LRFD- Steel Design Dr. Ali I. Tayeh First Semester Dr. Ali I. Tayeh First Semester

Steel Design Dr. Ali I. Tayeh Chapter 6-B

Beam-Columns Example 6.5 Solution

Beam-Columns

Example 6.6 Beam-Columns

Solution

MEMBERS IN UNBRACED FRAMES In a beam column whose ends are free to translate, the maximum primary moment resulting from the side sway is almost always at one end. As was illustrated in the next Figure the maximum secondary moment from the sides way is always at the end. As a consequence of this condition, the maximum primary and secondary moments are usually additive and there is no need for the factor Cm; in effect, Cm = 1.0. The amplification factor for the sides way moments, B2, is given by two equations. Either may be used; the choice is usually one of convenience: OR

Beam-Columns Evaluation of Cm The summations for P u and P e2 apply to all columns that are in the same story as the column under consideration. The rationale for using the summations is that B2

Beam-Columns Design of beam column The procedure can be plained as following :

Beam-Columns Evaluation of C m

Beam-Columns The detailed procedure for design is: Select an average b value from Table 6-1 (if bending appears more dominant than axial load, select a value of m instead). If weak axis bending is present, also choose a value of n. From Equation 6.5 or 6.6, solve for m or h. Select a shape from Table 6-2 that has values of b, nt, and n close to those needed. These values are based on the assumption that weak axis buckling control the axial compressive strength and that Ch==1.0. See Example 6.8

Beam-Columns See Example 6.8 Solution:

Beam-Columns

Design of Bracing A frame can be braced to resist directly applied lateral forces or to provide stability. The latter type, stability bracing, The stiffness and strength requirements for stability can be added directly to the requirements for directly applied loads. Frame bracing can be classified as nodal or relative. With nodal bracing, lateral support is provided at discrete locations and does not depend on the support from other part of the frame. The AISC requirements for stability bracing are given in Section C3 of the Specification. For frames, the required strength is

Beam-Columns See Example 6.11

Beam-Columns Design of Unbraced Beam-Columns The preliminary design of beam-columns in braced frames has been illustrated. The amplification factor BI was assumed to be equal to 1.0 for purposes of selecting a trial shape; B I could then be evaluated for this trial shape. In practice, BI with almost always be equal to 1.0. For beam-columns subject to sides way, the amplification factor B2 is based on several quantities that may not be known until all column in the frame have been selected. If AISC Equation C 1-4 is used for B2, the sides way deflection  oh may not be available for a preliminary design. If AISC Equation Cl-5 is used,  P e2 may not be known. The following methods are suggested for evaluating H2.

Beam-Columns Design of Un braced Beam-Columns in the United States contains a limit on the drift index, values of 1/500 to 1/200arc commonly used (Ad Hoc Committee on Serviceability, 1986). Remember that  oh is the drift caused by IH, so if the drift index is based on service loads, then the lateral loads H must also be service loads. Use of a prescribed drift index enables the designer to determine the final value of B2 at the outset. See Example 6.12

Beam-Columns TRUSSES WITH TOP-CHORD LOADS BETWEEN JOINTS If a compression member in a truss must support transverse loads between its ends, it will be subjected to bending as well as axial compression and is therefore a beam-column. This condition can occur in the top chord of a roof truss with purlins located between the joints. The top chord of an open-web steel joist must also be designed as a beam-column because an open-web steel joist must support uniformly distributed gravity loads on its top chord. To account for loadings of this nature, a truss can be modeled as an assembly of continuous chord members and pin-connected web members. The axial loads and bending moments can then be found by using a method of structural analysis such as the stiffness method. The magnitude of the moments involved, however, does not usually warrant this degree of sophistication, and in most cases an approximate analysis will suffice.

Beam-Columns TRUSSES WITH TOP-CHORD LOADS BETWEEN JOINTS The following procedure is recommended. 1.Consider each member of the top chord to be a fixed-end beam. Use the fixed end moment as the maximum bending moment in the member. The top chord is actually one continuous member rather than a series of individual pin-connected members, so this approximation is more accurate than treating each member as a simple beam. 2.Add the reactions from this fixed-end beam to the actual joint loads to obtain total joint loads. 3.Analyze the truss with these total joint loads acting. The resulting axial load in the top-chord member is the axial compressive load to be used in the design.

Beam-Columns TRUSSES WITH TOP-CHORD LOADS BETWEEN JOINTS This method is represented schematically in the next figure. Alternatively, the bending moments and beam reactions can be found by treating the top chord as a continuous beam with supports at the panel points. See Example 6.13

Beam-Columns -Steel Design End