{"loaderData":{"0-0-57":{"chapterData":{"_id":"66c67bc08d4ba352fd96023f","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"Center of Gravity—Distributed Force Systems—Fluid Statics","public_visibility":true,"book_slug":"statics","slug":"center-of-gravity-distributed-force-systems-fluid-statics","regular_authors":"","express_authors":"","regular_content":"

For every heavy body there is a definite point called a center of gravity, in which point we may suppose the weight of the body collected. — A Theorem of Archimedes.

","express_content":"","book_name":"Statics","permissions":{"book":"statics","chapter":"center-of-gravity-distributed-force-systems-fluid-statics","header1":"","header2":"","header3":"","bookType":"main","queryOn":"chapter","rolesData":[{"type":"PUBLIC","read":true,"write":false,"edit":false}]},"authors":[{"_id":"66c6369b8d4ba352fd95fb4b","full_name":"George W. Housner","image":"/user-images/Housnerpng-1724266258837.png","email":"housner@avidemia.com"},{"_id":"66c637d48d4ba352fd95fb6d","full_name":"Donald E. Hudson","image":"/user-images/Hudson1png-1724268841381.png","email":"hudson@avidemia.com"}]},"bookData":{"_id":"66c60f898d4ba352fd95fa97","category_id":"66cecf01c3d3f3f05eac01b6","author_id":["66c6369b8d4ba352fd95fb4b","66c637d48d4ba352fd95fb6d"],"book_name":"Statics","book_image":"/books/StaticsHousnerHudsonpng-1724256137605.png","book_description":"

This comprehensive textbook provides a solid foundation in the principles of statics, offering detailed explanations, illustrative diagrams, and practical examples to reinforce key concepts. Renowned for its clear and systematic approach, it serves as an essential resource for engineering students and professionals aiming to understand and apply the fundamental principles of statics in real-world scenarios.

Authored by George W. Housner and Donal E. Hudson, both leading figures in earthquake engineering and structural dynamics, the book offers added depth, particularly in understanding the relationship between static forces and dynamic conditions.

","have_express_version":true,"is_published":false,"status":"ACTIVE","slug":"statics","buy_regular_link":"","buy_express_link":"","chapter_name_type":1,"created_at":"2024-08-21T11:24:25.448Z","__v":0,"updated_at":"2024-08-28T07:18:24.266Z","chapter_data":[{"_id":"66c642fa8d4ba352fd95fc77","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"The Composition and Resolution of Force Systems","sequence":1,"chapter_content":"

Any number of forces are always reducible to a single force and a single couple whose plane is perpendicular to the direction of the force. So that there is always in space a certain determinate straight line . . . which may serve at the same time to represent the line of action of the resultant, and the axis of the resultant couple . . . this central axis . . . gives us so luminous a reduction of all of the forces of the system as to throw a light at the same time upon all the other equivalent reductions, and to group them, so to speak, into a single picture, in which we see at once order and mutual dependence.
—L. Poinsot, Éléments de Statique (1803).

Mechanics is the science of motion and has as its object the investigation of the position and configurations of systems of material bodies as a function of time. The aim of this investigation is to arrive at the simplest description of the facts which are observed in nature and, from this description, to form generalizations which will permit valid predictions as to the behavior of other systems.

The motions that occur in nature are the result of interactions between the various bodies which make up the system under consideration. That portion of the subject of mechanics which describes the motion of bodies, without reference to the causes of the motion, is called kinematics. That portion of the subject which studies the relationship between the mutual influences and the resulting motions is called kinetics. The subjects of kinematics and kinetics are often considered together under the name of dynamics. That portion of the subject which studies the conditions under which the interactions between bodies counteract each other, with a resultant state of rest or of uniform motion, is called statics. When the mutual influences between the bodies of a system counteract each other so that the system is either at rest or moves with a uniform velocity, the system is said to be in equilibrium. Statics, then, is the study of the conditions of equilibrium. In a large number of engineering problems the structures or mechanisms which are under consideration are in equilibrium, so that the subject of statics assumes an important place in the field of applied mechanics.

