If the member is manually meshed broken into segments, maintaining the integrity of the design algorithm becomes difficult. Manually, breaking a column member into several elements can affect many things during design in the program.
The unbraced length: The unbraced length is really the unsupported length between braces. If there is no intermediate brace in the member, the unbraced length is typically calculated automatically by the program from the top of the flange of the beam framing the column at bottom to the bottom of the flange of the beam framing the column at the top. If there are intermediate bracing points, the user should overwrite the unbraced length factor in the program. The user should choose the critical larger one.
Even if the user breaks the element, the program typically picks up the unbraced length correctly, provided that there is no intermediate bracing point. K-factor: Even if the user breaks the member into pieces, the program typically can pick up the K -factors correctly. However, sometimes it can not. The user should note the K -factors. All segments of the member should have the same K -factor and it should be calculated based on the entire member.
If the calculated K -factor is not reasonable, the user can overwrite the K -factors for all the segments. Cm factor:. The program already calculates the Cm factors based on the end moments of unbraced lengths of each segment. If the break-up points are the brace points, no action is required by the user. If the broken segments do not represent the brace-to-brace unsupported length, the program calculated Cm factor is conservative. If this conservative value is acceptable, no action is required by the user.
If it is not acceptable, the user can calculate the Cm factor manually for the critical combination and overwrite its value for that segment. B1 factor: This factor amplifies the factored moments for the P- effect.
In its expression, there are the Cm factor and the Euler Buckling capacity Pe. If the user keeps the unbraced length ratios l33 and l22 and the K -factors K 33 and K 22 correct, the B1 factor would be correct. If the axial force is small, the B1 factor can be 1 and have no effect with respect to modeling the single segment or multi-segment element. B2 factor: The program does not calculate the B2 factor. The program assumes that the user turns on the P-.
In such cases, B2 can be taken as equal to 1. That means the modeling with one or multiple segments has no effect on this factor. If the user models a column with a single element and makes sure that the L factors and K -factors are correct, the effect of B1 and B2 will be picked up correctly.
The factors Cm and Cb will be picked up correctly if there is no intermediate bracing point. The calculated Cm and Cb factors will be slightly conservative if there are intermediate bracing points. If the user models a column with multiple elements and makes sure that L factors and K -factors are correct, the effect of B1 and B2 will be picked up correctly.
The factors Cm and Cb will be picked up correctly if the member is broken at the bracing points. The calculated Cm and Cb factors will be conservative if the member is not broken at the bracing points. The effective buckling length is used to calculate an axial compressive strength, Pn, through an empirical column curve that accounts for geometric imperfections, distributed yielding, and residual stresses present in the cross-section. The first type of K -factor is used for calculating the Euler axial capacity assuming that all of the beam-column joints are held in place, i.
The resulting axial capacity is used in calculation of the B1 factor. This K -factor is named as K1 in the code. This K1 factor is always less than 1 and is not calculated. By default the program uses the value of 1 for K1. The program allows the user to overwrite K1 on a member-by-member basis. The other K -factor is used for calculating the Euler axial capacity assuming that all the beam-column joints are free to sway, i.
The resulting axial capacity is used in calculating Pn. This K -factor is named as K 2 in the code. This K 2 is always greater than 1 if the frame is a sway frame. The program calculates the K 2 factor automatically based on sway condition. The program also allows the user to overwrite K 2 factors on a. The same K 2 factor is supposed to be used in calculation of the B2 factor. However the program does not calculate B2 factors and relies on the overwritten values. If the frame is not really a sway frame, the user should overwrite the K 2 factors.
Both K1 and K 2 have two values: one for major direction and the other for minor direction, K1minor , K1major , K 2minor , K 2major. There is another K -factor. K ltb for lateral torsional buckling. By default, K ltb is taken as equal to K 2minor.
