THE USER SHOULD FULLY UNDERSTAND THE ASSUMPTIONS OF THE PROGRAM AND SHOULD INDEPENDENTLY VERIFY THE RESULTS. In the design of the columns, the program calculates the required longitudinal and shear reinforcement. Backup design information produced by the program is also provided for convenient verification of results.
Design Algorithms 5
D Effects
For lateral drift effects, SAP2000 assumes that a P-D analysis has been performed and that amplification is already included in the results. Normally, the unsupported length of the element is equal to the length of the element, ie. distance between END-I and END-J of the element. All equations and descriptions presented in the following chapters correspond to this specific system of units unless otherwise 14 Special Aspects of Seismic Loads.
Design for ACI 318-99 17
Shear reinforcement is designed for each loading combination in the major and minor directions of the column. The effects of axial forces on column moment capacities are included in the formulation. In the design of concrete frames with special moments (seismic design), the shear capacity of the beam is also checked for possible shear due to the possible moment capacities at the ends and the factored gravity load.
Design for AASHTO LRFD 1997 43
The effects of the force reduction factor,j, are included in the generation of the interaction surfaces. The non-rocking moment magnification factor, db, associated with the major or minor direction of the column is given by (AASHTO 4.5.3.2.2b), These are the lengths between the supporting points of the element in the respective directions.
For moment-resisting frames in Seismic Zones 3 and 4, column shear design is also based on the over-resisting moment capacities of the members in addition to the factored moments (AASHTO. The tensile steel required for compression balancing in the concrete is. The tensile steel for the compression balance in the steel is given by. If Mu > 0, the depth of the compression block is given by (see Figure IV-4).
Therefore, the momentum balance Muto carried by the web is given by Muw = Mu - Muf. For moment-resisting frames in Seismic Zones 3 and 4, the shear design of beams is also based on the over-resisting moment capacities of the members in addition to the factored moments (AASHTO. In the design of moment-resisting concrete frames in Seismic Zones 3 and 4, the strength of the design shear in a beam, Vu, is also calculated from the overbearing moment capacities of the beam.
The details of the design criteria used for the various framing systems are described in the following sections.
Design for CSA-A23.3-94 71
The moment magnification factor, db, for non-lateral moments associated with the major or minor direction of the column is given by. In the design of ductile moment-resisting concrete frames, the design shear force, Vf, in a given direction is also calculated from the possible column moment capacities coupled with the factored axial force acting on the column (CSA 21.7.2.2) . MI+, MI- = Positive and negative moment capacities at end I of column using a steel yield stress value of factors afy and noj (js =jc =1.0).
In the design of nominal moment resisting frames (seismic), the shear capacity of the column is also checked for the nominal shear due to the nominal (js =jc =1.0) moment capacities and the factored gravity load (CSA in addition to the design checks required for Ordinary moment resisting frames In the above equations dv the distance between the resultant of the tensile and compressive forces is conservatively taken as 0.9d The factored compressive force developed in the concrete alone is given by the factored moment resisted by the concrete and bottom steel become, is.
The required tensile steel for balancing the pressure in concrete is. is the tensile steel for balancing the compression in steel. Therefore, the balance of moment, Mf to be carried by the web is given by Mfw = Mf -M ff. The design of ductile moment resisting concrete frames (seismic design) also checks the shear capacity of the beam for the likely shear resulting from the likely moment capacities and the included gravity load, in addition to the design checks required for ordinary moment resisting frames.
In the above equation dv, the distance between the resultants of the tensile and compressive forces is conservatively taken to be 0.9d.
Calculate the capacity ratio or required reinforcement area for the factored axial force and biaxial (or uniaxial) bending moments obtained from each load combination at each station in the column. The coordinates of these points are determined by rotating a plane with linear deformation in three dimensions on the section of the column (BS 3.4.4.1). The stress in the steel is given by the product of the steel strain and the steel modulus of elasticity, esE and is limited to the design strength of the steel, fs y fy).
The additional moment in a braced column in a given plane is the product of the axial load and the lateral deflection of the column in that plane (BS 3.8.3). When calculating the value of the effective length, the b-factor is conservatively set to 1. K is the correction factor for the deflection to take into account the influence of the axial force and K is conservatively taken as 1.
The beam section is then designed for the maximum positive and maximum factored negative moments taken by all load combinations at that section. If M > Msingle, the compression gain area, As¢, is given by. where d¢ is the depth of the compression steel from the compression face of the concrete, and. With the flange in compression, the program analyzes the section considering alternative locations of the neutral axis.
If the stress block extends beyond the width of the flanges, then the contribution of the web to the bending strength of the beam is considered.
Design for Eurocode 2 119
MRd = Design moment resistance of the section, NSd = The axial force obtained from analysis, and. Finally, the design moments are calculated from the maximum of the three, MRd = max(NRdetot, NRdemin, Mfactored). The effect on the concrete shear capacity of any concentrated or distributed load in the span of the column between two beams is ignored.
Also, the effect of direct support on the columns provided by the beams is ignored. Obtain the design value of the applied shear force VSd from the SAP2000 analysis results. The contribution of the flange to the beam strength is ignored if the flange is on the tension side.
The effect of any concentrated or distributed load in the beam span between two columns on the shear capacity of the concrete is not considered. Also, the effect of direct support on the beams provided by the columns is neglected. The following steps of the standard method (EC2 4.3.2.1) are involved in the design of shear reinforcement for a given beam for a given combination of loads due to shear forces in a given direction.
Obtain the design value of the applied shear force VSd from the SAP2000 analysis results.
Design for NZS 3101-95 143
Mcol, joint,elastic = column moment at the center of the joint obtained by linear elasticity analysis. For earthquake-resistant ductile frames and frames with limited ductility, the shear design of the columns is based on the overload moments of the column (NZS. MI+, MI- = positive and negative moment capacities at the end of the I column using steel yield stress value ofafy and without factors j (j =1 ,0.
MJ+, MJ- = Positive and negative moment capacities at end J of the column using a steel yield stress value of afy and no j factors (j =1.0 and). The beam section is then designed for the maximum positive and maximum factored negative moments obtained from all load combinations. The compressive force developed only in concrete is given by. the moment resisted by the concrete and end steel is.
If a£ds (NZS 8.4.2), further calculations for As are exactly the same as previously done for the rectangular section design. Therefore, the moment balance, M*, to be carried by the mesh is given by Mw* = M* -M*f. For frames resisting seismic moments, the shear design of the beams is also based on the overload capacity of the members.
L hinge = 2h (NZS 8.5.3.1) Column shear reinforcement requirements reported by the program are based solely on the above findings.
Design Output 175
The graphic display in an active window can be printed in grayscale black and white from the SAP2000 program. The tabular design output includes input and output design information, which depends on the selected design code. The design details can be displayed for a specific load combination and for a specific station of a frame element.
The detailed design information can be accessed by right clicking on the desired frame member. Additional information can be obtained for column members by clicking the Redesign, Details and Interaction buttons in the dialog box. For beams, additional information can be obtained by clicking the Redesign and Details buttons in the dialog box.
Clicking the Interaction button displays the interaction diagram in three-dimensional space for the column section. The design axial force and biaxial moments are plotted on the interaction diagram to represent the stress state in the column. The interaction diagram can be viewed in any direction and the display can be manipulated from the interaction dialog.
New Zealand Standard NZS 3101, Standard for Concrete Structures, Part 1 - Design of Concrete Structures, Standards New Zealand, Wellington, New Zealand, 1995.
