrease the flange area, a thinner plate may be used. The thinner and thicker plates may then be butt welded. I

The self weight in kg may be taken as

Wl 400

-,

where W is the total superimposed

load in kg and 1 is the span in metres. The overall depth may be fixed from the formula

where,

D = overall depth M = maximum bending moment f = allowable stress

Flange: Each flange should preferably consist of a single section rather than of two or more sections superimposed, but the single section may comprise of series of sections laid end to end and effectively welded at their functions. Flange plates shall be joined by butt welds. These butt welds shall develop the full strength of the plates. Web: Assuming thickness of flange tf, the depth of web will be overall depth minus twice the thickness of flange = D - 2tf. The thickness of the web is fixed so that the average shear stress does not exceed 945 kg/cm2 and the ratio of depth of web to thickness of web does not exceed 200 if horizontal stiffeners are not to be provided. Flange design by approximate formula : The approximate formula for moment of resistance is given by

where,

D' = Distance between centre of flanges A = flange plate area A , = web plate area

Trial section can be fixed and checked by moment of inertia method and if found unsuitable, the section may be modified.

Minimum thickness-The thickness of the web plate shall be not less than the following: a) For unstiffened webs: the greater of

d

l G dl< dl and but not less than 1344 85 8 16

where,

dl' = depth of web as defined in 1.3 and

z,,,,,,

= calculated average stress in the web due to shear force.

webs: the greater of 11180 of the smallest clear panel b) For vertically, stiffened ddf d2 but not less than dimension and 3200 200

Design of Plate Girders

Members in Column Bases

&

C) For webs stiffened both vertically and horizontally with a horizontal stiffener at a distance from the compression flange equal to 215 of the distance from the compression flange to the neutral axis: the greater of 11180 of the smaller dl d2 dimension in each panel, and but not less than 4000 250 d) When there is also a horizontal stiffener at the neutral axis of the girder; the dl greater of 11180 of the smaller dimension in each pane1,and but not less 6400

fl

d2

than 400

In (b),(c) and (d) above, d2 is twice the clear distance from the compression flange angles, or plate, or tongue plate to the neutral axis. In the case of welded crane gantry plate girders intended for carrying cranes with a lifting load of 15 tonnes or more, the thickness of web plate shall be not less than 8 mm. The minimum thickness of web plates for different yield stress values are given in Table 6.'7 for information. Note: In no case shall the greater clear dimension of a web panel exceed 270. nor the lesser clear dimension of the same panel exceed 180 t, where t is the thickness of the web plate.

Table 7.1 : Minimum Thickness of Web Minimum Thickness of W e b for Yield Stress f y ( in MPa ) of

dZd& 3 2oo

dn

200

dn

dl

dz

200- 100 200

jg da 198

191

-d?_ 185

d > 179

d 174

d d1 d, r d dl dl _s __ 169

1G4

160

156

151

146

d2

d2

142 i38

Variation in Flange Thickness: The bending moment varies the span, therefore the flange thickness calculated for the maximum bending moment is not necessary to run throughout the span. Where bending moment is less, flange thickness may be reduced. The moment of resistance of the girder with reduced thickness of flange plate is calculated and the point at which the bending moment is equal to the calculated moment of resistance is worked out analytically or graphically and at that point the flange thickness may be reduced. The plates are butt welded at function to form continuous flange. Where the difference in thickness of the two plates is 6 mm or more, thicker plate shall, either be bevelled so that the slope of

(b)

Figure 7.4

surface from one part to the other is not steeper than 1 in 5 as shown in Figure 7.4(a), or the weld metal shall be built-up between the two parts as shown in Figure 7.4(b), provided the thickness of the thicker part is not more than 50% greater than that of the thinner plate.

Connection of Flange with Web: The web is machined and is in close contact with flange, therefore, the vertical loads are directly transmitted to the web by direct bearing. The bearing stress on the web should not exceed 1890 kg/cm2. The load is assumed to disperse at 30' through the flange. The connection of flange plate to web is done by intermittent welding. Horizontal shear per 1 cm

!

where,

F = shear force at the section I = moment of inertia A y = moment of area above the section about the N.A.

Using welds on both sides of the web of intermittent lengths I, of strength Sw per 1 cm length. 2Sw

11

Spacing of welds = Fh

..

11 --Fh Spacing of welds 2 Sw

The minimum ratio of effective length of intermittent weld to centre to centre distance of welds

- Fh -2 Sw

2 s w 11 Clearing spacing = -- 11 Flz

Web Stiffeners: Flates are used as stiffeners and are welded to the web. Welding between Stiffeners and Web: The size of the fillet welds should be in relation to the thickness of the web or stiffeners whichever is greater. Where intermittent welds are used, the distance between the effective lengths of any two welds, even if staggered on opposite sides of the stiffeners should not exceed 16 times thickness of the stiffener 30 cm. Where intermittent welds'are placed on one side of stiffener only or on both sides but staggered or where single plate stiffeners are butt welded to the web, the effective length of each weld should not be less than 10 times the thickness of the stiffener.

I

I

Where intermittent welds are placed in pairs, one weld on each side of the stiffener, the effective length of each weld should be not less than 4 times the thickness of the stiffener. For bearing stiffener the welding should, in addition, be sufficient to transmit to the web full reaction or load.



(a) Single .ingle Splice

(b) Double Angle Splice

(c) Splice .Angle and Plate

Figure 7.5: Flange Angle Splices

Where stiffeners are required to be welded to the flanges, they should not be welded to tension flange subjected to dynamic loads by welds transverse to the longitudinal axis of the girder.

7.4 DESIGN ASSUMPTIONS The approxilnate design is based on the following assumptions:

1)

The shear force is carried wholly by the web and the shear stress is uniformly distributed throughout the cross-sectional area of the web.