","chapter_express_content":"","public_visibility":true,"book_slug":"statics","slug":"the-composition-and-resolution-of-force-systems","regular_authors":"","express_authors":"","created_at":"2024-08-21T11:24:25.451Z","__v":0,"header_data":[{"sequence":1,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-concept-of-a-force","header_name":"The Concept of a Force","type":"header-1","header_data":[],"_id":"66c647678d4ba352fd95fc8c"},{"sequence":2,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-composition-and-resolution-of-forces","header_name":"The Composition and Resolution of Forces","type":"header-1","header_data":[],"_id":"66c671db8d4ba352fd95fe4d"},{"sequence":3,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"systems-of-parallel-forces","header_name":"Systems of Parallel Forces","type":"header-1","header_data":[],"_id":"66c672058d4ba352fd95fe62"},{"sequence":4,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-definition-of-a-moment","header_name":"The Definition of a Moment","type":"header-1","header_data":[],"_id":"66c6723c8d4ba352fd95fe77"},{"sequence":5,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-theorem-of-moments","header_name":"The Theorem of Moments","type":"header-1","header_data":[],"_id":"66c672608d4ba352fd95fe8c"},{"sequence":6,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-product-of-two-vectors","header_name":"The Product of Two Vectors","type":"header-1","header_data":[],"_id":"66c6728b8d4ba352fd95fea1"},{"sequence":7,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-scalar-or-dot-product","header_name":"The Scalar or Dot Product","type":"header-1","header_data":[],"_id":"66c672b28d4ba352fd95feb6"},{"sequence":8,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-analytical-description-of-a-vector","header_name":"The Analytical Description of a Vector","type":"header-1","header_data":[],"_id":"66c672da8d4ba352fd95fecb"},{"sequence":9,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-vector-or-cross-product","header_name":"The Vector or Cross Product","type":"header-1","header_data":[],"_id":"66c673048d4ba352fd95fee0"},{"sequence":10,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-moment-of-a-force-as-a-vector-product","header_name":"The Moment of a Force as a Vector Product","type":"header-1","header_data":[],"_id":"66c6732b8d4ba352fd95fef5"},{"sequence":11,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-characteristics-of-a-couple","header_name":"The Characteristics of a Couple","type":"header-1","header_data":[],"_id":"66c6734f8d4ba352fd95ff0a"},{"sequence":12,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-resolution-of-a-force-into-a-force-and-a-couple","header_name":"The Resolution of a Force into a Force and a Couple","type":"header-1","header_data":[],"_id":"66c673708d4ba352fd95ff1f"},{"sequence":13,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-resultant-of-the-general-force-system","header_name":"The Resultant of the General Force System","type":"header-1","header_data":[],"_id":"66c673918d4ba352fd95ff34"},{"sequence":14,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-composition-and-resolution-of-force-systems","slug":"the-isolation-of-a-mechanical-system-free-body-diagrams","header_name":"The Isolation of a Mechanical System — Free-Body Diagrams","type":"header-1","header_data":[],"_id":"66c673c18d4ba352fd95ff49"}]},{"_id":"66c6742e8d4ba352fd95ff85","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"The Equilibrium of Force Systems","sequence":2,"chapter_content":"

Prop. 6: Commensurable magnitudes balance at distances reciprocally proportional to their weights. Prop. 7: And now, if the magnitudes be incommensurable, they will likewise balance at distances reciprocally proportional to the magnitudes. — Archimedes (287-212 в.c.), On Plane Equilibrium.

In the preceding chapter the problem of reducing any type of force system to the simplest possible equivalent force system has been solved. In many practical problems the forces acting upon a system are balanced so that the resultant force is equal to zero. In the present chapter the conditions under which this equilibrium condition is obtained will be investigated. We shall first establish the equations of equilibrium for the general three-dimensional force system.

