plane and space trusses

Views:
 
     
 

Presentation Description

analysis of plane and space trusses

Comments

Presentation Transcript

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