However the user can overwrite this on a memberby-member basis. The rest of this section is dedicated to the determination of K 2 factors. The K -factor algorithm has been developed for building-type structures, where the columns are vertical and the beams are horizontal, and the behavior is basically that of a moment-resisting frame for which the K -factor calculation is relatively complex.
For the purpose of calculating K -factors , the objects are identified as columns, beam and braces. All frame objects parallel to the Z -axis are classified as columns. All objects parallel to the X - Y plane are classified as beams. The remainders are considered to be braces. The beams and braces are assigned K -factors of unity. In the calculation of the K -factors for a column object, the program first makes the following four stiffness summations for each joint in the structural model:.
If a rotational release exists at a particular end and direction of an object, the corresponding value of G is set to If all degrees of freedom for a particular joint are deleted, the G -values for all members connecting to that joint will be set to 1. Finally, if G I and G J are known for a particular direction, the column K -factors for the corresponding direction is calculated by solving the following relationship for :.
This relationship is the mathematical formulation for the evaluation of K -factors for moment-resisting frames assuming sidesway to be uninhibited.
For other structures, such as braced frame structures, the K -factors for all members are usually unity and should be set so by the user. The following are some important aspects associated with the column K -factor algorithm:. An object that has a pin at the joint under consideration will not enter the stiffness summations calculated above.
Also, beam members that have no column member at the far end from the joint under consideration, such as cantilevers, will not enter the stiffness summation. If there are no beams framing into a particular direction of a column member, the associated G-value will be infinity. If the G-value at any one end of a column for a particular direction is infinity, the K -factor corresponding to that direction is set equal to unity.
If rotational releases exist at both ends of an object for a particular direction, the corresponding K -factor is set to unity. Effective Length Factor K 2 - The automated K -factor calculation procedure can occasionally generate artificially high K -factors , specifically under circumstances involving skewed beams, fixed support conditions, and under other conditions where the program may have difficulty recognizing that the members are laterally supported and K -factors of unity are to be used.
All K -factors produced by the program can be overwritten by the user. These values should be reviewed and any unacceptable values should be replaced. The calculated K 2 factors and their overwritten values are not considered in design. Framing Type.
Implementing those three types of framing require further information about modeling. The steel beam frames in a direction parallel to the column major direction, i. The steel beam frames in a direction parallel to the column minor direction, i. For connection conditions described in the last two bullet items, the thickness of such plates is usually set equal to the flange thickness of the corresponding beam.
However, for the connection condition described by the first bullet item, where the beam frames into the flange of the column, such continuity plates are not always needed. The requirement depends upon the magnitude of the beam flange force and the properties of the column. The program investigates whether the continuity plates are needed based on the requirements of the selected code.
Columns of I-sections supporting beams of I-sections only are investigated. The program evaluates the continuity plate requirements for each of the beams that frame into the column flange and reports the maximum continuity plate area that is needed for each beam flange.
The continuity plate requirements are evaluated for moment frames only. Shear stresses seldom control the design of a beam or column member. However, in a moment resisting frame, the shear stress in the beamcolumn joint can be critical, especially in framing systems when the column is subjected to major direction bending and the web of the column resists the joint shear forces. In minor direction bending, the joint shear is carried by the column flanges, in which case the shear stresses are seldom critical, and the program does therefore not investigate this condition.
Shear stresses in the panel zone, due to major direction bending in the column, may require additional plates to be welded onto the column web, depending upon the loading and the geometry of the steel beams that frame into the column, either along the column major direction, or at an angle so that the beams have components along the column major direction.
See Figure When code appropriate, the program investigates such situations and reports the thickness of any required doubler plates. Only columns with I-shapes and only supporting beams with I-shapes are investigated for doubler plate requirements. Also, doubler plate requirements are evaluated for moment frames only. The codes are based on a specific system of units. All equations and descriptions presented in the subsequent chapters correspond to that specific system of units unless otherwise noted.
However, any system of units can be used to define and design a structure in the program. References also are made to IBC in this document. Compressive residual stress in flange assumed Effective length K-factors in the major and minor directions for appropriate braced K1 and unbraced K2 condition.
