Theory of Plates and Shells (McGraw-Hill Classic Textbook by S. Timoshenko

By S. Timoshenko

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Extra resources for Theory of Plates and Shells (McGraw-Hill Classic Textbook Reissue Series)

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Structural components As structural components, cables in beam-like forms sustain tensional components of internal moments, forming free-standing cable networks. Tensegrity grids and new cable-strut grids with extended concept belong to the type. 2). Tensegrity concept is introduced in the following section. 3 Introduction to tensegrity ‘Tensegrity’ attracted wide attention since its mysterious origin and its unique characteristics in architecture. Although some similar ideas occurred occasionally in 1920s (Motro 1996), topic studies were led by Buckminister Fuller, the originator of geodesic geometry.

A system with high-order infinitesimal mechanisms cannot be rigidified by one state of self-stress. A system with finite mechanisms cannot be rigidified at all. However, these mechanisms may actually reach a stable final position under load after experiencing large displacement (including rigid body movement) despite that singularity in stiffness matrix hinders efficient analysis. 5 A cable string (containing first-order infinitesimal mechanisms). ● Loading process due to cable slackening. During the loading process, some cables may slacken.

4 Force equilibrium diagram at an arbitrary joint i. 8) Ј , Pi,y Ј , Pi,z Ј by amounts ␦Pi,x, ␦Pi,y, ␦Pi,z, When the loads are increased to Pi,x the nodes i and j deflect to xiЈ, yiЈ, ziЈ through ␦xi, ␦yi, ␦zi, and to xjЈ, yjЈ, zjЈ through ␦xj, ␦yj, ␦zj, respectively. Meanwhile, the force Fe and length le increase by ␦Fe to FeЈ and ␦le to leЈ, respectively. 11) e in which EAe is the sectional modulus of element e. 15) in which [K] is the stiffness matrix ranked 3Nj ϫ 3Nj (Nj is the total number of joints), {d} is the displacement vector ranked 3Nj ϫ 1, and {R} is the nodal in-equilibrium force vector ranked 3Nj ϫ 1.

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