in Fig. 2, while a through plate girder highway bridge is shown in Fig. 3. As a through plate girder bridge can have only a lower lateral system, the upper flanges are braced by side braces with gusset plate connections.

Short spans up to 70 or 80 feet have one end fixed while the other end is allowed to move on a sliding plate. For greater lengths of span the expansion end is supported on nests of rollers. The ordinary limit of plate girder spans is about 100 feet, although railroad plate girders having a span of 126 feet have been built. Plate girders of more than 100 feet span have a depth that makes transportation by rail very difficult.

Thickness of Web.-Standard specifications limit the minimum thickness of the web plates to inch for railroad bridges and inch for highway bridges. For heavy loads and long spans the web plates are made much thicker than the minimum thickness. Thin webs require more stiffeners and give a much shorter life to the bridge.

Flanges. The simplest form of a flange consists of a pair of unequal-legged angles with the long legs placed out and riveted to the web plate. When additional rivets are required in the connection of the flanges to the web plate, equal-legged angles with two rows of rivets are used. When additional area is required, one or more cover plates are usually riveted to the horizontal legs of the angles. The thickness of the flanges should be limited so that the rivets will not be longer than five times the diameter of the rivet. Flange angles should never be thinner than the web plates to which they are fastened. Where more than one plate is used, one plate should extend the full length of the girder, the others being continued a short distance (not less than one foot) beyond the point where the area is required. For steam or electric railway plate girder bridges the rivet heads and the variation in the thickness of the flange plates makes it necessary to notch the cross-ties unequally, so that other forms of flange are sometimes used for the upper flanges of long girders. It is quite the common practice to design the tension, or bottom, flange to take the stresses and then make the compression, or upper, flange with the same gross

area.

FIG. 3.

←7-0"

HIGHWAY THRough Plate GIRDER BRIDGE WITH SOLID FLOOR. (AMERICAN BRIDGE

COMPANY.)

Moments and Shears.-The moments and the shears in through plate girder bridges, as in Fig. 2 and Fig. 3, are found in the panels in the same manner as for a truss. In a deck bridge the moments and the shears are calculated in a similar manner, at intervals. The load on the girder produces shearing stresses in the girder, which in turn develop tensile and compressive stresses. In a solid rolled beam the entire section carries both shear and bending moment. In plate girders it is usual to assume that all the shear is carried by the web and that all the bending moment is taken by the flanges.

Nomenclature.-The following nomenclature will be used.

M = resisting moment of section.

V = vertical shear at section.

h

h'

d

=

=

=

==

=

distance between gage lines of rivets in tension and compression flanges.

distance back to back of angles in flanges.

distance from neutral axis to extreme fiber.

pitch of rivets in flanges.

= allowable resistance of one rivet.

=

concentrated load per unit length of rail

=

P/ where P

= concentrated load and

2n

1 = distance over which the load, P, is considered as distributed.

= number of rivets on one side of web splice.

Resisting Moment.-There are four methods now in use for determining the resisting moment of a plate girder section.

(1) Assuming that all the bending moment is carried by the flanges,

M = Ap'.f.h

(2) Assuming that one-eighth the gross area of the web is available as flange area. Then the total resisting moment of the girder is

(1)

On account

This shows that approximately one-sixth of the web is available as flange area. of the reduction of the area due to rivet holes, one-eighth of the area of the web is commonly taken as available as flange area wherever this method is used.

(4) By moment of inertia of gross section (used by American Bridge Co. for plate girders for buildings),

Rivets in Flanges Which do not Carry Concentrated Loads.

(1) Assuming that all bending moment is carried by flanges.

The loads produce shearing stresses in the web, which are transferred to the flanges by means of rivets in the flanges. In (c) Fig. 4 let p be the pitch of the flange rivets, V be the vertical shear at section, h' be the distance between lines of rivets in compression and tension flange, and r be the allowable resistance of a rivet; then taking moments about the lower right hand rivet,

(2) Assuming that one-eighth the gross area of web is available as flange area,

(8)

H

Rivets in Flanges Carrying Concentrated Loads.

(1) Assuming that all the bending moment is carried by the flanges,

(2) Assuming that one-eighth the gross area of the web is available as flange area,

(1) and (2). Assuming that all the bending moment is carried by the flanges, or that oneeighth the gross area of the web is available as flange area,

=

distance between centroids of all cover plates in tension flange and all cover plates in compression flange.

(4) By moment of inertia of gross section,

where Ac he

(18)

distance between centroids of all cover plates in tension flange and all cover plates in compression flange.

Web Splice. An ordinary web splice is shown in Fig. 4. Where splice plates are designed to carry part of the moment as well as the shear the splice shown in Fig. 5 is sometimes used. Plates AB and A'B' are assumed to transfer that part of the moment carried by the web, and plate CD to transfer the shear. Two lines of rivets should be used in each section of the web spliced. The number and spacing of rivets in a web splice can be determined only by trial, except when the first method for proportioning the section is used. The rivet most remote from the neutral axis is the most severely stressed.

(1) Assuming that all the bending moment is carried by the flanges,

(2) Assuming that one-eighth the area of web is available as flange area. The stress in the outermost rivet is given by the formula, where M' is moment carried by web.

(3) By moment of inertia of net section. The stress in the outermost rivet is given by the formula

(4) By moment of inertia of gross section. The stress in the outermost rivet is given by the formula

Flange Splice.-Flanges should never be spliced unless it is impossible to get material of the required length. Flange splices should always be located at points where there is an excess of flange section, no two parts of the flange should be spliced within two feet of each other. Rivets in splice plates and angles should be located as close together as possible in order that the transfer may take place in a short distance. No allowance should be made for abutting edges of spliced members of the compression flange.

Flange angles should be spliced with a splice angle of equal section riveted to both legs of the angle spliced. Where this is impossible the largest possible splice angle should be used and the difference made up by a plate riveted to the vertical leg of the opposite angle. The number of rivets required in the splice angle on each side of the joint in the angle is given by the formula

=

where f the allowable unit stress in the flange, A = area of spliced angle, and r = the allowable stress on one rivet. Rivets which are already considered as transferring the shear may be considered as splice rivets if they are included in the splice angle.

Cover plates should be spliced with a splice plate of equal section. The number of rivets