Nominal dimension of plate in a section, in longer leg of angle sections, bf 2tw for welded and bf 3tw for rolled box sections, and the like. Clear distance between flanges less fillets, in assumed d 2k for rolled sections, and d 2tf for welded sections. Design Loading Combinations The structure is to be designed so that its design strength equals or exceeds the effects of factored loads stipulated by the applicable design code. The default design combinations are the various combinations of the already defined load cases, such as dead load DL , live load LL , roof live load RL , snow load SL , wind load WL , and horizontal earthquake load EL.
AISC refers to the applicable building code for the loads and load combinations to be considered in the design, and to ASCE in the absence of such a building code. Most of the analysis methods recognized by the code are required to consider Notional Load in the design loading combinations for steel frame design.
The program allows the user to define and create notional loads as individual load cases from a specified percentage of a given gravity load acting in a particular lateral direction. These notional load patterns should be considered in the combinations with appropriate factors, appropriate directions, and appropriate senses. Currently, the program automatically includes the notional loads in the default design load combinations for gravity combinations only.
The user is free to modify the default design load combinations to include the notional loads. For further information, refer to the "Notional Load Patterns" section in Chapter 2. The program automatically considers seismic load effects, including overstrength factors ASCE The factor SDS is described later in this section. Effectively, the special seismic combinations that are considered for the LRFD provision are 0.
The program assumes that the defined earthquake load is really the strength level earthquake, which is equivalent to QE as defined in Section Effectively, the seismic load combination for the LRFD provision becomes: 1. The seismic load combinations for the ASD provision become: 1. The program assumes that the seismic loads defined as the strength level load is the program load case. Otherwise, the factors , o , and SDS will not be able to scale the load to the desired level.
The combinations described herein are the default loading combinations only. They can be deleted or edited as required by the design code or engineer-ofrecord. Classification of Sections for Local Buckling The nominal strengths for axial, compression, and flexure are dependent on the classification of the section as Seismically Compact, Compact, Noncompact, Slender, or Too Slender.
Compact or Seismically Compact sections are capable of developing the full plastic strength before local buckling occurs. Noncompact sections can develop partial yielding in compression, and buckle inelastically before reaching to a fully plastic stress distribution.
Slender sections buckle elastically before any of the elements yield under compression. Seismically Compact sections are capable of developing the full plastic strength before local buckling occurs when the section goes through low cycle fatigue and withstands reversal of load under seismic conditions.
For a section to qualify as Compact, its flanges must be continuously connected to the web or webs and the width-thickness ratios of its compression elements must not exceed the limiting width-thickness ratios p from Table B4. If the widththickness ratio of one or more compression elements exceeds p, but does not exceed r from Table B4. If the width-thickness ratio of any element exceeds r but does not exceed s, the section is Slender.
If the width-thickness ratio of any element exceed s, the section is considered Too Slender. The limit demarcating Slender and Too Slender has been identified as s in this document. The table uses the variables kc, FL, h, hp, hc, bf, tf, tw, b, t, D, d, and so on.
The variables b, d, D and t are explained in the respective figures inside the table. The variables bf, tf, h, hp, hc, and tw are explained in Figure For Doubly Symmetric I-Shapes, h, hp, and hc are all equal to each other.
This is the same as the y-y axis. This is the same as the x-x axis. For unstiffened elements supported along only one edge parallel to the direction of compression force, the width shall be taken as follows: a For flanges of I-shaped members and tees, the width b is one-half the fullflange width, bf.
For stiffness elements supported along two edges parallel to the direction of the compression force, the width shall be taken as follows: a For webs of rolled or formed sections, h is the clear distance between flanges less the fillet or corner radius at each flange; hc is twice the distance from the centroid to the inside face of the compression flange less the fillet or corner radius.
