CE 416 STRUCTURAL STEEL DESIGN ENGR. AMIE LOU G. CISNEROS, ENP, MSCE COLLEGE OF ENGINEERING AND TECHNOLOGY, COR JESU COLLEGE, DIGOS CITY COMPRESSION MEMBERS COMPRESSION MEMBERS structural elements that are subjected only to axial compressive forces; that is the loads are applied along a longitudinal axis through the centroid of the member cross section TYPES OF COMPRESSION MEMBERS Columns straight vertical members whose lengths are considerably greater than their thickness Struts Short vertical members subjected to compressive loads Top chords of trusses Bracing members Compression flanges of rolled beams 3 GENERAL MODES BY WHICH AXIALLY LOADED COLUMNS FAIL 1. FLEXURAL BUCKLING (EULER BUCKLING) The primary type of buckling Members are subject to flexure or bending, when they become unstable 2. LOCAL BUCKLING Occurs when some part or parts of the cross section of a column are so thin that they buckle locally in compression before the other modes of buckling can occur. The susceptibility of a column to local buckling is measured by the width – thickness ratio of the parts of its cross – section. 3 GENERAL MODES BY WHICH AXIALLY LOADED COLUMNS FAIL 3. FLEXURAL TORSIONAL BUCKLING May occur in columns that have certain cross – sectional configurations These columns fail by twisting (torsion) or by a combination of torsional and flexural buckling EULER’S COLUMN BUCKLING THEORY EULER’S COLUMN BUCKLING THEORY Column design and analysis was based on the Euler buckling load theory. His analysis is based on the differential equations of the elastic curve. Theory: “When a column is loaded with the buckling load or Euler load, a column will fail by sudden buckling or bending.” EULER’S COLUMN BUCKLING THEORY If the column is hinged at both ends, the Euler critical load is given as: 𝟐 𝒆 𝟐 And the Euler critical stress is: 𝟐 𝟐 𝒆 𝒆 𝟐 𝟐 𝒆 EULER’S COLUMN BUCKLING THEORY And the Euler critical stress is: Thus, = slenderness ratio EFFECTIVE LENGTH EFFECTIVE LENGTH The restraints placed on a column’s ends greatly affects its stability. To counter these effects, an effective length factor, K, is used to modify the unbraced length. This length approximates the length over which the column actually buckles and this may be shorter than the actual unbraced length. Thus, EFFECTIVE LENGTH SLENDERNESS RATIO SLENDERNESS RATIO Steel columns are usually subdivided into two groups: long and intermediate columns depending on their slenderness ratio. The values of slenderness ratio are: SLENDERNESS RATIO The critical slenderness ratio corresponds to the upper limit of elastic buckling failure, which is defined by an average column stress equal to 0.50 , thus: MINOR AND MAJOR AXIS BUCKLING LIMITING SLENDERNESS RATIO Acc. Section 502.8 (NSCP), the limiting slenderness ratio for members whose design is based on compressive force preferable shall not exceed 200. For members whose design is based on tensile force, the limiting slenderness ratio preferable should not exceed 300. NSCP ALLOWABLE COMPRESSIVE STRESS The allowable column slenderness ratio. stress Inelastic buckling occurs when buckling occurs when For intermediate columns, . varies with the and elastic NSCP ALLOWABLE COMPRESSIVE STRESS 𝟑 𝒄 For long columns, where 𝒌𝑳 𝒓 𝒄 𝟑 > 𝒄 𝟐 𝒂 𝟐 Where 𝒌𝑳 𝒓 is the larger value of 𝑲𝒙 𝑳𝒙 𝒓𝒙 and 𝑲𝒚 𝑳𝒚 𝒓𝒚 LOCAL BUCKLING LOCAL BUCKLING Local buckling of a plate element in a rolled shape or built – up compression member may occur before Euler buckling. The ability of plate sections to carry compressive loads without buckling is determined by the width – thickness ratio, . LOCAL BUCKLING Compression members are divided into stiffened and unstiffened elements. STIFFENED ELEMENTS Are supported along two parallel edges UNSTIFFENED ELEMENTS Supported along one edge only LOCAL BUCKLING To prevent local buckling, the following equation must be met if the plates are to be fully effective. 𝒚 For circular tubular sections whose ratios of outside diameter to wall thickness to be fully effective, the following equation must be met. 𝒚 UNSTIFFENED ELEMENTS ELEMENTS H • Stems of tees 333 • Double angles in contact 250 • Compression Flanges of beams 250 • Angles or plates projecting from girders, columns, or other members and compression flange of plate girders compression 250 𝐤𝐜 • Stiffeners on plate girders 250 • Flanges of tees and I – beams (use bf/2) 250 • Single – angle struts or separated double – angle struts 200 LOCAL BUCKLING LOCAL BUCKLING If , Otherwise, STIFFENED ELEMENTS ELEMENTS H • Square and rectangular box sections 625 • cover plates with multiple access holes 832 • other uniformly compressed members 664 UNSTIFFENED COMPRESSION MEMBERS UNSTIFFENED COMPRESSION ELEMENTS The allowable stress of unstiffened compression elements whose width – thickness ratio exceeds the applicable non – compact limit given shall be subject to a reduction factor 𝒔 . For single angles, When 𝟐𝟎𝟎 𝑭𝒚 𝒃 𝒕 𝟒𝟎𝟕 𝑭𝒚 𝒔 𝒚 UNSTIFFENED COMPRESSION ELEMENTS When 𝒚 UNSTIFFENED COMPRESSION ELEMENTS For angles and plates projecting from columns or other compression members, and for projecting elements of compression flanges of beams and girders: When 𝑭𝒚 𝑭𝒚 𝒌𝒄 𝒔 𝒌𝒄 UNSTIFFENED COMPRESSION ELEMENTS When 𝑭𝒚 𝒌𝒄 ALLOWABLE STRESSES FOR UNSTIFFENED COMPRESSION MEMBERS ALLOWABLE STRESSES FOR UNSTIFFENED COMPRESSION MEMBERS The allowable stress for axially loaded compression members containing unstiffened elements shall not exceed the following: When 𝒌𝑳 𝒓 𝒄 𝟐 𝒚 𝒂 𝟐 𝒄 ALLOWABLE STRESSES FOR UNSTIFFENED COMPRESSION MEMBERS 𝟑 𝟑 𝒄 𝒄 𝟐 𝒄 𝒚 ALLOWABLE STRESSES FOR UNSTIFFENED COMPRESSION MEMBERS Cross sections composed entirely of unstiffened elements, 𝒔 Cross sections composed entirely of stiffened elements, 𝒂 Cross sections composed of both stiffened and unstiffened elements, 𝒔 𝒂 ALLOWABLE STRESSES FOR UNSTIFFENED COMPRESSION MEMBERS When