","chapter_express_content":"","public_visibility":true,"book_slug":"statics","slug":"the-equilibrium-of-force-systems","regular_authors":"","express_authors":"","created_at":"2024-08-21T11:24:25.451Z","__v":0,"header_data":[{"sequence":1,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-equilibrium-of-force-systems","slug":"conditions-of-equilibrium","header_name":"Conditions of Equilibrium","type":"header-1","header_data":[],"_id":"66c676508d4ba352fd95ffd4"},{"sequence":2,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-equilibrium-of-force-systems","slug":"three-forces-in-equilibrium","header_name":"Three Forces in Equilibrium","type":"header-1","header_data":[],"_id":"66c6766c8d4ba352fd95ffe9"},{"sequence":3,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-equilibrium-of-force-systems","slug":"complete-constraint-of-a-rigid-body-in-space","header_name":"Complete Constraint of a Rigid Body in Space","type":"header-1","header_data":[],"_id":"66c6768d8d4ba352fd95fffe"},{"sequence":4,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-equilibrium-of-force-systems","slug":"degrees-of-freedom","header_name":"Degrees of Freedom","type":"header-1","header_data":[],"_id":"66c676b48d4ba352fd960013"}]},{"_id":"66c677be8d4ba352fd96006a","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"The Principle of Virtual Displacements","sequence":3,"chapter_content":"

In general, I believe that I may assert that all the general principles which may still be discovered in the science of equilibrium will be only this same principle of virtual velocities, looked at from different points of view, and differing from it only in the form of statement.—Lagrange, Mécanique Analytique (1788).

In the development of the principles of statics outlined in the preceding pages, we have adopted only one of several possible points of view concerning the basic elements of the subject. In considering such a problem as the equilibrium of two weights, Fig. 1a, we have emphasized the fact that the significant quantities involved are the magnitudes \\(W_{1}\\) and \\(W_{2}\\) of the forces and the distances \\(a\\) and \\(b\\) of the forces from the pivot point. The development of these ideas, starting with Archimedes, and brought to their modern form by Varignon, finally culminated in the concept of the moment of a force about a point. In the problem of Fig. 1, this concept of a moment would lead to the following equilibrium equation: \\(\\left(W_{1}\\right)(a)=\\left(W_{2}\\right)(b)\\). It was perceived, however, by Galileo and Stevinus, that it would be just as logical to focus the attention upon another significant quantity. Suppose (Fig. 1b) that we imagine that the lever and weight system has tipped through some small angle, thus raising \\(W_{1}\\) through a distance \\(c\\) and lowering \\(W_{2}\\) through a distance \\(d\\). From similar triangles we can say that \\(a / c=b / d\\); substituting this in the above equilibrium equation, we find \\(\\left(W_{1}\\right)(c)=\\left(W_{2}\\right)(d)\\). We may now consider as the significant quantities in the problem, the forces \\(W_{1}\\) and \\(W_{2}\\) and the distances \\(c\\) and \\(d\\), through which the weights have moved.

This second form of the equation is equivalent to the previous statement, so far as any practical solution of the problem is concerned. We have, however, approached the problem in a somewhat different way. In the first case we balance the moments of the system about the pivot point; in the second case we examine the work which is done by the forces of the system during some possible motion of the system. The universal applicability of this second point of view to the problems of mechanics was first indicated in 1717 by John Bernoulli, and this Principle of Virtual Displacements was taken as the foundation for the science of mechanics by Lagrange in his Mécanique Analytique.

Since the principle of virtual displacements introduces no new information into the science of mechanics, we cannot, by its use, solve problems which we would be unable to solve by the methods previously discussed. For certain types of problems, however, the principle leads directly to particularly simple results, and it is for this reason, and for the additional reason that the principle is the starting point for several important developments in dynamics, that we shall here consider the principle of virtual displacements.