For webs of rectangular HSS, h is the clear distance between the flanges less the inside corner radius on each side. If the corner radius is not known, b and h shall be taken as the corresponding outside dimension minus three times the thickness. The design wall thickness, t, for hollow structural sections, such as Box and Pipe sections, is modified for the welding process AISC B3. The Overwrites can also be used to change the reduction factor. The variable kc can be expressed as follows:.
Seismically Compact sections are compact sections that satisfy a more stringent width-thickness ratio limit, ps. This limit ps is presented in Table in Chapter 4, which is dedicated to the seismic code. In classifying web slenderness of I-Shapes, Box, Channel, Double Channel, and all other sections, it is assumed that there are no intermediate stiffeners.
Double angles and channels are conservatively assumed to be separated. Stress check of Too Slender sections is beyond the scope of this program. Calculation of Factored Forces and Moments The factored member loads that are calculated for each load combination are Pr, Mr33, Mr22, Vr2, Vr3 and Tr corresponding to factored values of the axial load, the major and minor moments and shears, and torsion, respectively.
These factored loads are calculated at each of the previously defined stations. The factored forces can be amplified to consider second order effects, depending on the choice of analysis method chosen in the Preferences. Second-order effects due to overall sway of the structure can usually be accounted for, conservatively, by considering the second-order effects on the structure under one set of loads usually the most severe gravity load case , and performing all other analyses as linear using the stiffness matrix developed for this one set of P-delta loads see also White and Hajjar For a more accurate analysis, it is always possible to define each loading combination as a nonlinear load case that considers only geometric nonlinearities.
For both approaches, when P- effects are expected to be important, use more than one element per line object accomplished using the automatic frame subdivide option; refer to the program Help for more information about automatic frame subdivide. Hence the analysis results are amplified using B1 and B2 factors using the following approximate second-order analysis for calculating the required flexural and axial strengths in members of lateral load resisting systems.
M a M b is positive when the member is bent in reverse curvature, negative when bent in single curvature. When Mb is zero, Cm is taken as 1. The user can overwrite the value of Cm for any member. Cm can be expressed as follows:. AISC Cb. It is taken to be equal to 1. The Overwrites can be used to change the value of K1 for the major and minor directions.
The Overwrites can be used to change the value of K2 for the major and minor directions. In the expression of B1, the required axial force Pr is used based on its first order value. The magnification factor B1 must be a positive number. Therefore, Pr must be less than Pe1. If Pr is found to be greater than or equal to Pe1 a failure condition is declared. If the program assumptions are not satisfactory for a particular structural model or member, the user has the choice to explicitly specify the values of B1 for any member.
Currently, the program does not calculate the B2 factor. The user is required to overwrite the values of B2 for the members. Calculation of Nominal Strengths The nominal strengths in compression, tension, bending, and shear are computed for Compact, Noncompact, and Slender members in accordance with the following sections.
The nominal flexural strengths for all shapes of sections are calculated based on their principal axes of bending. For the Single Angle sections, the principal axes are determined and all computations except shear are based on that. For all sections, the nominal shear strengths are calculated for directions aligned with the geometric axes, which typically coincide with the principal axes.
Again, the exception is the Single Angle section. If the user specifies nonzero nominal capacities for one or more of the members on the Steel Frame Overwrites form, those values will override the calculated values for those members. The specified capacities should be based on the principal axes of bending for flexure, and the geometric axes for shear. Although there is no maximum slenderness limit for members designed to resist tension forces, the slenderness ratio preferably should not exceed AISC D1.
A warning message to that effect is printed for such slender elements under tension. The design tensile strength, tPn, and the allowable tensile strength, Pn t , of tension members is taken as the lower value obtained according to the limit. The effective net area, Ae, is assumed to be equal to the gross cross-sectional area, Ag, by default. For members that are connected with welds or members with holes, the Ae A g ratio must be modified using the steel frame design Overwrites to account for the effective area.