2)

The bending moment is resisted by the flanges. The distribution of bending stress in the flanges is uniform.

7.5 DESIGN OF FLANGE SPLICE When plate girders are longer the elements of their flanges, i.e., flange angles and flange plates may not be available in the required lengths so their splicing becomes necessary. A joint in the flange element provided to increase the length of the flange angle or plate is known as flange splice. The flange splices should be avoided as far as possible. In general the flange angles and flange plates can be obtained for full length of the plate girder. In spite of availability of full length of flange angles and flange plates, sometimes it becomes necessary to make flange splices, for example, the transportation facilities ,may not permit transportation of plate girder for the entire span as one piece. The flange splices should be located at the section where some excess of flange area is available and not at the points where web splice is done. In locating the flange splice, care should be taken to see that it is not located at the points of maximum stress. The centre of gravity of the splice plate should be kept as close to the c.g. of the flange element spliced as possible. There shall be enough rivets or welds on each side of the splice to develop the load in the element spliced plus 5 per cent, but in no case should the strength developed be less than 50 per cent of the effective strength of the material spliced. In welded connection the flange splice is done through a full strength butt weld or through a single cover butt or double cover butt joint for the flange force at the section.

7.5.1 Splice of Flange Angles When one flange angle is spliced at a section, a single splice angle may be provided in case it provides sufficient area. The two flange angles should not be spliced at the same section preferably one flange angle should be spliced in one

half and the other flange angle in the other half of span of the girder. Splicing of angles can be achieved in either of the following three ways:

i)

by one angle on the side of flange

ii)

by two angles on either side of the flange

iii) by one angle on the spliced side and additional plate on the other side The splice angle should be suitably shaped at the heel to match with the fillet of the spliced angle. The splice shown in Figure 7.5(a) is the direct splice as the area of spliced angle there is spliced by the area of splice angle which is in direct touch with the force. The shear force between the web plate and the flange angle in this case is not affected by splicing. So no additional rivets are required to connect the splice angle with the spliced angle, the length of splice angle should be sufficient to accommodate the sufficient number of rivets already used for connecting flange angle with the web plate so that full strength of splice angle is developed. However, in the case of splicing with two angles or one angle and one plate on the two sides [Figure 7.5(a) and (c)] the shear force between the web and flange angle is increased by the amount of force carried by the splice plate. The force in the flange angle is assumed to be distributed to the elements of the splice in proportion to their cross-sectional area. The strength to be transmitted by rivets connecting splice plate is equal to force in splice plate plus force due to horizontal shear. Therefore, (n R, = Y where,

+ Horizontal shear)

n = no of rivets required to connect splice plate on each side of splice P = force to be carried by splice plate

R, = strength of rivet in single shear. The strength of rivets in considered single shear because P is force to be carried in one plane only. The horizontal shear per unit length T~f.cal= (V'de)

The horizontal shear per unit length in one plane

The horizontal shear per unit length in one plane

where,

p = pitch of rivets

V = shear force at the splice section de = effective depth of the girder

.. 7.5.2

P 1 n=[Rs-5

v

Splice of Flange Plates

In case it becomes necessary to splice an outer flange plate a splice plate of same cross-section as the plate is provided. The length of splice plate is kept sufficient to accommodate necessary number of rivets. The strength of rivet is found in


Slembers in Flexure & C:ulumn Bases

single shear. The splice plate is in direct contact. Therefore, the force to be transmitted by splice plate is not affected.

In case, it becomes necessary to splice an inner flange plate, the 'splice may be located at the theoretical cutoff of the next outer plate. The outer plate is extended. This serves as a splice plate splicing of an inner plate is also done by providing an extra plate, which is placed outside of all flange plates. The area of cross-section of splice plate is kept equal to the cross-sectional area of flange plate cut. The rivets may be designed to take full strength of flange plate cut and the shearing stress due to transmission of flange increment is neglected.

3.6 DESIGN OF WEB SPLICE When the requiretl length of the web plate is longer than that which can be secured from the rolling mills, the web plate must be spliced. A joint in the web plate provided to increase the length is known as web splice. The splicing of web plates is achieved by fixing splice plates on both sides. As the best design, the splice plates should directly take up all stresses borne by the web plates covered by them. In many cases, the web has to be spliced due to the limitations of the handling equipment. Supposing we have to fabricate a plate girder with web 25 m long 2.5 m deep and 8 mm thick, the weight of the web alone will be 3.9 tonnes. The size and the weight of the plate are fairly large and it will be convenient to splice the plate. The web of a plate girder carries both bending and shearing stresses. As far as possible, web splices may be located at sections where excess flange areas are available. The excess flange areas are available at sections prior to the curtailment of flange plates preferably, splices may be located under stiffeners. The stiffeners provide additional strength to the splice. The splices should not be located at the sections, where maximum bending moments occur. In case, only one splice may suffice for full length of the girder, it may be located at such sections. The web splice are designed to resist the shears and moments at the spliced sections the splice plates are provided on each side of the web. There are following three types of web splices which are commonly used. 1)

Rational Splice

2)

Moment Splice

3)

Shear Splice

7.6.1 Web Splice (Rational Splice) This type of web splice is shown in Figure 7.6(a). The stresses are transmitted directly in this type. This type is most satisfactory than other two types. The splice plates A as shown in Figure 7.6(a) are provided between flange angles. A clearance of 6 mm is left between splice plates and flange angles. The splice plates B are provided for portion of web underneath the flange angles. If sufficient excess flange area is available at the splice section. The splice plates B need not be provided. These plates are designed for shear and moment which would be resisted by the portion of the web, if the web was not spliced. The rivets are provided at uniform spacing in this type. The pitch of rivets connecting splice rivets to the web is found as under: Vertical shear per unit depth.

