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A text book on roofs and bridges
A TEXT BOOK ON ROOFS AND BRIDGES
PART I. STRESSES IN SIMPLE TRUSSES
PART II. GRAPHIC STATICS
PART III. BRIDGE DESIGN
PART IV. HIGHER STRUCTURES
BY MANSFIELD MERRIMAN,
PROFESSOR OF CIVIL ENGINEERING IN THE LEHIGH UNIVERSITY.
NEW YORK; JOHN WILEY & SONS; 1888,
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PREFACE
The course of instruction in roofs and bridges given to students of civil engineering in Lehigh University consists of four parts; first, the computation of stresses in roof trusses and in all the common styles of simple bridge trusses; second, the analysis of stresses by graphic methods; third, the design of a bridge, which includes the proportioning of details and the preparation of working drawings; and fourth, the discussion of cantilever, suspension, continuous and arched bridges. In the following pages the first part of this course is presented.
The plan adopted in arranging this text-book on the computation of stresses is similar to that followed in the author's “Mechanics of Materials” The principles and methods are first established, and then numerous numerical examples are fully worked out to illustrate them and their application to different forms of trusses, while a number of problems are stated as exercises for the student As no work is so valuable to a student as that done by himself, each alternate leaf throughout the text has been left blank, so that his solutions of these problems may be recorded in permanent form.
In view of the importance of designing members for repeated stresses and shocks, particularly in bridge trusses, it has been thought well to compute in most cases the minimum as well as the maximum stresses. The range of stress thus becomes known for each member. It is believed that this feature will assist students in forming clear ideas as to the influence of the live load upon different members of the truss.
In the Chapter on roof trusses the fundamental principles are deduced, and directly applied to the computation of stresses caused by dead load, snow and wind. The simpler forms of roof trusses are well adapted to the elucidation of general principles, which in bridge trusses usually become of a special nature, owing to the parallelism of the chords.
In bridge trusses all methods of live loading are considered, beginning with that of a uniform load, passing to that of a locomotive excess over one or more panels, and concluding with that now in most general use - the actual locomotive wheel concentrations, followed by a uniform train load. Although the propriety of specifying typical locomotive wheel loads may perhaps be questioned, there can be no doubt but that, when once specified, the true static stresses should be computed for the given data, and not the approximate stresses from a so-called equivalent uniform load. The author has endeavored to present this subject in a simple manner and in accordance with the methods used in practice, and he acknowledges his indebtedness to the Phoenix Bridge Company for the convenient diagram for tabulating wheel moments.
The course of instruction in roofs and bridges given to students of civil engineering in Lehigh University consists of four parts; first, the computation of stresses in roof trusses and in all the common styles of simple bridge trusses; second, the analysis of stresses by graphic methods; third, the design of a bridge, which includes the proportioning of details and the preparation of working drawings; and fourth, the discussion of cantilever, suspension, continuous and arched bridges. In the following pages the first part of this course is presented.
The plan adopted in arranging this text-book on the computation of stresses is similar to that followed in the author's “Mechanics of Materials” The principles and methods are first established, and then numerous numerical examples are fully worked out to illustrate them and their application to different forms of trusses, while a number of problems are stated as exercises for the student As no work is so valuable to a student as that done by himself, each alternate leaf throughout the text has been left blank, so that his solutions of these problems may be recorded in permanent form.
In view of the importance of designing members for repeated stresses and shocks, particularly in bridge trusses, it has been thought well to compute in most cases the minimum as well as the maximum stresses. The range of stress thus becomes known for each member. It is believed that this feature will assist students in forming clear ideas as to the influence of the live load upon different members of the truss.
In the Chapter on roof trusses the fundamental principles are deduced, and directly applied to the computation of stresses caused by dead load, snow and wind. The simpler forms of roof trusses are well adapted to the elucidation of general principles, which in bridge trusses usually become of a special nature, owing to the parallelism of the chords.
In bridge trusses all methods of live loading are considered, beginning with that of a uniform load, passing to that of a locomotive excess over one or more panels, and concluding with that now in most general use - the actual locomotive wheel concentrations, followed by a uniform train load. Although the propriety of specifying typical locomotive wheel loads may perhaps be questioned, there can be no doubt but that, when once specified, the true static stresses should be computed for the given data, and not the approximate stresses from a so-called equivalent uniform load. The author has endeavored to present this subject in a simple manner and in accordance with the methods used in practice, and he acknowledges his indebtedness to the Phoenix Bridge Company for the convenient diagram for tabulating wheel moments.
