Statics
A Text-Book for the Use of the Higher Divisions in Schools and for First Year Students at the Universities
By Arthur Stanley Ramsey
Publisher: Cambridge University Press
Print Publication Year: 2009
Online Publication Date:September 2010
Original Publication Year:1934
Online ISBN:9780511693625
Paperback ISBN:9781108003155
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511693625.007
Subjects: History of Mathematical Texts
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We have found that conditions sufficient to ensure the equilibrium of a rigid body under the action of coplanar forces are three in number, and may be summarized asâ€”
two resolutions and one equation of moments,
or one resolution and two equations of moments,
or three equations of moments.
The student will do well to bear in mind that, in the solution of a problem, no additional information can be obtained by writing down more than three such equations of moments or resolutions for one and the same body.
It follows that many statical problems are indeterminate or insolvable without further hypotheses as to the elastic properties of the body acted upon. For example, if a beam or bar under the action of given forces has its ends fixed, it is not possible to determine the magnitude and direction of the reactions at the fixed ends, because this means four unknown quantities, two magnitudes and two directions, and the conditions of equilibrium give only three equations between the four unknown quantities.
Constraints and Degrees of Freedom. The position of a plane body in its plane is determined by three quantities, such as the rectangular co-ordinates of one specified point of the body and the angle which a line fixed in the body makes with a line fixed in the plane. Hence a body free to move in a plane has three degrees of freedom. We may also express this fact by saying that it is free to have a motion of translation with components in either or both of two perpendicular directions and also free to rotate.
pp. i-iv
pp. v-vi
pp. vii-xii
Chapter I - INTRODUCTION : Read PDF
pp. 1-3
Chapter II - VECTORS : Read PDF
pp. 4-11
Chapter III - FORCES ACTING AT A POINT : Read PDF
pp. 12-30
Chapter IV - MOMENTS. PARALLEL FORCES. COUPLES : Read PDF
pp. 31-55
Chapter V - COPLANAR FORCES : Read PDF
pp. 56-66
Chapter VI - THE SOLUTION OF PROBLEMS : Read PDF
pp. 67-94
Chapter VII - BENDING MOMENTS : Read PDF
pp. 95-106
Chapter VIII - GRAPHICAL STATICS : Read PDF
pp. 107-133
Chapter IX - FRICTION : Read PDF
pp. 134-159
Chapter X - CENTRES OF GRAVITY : Read PDF
pp. 160-186
Chapter XI - WORK AND ENERGY : Read PDF
pp. 187-229
Chapter XII - FLEXIBLE CHAINS AND STRINGS : Read PDF
pp. 230-254
Chapter XIII - ELASTICITY : Read PDF
pp. 255-274
Chapter XIV - FORCES IN THREE DIMENSIONS : Read PDF
pp. 275-296