plane and space trusses

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Information about plane and space trusses
Science-Technology

Published on December 26, 2008

Author: touqanar2000

Source: authorstream.com

Theory of plane and space trusses : Theory of plane and space trusses Dr. Abdul Razaq Touqan Department of Civil Engineering Local versus global coordinates : Local versus global coordinates Element axes are not all the same. So there is a need for a coordinate transformation Coordinate transformations from local to global : Coordinate transformations from local to global Coordinate transformations from local to global : Coordinate transformations from local to global Coordinate transformations from local to global : Coordinate transformations from local to global Transformation matrix from global to local T is: Notice for an orthogonal matrix, the inverse transformation from local to global is quite easy because: Coordinate transformations from local to global : Coordinate transformations from local to global -The element stiffness matrix in local coordinates is: -since truss member connects two nodes, the transformation: Coordinate transformations from local to global : Coordinate transformations from local to global -element equation in local coordinate: -transform to global -multiply both sides by T-1 Global stiffness matrix : Global stiffness matrix Plane truss example : Plane truss example Analyze the truss shown, given: Slide 10: Plane truss example (continues) Member connects nodes 1?j Plane truss example (continues) : Plane truss example (continues) Plane truss example (continues) : Plane truss example (continues) Stress equation for PT : Stress equation for PT Space truss : Space truss 3D trusses Space truss : Space truss Space truss global stiffness : Space truss global stiffness Example : Example Analyze the truss shown, given ST example (solution) Member connects nodes 1?j : ST example (solution) Member connects nodes 1?j member(1):1 to 2 ST example (solution) : ST example (solution) member(2): 1 to 3 ST example (solution) : ST example (solution) -member (3): 1 to 4 ST example (solution) : ST example (solution) -combining equations ST example (solution) : -equation of stress becomes ST example (solution) ST example (solution) : ST example (solution) Slide 24: End of PT and ST analysis Let Learning Continue

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