CONTENTS: PART I. STRESSES IN SIMPLE TRUSSES
Chapter I
STRESSES - IN ROOF TRUSSES
- Definitions
- Loads on Roof Trusses
- Apex Loads and Reactions
- Relations between External Forces and Internal Stresses
- The Method of Moments
- Lever Arms
- The Method of Resolution of forces
- Dead Load Stresses
- Snow Load Stresses
- Ambiguous Cases
- The Ends of Roof Trusses
- Wind Loads
- Reactions Due to Wind Loads
- Wind Stresses in Trusses with Fixed Ends
- Wind Stresses in Trusses with One End Fixed and the Other Free
- Final Maximum and Minimum Stresses
- Crescent Roofs
- Purlins
- Flexural Stresses in Members
- Investigation of Roof Trusses
- Design of Roof Trusses
Chapter II
HIGHWAY BRIDGE TRUSSES
- Definitions
- Dead Loads
- Kinds of Trusses
- Stresses in Web Members
- Stresses in Chords
- Dead Load Stresses
- Live Loads
- Chord Stresses Due to Live Load
- Maximum Chord Stresses
- Vertical Shears Due to Live Load
- Maximum and Minimum Shears
- Web Stresses in the Warren Truss
- Panel Counter-Braces
- Web Stresses in Howe and Pratt Trusses
- Ranges of Stress
- The Bowstring Truss
- The Parabolic Bowstring Truss
- Other Forms of Trusses
- Snow Load Stresses
- Wind Stresses
- Final Maximum and Minimum Stresses
- Investigation and Design
Chapter III
RAILROAD BRIDGE TRUSSES
- Dead Loads
- Live Loads
- Snow, Wind and Impact
- Kinds of Trusses
- The Warren Truss with Sub-Verticals
- The Double System Warren Truss
- The Whipple Truss
- The Bollman Truss
- The Fink Truss
- The Baltimore Truss
- The Post Truss
- True Live Load Shears
- One Concentrated Excess Load
- Two Concentrated Excess Loads
- Locomotive Wheel Loads
- Shears from Wheel Loads
- Moments from Wheel Loads
- Tabulation for Locomotive Wheels
- Stresses from Locomotive and Train Loads
- Remarks on Double Systems
- Example of a Double System Truss
- Triple and Quadruple Systems
- Unsymmetrical Trusses
- The Lateral Bracing
- The Economic Depth of Trusses
CONTENTS: PART II. GRAPHIC STATICS
Chapter I. PRINCIPLES AND METHODS.
- The Force Triangle
- The Force Polygon
- Conditions of Equilibrium
- Stresses in a Crane Truss
- Stresses in a Polygonal Frame
- The Equilibrium Polygon
- Properties of the Equilibrium Polygon
- Reactions of Beams
- Simple Beams under Concentrated Loads
- Simple Beams under Uniform Loads
- Overhanging Beams
- Center of Gravity of Cross- Sections
- Moment of Inertia of Cross-Sections
- Graphical Arithmetic
Chapter II. ROOF TRUSSES.
- Definitions and Principles
- Dead and Snow Loads
- Stresses Due to Dead and Snow Loads
- A Triangular Roof Truss
- Wind Loads
- A Truss with Fixed Ends
- A Truss with One End Free
- Abbreviated Methods for Wind Stress
- Complete Stresses for a Triangular Truss
- Complete Stresses for a Crescent Truss
- Ambiguous Cases
- Unsymmetrical Loads and Trusses
Chapter III. BRIDGE TRUSSES.
- Loads on Bridge Trusses
- Dead Load Stresses
- Live Load Stresses in a Warren Truss
- Live Load Stresses in a Pratt Truss
- Snow Load Stresses
- Wind Stresses
- Stresses Due to Initial Tension
- Final Maximum and Minimum Stresses
- The Bowstring Truss
- The Parabolic Bowstring Truss
- Application of the Equilibrium Polygon
- Excess Loads
Chapter IV. LOCOMOTIVE WHEEL LOADS.
- Standard Typical Loads
- Analysis of a Plate Girder
- Analysis of a Pratt Truss
- Moments in Plate Girders
- Shears in Plate Girders
- Simultaneous Moments
- Shears in Trusses
- Floor beam Reactions
- Moments in Trusses
Chapter V. TRUSSES WITH BROKEN CHORDS.
- Points of Division in Panels
- Position of Wheel Loads
- Resolution of the Shear
- Example - Maximum Chord Stresses
- Example - Maximum Stresses in Diagonals
- Example - Maximum Stresses in Verticals
- Example - Minimum Stresses in Vertical
- Stresses due to Wind
Chapter VI. MISCELLANEOUS TRUSSES.
