THEORY OF STRUCTURES TEXTBOOK FREE DOWNLOAD PDF CIVILENGGFORALL

TOPICS COVERED

ELEMENTS OF PLANE STATISTICS
CONCURRENT FORCES IN A PLANE
THREE FORCES IN EQUILIBRIUM
EQUATIONS OF EQUILIBRIUM
INTERNAL FORCES
FUNICULAR POLYGON
APPLICATIONS OF THE FUNICULAR POLYGON
FUNICULAR CURVES FOR DISTRIBUTED FORCE
FLEXIBLE SUSPENSION CABLES
GRAPHICAL CONSTRUCTION OF BENDING MOMENT DIAGRAMS
PRINCIPLE OF VIRTUAL DISPLACEMENTS
STATICALLY DETERMINATE PLANE TRUSSES
SIMPLE TRUSSES
REACTIONS
METHOD OF JOINTS
MAXWELL DIAGRAMS
METHOD OF SECTIONS
COMPOUND TRUSSES
GENERAL THEORY OF PLANE TRUSSES
COMPLEX TRUSSES
HENNEBERG’S METHOD
METHOD OF VIRTUAL DISPLACEMENTS
INFLUENCE LINES
INFLUENCE LINES FOR BEAM REACTIONS
INFLUENCE LINES FOR SHEARING FORCE AND BENDING MOMENT
GIRDERS WITH FLOOR BEAMS
INFLUENCE LINES FOR THREE HINGED ARCH RIBS, SIMPLE TRUSSES AND COMPOUND TRUSSES
STATICALLY DETERMINATE SPACE STRUCTURES
CONCURRENT FORCES IN SPACE
SIMPLE SPACE TRUSSES : METHOD OF JOINTS
STATICALLY DETERMINATE CONSTRAINT OF A RIGID BODY IN SPACE
COMPOUND SPACE TRUSSES : METHOD OF SECTIONS
GENERAL THEORY OF STATICALLY DETERMINATE SPACE TRUSSES
ANALYSIS OF COMPLEX SPACE TRUSSES
HENNEBERG’S METHOD
GENERAL THEOREMS RELATING TO ELASTIC SYSTEMS
STRAIN ENERGY IN TENSION, TORSION AND BENDING
PRINCIPLE OF SUPERPOSITION
STRAIN ENERGY IN GENERALIZED FORM
CASTIGLIANO’S FIRST THEOREM
CASTIGLIANO’S SECOND THEOREM
THEOREM OF LEAST WORK
THE RECIPROCAL THEOREM
DEFLECTION OF PIN-JOINTED TRUSSES
APPLICATIONS OF CASTIGLIANO’S THEOREM
MAXWELL-MOHR METHOD OF CALCULATING DEFLECTIONS
GRAPHICAL DETERMINATION OF TRUSS DEFLECTIONS
METHOD OF FICTITIOUS LOADS
ALTERNATIVE METHOD OF FICTITIOUS LOADS
STATICALLY INDETERMINATE PIN-JOINTED TRUSSES
GENERAL CONSIDERATIONS
TRUSSES WITH ONE REDUNDANT ELEMENT
TRUSSES WITH SEVERAL REDUNDANT MEMBERS
ASSEMBLY AND THERMAL STRESSES IN STATICALLY INDETERMINATE TRUSSES
INFLUENCE LINES FOR STATICALLY INDETERMINATE TRUSSES
STATICALLY INDETERMINATE SPACE STRUCTURES
ARCHES AND FRAMES
INTRODUCTION
SYMMETRICAL TWO-HINGED ARCHES
SYMMETRICAL HINGELESS ARCHES
NUMERICAL CALCULATIONS OF REDUNDANT ELEMENTS
FUNICULAR CURVE AS THE CENTER LINE OF AN ARCH
UNSYMMETRICAL ARCHES
FRAMES WITHOUT HINGES
FRAMES WITH HINGES
EFFECTS OF TEMPERATURE CHANGES AND SUPPORT SETTLEMENT
RINGS
CONTINUOUS BEAMS AND FRAMES
SLOPE-DEFLECTION EQUATIONS
BEAMS WITH FIXED ENDS
CONTINUOUS BEAMS
BEAMS OF VARIABLE CROSS SECTION
CONTINUOUS FRAMES WITH PRISMATIC MEMBERS
MOMENT-DISTRIBUTION METHOD
ANALYSIS OF BUILDING FRAMES
FRAMES WITH NON PRISMATIC MEMBERS
MATRIX METHODS IN STRUCTURAL ANALYSIS
FORCE AND DEFORMATION METHODS
ELEMENTS OF MATRIX ALGEBRA
APPLICATION OF MATRIX METHODS TO PLANE TRUSSES
MATRIX ANALYSIS OF CONTINUOUS BEAMS
MATRIX TREATMENT OF ARCHES AND FRAMES
MATRIX ANALYSIS OF CONTINUOUS FRAMES

