CONTENTS.

LONG-SPAN RAILWAY BRIDGES.

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Formulæ for depth,

General formulæ for

8-13

Position of plate and

Definition of long-span bridge - Circumstances justifying adoption

General problem of indefinite solution - Importance of superstruc-

ture Want of information on the subject - Possible to approximate

— Object of paper, and method proposed to be adopted.. Pages 1-5

Relative strains on webs and flange - Lattice and plate webs - Mini-

mum thickness of plate governs depth — Limit of depth for lattice —

Method for arriving at weight of ironwork necessary - Limiting

strain- Types of construction to be investigated in iron and

steel

5-8

Type 1. Box girders — Economic depth small - Buckling of plates

and waste of metal at centre-Weight of web governs depth-

General principles determining proper depth

and minimum thickness of plate allowable-

strains and multiples - Tables of same

Theoretical deductions overruled by practical

lattice reversed - Advantage of lattice on account of increased

economic depth — Stiffness

- Inves-

American and English lattice-
tigation of strains, and proper depths of Type 2- Lattice girders —
Tables of strains and multiples ..
Type 3. Bowstring girders - Uniform and unequal loads Bracing
requires little metal, otherwise proves disadvantageous - Stiffness
Investigations of mass required-Influence of load-Strain on
diagonals - Tables of strains and multiples
16-23

Type 4. Straight-link girders - No example in this country - Chep-

stow Bridge - Bollman truss - Discussion at Institution — Similarity

to bowstring-Influence of load - Reversed conditions-Inclina-

tion of bows - Deflections peculiar - Practical difficulties - Strains,

masses, and multiples - Tables - Conclusion of first stage.. 23-31

Type 5. Cantilever-Appearance same as Type 2-Web same also
- Mass and moment of flange theoretically less - Extra metal in
adjacent spans diminish economy Mass of metal-Tables of con-
stants, strains, and multiples
31-36

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13-16

Type 6. Cantilever varying depth - Modification of form desirable—
Curved-top flanges diminish strain on web-Depth and stiffness
greater― Mr. Fowler's Severn Bridge — Tables of multiples, &c.

Pages 36-38
Type 7. Continuous Maximum span - Sedley's bridge no prac-
tical difficulty - Economical results surpass other systems —
Tables

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38-43
Type 8. Arched rib-Early form of long-span bridge - Indefinite-
ness of opinions concerning it—Hypotheses vary — Rib jointed at
three points — Nicety in proportioning metal to strain — Expansion
and contraction entail no additional strain - Investigation of strains
- Tables, &c.
43-49
Type 9. Suspension with stiffening girder - Lightness and strength
of rope between supports - Earliest form of long span - Instability
at first inadequately appreciated — Check ties — No important diffi-
culty in obtaining any required amount of stability - Transverse
strength necessary Vibration always exists, but not detrimental
Great variety of design for rigid bridges - Investigation of strains
on chains and stiffening girders — Tables, &c.
Type 10. Suspended girder-Reasons for rigidity of girder as com-
pared with suspension - Inverted bowstring - Reduction of mass by
initial tension on boom-Mr. Fowler's Thames Bridge - Freedom
from vibratory impulses -- Expansion provisions — Investigation of
strains, masses, &c. - Tables

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49-55

55-60

Rolling, dead,
60-62

Type 11. Same as straight-link girder, less the boom
and mixed loads - Tables of strains and multiples
Conclusion of tables of multiples - Investigation of specific loads
Weights of platform-Cross girders - Useful load Formulæ and
classification - Gross loads

Tables of loads and weight of iron in cwts. per foot run ..
Adaptation of formula to steel structures -Available strength for
useful load higher ratio than limiting strains Tables of multiples,
strains, and weight of metal
Summary of results, illustrated by diagrams-Comparative economy
refers to superstructure only - Expense of piers influences economy
- Fairest comparison obtained by taking average weight per foot of
viaduct Tables of same-Difference less marked - Influence of
cost of scaffolding on designs for long-span bridges

SHORT-SPAN RAILWAY BRIDGES.