- The Pegram Truss
- The Pennsylvania Truss
- The Baltimore Truss
- Unsymmetrical Trusses
- Double and Quadruple Systems
- The Greiner Truss
- Horizontal Shear in a Beam
- Roof Truss with Counterbraces
- A Ferris Wheel with Tensile Spokes
- A Bicycle Wheel with Tensile Spokes
Chapter VII. ELASTIC DEFORMATION OF TRUSSES
- The Displacement Diagram
- Deformation of a Truss
- Deflection of a Truss
- Truss Deflection under Locomotive Wheel
- Loads
CONTENTS: PART III. BRIDGE DESIGN
Chapter I. HISTORY AND LITERATURE.
- Bridge Design prior to 1800
- Progress from 1800 to 1850
- Truss Development since 1850
- Materials used in Bridges
- Joint Connections
- Literature of Bridge Design
Chapter II. PRINCIPLES OF ECONOMIC DESIGN.
- Number of Piers and Spans
- Choice of Kind of Bridge
- Theoretic Comparisons of Trusses
- Economic Depth
- Practical Considerations
Chapter III. TABLES AND STANDARDS.
- Manufacturers' Pocket Books
- Standard Loads for Bridges
- Rivet Proportions
- Rivet Spacing in Angles
- Pin Plates and Rivets
- Properties of Channels
- Eyebars
- Standard Bridge Floor
- Expansion Bearings
- Conventional Signs on Drawings
Chapter IV, DESIGN OF A ROOF TRUSS.
- Data and Specifications
- Rafters and Purlins
- Loads and Stresses
- Main Sections
- Bearing Areas
- Design of End Joint
- Chord Splices
- Weight of the Truss
Chapter V. DESIGN OF A PLATE-GIRDER BRIDGE.
- Specifications
- Live-load Stresses
- The Track
- Loading
- Sectional Area of Flanges
- Composition of Flanges
- Web Section
- Web Splices
- Web Stiffeners
- Rivet Spacing in Flanges
- Lengths of Cover Plates
- Flange Splices
- Bed Plates and Expansion Rollers
- Upper Lateral System
- Lower Lateral System
- Transverse Bracing
- Final Estimate of Weight
- Discussion of Economic Depth
Chapter VI. DESIGN OF A PIN BRIDGE.
- Data and Specifications
- Floor Timbers and Stringers
- Floor Beams
- Stresses in Trusses
- Sections of Intermediate Posts
- Sections of Ties and Lower Chord
- Pins and Eyebar Heads
- Upper Chord Sections
- Section of the End Post
- Lateral and Transverse Bracing
- Pin Plates
- Stay Plates and Latticing
- Connections of Wind Bracing
- Pedestal, Expansion Rollers, and Bed Plates
- Minor Details and Camber
- Final Estimate of Weight
- Concluding Remarks
Chapter VII. DESIGN OF A RIVETED BRIDGE.
- Data and Specifications
- Floor System
- Stresses
- Sections of Truss Members
- Joint Details
- Shoes and Bed Plates
- Estimate of Weight
Chapter VIII. CLASS-ROOM DESIGNS.
- Plan for Class Work
- Data for a Pratt Truss Bridge
- Steps of the Design
- Estimate of Weight and Cost
- Comparison of Class Designs
- Exercises and Problems
Chapter IX. BRIDGE LETTINGS AND OFFICE WORK.
- Specifications
- Estimates and Proposals
- Lettings and Contracts
- Drafting Office Practice
Chapter X. BRIDGE SHOPS AND BUILDINGS.
- General Considerations
- The Forge Shop
- The Machine Shop
- The Pattern and Templet Shop
- The Truss Shop
- Roof of the Truss Shop
- Weight and Cost of Truss Shop
Chapter XI. SHOP PRACTICE.
- Preliminary
- Standards of Measure
- Templets
- Riveted Work
- Eyebars
- Smith Work
- Machine Work
- Foundry Work
- Inspection
- Painting and Shipping
- Cost of Manufacture
Chapter XII. A BALLAST-FLOOR PLATE-GIRDER BRIDGE.
- Description
- Loads and Stresses
- Specifications for Construction
- Specification for Steel
- Central and Hudson River Railroad
Chapter XIII. A HALF-THROUGH SKEW LATTICE BRIDGE.
- Description
- Bridge Specifications
- Norfolk and Western Railroad
- Design of the Floor System
- Design of the Trusses
- A Through Skew Riveted Bridge
Chapter XIV. A PONY LATTICE BRIDGE;
Chapter XV. A THROUGH PIN BRIDGE; UNION BRIDGE COMPANY.
