tailieunhanh - Effective Length of Compression Members

Effective Length of Compression Members Introduction Isolated Columns Framed Columns — Alignment Chart Method Alignment Chart Method • Requirements for Braced Frames • Simplified Equations. to Alignment Charts Modifications to Alignment Charts Different Restraining Girder End Conditions • Consideration of Partial Column Base Fixity • Columns Restrained by Tapered Rectangular Girders Lian Duan California Department of Transportation Framed Columns — Alternative Methods LeMessurier Method • Lui Method • Remarks Crossing Frame System Latticed and Built-Up Members Latticed Members • Built-Up Members Wai-Fah Chen Purdue University Tapered Columns Summary. | Duan L. and Chen W. Effective Length of Compression Members Bridge Engineering Handbook. Ed. Wai-Fah Chen and Lian Duan Boca Raton CRC Press 2000 52 Effective Length of Compression Members Introduction Isolated Columns Framed Columns Alignment Chart Method Alignment Chart Method Requirements for Braced Frames Simplified Equations. to Alignment Charts Modifications to Alignment Charts Different Restraining Girder End Conditions Consideration of Partial Column Base Fixity Columns Restrained by Tapered Rectangular Girders Framed Columns Alternative Methods LeMessurier Method Lui Method Remarks Lian Duan California Department 52 7 of Transportation . Crossing Frame System Latticed and Built-Up Members Latticed Members Built-Up Members Wai-Fah Chen 52 8 Purdue University Tapered Columns Summary Introduction The concept of effective length factor or K factor plays an important role in compression member design. Although great efforts have been made in the past years to eliminate the K factor in column design K factors are still popularly used in practice for routine design 1 . Mathematically the effective length factor or the elastic K factor is defined as K cr cr where Pe is Euler load elastic buckling load of a pin-ended column Pcr is elastic buckling load of an end-restrained framed column E is modulus of elasticity I is moment of inertia in the flexural buckling plane and L is unsupported length of column. Much of the material of this chapter was taken from Duan L. and Chen W. F. Chapter 17 Effective length factors of compression members in Handbook of Structural Engineering Chen W. F. Ed. CRC Press Boca Raton FL 1997. 2000 by CRC Press LLC FIGURE Isolated columns. a End-restrained columns b pin-ended columns. Physically the K factor is a factor that when multiplied by actual length of the end-restrained column Figure gives the length of an equivalent pin-ended column Figure whose buckling load is the same