In the determination, the effective length factor K2 is used as the K-factor. If the user overwrites the K2 factors, the overwritten values are used. If the chosen analysis method is one of any Direct Analysis Methods, the effective length. The overwritten value of K2 will have no effect for the latter case. The nominal axial compressive strength, Pn , depends on the slenderness ratio, Kl r , where. For Single Angles, the minimum principal radius of gyration, rz , is used instead of r22 and r33 , conservatively, in computing Kl r.
K33 and K22 are two values of K2 for the major and minor axes of bending. Although there is no maximum slenderness limit for members designed to resist compression forces, the slenderness ratio preferably should not exceed AISC E2. A warning message to that effect is given for such slender elements under compression.
The members with any slender element and without any slender elements are handled separately. The limit states of torsional and flexural-torsional buckling are ignored for closed sections Box and Pipe sections , solid sections, general sections, and sections created using Section Designer.
The flexural buckling stress, Fcr , is determined as follows:. The flexural buckling stress, Fc , is determined as follows. For angle sections, the principal moment of inertia and radii of gyration are used for computing Fe. Also, the maximum value of KL, i. The principal maximum value rmax is used for calculating Fe33 , and the principal minimum value rmin is used in calculating Fe The flexural buckling stress, Fcr , is determined as follows: QFy Q 0. The reduction factor, Qs , for slender unstiffened elements is defined as follows:.
For T-Shapes, the Qs is calculated for the flange and web separately, and the minimum of the two values is used as Qs. For Angle and Double Angle sections, Qs is calculated based on the leg that gives the largest b t and so the smallest Qs. The reduction factor, Qa, for slender stiffened elements is defined as follows:. The members are assumed to be loaded in a plane parallel to a principal axis that passes through the shear center, or restrained against twisting.
When determining the nominal flexural strength about the major principal axis for any sections for the limit state of lateral-torsional buckling, it is common to use the term Cb, the lateral-torsional buckling modification factor for nonuniform moment diagram. If the member is under tension and if the section is doubly symmetric, Cb is increased by a factor fcb where Ra is given as follows:. Cb should be taken as 1. However, the program is unable to detect whether the member is a cantilever.
The user should overwrite Cb for cantilevers. The program also defaults Cb to 1. The Overwrites can be used to change the value of Cb for any member. The nominal bending strength depends on the following criteria: the geometric shape of the cross-section; the axis of bending; the compactness of the section; and a slenderness parameter for lateral-torsional buckling. The nominal bending strength is the minimum value obtained according to the limit states of yielding, lateral-torsional buckling, flange local buckling, web local buckling, tension flange yielding as appropriate to different structural shapes.
AISC, in certain cases, gives options in the applicability of its code section, ranging from F2 to F In most cases, the program follows the path of the sections that gives more accurate results at the expense of more detailed calculation. In some cases, the program follows a simpler path.
Table 3. Fcr , Lp , and Lr are given by:. The provisions of lateral-torsional buckling for "Compact Web and Flanges" as described in the provision pages also apply to the nominal flexural strength of I-Shapes with compact webs and noncompact or slender flanges bent about their major axis.
Rpg is the bending strength reduction factor, which has been described in the previous section. AISC F, F, F and , pf, and rf are the slenderness and the limiting slenderness ratios for compact and noncompact flanges from Table 3. It is determined as follows:. Rpg is the bending strength reduction factor, which has been described in a previous section.
AISC F, F, F -9 and , pf, and rf are the slenderness and the limiting slenderness ratios for compact and noncompact flanges from Table 3. Fcr , Lp and Lr are given by. If the web is compact,. The program uses the same set of formulas for both major and minor direction bending, but with appropriate parameters.
The nominal flexural strength is the lowest value obtained according to the limit states of yielding plastic moment , flange local buckling and web local buckling. Note that the code does not cover the Box section flexure strength if the web is slender. The program uses the same flexure strength formula for Box sections with noncompact and slender webs, even though the formula applies only to noncompact section.