The bending stress up to the level of rivets connecting flange angles

Design UP Plate CirUers

I

6mm clearance

I

-I t + + : + + + I I

I

I

I

I+ + + I +

++

I

Slice plate B k s l i c e plate A

I

'Y

I

Figure 7.6(a) : Web Splice (Rational Splice Method)

where,

M = bending moment at the splice section

1= moment of inertia of the girder y,

= distance upto the level of rivets connection flange angles from neutral axis

.

The horizontal force per unit length due to moment

If the rivets are provided in one vertical row and P is the pitch of rivets, the resultant of vertical and horizontal forces per pitch should not exceed the rivet value, R

If the computed pitch of rivets is less than minimum pitch, rivets are provided in two or three vertical rows. The rivets are provided at spacing of twice pitch computed above, if rivets are provided in two vertical rows. The rivets are provided at spacing of three times the pitch computed above if rivets are provided in three vertical rows. The thickness of splice plates A is kept equal to half the thickness of web, but not less than 6 mm. The width of splice plates A is kept sufficient to accommodate the rivets. The horizontal force in the portion of web beneath flanges due to moment. The horizontal shear force per pitch length

'

The pitch of rivets is assumed

Af= gross area of flange excluding web equivalent P = pitch of rivets, which one is assumed The horizontal force in the portion of web beneath flange angle6 due to moment P2 =

M.

x (Area of portion of web beneath flange angles)

where, y is the distance of rivets connecting splice plates B to the flange angles ftom the neutral axis if n is the number of rivets required

n = P 2 / ( R - P,) The rivets connecting splice plates B to flange are provided at close spgcing, so that their length is small.

7.6.2

Web Splice (Moment Splice)

This type of web splice is shown in Figure 7.6(b). There are four moment plates (two on each face), marked as splice A plates and two shear plates (one on each face) marked as splice plate B. It is assumed that moment plates resist moment resisted by web, and shear plates resist shear resisted by web. In fact, each set of plate resist shear as well as moment, but in case of deep girders, shear resisted by splice plates A is small compared with plates B. Similarly the moment resisted by splice plates B is small compared with splice plates A. This type of splice may be used for girders about 2 m deep. A clearance of 6 mm is provided between splice plates A and flange angles and between splice plates B. The web splice (moment splice) is designed as under: The moment resisted by the web plate is as under

-

+

+

+

t

+

+

4

+

+ + + + + + + +

+ + + + . + + + + +

Splice plate A 4

*. Splice

.-.

B

S lice

I'

,, ,p a t e A

.-a

+ + ++ ++ ++ ++ ++ + + + +

+ + + - c + + + + + + + + + + +

r

Figure 7.6(b): Web Splice (Moment Splice Method)

where,

I, = gross moment of inertia of the web, I = gross moment of inertia of the girder, and

M = bending moment at the web splice section. Moment Plates The moment of resistance of four moment plates (splice plates A) is equal to moment resisted by web. The moment of resistance of four moment plates is A , . al . d, where, A, = net area of two moment plates, d , = distance between centre to centre of splice plate A (moment plates),

a,= bending stress at the centre of splice plate A, and assumed uniform in these plates. Therefore, Mw = A, . ab, . d,

where,

(Tbc,cal

is the bending stress at the extreme fibre of the web plate

Let t, be the thickness of the moment plate

where,

d, = depth of moment plate,

nl = number of rivets in one vertical row, and d = diameter of rivets.

The horizontal force in the two moment plates A = (Al x obi) The number of rivets required to connect moment plates A to the web plate on each side of web splice is given by n = (A, . abl/R)

where,

R = rivet value.

Shear Plates The shear plates B resists shear at the web splice section. The combined thickness of these plates is designed to resist shear at web splice section. The width of the splice plates B is kept sufficient to accommodate rivets. The number of rivets, required to resist shear

Members in Flexure & Colun~nBases

n = (V/R)

where, V is the shear at the web splice and R is the rivet value.

7.6.3 Web Splice (Shear Splice) In this type of web splice the splice plates are provided between flange angles. A clearance of 6 mm is left between splice plates and flange angles. The web splice (shear splice) is designed as under : The moment of resistance of splice plate is kept equal to moment of resistance of web plates

where,

B,,

is the bending stress at the extreme fibre of splice plate and obcthe

bending stress at the extreme fibre of web plate. From the triangular distribution of bending stress,

Thus where,

A, and d, = Area and depth of splice plates A, and d, = Area and depth of web plate.

Total thickness of splice plates Area of the splice plate Width of the splice plate

Figure 7.6(c):Web Plates (Shear Splice Method)

The splice plates are designed to resist shear and moment which would be resisted by web, if web was not spliced

where,

I, = gross moment of inertia of the web I = gross moment of inertia of the girder

M = bending moment at the splice section The splice plates resist a total moment M, = (Me + M,) The rivets connecting splice plates to the web are designed to resist a vertical force ' V ' and a moment 'Me' or shown in Figures 7.7(a) and (b).

I

I

v

+VXe qi

I Mc

pet 1 te", + I

C,G.of rivets

*

!

I

' + L

I

6.C .of rivets

I I

I I I

I

(b) Figure 7.7

7.7 STIFFENERS The web of a plate girder buckles locally either under pure shear due to diagonal compression or under flexure due to bending compressive stress, or under concentrated loads due to bearing compressive stress. This local buckling of the web is prevented by stiffeners. In riveted plate girders, angle sections are used as stiffeners and in welded plate girders, plates are used as stiffeners.

