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CE 636 - Design of Multi-Story Structures T. B. Quimby UAA School of Engineering.

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Presentation on theme: "CE 636 - Design of Multi-Story Structures T. B. Quimby UAA School of Engineering."— Presentation transcript:

1 CE 636 - Design of Multi-Story Structures T. B. Quimby UAA School of Engineering

2  Preliminary  Very rapid and simple approximate analysis  Gross approximations are made  Deflections and member forces should be within 15% of what a final analysis would give.  Final Analysis  Gives accurate deflections and member forces  Hybrid Analysis  Combines both preliminary and final analysis

3  Necessary to reduce the problem to a viable size  Materials of the structure and components are linear.  Only the primary structural components participate in the overall behavior.  Floor slabs are assumed to be rigid in plane.  Component stiffness of relatively small magnitude are assumed to be negligible.  Deformations that are relatively small, and of little importance, are neglected.  The effects of cracking in reinforced concrete members due to flexural tensile stresses are assumed to be representable by a reduced moment of inertia.

4  Loads from gravity forces result from tributary areas supported by members.  Resistance to external moment is provided by flexure of the vertical components and their axial action acting as the chords of a vertical truss. (See next slide)  Horizontal shear is resisted by:  Shear in the vertical components  the horizontal components of axial force in diagonal braces  Torsion on a building is resisted mainly by:  Shear in the vertical components  the horizontal components of axial force in diagonal braces  the shear and warping torque resistance of elevator, stair, and service shafts.

5  Resistance to bending and torsion can be significantly influenced by the vertical shearing action between connected orthogonal bents or walls. (Flange action)  Horizontal force interaction occurs when a horizontally deflected system of vertical components with dissimilar lateral deflection characteristics is connected horizontally.

6  The stiffer the shear connection, the larger the proportion of external moment that is carried by external forces.

7

8  Simplify analysis by replacing complex structures with “simple” structures having the same lateral characteristics.  Shear Walls and Braced Frames (deflection controlled by flexure) can be modeled with an “equivalent beam”.  Multibay Frames can be represented by a single bay Frame.  More complex coupled systems can be represented by assemblies of simple structures that each represent a particular type of bent. May need to include “rigid” arms to account for geometric bent width.  Nonplanar assemblies can be represented by a column located at the shear center.

9  Model needs yield accurate deflections and member forces.  Current computer analysis techniques use finite elements (stiffness method) and are capable of solving large, complex problems.  Input actual members, not simplified approximations.  Only include members that contribute/effect to the lateral force system.  Include all gravity and lateral forces carried by members in the model.

10  See text Figure 5.12  Truss element. 2 DOF (one translational at each node).  Beam element. 12 DOF (three translational and three rotational at each node).  Quadrilateral membrane element: 8 DOF (two translational at each node).  Quadrilateral plate bending element. 12 DOF (1 translational, 2 rotational at each node).

11  Used for modeling of shear walls.  Only translational DOF  All DOF are in one plane  Cannot apply moment at the nodes  Need to add a fictitious element to approximate a rigid connections (see Figure 5.17 in text)  Non rectangular bodies will require generation of a transitional mesh.

12  Use beam elements for frames  Deform axially, in shear and bending in two transverse directions, and twist  Need area, two shear areas, two moments of inertia, and torsional constant.  omitting or using large values for member properties can simplify the problem.

13  Use plane stress membrane elements since shear and bending are in-plane.  Story height, wall width elements are generally suitable. They give shear and chord forces at the node.  Rigidly connected links to other systems require the use of fictitious beams in the wall that are very rigid. (See text Figures 5.19 and 5.20).

14  The text shows two methods for modeling for P-Delta effects if your program does not include analysis of P-Delta effects.  Use either negative shear area or negative moment of inertia to simulate the “softening” effects of gravity loads (i.e. P-delta effects).

15  Large buildings can result in very complex models.  Reduced models must have the same deflections and member forces as the full model.  Use of symmetry and antisymmetry simplify the model and you get two benefits:  Reduced computer time and size requirements.  Less chance for error when adjusting member sizes.  Two dimensional models of three dimensional systems.  can use 2d beam elements with 6 DOF  Lumping like bents together in a 2D model  Wide Column and Deep Beam analogies

16  Must have symmetry or antisymmetry in both structure and loading.  Model 1/2 of the building with 1/2 the loads.  Be careful with the restraints at the “cut”. They must cause the restraint that the other half of the structure would provide.  See text Figures 5.23 and 5.24.  If a building is doubly symmetric (both symmetric and antisymmetric) you can model only one quarter of the structure.

17  put all bents in the same plane with axially rigid truss element links to represent the connecting rigid slab (see text Figure 5.25)  If orthogonal frames are mobilized (via stiff shear elements) they can also be included with a little work.  Connection to orthogonal frames is shear only so connecting link must be very rigid in shear and flexure while not transferring any axial force. (see text Figure 5.26).  Intersection columns are represented twice. Area is assigned to representation in parallel frame. Other representation gets zero area.

18  Translation in two orthogonal directions with twist is same a twist about a point somewhere else in the plane. (see text Figure 5.27)  Twisting generally occurs in asymmetric structures.  Technique is conceptually complex.

19  Combination of several of a structure's similar, and similar behaving, components or assemblies of components into an equivalent single component or assembly.  Lateral Lumping  combining similar bents (text Figure 5.29)  lumped assembly's behavior must be the sum of all the represented assemblies' behaviors.  Vertical Lumping  Can be used in structures having repetitive beam sizes and story heights.  Combine 3-5 levels of beams together at the middle beam location.  Lateral loads lumped at same levels

20  Shear walls can be modeled by “wide columns”. This gives you shear and moment at top and bottom of wall.  Must use “rigid” links for connections to beams or beams will be longer than they really are, increasing deflections and resulting in an oversized beam.  Same ideas hold true for deep beams connected to columns.  See text figures 5.32 through 5.34


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