","chapter_express_content":"","public_visibility":true,"book_slug":"statics","slug":"the-principle-of-virtual-displacements","regular_authors":"","express_authors":"","created_at":"2024-08-21T11:24:25.451Z","__v":0,"header_data":[{"sequence":1,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-principle-of-virtual-displacements","slug":"the-principle-of-virtual-displacements-for-a-free-particle","header_name":"The Principle of Virtual Displacements for a Free Particle","type":"header-1","header_data":[],"_id":"66c677e18d4ba352fd96007f"},{"sequence":2,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-principle-of-virtual-displacements","slug":"the-principle-of-virtual-displacements-for-a-constrained-particle","header_name":"The Principle of Virtual Displacements for a Constrained Particle","type":"header-1","header_data":[],"_id":"66c677fe8d4ba352fd960094"},{"sequence":3,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-principle-of-virtual-displacements","slug":"the-principle-of-virtual-displacements-for-a-system-of-particles","header_name":"The Principle of Virtual Displacements for a System of Particles","type":"header-1","header_data":[],"_id":"66c678438d4ba352fd9600a9"},{"sequence":4,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-principle-of-virtual-displacements","slug":"the-generality-of-the-principle-of-virtual-displacements","header_name":"The Generality of the Principle of Virtual Displacements","type":"header-1","header_data":[],"_id":"66c6787f8d4ba352fd9600be"},{"sequence":5,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-principle-of-virtual-displacements","slug":"the-potential-energy-of-systems-in-equilibrium","header_name":"The Potential Energy of Systems in Equilibrium","type":"header-1","header_data":[],"_id":"66c679968d4ba352fd960164"},{"sequence":6,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"the-principle-of-virtual-displacements","slug":"stable-unstable-and-neutral-equilibrium","header_name":"Stable, Unstable, and Neutral Equilibrium","type":"header-1","header_data":[],"_id":"66c679bf8d4ba352fd960179"}]},{"_id":"66c67bc08d4ba352fd96023f","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"Center of Gravity—Distributed Force Systems—Fluid Statics","sequence":4,"chapter_content":"

For every heavy body there is a definite point called a center of gravity, in which point we may suppose the weight of the body collected. — A Theorem of Archimedes.