7.7.1 Intermediate Web Stiffeners The intermediate stiffeners are used for the economical design of the web plate of the plate girder. They are used to avoid diagonal buckling of the web depending upon the ratio of clear depth to the thickness of web (dlt,), vertical stiffeners, horizontal stiffeners are provided throughout the length of the girder. The vertical intermediate stiffener divide the web plate into small panels. These panels are supported along the lines of stiffeners. The resistance of web plate to buckling is measurably increased. These stiffeners also have a second function. When the vertical stiffeners are fitted against the top and bottom flanges, then they maintain the original 90' angle between the flanges and the web when the dimensions of the web are very large, then the panel dimensions are reduced by providing the horizontal stiffeners on the compression side of the web. When the thickness of the web is less than the limits specified in IS: 800 6.7.3.1(a) vertical stiffeners shall be provided through-out the length of the girder. When the thickness of the web is less than the limits specified in IS: 800 6.7.3.1(b) horizontal stiffeners shall be provided in addition to the vertical stiffeners.

Design or Plate Girders

--In Cotunul Bases

In no case shall the greater unsupported clear dimension of a web panel exceed 270t nor the lesser unsupported clear dimension of the same panel exceed 180t, where t is the thickness of the web plate.

Vertical Stiffeners The vertical stiffeners are also termed as transverse stiffener. The vertical stiffeners are provided throughout the length of the girder when the thickness of web is less than the limits specified for the minimum thickness of the web plate. They are joggled or ciimpled. They may be provided straight in that case, filler plate of thickness equal to that of flange angles is inserted between the stiffener and web plate. They are fitted tightly between outstanding legs of top and bottom flange angles. The vertical stiffeners are provided at spacing not greater than 1.5 d and not less than 0.33 d where, d is the distance between the flange angles. The vertical stiffeners divide the web plate into number of panels. The greater unsupported clear dimension of web panel should not be greater than 270 times the thickness of web, and the lesser unsupported clear dimension of the same web panel should not be greater than 180 times the thickness of web. The length of outstanding leg of vertical stiffener may be taken equal to 1/30 of the clear depth plus 50 mm. The length of the connected leg of vertical stiffener should be sufficient to accommodate the rivets connecting the stiffener to the web. The moment of inertia I of the stiffener selected should not be less than

where,

I = the M.I. of a pair of stiffener about the centre line of web, t,

= the minimum required thickness of the web, and

C = the maximum permitted clear distance between vertical stiffeners.

Horizontal Stiffener The horizontal stiffener are also termed as longitudinal stiffeners. They are used to safeguard the web against buckling due to longitudinal bending compression. When the ratio of dlt, is larger than 200, a longitudinal stiffener is used on the web at a distance of dl5 from the compression flange. The requirement for moment of inertia for horizontal stiffeners should not be less than 4c15 where, C1 is the actual distance between the vertical stiffeners. The M.I. of the stiffener should be calculated about the centre line of the web if the stiffener consists of a pair of angles and about the face of the web if the stiffener is made up of one angle only. If dlt, ratio of the web exceeds 200, another horizontal stiffener should be used. This should be placed at the neutral axis of the web. The M.I. of this stiffener should be not less than d l t; Longitudinal stiffeners need not be continuous and may be cut at their intersections with transverse stiffeners. The outstand of the stiffeners should not exceed 16 times their thickness.

Connection of Intermediate Vertical and Horizontal Stiffeners Intermediate vertical and horizontal stiffeners not subjected to external loads shall be connected to the web by rivets of welds, so as to withstand a shearing force, between each component of the stiffener and the web of not less than

Design of Plate Gird.. ,.

where,

t = the web thickness in mm, and

h = the outstand of stiffener in mm For stiffeners subjected to external loads, the shear between the web and stiffeners due to these loads shall be added to the above values.

Bearing Stiffener

7.7.2

Bearing stiffeners in addition to accomplishing their primary function of stiffening the web of the plate girder help in relieving the rivets connecting flange angles and web from vertical force. When these stiffeners are provided at ends, they are termed as end bearing stiffeners. Bearing stiffeners are required at the point of application of concentrated loads known as load bearing stiffeners. For all sections, load bearing stiffeners should be provided, where the concentrated load or reaction of girder exceeds. A bearing stiffener consists of one or more pairs of angles connected on both sides of the web. As the purpose of the bearing stiffeners make it clear, the flange angles should transfer the vertical concentrated load directly to the bearing stiffener through bearing. Filler plates of thickness equal to the thickness of flange angles should be connected on both sides of the web (see Figure 7.8(b). Thus the net bearing area to be provided by the outstanding legs should be sufficient so that the bearing stress is within the allowable limit i.e., 1890 kg/cm2. For any section, load bearing stiffeners shall be provided at points of concentrated load (including points of support) where the concentrated load or reaction exceeds the value of

where,

o,, = the maximum permissible axial stress for columns as given under 5.1 for a dl

slenderness ratio -&., t t

r

= web thickness,

B = the length of the stiff portion of the bearing plus the additional length given by dispersion at 450 to the level of the neutral axis, plus the thickness*of the scating angle, if any. The stiff portion of a bearing is that length which cannot deform appreciably in bending and shall not be taken as greater than half the depth of beam for simply supported beams and the full depth of the beams continuous over a bearing; and ci, = clear depth of web between root fillets.

Load bearing stiffeners shall be symmetrical about the web, where possible.

Design of Bearing Stiffener 1)

Load bearing stiffeners should be designed as columns, assuming a section to consist of the pair of stiffener together with a length of web on each side of the centre line of stiffeners equal to 20 times the web thickness. The effective length of the column is equal to 0.7 times the length of the stiffener.

2)

The outstand of the pair of stiffener should be clear of the flange root or weld and the calculated bearing stress should be less than the permissible value.


3)

Stiffeners shall be symmetrical about the web, where possible and at points of support shall project as nearly as practicable to the outer edges of the flanges.