The nominal flexural strength is the lowest value obtained according to the limit states of yielding plastic moment and local buckling. The same set of formulas is used for both major and minor axes of bending.
Sxc is the elastic section modulus about the compression flange, and Fcr is determined as follows:. When the flange is in tension, i. The nominal flexural strength about the major principal axis is the lowest value obtained according to the limit states of yielding plastic moment , lateral-torsional buckling, and leg local buckling. A limit on Cb is imposed Cb 1. It is taken as the max L22, L33 in the program because L22 and L33 are not defined in the principal direction, in.
If the long leg is in compression anywhere along the unbraced length of the member, the 3 - It is conservatively taken as negative for unequal-leg angles.
The loading for this method is the same as shown in Figure 2, except for the addition of a notional load of 2. To determine which interaction equation is applicable, the ratio of the required axial compressive strength to available axial compressive strength must be determined. Direct Analysis Method Appendix 7 It was previously determined in the illustration of design by second-order analysis example that the second-order drift is less than 1.
The first-order drift ratio is determined from the amplified drift of 0. The lateral load required to produce the design story drift limit is: 15 kips 1, in.
Because this multiplier is less than 1. Additionally, because the multiplier is equal to 1. Summary for the Three-Bay Frame As before, all methods produce similar designs. The result of the beam-column interaction equation for each method is: Method Interaction Equation Second-Order 0. If conservative assumptions are acceptable, the easiest method to apply is the Simplified Method, particularly when the drift limit is such that K can be taken equal to 1.
The First-Order Analysis Method and Direct Analysis Method both eliminate the need to calculate K, which can be a tedious process based upon assumptions that are rarely satisfied in real structures.
Nonetheless, those who prefer to continue to use the approach of past specifications, the Effective Length Method, can do so, provided they incorporate the new requirement of a minimum lateral load in all load combinations. This should not be taken as a blanket indication that the use of a drift limit eliminates the need to consider stability effects. Rather, it simply means that drift-controlled designs may be less sensitive to secondorder effects because the framing is naturally stiffer and provides reserve strength.
Geschwindner, L. Lim, L. Open navigation menu. Close suggestions Search Search. User Settings. Skip carousel. Carousel Previous. Carousel Next. What is Scribd? Explore Ebooks. Bestsellers Editors' Picks All Ebooks. Explore Audiobooks. Bestsellers Editors' Picks All audiobooks.
Explore Magazines. Editors' Picks All magazines. Explore Podcasts All podcasts. Difficulty Beginner Intermediate Advanced. Explore Documents. Aisc Uploaded by Mugamputhagam. Did you find this document useful? Is this content inappropriate? The material in Section E5 c asic been moved to Section E5 with the exception of the specific examples of different end conditions, requiring the use of Chapter H provisions, which has been removed.
A user note has been added to this section stating that the strength of a bolt group be taken as the sum of the effective strengths of the individual fasteners, where the effective strength of an individual may be taken as the lesser of the fastener shear strength based on the provisions of this section or that of the bearing strength at the bolt hole from the provisions of Section J3.
In Equation G, the variable, a, has been changed to b. No Evidence of Composite Beam Design. Note that the definitions of M1 and M2 have not changed from the Specification. This chapter replaces Section M5 of the Specification. Torsional Bracing The first and last sentences of this section have been removed.
The elastic shear modulus, G, has also been added to these terms. You should refer to the individual codes for more details.
Noncompact and slender members are now allowed by the provisions without justification by testing or analysis. Load Transfer This section now refers to Section I6 for load transfer requirements for encased composite members. Material Properties and Yield Criteria This section includes material properties and yield criteria that must be included in the inelastic analysis that were previously specified in Sections 1. Qualification Standards No changes have been made to this section.
SCOPE The scope of the Specification has been expanded by including systems with structural steel acting compositely with reinforced concrete. Out of these cookies, the cookies that are categorized as necessary are stored on your browser as they are as essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website.
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