MT-16.20 al.2002 The logical extension of discrete mass systems is one of an infinite number of masses In the limit this is a continuous syStem T ake the generalized beam-column as a generic representation d dw El F dx 23-1) Figure 23.1 Representation of generalized beam-column dF dx 和x This considers only static loads Must add the inertial load(s Since the concern is in the z-displacement(w) Inertial load /unit length mw (232) where: m(x =mass/unit length Paul A Lagace @2001 Unit 23-2MIT - 16.20 Fall, 2002 The logical extension of discrete mass systems is one of an infinite number of masses. In the limit, this is a continuous system. Take the generalized beam-column as a generic representation: 2 d 2 EI dw  dx2  dx2  − d F dw  = pz (23-1) dx  dx  Figure 23.1 Representation of generalized beam-column dF = − px dx This considers only static loads. Must add the inertial load(s). Since the concern is in the z-displacement (w): Inertial load unit length = mw ˙˙ (23-2) where: m(x) = mass/unit length Paul A. Lagace © 2001 Unit 23 - 2