4)

The connection to the web should be capable of carrying the full load. The end of stiffeners should be tight fitted for full bearing. At points of support this requirement should be satisfied at both flanges.

5)

The ends of load bearing stiffeners shall be fitted to provide a tight and uniform bearing upon the loaded flange unless welds or rivets designed' to transmit the full reaction or load are provided bet&een the flange and stiffener. At points of support this requirement shall apply at both flanges;

6)

Bearing stiffeners shall not be joggled and shall be solidly packed throughout; and

7)

The moment of inertia of the stiffener is

where, D = overall depth of the girder,

T = maximum thickness of comp flange, R = reaction on the bearing, and

W = total load on girder.

Figure 7.8(a): Intermediate Stiffeners

Figure 7.8(b): Bearing Stiffeners

The load carrying capacity of the bearing stiffeners as a column should be greater than or equal to the applied load or the reaction.

SAQ 1 1)

Define plate girder and discuss the elements of a plate girder.

2) Bring out the differences between the riveted and welded plate girder. 3)

Explain the basic concepts in the design of flange splice.

4)

Discuss the various types of web splices and explain when they are adopted.

5)

What is the function of a stiffener in a plate girder and describe the various types of stiffeners used.

h i p of Plate Girdem

7.8 DESIGN PRBBLENIS Example 7.1 Design a welded plate girder to carry a superimposed load of 10 tonnes per metre on an effective span of 24 metres.

Solution Total superimposed load = 10 x 1000 x 24 = 240,000 kg

Assuming self weight

= 240,000

Total load Maximum B.M.

=

+ 14,400 = 254,400 kg

2 5 , 4 0 0 ~2400 8

kg. cm.

= 76,320,000 kg. cm.

Assuming girders to be laterally supported throughout so that maximum allowable stresses both in tension and compression are 1575 kg/cm2

= 182.3 cm

Use overall depth of 180 cm. Taking flange plate thickness as 5 cm, depth of web will be 170 cm Maximum shear

- 2549400= 127,200kg - 2

At the average shear stress of 945 kg/cm2 Thickness of web =

127,200 = 0.79 1cm 945 x 170

d As - should be less than 200 if horizontal stiffeners are not to be provided, r web thickness of 1 em is used.

Design by Approximate Formula

where,

f = maximum allowable stress

D ' = distance between centre to centre of flanges A = flange plate area


A, = web plate area

w:,:

P.

248.57 ange plate = - 49.71 5

Width provided is 52 cm.

Check by Moment of Inertia Method

- 4,404,300 Ymax 90

z=--I

Maximum stress =

76,320,000 48,973

= 15559kg/cm2 < 1575kg/cm2

Variation of Flange Thickness

The flange outside should not be greater than 12 times the thickness of the flange.

.:

The minimum allowable flange thickness

Use flange thickness of 5 cm, 4 cm, and 2.5 cm for different positions.

-

Design

Moment of inertia with 4 cm flange thickness

I=

52 ( 1 7 f - 1703 1 x 17d + 12 12

= 3,154,000+ 409,300 = 3,563,300 cm4

Moment of resistance

E

-- - f X , Ymax

-- 1575 x 356,300

E

-7-

89

= 63,050,000kg.cm

Figure 7.9(b)

Let x metres be the distance from end where 5cm. Flange will be terminated. B.M. at this section will be equal to moment of resistance of section with 4cm flange thickness.

Total load 2 5 4 , 4 0 0 1 ~ ~ ~

254,400 /2

254,400/2 Figure 7.9(c)

=17m and 7 m Moment of resistance with 2.5 cm flange thickness

-&I Ymax

(175" - 17$)

---

87.5

[1,936,000+ 409,300]

---1575 x 2,354,300 87.5

1x1031

+12

Plate

I -.

.

Members in column

&

Distance x from left support, where BM is equal to moment of resistance is given

= 79.64 (X

- 12)'

= -79.64

+ 144 = 64.30

x = - + 8 . 0 2 + 12 = 3.98 m and 20.02 m

The variation of flange thickness is shown in Figure 7.9(ej.

6mm weld at 30cm centres

i

Figure 7.9(e)

Connection of Flange with Web Horizontal shear for 1 cm length

Used 6 rnm weld Strength of weld per 1 cm length

S,= 1025x0.7x0.6=431 kg

..

Effective length = 0.705 Centre to centre of welds

Use 22.5 m weld with effective length 21.3 cm and centre to centre of weld 30 cm. The clear distance between the effective welds will be 8.7 cm. Allowable maximum clear spacing is 16t = 16 x 1 = 16 cm. Use 14 intermittent welds.

Shear force at 4 metres =

254,400 - 254,400 x 40 2 24


Use 6 mm weld

Use 11 cm weld having 9.8 cm effective length of weld and centre to centre of weld 20 cm. The clear distance between effective welds will be 10.2 cm. This spacing is maintained for the remaining position up to the centre.

End Bearing Stiffeners Stiffeners width is taken as 24 cm. As the outstand should not exceed 12t, minimum thickness required will be 2 cm used 2 flats as shown in Figure 7.10 Area of stiffener = 2 x 24 x 2 + 20 x 1

Bearing area of the stiffener taking that flat is splayed 1 cm to fit on the weld

Bearing stress

=

127,200 92

= 1380kg/cm2 < 1890 kg/cm2,

Safe.

2 ~ 4 918x13 ~ Moment of inertia = -+ 12 12

Figure 7.10(b)

Allowable stress from IS code is 1246.3 kg/cm2

:.

