Plane And Space Trusses

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analysis of plane and space trusses

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Added: December 26, 2008 This Presentation is Public 
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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