Understanding Effective Length Factor in Structural Analysis

1. Effective Length Factor - Real Conditions The effective length factor (K) was introduced in page (C-7) for six ideal conditions, these are not encountered in practical field conditions. LRFD commentary provides both real conditions and standard ideal conditions (C-C2.2) (page 16.1-239 to 242) Braced Frames: Unbraced Frames: No lateral movement is allowed (0.5 < K < 1.0) (sideway prevented) Lateral movement possible (1.0 < K < 20.0) (sideway allowed) • Diagonal • bracing b) Shear Walls (masonry, reinforcement concrete or steel plate) C-23

2. Alignment Charts (LRFD P-16.1 - 241) where A is top of column where B is bottom of column * For fixed footing G = 1.0 * For pinned support G = 10.0 C-24

3. W12 x 96 12' W24 x 68 W24 x 55 A W12 x 120 12' W24 x 55 W24 x 68 B W12 x 120 15' C 18' 20' 20' Use of Alignment Charts Example C – 8 :- In the rigid frame shown below, Determine Kx for columns (AB) & (BC). Knowing that all columns webs are in the plane. Solution: Column (AB): Joint (A): C-25

4. For joint B,:- From the alignment chart for sideways uninhibited, with GA = 0.94 and GB = 0.95, Kx = 1.3 for column AB. Column (BC): For joint B, as before, G = 0.95 For joint C, at a pin connection the situation is analogous to that of a very stiff column attached to infinitely flexible girders – that is, girders of zero stiffness. The ratio of column stiffness to girder stiffness would therefore be infinite for a perfectly frictionless hinge. This end condition is only be approximated in practice, so the discussion accompanying the alignment chart recommends that G be taken as 10.0. From the alignment chart with GA = 0.95 and GB = 10.0, Kx = 1.85 for column BC. C-26