Allowable load

= 1246.3 x 116

Mea~BersIn Ftenure & CGhEUl

= 144,500 kg. > 120.200 kg

&IS~?E

Safe. Use 6 mm, intermittent welding on both sides of the stiffener. Strength of weld per cm = 1025 x 0.7 x 0.6 = 431 kg Shear per cm. length of web = 277200= 747.1 kg 170

Effective Length of Weld 747.1 Centre to centre of web = -= 0.43 4x431 Use 10 cm, length of weld with effective length of 8.8 cm and centre to centre of welds 20 cm. This gives clear distance of 11.2 cm between effective welds which is permissible. The stiffeners are connected to flanges by 6 cm weld.

Intermediate Stiffeners Use single flat stiffeners alternately one on either side of the web

Average shear stress = 127'200 = 748 k g c m 2 170 x 1 Stiffeners spacing for these values of dlt ratio and average shear stress is 1.2 d i.e., 1.2 x 170 = 204 cm Use stiffeners at 200 cm centres Moment of inertia required =

1.5d3ti

E

1

p-52~~1

u i

---(

m

C

aI

t , = 0.791 cm

I

!

Minimum width of stiffener

Use 12 cm x 1 cm flat as stiffener

=576cm4 >91.14cm4 Connection to web: t

Shear in tonnes per cm = 2h where.

t =: web thickness

-

Safe.

Figure 7.10(c)

h = outstand of stiffener in cm

.:

1

Shear per cm = --x1OOO 2 x 12

= 41.67 kg

Use 5 mm inter~ediateweld on both sides of stiffener

-

Effective length Centre to centre of weld

Use 5 cm weld with effective length 4 cm and centre to centre of welds 20 cm. This gives clear distance of 16 cm between effective length of welds which is permissible.

Example 7.2 Design a riveted plate girder to carry a superimposed load of 10 tonnes'per metre on an effective span of 24 m. Assume girder to be laterally supported throughout.

Solution Total superimposed load

= 10 x 24 = 240 tonnes = 240,000 kg

Self weight may be taken as where,

w1

-

380

W = total superimposed load

2 = Span in metres Self weight =

2407000

3 80

24 = 15,158 kg

= say 16,000 kg

:.

Tota load = 240,000

+ 16,000 = 256,000 kg

Maximum bending moment

Assume girder to be laterally supported throughout so that maximum allowable stress in tension and compression is 1575 kg/cm2 Depth over angles 0 = 5.5

Adopt 201 cm depth over angles keeping a gap of 0.5 cm between web is the flange plates.

Depth of web = 201 - 1 = 200 cm

Taking length of angle leg is 15 cm d = 201 - 2 x 15 = 171 cm W Maximum shear force = 2

Minimum thickness of web required

:.

Use 0.8 cm thickness of web

'

d t

If horizontal stiffeners are not be' used, - should be less than 200 mm

:.

Use 1 cm thickness of web

= 243.50- 25.00= 218.50cm2 Use 2 c s 150 mm x 150 mm x 15 mm Gross area = 2 x 42.78 = 85.56 cm2

2 plates 44 cm x 2 cm Gross area = 2 x 88 = 176.00 cm2

Total gross area = 261.56 crn2 Using 20 mm diameter rivets d = 2.15 cm

Let the plates be connected to the flange angles by two rivets in each angle by staggered riveting. Deduction due to holes in flange plates

= 2 x 2 . 1 5 ~ ( 2 + 2 +1.5)=4.3x5.5=23.65cm2 Deduction due to holes in legs connected to web

=2x2.15[2x 1 . 5 ] = 4 . 3 ~ 3 = 12.9cm2

Total deduction = 23.75 + 12.9 = 36.55 cm2

Net flange area = 261.56

-

Design

36.55 = 225.01 cm2

The plate girder section i s shown in Figure 7.11.

(b)

Figure 7.11

Check by Moment of Inertia Method Moment of inertia of gross section

= moment of inertia of plate inertia of web

+ moment of inertia of angles + moment

Maximum tensile stress on gross area

Gross flange area = area of flznge plates

+ area of angles

+ area of web between the angles

Deduction for rivet holes Due to connection of flange plates to flange angles

Due to connection of flange angles to web

of

Plate

MembvsIn-rr& C ~ U B-~ R

Total deduction = 23.65 Net flange area = 276

+ 17.2 = 40.85 cm2

- 40.85 = 235.21

Actual maximum tensile stress

-- 1351

276'06 = 1588 kg/cm2 > 1575 235.21

:.

Not safe.

The section is revised by providing flange plate of width 45 cm Moment of inertia of gross area

45 12

+

= - [20g3- 2013] 1,588,787+ 666,667

= 3,768,750 + 1,588,787 + 666,667 = 6,024,204 cm4

Maximum tensile stress on gross area

Gross flange area

= 2 x 90

+ 85.56 + 14.5 = 280.06 cm2

Net flange area

= 280.06

- 40.85

= 239.21 cm2

Actual maximum tensile stress = 1332 280.06 = 1564 kg/cm2 Safe. 239.21 Curtailment of top plate: Taking one plate throughout the top plate can be curtailed at a point as calculated below.

Total effective flange area = area of flange plates -

+ area of

angles

1

+ -8 web area

deduction for holes

+ 2 x 42.78 + 25.00 - 36.55 = 180 + 85.56 + 25.00 - 36.55

= 2 x 90

= 254.01 cm2 a = net area of flange to be curtailed

= 90 - 2 x 2.15 x 2 = 90

- 8.6 = 81.4 cm2

= 130.0 metres. Maximum stress at theoretical curtailments point r

2

1

Figure 7;12

= 1105 kg/cm2 Force in curtailed plate = 45 x 2 x 1105 = 99,470 kg

Strength of one 20 mm diameter rivet = 3430 kg

997470- 29.00 Number or rivets required = -----3430 Using 4 rivets in a row, number of rows required will be 8. Using the minimum pitch of 5.5 cm the extended length of plate beyond theoretical cut-off point will be 44 cm. Length of top plate

= 13.0 + 2 x 0.44 = 13 + 0.88 = 13.88 say 14 metres

Riveting i)

Connecting of flange plate to flange angles Shear per 1 cm length of web

-

28'000 = 640 kg depth of web= 200 F

Use 20 rnrn diameter rivets Strength of two rivets = 2 x 3430 = 6860 kg.