Chapter XVI. A THROUGH PIN BRIDGE; PENCOYD BRIDGE CO.
Chapter XVII. A DECK THREE-TRUSS BRIDGE; PHCENIX BRIDGE COMPANY.
Chapter XVIII. ELEVATED RAILROAD STRUCTURES.
- General Considerations
- Specifications of the Brooklyn Elevated Railroad Company
- Maximum Moments and Shears
- Economic Depth
- Design of Longitudinal Plate Girders
- Transverse Girders
- Supporting Columns
- Drawings
- Estimate of Weight
- Erection
Chapter XIX. A HIGHWAY BRIDGE FOR ELECTRIC-CAR TRAFFIC.
CONTENTS: PART IV. HIGHER STRUCTURES
Chapter I. CONTINUOUS BRIDGES.
- Introduction
- Vertical Shears and Bending Moments
- Reactions of Supports
- The Theorem of Three Moments
- Reactions for Two Equal Spans
- Reactions for Three Spans
- Loadings for Maximum Shears
- Loadings for Maximum Moments
- A Two-Span Warren Truss
- A Three-Span Pratt Truss
- Supports on Different Levels
- Advantages and Disadvantages
- General Formulas
Chapter II. DRAW BRIDGES.
- Classification
- Swing Bridges
- A Center-Bearing Continuous Truss
- Plate Girder Swing Bridges
- A Rim-Bearing Continuous Truss
- Partially Continuous Swing Bridges
- A Partially Continuous Truss
- Deflection of a Swing Truss
- True Reactions for Swing Trusses
- Double Swing Bridges
- Simple Swing Bridges
- Horizontal Rolling Draw Bridges
- Hinged Lift Bridges
- Rolling Lift Bridges
- Other Forms of Movable Bridges
Chapter III. CANTILEVER BRIDGES.
- Fundamental Principle
- Classification
- Historical and Descriptive Notes
- The Cantilever Arm
- The Anchor Span
- An Anchor Truss
- The Intermediate Span
- An Intermediate Truss
- Influence Lines
- Economic Lengths
- Deflections
- Comparison with Simple Trusses
- General Comparisons
Chapter IV. SUSPENSION BRIDGES.
- Historical Notes
- Stresses in the Cable
- Deflection of the Cable
- Approximate Methods
- Effect of Temperature
- Effect of a Single Load
- Hangers and Stays
- Cable Connections
- Stiffening Trusses
- The Truss without Hinges
- The Truss with Center Hinge
- Discussion of Truss Theories
- Temperature Stresses in Trusses
- Limiting and Practicable Spans
- Unsymmetrical Spans
- Stiffened Cables
- Concluding Remarks
Chapter V. THREE-HINGED ARCHES.
- Metallic Arched Roofs
- Reactions of the Supports
- Stresses in Roof Arches
- Metallic Arched Bridges
- Live Loads for Maximum Stresses
- Computation of Stresses
- Parabolic Lower Chord
- Graphic Analysis of Stresses
- Position of Wheel Loads for Chords
- Position of Wheel Loads for Web Members
- Stresses due to Wheel Loads
- Excess Loads
- Wind Stresses
- Arch Rib with Soud Web
- Deflection
- Influence Lines
Chapter VI. TWO-HINGED ARCHES.
- Historical Notes
- Reactions for an Arch Rib
- Solid Arch Ribs
- Parabolic Arch Rib
- Position and Moments for Live
- The Axial Thrust
- Rib Shortening
- Influence of Temperature
- Flange Stresses
- Shear
- Arch Rib with Open Web
- Theory of Arch Rib Design
- Reactions for a Braced Arch
- Graphic Method for Reactions
- Live Load Stresses
- Temperature Stresses
- Final Horizontal Reactions
- Effect of Yielding Supports
- Weight of Spandrel-Braced Arches
- Comparative Methods for Horizontal Thrust
- Relation of Design and Construction
- Deflection
Chapter VII. ARCHES WITHOUT HINGES.
- Historical Notes
- Conditions of Equilibrium
- The Parabolic Arch Rib
- Position of the Live Load
- Determination of Stresses
- Rib Shortening
- Temperature Stresses
- Concluding Remarks
Chapter VIII. REFERENCES TO ENGINEERING LITERATURE.
- Explanatory Note
- Draw Bridges
- Cantilever Bridges
- Suspension Bridges
- Three-Hinged Archf5
- Two-Hinged Arches
- Arches without Hinges
CHAPTER V - DESIGN OF A PLATE-GIRDER BRIDGE
Art. 30. Specifications.