","chapter_express_content":"","public_visibility":true,"book_slug":"statics","slug":"center-of-gravity-distributed-force-systems-fluid-statics","regular_authors":"","express_authors":"","created_at":"2024-08-21T11:24:25.451Z","__v":0,"header_data":[{"sequence":1,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"center-of-gravity","header_name":"The Center of Gravity","type":"header-1","header_data":[],"_id":"66c67d328d4ba352fd9602e7"},{"sequence":2,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-center-of-mass","header_name":"The Center of Mass","type":"header-1","header_data":[],"_id":"66c67d638d4ba352fd9602fc"},{"sequence":3,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"centroids-of-areas-lengths-and-volumes","header_name":"Centroids of Areas, Lengths, and Volumes","type":"header-1","header_data":[],"_id":"66c67d958d4ba352fd960311"},{"sequence":4,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-computation-of-centroidal-distances-and-of-moments-of-inertia-of-areas","header_name":"The Computation of Centroidal Distances and of Moments of Inertia of Areas","type":"header-1","header_data":[],"_id":"66c67e258d4ba352fd960326"},{"sequence":5,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-transfer-theorem-for-moments-of-inertia","header_name":"The Transfer Theorem for Moments of Inertia","type":"header-1","header_data":[],"_id":"66c67e578d4ba352fd96033b"},{"sequence":6,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-polar-moment-of-inertia-of-an-area","header_name":"The Polar Moment of Inertia of an Area","type":"header-1","header_data":[],"_id":"66c67e808d4ba352fd960350"},{"sequence":7,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-product-of-inertia-of-an-area","header_name":"The Product of Inertia of an Area","type":"header-1","header_data":[],"_id":"66c67eab8d4ba352fd960365"},{"sequence":8,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-moment-of-inertia-of-an-area-about-an-inclined-axis","header_name":"The Moment of Inertia of an Area about an Inclined Axis","type":"header-1","header_data":[],"_id":"66c67ee58d4ba352fd96037a"},{"sequence":9,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"distributed-forces","header_name":"Distributed Forces","type":"header-1","header_data":[],"_id":"66c67f038d4ba352fd96038f"},{"sequence":10,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"hydrostatics","header_name":"Hydrostatics","type":"header-1","header_data":[],"_id":"66c67f238d4ba352fd9603a4"},{"sequence":11,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-pressure-in-a-fluid","header_name":"The Pressure in a Fluid","type":"header-1","header_data":[],"_id":"66c67f538d4ba352fd9603b9"},{"sequence":12,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-pressure-in-a-fluid-under-gravity-forces","header_name":"The Pressure in a Fluid Under Gravity Forces","type":"header-1","header_data":[],"_id":"66c67f718d4ba352fd9603ce"},{"sequence":13,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"hydrostatic-force-on-plane-areas","header_name":"Hydrostatic Force on Plane Areas","type":"header-1","header_data":[],"_id":"66c67f8f8d4ba352fd9603e3"},{"sequence":15,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"the-equilibrium-and-stability-of-floating-bodies","header_name":"The Equilibrium and Stability of Floating Bodies","type":"header-1","header_data":[],"_id":"66c67ffe8d4ba352fd96040d"},{"sequence":16,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"center-of-gravity-distributed-force-systems-fluid-statics","slug":"hydrostatic-force-on-any-curved-area--buoyant-forces","header_name":"Hydrostatic Force on Any Curved Area. Buoyant Forces","type":"header-1","header_data":[],"_id":"66c680f28d4ba352fd960500"}]},{"_id":"66c6813d8d4ba352fd960515","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"Friction: The Application of Statics to Machine Design","sequence":5,"chapter_content":"

The physical cause of the resistance offered by friction to the motion of surfaces which slide on each other can be explained either by supposing an interlocking of the roughnesses of the surfaces, which cannot be separated unless they yield or break or are lifted over the tops of one another; or by supposing that the molecules of the surfaces of the two planes in contact are so close together that they develop a cohesion which must be overcome to produce the motion; experiment alone can enable us to determine the reality of these different causes. —Coulomb, Théorie des Machines Simples (1779).

For the present chapter we shall consider the application of the principles of statics to the solution of a number of problems taken from the field of machine design.

An analysis of the forces involved in the various members of a machine is one of the first steps in the design of any machine, and we shall find that the principles of statics, as we have developed them above, play a very important part in this force analysis.

In many of the problems which we have solved, we have stated that the forces between surfaces in contact are normal to the surfaces in contact, i.e., that the reactions were frictionless. We now wish to investigate more exactly the true nature of these reactions, and to include in our analysis the effects of frictional forces which in all physical problems must be present in some degree.

These frictional forces will sometimes represent undesirable elements of a physical situation, in that there will be associated with them an energy dissipation. At other times we may wish to take advantage of the frictional forces, as in the case of brakes, clutches, and some types of propulsion systems.