.

6860 Spacing of staggered rivets = -= 10.8 cm 640

Use pitch of 10 cm. ii)

Connection of flange angles to web Horizontal shear per cm =

A+-

Vertical load per km = Resultant force

10 1000

r = 4577.0

= 100 kg

+ loo2

= 586 kg. Use 20 mm diameter rivets Strength of two rivets in bearing against web

= 2 x 2.15 x 1 x 2125 = 9137.5 kg Double shear strength of two rivets = 2 x 2 x 3430 = 13,720 kg

Pitch of rivets = ------ 15.6 cm 586

Figure 7.13

Use same pitch of 10 cm as for connection between flange angles and flange plates. Intermediate stiffeners

d = 171 t

Members In Flenure & Column Bases

Average shear stress = 128'ooo = 749 k d c m 2 171 x 1 From IS 800 - 1962 centre to centre distance of stiffeners = 1.2 x 17 1

= 205.2 cm say 200 cm Use 2Ls 80 mm x 80 mm x 6 mm as stiffeners clear distance between stiffeners C = 200 - 8 I

1.5 d3t: I section required = -- where t , = minimum required thickness of

c?

web

I = 2 [560 + 9.29 x (2.18 + 0.5)~]

I

= 2 [56.0+ 9.29 x 2.682]

I

= 2 [56.0+ 69.581

= 2 x 125.58 = 251.16 cm4 > 101.0 cm4

Connection of Stiffeners to Web I

t2 Shear in tonnes per cm = 2h

where, t = web thickness h = outstand of stiffeners in cm 12

-- 1

:.

tonne~

Shear per cm = 62.5 kg

130 x 130 x 15mn length

u '7 Itm. th~ckweb

Figure 7.14

:.

Safe.

Use 20 mm diameter rivets single shear strength of 3430 kg will be least 3430 62.5 - 54.9 cm Pitch of rivets = Use pitch of 16 cm as allowable pitch is =16t=16x1=16cm Bearing stiffeners use 4 L s 130 mm x 130 mm x 15 mm Maximum shear force at the end = 128,000 kg Area of outstanding legs clear of root of flange angles

= 4 [13 - 0.81 x 1.5 = 4 x 12.2 x 1.5 = 73.2cm2 Stress =

128,000 73.2

= 1748 kg/cm2 c 1890 kg/cm2

:.

Safe.

Length of stiffener = 201 - 2 x 1.5 = 198 cm Effective length = 0.7 x 198 Area

= 4 x 36.81

+ 40 x

= 138.6 cm

1

= 147.24 + 40 = 187.24 cm2

Allowable stress from IS = 1237.80 kg/cm2 Safe load on stiffener = 167.24 x 1237.80 = 206,500 kg > 128,000 kg. Safe Connection of stiffener to web use 20 mm diameter rivets Strengh of one rivet in bearing in web = 1.25 x 1 x 2125 = 4568.75 kg Double shear strength of rivet = 6860 kg Number of rivets =

128,000 = 28 4568.57

Rivets we shown in Figure 7.15. E ~ t r a14 rivets are provided in packing plate. Weight of plate girder total volume of web s 200 x 1 x 2400 = 480,000 cm3

>l\lemRers in ~1e;carr & Column Bascs

Figure 7.15

4 flange L S = 4 x 4 2 . 7 8 ~2400 = 410,700 crn3

First flange plate (top and bottom) = 2 x 45 x 2 x 2400 = 432,000 cm3 Second flange plate (top and bottom)

11 Intermediate stiffeners = 11 x 2 x 198 x 9.29 = 40,500 cm3 2 bearing stiffeners = 2 x 4 x 198 x 36.81 = 58,300 cm3 4 filter plates = 4 x 170 x 40 x 1.5 = 40,800 cm3

Total = 480,000

+ 410,700 + 432,000 + 252,000 + 40,500 + 58,300 + 40,800

Add 295% for rivets = 42,650 cm3 Grand total = 1,757,160 cm3 Total weight of girder = 1,736,250 x 0.00785 = 13,794 kg Assumed weight

= 16,000 kg

Assumed weight is alright.

Example 7.3 A simply supported plate girder spans 20 m and carries a uniformly distributed load (including its own weight), of 3000 kN. The section of plate girder at supports is shown in Figure 7.16. Design end bearing stiffeners. Also design the necessary intermediate stiffeners.

Solution Step 1 Design of bearing stiffener (end reaction). The uniformly distributed load including own weight of plate girder is 3000 kN. Support reaction = 1500 kN. Allowable bearing stress (Yield stress for steel 250 ~ 1 1 - n ~ )


Step 2 Bearing area required

[

)

1500 x 1000 = 8000 mm2 18.5

From JSI Handbook No. 1, select 4 ISA 150 mm x 115 mm x 15 mm (4 ISA 150 115, @ 0.394 kNIm) Radius at root, r, for the flange angle is 13.5 mm Bearing are provided = 4 (150

-

13.5) x 15 = 8190 mm2

The bearing provided is greater than bearing are required. Provide 18 mm thick filler plates, as shown in Figure 7.16.