SUSPENSION BRIDGES
PARABOLIC FUNICULAR CURVE
DEFLECTION OF UNSTIFFENED SUSPENSION BRIDGES
FUNDAMENTAL EQUATIONS AND STIFFENED SUSPENSION BRIDGES
ANALYSIS OF STIFFENING TRUSSES
APPLICATION OF TRIGONOMETRIC SERIES IN CALCULATING DEFLECTIONS
THREE-SPAN SUSPENSION BRIDGE WITH SIMPLY SUPPORTED STIFFENING TRUSSES
THREE-SPAN SUSPENSION BRIDGE WITH CONTINUOUS STIFFENING TRUSS
STIFFENING TRUSS OF VARIABLE CROSS SECTION
STRUCTURAL DYNAMICS
FREE VIBRATIONS : ONE DEGREE OF FREEDOM
BAYLEIGH’S METHOD
FORCED VIBRATIONS IN STEADY STATE
GENERAL CASE OF A DISTURBING FORCE
NUMERICAL INTEGRATION
GRAPHICAL INTEGRATION
STATICAL AND DYNAMIC STRESSES IN RAILS
LATERAL VIBRATIONS OF PRISMATIC BEAMS
VIBRATION OF BRIDGES
STRUCTURES SUBJECTED TO EARTHQUAKES

THEORY OF STRUCTURES INTRODUCTION

A structure (from the Latin struere) is anything built: say an arched bridge or cathedral from stone; a ship or a roof (and perhaps a spire) from timber; an earth dam or an excavation in soil for a fortification; or (as isolated usages) iron bars (in China first) or vegetable ropes to form suspension chains in bridges. Before the Renaissance all these structures were built without calculation, but not without theory’, or what today would be called a code of practice.

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Mignot’s statement in 1400, at the expertise held in Milan, that ars sine scientia nihil est (practice is nothing without theory), testifies to the existence of a medieval rule-book for the construction of cathedrals: the few pages of a builder’s manual bound in with the book of Ezekiel in about 600 BC show that there were yet earlier rules. These rules, for construction in the two available materials, stone and wood, were essentially rules of proportion and, as such, are effectively correct Stresses in ancient structures are low, and this has helped to ensure their survival. The stone in medieval cathedral, or in the arch ring of a masonry bridge, is working at a level of one or two orders of magnitude below its crushing strength. Similarly, deflexions of such structures due to loading are negligibly small (although the movements imposed by warping of the material or by slow movements of foundations may often be seen).

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What is necessary is that ancient structures should be of the right form; a lying buttress must be of the right shape, an arch ring must have a certain depth, and a river pier must have a minimum width. Correct form is a matter of correct geometry, and the ancient and medieval rules of proportion were established empirically to give satisfactory designs The introduction two centuries ago of iron. and then steel, as a structural material generated new structural forms, such as the large-span lattice girder. or truss, and the high-rise framed building; and the advent of reinforced concrete made possible such attenuated construction as the thin shell roof These ‘modern’ structures work their materials harder than earlier buildings in stone and wood: a slender steel truss will have ambient stresses which are a sensible proportion of the yield stress (say one half or more).

Further, higher stresses will lead to larger elastic deformations of the components of the structure; these may be small in themselves, but overall deformations may now be of importance. This higher performance, coupled with the increase in complexity of structural form, dictated the need for a structural theory no longer based on empirical rules of proportion could assess whether or not a particular construction would fulfil its design – a theory which criteria. There are three main criteria which must be satisfied if a structure is to be successful (and a large number of other minor criteria that the modern designer will also take into account); they are those of strength, stiffness and stability.

The homely example of a four-legged table may make clear the three aspects of performance that are being examined. The legs of the table must not break when a (normal) weight is placed on top, and the table top itself must not deflect unduly, (Both these criteria will usually be satisfied easily by the demands imposed by criterion may be manifest locally, or overall. If the legs of the table are slender, they may buckle when the overall load on the table is increased a dinner party.) Finally, the stability Alternatively, if the legs are not at the four corners, but situated so that the top overhangs them, then placing a heavy weight near an edge may result in the whole table overturning.

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The Virtual Work

The theory of structures deals with the mechanics of slightly deformable bodies. The ‘slight deformations are such that, viewed overall, the geometry of the structure does not appear to alter, so that, for example, equilibrium equations written for the original structure remain valid when the structure is deformed. A familiar example for pin-jointed trusses arises in the resolution of forces at nodes; the inclinations of the bars are assumed to remain fixed with respect to a set of reference axes. For beams and frames, deflexions within the length of a member are ‘small’ compared with the length of that member, and so on.

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The equation of virtual work is altered profoundly when the body being studies suffers slight deformations. Not only will external forces acting On the body be involved; account must somehow be taken of the internal forces in equilibrium with those external forces. In the general application of the equation of virtual work, full use is made of the implication of the words in equilibrium with; the internal forces may be any one of the (infinitely many) sets which satisfy the equilibrium equations.

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