","chapter_express_content":"","public_visibility":true,"book_slug":"statics","slug":"friction-the-application-of-statics-to-machine-design","regular_authors":"","express_authors":"","created_at":"2024-08-21T11:24:25.451Z","__v":0,"header_data":[{"sequence":1,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"friction-the-application-of-statics-to-machine-design","slug":"dry-friction","header_name":"Dry Friction","type":"header-1","header_data":[],"_id":"66c6817b8d4ba352fd96052a"},{"sequence":2,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"friction-the-application-of-statics-to-machine-design","slug":"thick-film-and-boundary-lubrication","header_name":"Thick-Film and Boundary Lubrication","type":"header-1","header_data":[],"_id":"66c6819c8d4ba352fd96053f"},{"sequence":3,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"friction-the-application-of-statics-to-machine-design","slug":"rolling-friction","header_name":"Rolling Friction","type":"header-1","header_data":[],"_id":"66c681ba8d4ba352fd960554"},{"sequence":4,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"friction-the-application-of-statics-to-machine-design","slug":"friction-problems-in-machine-design","header_name":"Friction Problems in Machine Design","type":"header-1","header_data":[],"_id":"66c681d88d4ba352fd960569"},{"sequence":5,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"friction-the-application-of-statics-to-machine-design","slug":"pivot-friction","header_name":"Pivot Friction","type":"header-1","header_data":[],"_id":"66c681f88d4ba352fd96057e"},{"sequence":6,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"friction-the-application-of-statics-to-machine-design","slug":"screw-threads","header_name":"Screw Threads","type":"header-1","header_data":[],"_id":"66c6821b8d4ba352fd960593"},{"sequence":7,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"friction-the-application-of-statics-to-machine-design","slug":"brake-band-or-belt-friction","header_name":"Brake-Band or Belt Friction","type":"header-1","header_data":[],"_id":"66c682508d4ba352fd9605a8"}]},{"_id":"66c6828e8d4ba352fd9605f7","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"Elementary Theory of Statically Determinate Structures","sequence":6,"chapter_content":"

The use of diagrams is a particular instance of that method of symbols which is so powerful an aid in the advancement of science. A diagram differs from a picture in this respect, that in a diagram no attempt is made to represent those features of the actual material system which are not the special objects of our study . . . when studying the equilibrium of a framework . . . in which each piece acts only by tension or pressure between its extremities, it is not necessary to know whether a particular piece is straight or curved or what may be the form of its section. In order, therefore, to exhibit the structure of the frame in the most elementary manner we may draw it as a skeleton in which the different joints are connected by straight lines. — James Clerk Maxwell, “On Bow’s Method of Drawing Diagrams in Graphical Statics” (1876), Scientific Papers, Vol. II, p. 492.

Many of the most important applications of the theory of statics are in the field of structural design. One of the first steps in the design of any structure is the calculation of the forces which act in the various members of the structure. Some of the special applications of statics which are used extensively in this field will be discussed in the following pages.

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Trusses","type":"header-1","header_data":[],"_id":"66c682eb8d4ba352fd960621"},{"sequence":3,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"the-method-of-joints","header_name":"The Method of Joints","type":"header-1","header_data":[],"_id":"66c6830a8d4ba352fd960636"},{"sequence":4,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"the-method-of-sections","header_name":"The Method of Sections","type":"header-1","header_data":[],"_id":"66c683268d4ba352fd96064b"},{"sequence":5,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"graphic-statics","header_name":"Graphic Statics","type":"header-1","header_data":[],"_id":"66c6834c8d4ba352fd960660"},{"sequence":6,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"the-graphical-solution-of-a-coplanar-force-system","header_name":"The Graphical Solution of a Coplanar Force System ","type":"header-1","header_data":[],"_id":"66c6836d8d4ba352fd960675"},{"sequence":7,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"equilibrium-problems-by-graphical-methods","header_name":"Equilibrium Problems by Graphical Methods","type":"header-1","header_data":[],"_id":"66c6838e8d4ba352fd96068a"},{"sequence":8,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"the-funicular-polygon-as-a-moment-diagram","header_name":"The Funicular Polygon as a Moment Diagram","type":"header-1","header_data":[],"_id":"66c683c28d4ba352fd96069f"},{"sequence":9,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"the-graphical-analysis-of-a-truss","header_name":"The Graphical Analysis of a Truss","type":"header-1","header_data":[],"_id":"66c683eb8d4ba352fd9606b4"},{"sequence":10,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"beams-and-beam-reaction-forces","header_name":"Beams and Beam Reaction Forces","type":"header-1","header_data":[],"_id":"66c6840f8d4ba352fd9606c9"},{"sequence":11,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"shearing-forces-and-bending-moments-in-beams","header_name":"Shearing Forces and Bending Moments in Beams","type":"header-1","header_data":[],"_id":"66c6842d8d4ba352fd9606de"},{"sequence":12,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"relationship-between-shear-force-and-bending-moment-diagrams","header_name":"Relationship between Shear Force and Bending Moment Diagrams","type":"header-1","header_data":[],"_id":"66c684638d4ba352fd9606f3"},{"sequence":13,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"flexible-cables","header_name":"Flexible Cables","type":"header-1","header_data":[],"_id":"66c6848c8d4ba352fd960708"},{"sequence":14,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"cable-with-horizontally-distributed-load","header_name":"Cable With Horizontally Distributed Load","type":"header-1","header_data":[],"_id":"66c6864c8d4ba352fd960794"},{"sequence":15,"public_visibility":true,"header_type":"TEXT","book_slug":"statics","chapter_slug":"elementary-theory-of-statically-determinate-structures","slug":"cable-loaded-by-its-own-weight","header_name":"Cable Loaded by Its Own Weight","type":"header-1","header_data":[],"_id":"66c6867c8d4ba352fd9607a9"}]},{"_id":"66c687168d4ba352fd9607be","book_id":"66c60f898d4ba352fd95fa97","chapter_name":"Appendix","sequence":7,"chapter_content":"

