Chapter Structural Analysis - Ahmed Mansour

1 3-1 Chapter Structural Analysis The Structural Analysis collection includes frame Analysis and also some specialised finite element and beam Analysis modules. Structural Analysis using PROKON 3-2 Quick Reference Structural Analysis using PROKON 3-3 Frame Analysis 3-5 Plane Stress/Strain Analysis 3-78 Single Span Beam Analysis 3-78 Beam on Elastic Support Analysis 3-78 3-3 Structural Analysis using PROKON The accent of the Analysis modules falls on user friendliness, speed and efficiency. The frame Analysis module is ideally suited for the Analysis of small to medium sized structures, not to say that the analyses of large structures are not possible.

2 Frame has a comprehensive array of static and dynamic Analysis modes. Extensive use is made of interactive graphic representations during both the input and output phases. The input modules incorporate error checking to help eliminate input errors as they occur. Frame Analysis Frame can take account of own weight, temperature changes, prescribed displacements and elastic supports. Loads are entered as load cases and grouped in load combinations at ultimate and serviceability limit states. The following static Analysis modes are available: Linear Analysis : Normal elastic frame Analysis .

3 Second order Analysis : Models sway behaviour by incorporating P-delta effects. The solution is obtained by iterative Analysis , thereby allowing for options like tension elements. Non linear Analysis . This takes the second order Analysis a bit further. The load is applied in steps and the deflected structure at the end of each step is used to apply the next step. Material non linearity is not yet supported. Buckling Analysis : For calculating safety factors for Structural instability due to buckling. Dynamic Analysis modes available include: Modal Analysis : Calculation of a frame s natural modes of vibration.

4 Harmonic Analysis : For determining a frame s response to harmonic loading. Earthquake Analysis : Quasi-dynamic Analysis of a frame subjected to ground acceleration. Structural Analysis using PROKON 3-4 Finite element Analysis Frame allows you to use finite shell elements and solid elements alongside normal beam elements. The shell elements enables you to model the combination of plate bending and membrane action in 3D. To model plate bending in concrete slabs, you may prefer using the Finite Element Slab Design see Chapter 6 for details. You can also use the Plane Stress/Strain Analysis module to perform a finite element Analysis of any general plane geometry subjected to plane stress or strain.

5 The module features an automated element grid generation facility to help speed up the input and Analysis processes. Beam Analysis Modules are available for the Analysis of simple beams and beams on elastic supports. Post-processing of Analysis results Linear and second-order Analysis output can be post-processed by the steel member design modules, Strut and Com, to evaluate and optimise section profiles. The Space Frame Analysis module can also design finite shell elements as reinforced concrete members. 3-5 Frame Analysis Frame can be used for the Analysis of the following types of structures by selecting a domain on the General input tab: Plane Frames: Analysis of a frames in a vertical (X-Y) plane.

6 Grillages: Analysis of a structure in a horizontal (X-Z) plane. Space Frames: Analysis of three-dimensional structures made up of beam and/or shell elements and design of concrete shells. Space Trusses: Analysis of three-dimensional trusses where only axial forces are considered. Frame Analysis results can be post-processed using the steel member design modules for axial and combined stress, namely Strut and Com. Frame Analysis 3-6 3-7 Theory and application The following text explains the sign conventions used and gives a brief background of the Analysis techniques.

7 Sign conventions Frame input and output uses a mixture of global axis and local axes values. Global axes The global axis system is nearly exclusively used when entering frame geometry and loading. Global axes are also used in the Analysis output for deflections and reactions. The global axes are defined as follows: For the sake of this definition, the X-axis is chosen to the right. The Y-axis always points vertically upward. Using a right-hand rule, the Z-axis points out of the screen. Note: Unlike some other 3D programs that put the Z-axis vertical, Frame take the Y-axis as being vertical.

8 Beam element local axes Local axes are used in the output for element forces. You can also apply loads in the direction of a beam element s local y-axis. Frame Analysis 3-8 The local axes for beam elements are defined as follows: The local z-axis and axial force is chosen in the direction from the smaller node number to the larger node number. The y-axis is taken in a vertical plane perpendicular to the z-axis. The y and z-axes thus describe a vertical plane with the y-axis pointing vertically or diagonally upward. The x-axis is taken perpendicular to the y and z-axes, using a left-hand rule.

9 One special case exists: In the case of a vertical member, the z-axis is taken parallel to the global Y-axis. A unique definition of the y-axis is obtained by taking it parallel to the global X-axis. Shell element local axes For shell elements, the local axes are defined as follows: The local x and y-axes are chosen in the plane of the shell in such a way that the x-axis is horizontal and the y-axis lies perpendicular to and upward from the x-axis. Using a right-hand rule the z-axis is taken perpendicular to the shell element to point diagonally upward.

10 Two special cases exist: Horizontal elements: The local x is chosen parallel to the global X-axis and the y-axis parallel to the negative Z-axis. The z-axis is then taken parallel to the Y-axis. Vertical elements: The y-axis is taken vertically upward, parallel to the global Y-axis. The x-axis is taken horizontal in the plane of the shell and z-axis is taken horizontal perpendicular to the shell. The z-axis points towards you if the shell s nodes are defined in an anti-clockwise direction and away if defined clockwise. To simplify the Analysis output, the orientation of the local shell axes can sometimes be manipulated by slight rotation of the shell elements.