I S A 125 x 95 x 8 m m

Web 8 m m thick

Figure 7.16

Step 3 Check for load carrying capacity. The bearing stiffener acts as a column Actual length of bearing stiffener

Effective length of column

Cross-sectional area of column section A = (4 x 37.52

+ (40 x 0.8) x 0.8) x

100 = 17568 mm2

The moment of inertia of column section about the centre line of web,

The radius of gyration of column section about the centre line of web 1 /2

r

=(

1 0 5 9 5 . 3 6 ~lo4 17568

j"'

= 77.66 mm

Slenderness ratio of column section

From IS 800 - 1984, allowable stress is axial compression, for the steel having yield stress as 250 ~ l m m *

Members in Flenure & Column Bases

a = 147.331 ~ / m m ~ Load carrying capacity of stiffener

(

147'331x 17568 = 2588.31 kN > 1500 kN 1000

(Support reaction)

Hence design of bearing stiffener is safe. Step 4

Connection of bearing stiffener to web plate use 22 mm diameter power driven rivets. Strength of rivet in double shear

Strength of rivet in bearing

Rivet value, R = 56.4 kN. Number of rivets required to transmit reaction = (1500156.4) = 26.59 The filler plates are provided on both the sides of web plate. Thickness of filler plate = 18 mm. The filler plate (packings) are properly fitted with the bearing stiffeners. These filler plates are subjected to direct compression only. Provided 30 rivets in 2 rows at pitch p = 130 mm

Step 5 Design of intermediate stiffeners clear depth between flange angles of plate girder d = (2500

Thickness of web

t,

-2 x

150) = 220 mrn

= 8 mm.

In case, the web plate is to be unstiffened, the minimum thickness of web needed is found as under. Calculated average stress in the web plate due to shear force.

ii>

[

tW.rnin-

.fin -- 2200 x 25dI2

d2 134

1344

I

=25.88 mm; or

Actual thickness of the web 8 mm is less than the above values of t,,,,,, such the vertical stiffeners are required. In case, the vertical stiffeners are used only, then the thickness of web required is as under (d2 = 2200 mm).

as


ii) Actual thickness of the web 8 mm is less than t,.,,,, and horizontal stiffeners become necessary.

then, both, the vertical

Therefore, thickness required shall be as below, (d2 = 2200 mm)

a horizontal Since, actual thickness of web 8 mm is still less than that t,,, stiffener is also necessary at the neutral axis, in which case, the minimum thickness of web needed is as follows (d7 = 2200 mm)

Therefore, the web of 8 mm thickness has to be stiffened using vertical and horizontal stiffeners at a distance from the compression equal to 215'~ of the distance from the compression flange to the neutral axis (215.1 100 = 440 mm) and also at the neutral axis of the plate girder.

Step 6 Design of vertical stiffeners. At support, shear force = 1500 kN Actual average shear stress in web plate

The smaller clear panel dimensions for the actual thickness of web = 180 x 8 = 1440 mm.

The great clear panel dimension for the actual thickness of web = 270

x 8 = 2160 m.

The vertical stiffeners may be provided at spacing smaller than 1440 mm. Let the spacing of vertical stiffeners be = (0.6

x 4 = 0.6 x 2200 = 1320 mm

From IS: 800-1984, Table 6.6(A), the permissble average shear stress, z, in and~ 0.6 d spacing and the stiffened web plate of steel with fy = 250 ~ l m m d/tw ratio

Members in Flenure & Column Bases

Length of outstanding leg of the vertical stiffener

($x clear depth of girder + 50

1

mm

Provide ISA 125 mm x 95 mm x 8 mm (ISA 125,95, @ 0.133 kN-m). The length of outstanding leg of the angle section is 90 mm. Clear distance between vertical stiffeners

Depth of plate girder = 2500 mm Minimum required thickness of web

Required moment of inertia,

.

= 409 x lo4 mm4

Moment of inertia about the face of web plate provided

Step 7 Connection of vertical stiffener to web plate. Shear force =

($1

(

= l2;:

8 2 ) = 88.89 kN/m

Use 22 mm diameter power driven field rivets strength of power driven rivet in single shear

Strength of rivet in bearing

Rivet value R = 43.35 kN Pitch of rivets =

(:::::) -

= 0.487 m = 487 mm

Provide rivets at a pitch of 200 mm Provide ISA : 125 mm x 95 min x 8 mm and 22 m rivets to connect the stiffener with the web at 200 mm pitch.

Dealgn of Plate Girders

SAQ 2 1)

Design a plate girder of effective span 16 m and simply supported at ends. It carries a UDL of 50 kN/m and two concentrated loads of 800 kN at 4 m from each support. The girder is effectively supported in the lateral direction.

2)

The bending moment and shear force at a particular section of a plate girder are 5760 kN-m and 1080 kN respectively. Design the web splice 22 mm power driven rivets are used.

3)

Design a flange splice for a section of riveted plate girder, having I = 2.75 x lo6 cm4 and subjected to B.M. of 280 t-m. 22 mm dia rivets have been used at 8 cm pitch and horizontal shear per cm length between web and flange angles is 450 kg.

7.9 SUMMARY Let us conclude this unit by summarising what we have covered in it. In this unit we have 1)

Introduced the concept of plate girder.

2)

Discussed the elements of a plate girder.

3)

Studied the design of welded and riveted plate girder.

4)

Described thk design of flange splice, web splice.

5)

Evaluated the design of web splice and differentiated among various types of web splices.

6)

Studied the function of stiffeners.

7)

Understood the design concept of intermediate (Hor and Ver) and bearing stiffeners.

7.10 ANSWERS TO SAQs -

-

-

--

SAQ 1 1)

Refer Section 7.1 and 7.2

2)

Refer Section7.3

3)

Refer Section 7.5

4)

Refer Section 7.6

7T

Member-s in Flc Column Bases

5)

Refer Section 7.7

SAQ 2 Refer examples given in the text.

Design of Plate Girders

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