PROPERTIES OF PLANE SECTIONS

The following symbols will be used:

\\(A=\\) Area
\\(x_0, y_c=\\) Coordinates of centroid of section in \\(x y\\) coordinate system.
\\(I_{x_c}, I_{\\nu_c}=\\) Moment of inertia about an axis through the centroid parallel to the \\(x y\\) axes.
\\(r_{x_c}, r_{y_c}=\\) Radius of gyration of the section with respect to the centroidal axes parallel to the \\(x y\\) axes.
\\(I_{x_c y_c}=\\) Product of inertia with respect to the centroidal axes parallel to the \\(x y\\) axes.
\\(I_x, I_y=\\) Moment of inertia with respect to the \\(x y\\) axes shown.
\\(r_x, r_y=\\) Radius of gyration of the section with respect to the \\(x y\\) axes shown.
\\(I_{x y}=\\) Product of inertia with respect to the \\(x y\\) axes shown.
\\(I_P\\) (same as \\(J_O\\)) \\(=\\) Polar moment of inertia about an axis passing through the centroid.
\\(r_{P}=\\) Radius of gyration of the section about the polar axis passing through the centroid.
\\(G\\) marks the centroid.

PROPERTIES OF HOMOGENEOUS BODIES

The following symbols will be used:

\\(\\rho=\\) Mass density
\\(M=\\) Mass
\\(x_c, y_c, z_c=\\) Coordinates of centroid in \\(x y z\\) coordinate system.
\\(I_{x_c}, I_{y_c}, I_{z_c}=\\) Moment of inertia about an axis through the centroid parallel to the \\(x y z\\) axes shown.
\\(r_{x_c}, r_{y_c}, r_{z_c}=\\) Radius of gyration of the body with respect to the centroidal axes parallel to the \\(x y z\\) axes shown.
\\(I_{x_c y_c}, I_{x_c z_c}\\), etc. = Product of inertia with respect to the centroidal axes parallel to the \\(x y z\\) axes shown.
\\(I_x, I_y, I_z=\\) Moment of inertia with respect to the \\(x y z\\) axes shown.
\\(r_x, r_y, r_z=\\) Radius of gyration of the body with respect to the \\(x y z\\) axes shown.
\\(I_{x y}, I_{x z}\\), etc. \\(=\\) Product of inertia with respect to the \\(x y z\\) axes shown.
\\(I_{A A}, r_{A A}=\\) Moments of inertia and radii of gyration with respect to special axes shown.
\\(G\\) marks the centroid

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Center of Gravity—Distributed Force Systems—Fluid Statics

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