Let the design be that of a deck plate-girder bridge for a single-track railroad, the span being 80 feet between centres of bearing plates. The bridge is to be located on a straight track, and its material, with the exception of the track and the rivets, is to be medium steel. The specifications to be used are those of F. H. Lewis contained in a pamphlet entitled Soft Steel in Bridges, first published in the Proceedings of the Engineers' Club of Philadelphia, Vol. IX, January, 1892. By permission, so much of the specifications as relates to the design of plate girders of the above span is here reprinted.
Specifications for First-class Bridge Superstructure.
General Description,
2. Ties on tangents will be 8 inches by 10 inches, laid on 8-inch face and spaced 14 inches between centers; guard-rails will be 7 inches by 8 inches, spaced 8 feet between centers... Ties will be notched ¾ inch over stringers, and guard-rails f inch over ties. Guard-rails ¾ will be bolted to each end of every other tie; and ties and guard-rails will be secured to stringers by hook bolts at each end of every fourth tie.
3. For spans of 16 feet or less, rolled beams will be used, and from 16 feet to 100 feet, riveted plate girders. All spans over 100 feet will be pin-connected trusses.
4. Beams or deck girders on masonry will be spaced 7 feet o inches center to center (ties 10 feet long)...
10. All structures will be simple in design, and admit of accurate calculation of the stresses in each member.
18. Live loads will be as per diagram furnished by the Chief Engineer.
19. The structure will be proportioned to carry the live loads as per diagram, and the live- load stresses will be the maximum stresses produced by the rolling load considered as stationary or as moving in either direction...
20. The dead load shall consist of the entire structure, including the floor system and rails and fastenings. The weight of the ties, guard timbers, rails, spikes, etc., shall be taken at 400 pounds per linear foot for each track. The load of the structure when complete shall not exceed the dead load used in calculating the stresses.
Wind in Trusses.
22. The bottom lateral bracing in deck bridges and the top lateral bracing in through bridges must be proportioned to resist a uniformly distributed lateral force of 150 pounds per linear foot of bridge for all spans of 200 feet and under, and an additional force of 10 pounds per lineal foot for every 25 feet increase in length of span over 200 feet.
23. The bottom lateral bracing in through bridges and the top lateral bracing in deck bridges must be proportioned to resist a uniformly distributed force the same as above, and an additional force of 300 pounds per linear foot of bridge, which shall be treated as a moving load.
Centrifugal Force,
25. When the bridge is on a curve add to the maximum wind stresses a moving lateral stress equal to 3 per cent of the live load on all tracks (acting in the direction of centrifugal force) for each degree of curvature.
26. The effects of wind and centrifugal force in the lateral system of structures must be fully provided for at unit stresses given below.
Longitudinal Bracing and Anchorage,
27. Longitudinally the bracing of trestle towers and the attachments of the fixed ends of all trusses shall be capable of resisting the greatest tractive force of the engines or any force induced by suddenly stopping the assumed maximum trains, the coefficient of friction of the wheels upon the rails being assumed to be 0,20...
Temperature.
28. Variations in length from change of temperature to the amount of I inch in 100 feet shall be provided for.
Calculations and Unit Stresses.
29. All parts of the structure will be proportioned to sustain the maximum stresses produced by the live and dead loads specified above, and by the wind and centrifugal forces under special conditions provided in paragraphs 26, 32 and…
30. In calculating strains, conventional assumptions will be used throughout. The lengths of spans will be the distance between centers of end pins of trusses, and between centers of bearing plates of beams and girders. The length of stringers will be the distance between centers of floor beams, and the length of floor beams the distance between centers of trusses. The depth for calculation of girders will be the distance between centers of gravity of flange sections, provided it does not exceed the distance out to out of angles, in which case the latter amount shall be considered the depth.
Formulas far Unit Stresses.
32. In case the maximum stresses in chords, girder flanges, trestle posts, or the bending effects on posts due to wind or centrifugal force, shall exceed 25 per cent of stresses due to dead and live load, the sections will be increased until the total strain per square inch will not exceed by more than 25 per cent the maximum fixed for live and dead load only.
34. The effects of the weights of horizontal or inclined members in reducing their strength as columns must be provided for. It will also be considered in fixing the position of pin centers.
35. Plate girders shall be proportioned upon the supposition that the bending or chord strains are resisted entirely by the upper and lower flanges, and that the shearing or web strains are resisted entirely by the web plate.
Details of Construction and Workmanship. General
40. All details must be of approved forms and satisfactory to the Chief Engineer.
41. Preference will be had for such details as will be most accessible for inspection, cleaning, and painting.
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