Essential difference between short and long span bridges - Rolling

load proportionally large in former, and different design required to

attain economy

Pages 87-89

Special action of rolling load as compared with dead load is of a three-
fold nature: Greater bending stress, frequent deflections, and
consequent vibrations - Modifying action of springs-Increased
deflection under rolling load indicated by theory-Practical con-
ditions modifying these conclusions
89-95
Large increase in bending moment must be provided for in short
girders - Baron Von Weber's experiments as to variations of load
on engine springs - Increase on normal load nearly cent. per
cent.
95-98

Other pressures not transmitted through springs - Obliquity of con-

necting rod and centrifugal force of unbalanced masses -Practical

illustration of destructive action of heavy tank engines 98-105

Effect of repeated bendings upon the endurance of girders — Herr

Wohler's experiments - Influence of varying proportions of dead

and live load-Fairbairn's experiments upon cast-iron bars - Truth

of conclusions illustrated by failure of Somerset House girders-

Effect of rolling load, provided for in ensuing Tables, partly by

assuming an increased load, and partly by adopting a diminished

unit strain

105-111

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Actual rolling loads to which existing bridges are liable- Great

Northern express engine and tender - Do. goods engine and tender

- London and Brighton goods engine - St. John's Wood tank engine

- General summary and table of normal rolling loads for short-span

bridges

111-116

Increase upon normal rolling load adopted in calculations — Decreased
working strain in short spans - Dead load upon the several spans
-Type form of bridges proposed to be considered

Type 1, Division (a), two main plate girders, with cross girders secured

to lower flanges-Modern practice with respect to cross girders-

Deficient strength of old cross girders- Advantage of increased

depth - Horizontal bracing-Weight of cross girders and bracing

-Table of weights of main girders and of total ironwork per foot

run in bridges of different spans

116-119

119-126

Type 1, Division (b), three main plate girders with cross girders secured

to lower flanges-Saving in weight is effected, but not necessarily a

saving in cost — Tables of weight of iron required in construction of

bridges of this class up to 100 feet span

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Pages 126-128

Type 1, Division (c), two main plate girders with cross girders on top

-Saving effected at all spans -Weight of iron required in main

girders, &c.

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128-130

135-137

Type 1, Division (d), three main girders with cross girders on top,

and Division (e), four main girders with bracing Tables of

weights

130-132

Type 2, Division (a), two main lattice girders with cross girders at lower
flanges-Reduced weight of web-Lattice girder not necessarily
lighter than plate girder - Weight of iron required in this division
and also in Division (6), which comprises three main lattice girders
with cross girders at lower flanges
132-135
Type 3, bowstring girders, or lattice girders of special construction —
Reduced weight effected at cost of increased labour-Weight of iron
in main and cross girders
Type 4, Division (a), two main plate continuous girders with cross
girders at bottom flange-Reduced weight in consequence of
modified strains on flanges - Small advantage in short spans -
Tables of loads, weight of iron, and sectional area required in terms
of that necessary in an independent girder of equal span 137-140
Type 4, Division (b), same as preceding, but with lattice girders of
ordinary construction, and in Division (c) with lattice girders of
special construction - Tables of weights and loads
Bridges of all varieties of design, so far as regards weight of iron
required in construction, will be included in preceding Tables
Mr. Fowler's wrought-iron arched bridge same weight as lattice
girder — Tables are not simple records of actual weights of existing
bridges, but are based upon such weights duly collated and rectified
- Example of long-span bridge recently erected, and comparison of
actual weight with that previously published in the Tables - Contract
weight of Mr. Fowler's 600 feet Severn Bridge - Comparative
weights of different existing independent lattice-girder bridges —
Practical illustration of statement that lattice girder not necessarily
lighter than plate girder - Example of great economy that may be
attained in a well-designed lattice girder
141-147

Comparison between weights of iron in different existing continuous lat-

tice-girder bridges - Remarkable discrepancies evidenced 147-149

Examples of similar inconsistencies in the case of plate girders
Evidence as to same differences obtaining in the shorter

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spans
Pages 149-150
General conclusion to be drawn from preceding evidence is that the
Tables fairly represent the weight of iron required in a well-designed
bridge in each case Justification of provision made for rolling load
- Strain upon permanent way much higher than that assumed in
the calculations upon which the Tables are based — Variation in the
weights of existing structures much greater than it would be were
some standard before the designer, informing him what the weight
should be―The practice of individual designers may legitimately
vary considerably from time to time- General conclusion

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150-157