Determine the deflection at the center the radial

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Unformatted text preview: S IP, Inc. 1–301 VM135: Bending of a Beam on an Elastic Foundation Overview Reference: S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 12, article 2. Analysis Type(s): Static Analysis (ANTYPE = 0) Element Type(s): 2-D Elastic Tapered Unsymmetric Beam Elements (BEAM54) Input Listing: vm135.dat Test Case A long (semi-infinite) beam on an elastic foundation is bent by a force F and a moment M applied at the end as shown. Determine the lateral end deflection of the beam δend. The elastic foundation stiffness k is based on 0.3 inches deflection under 10,000 lb loads spaced 22 inches apart. Figure 135.1 Beam Problem Sketch Material Properties k = 1515.15 lb/in2 E = 30 x 106 psi Geometric Properties A = 23 in2 I = 44 in4 Loading F = 1000 lb M = 10,000 in-lb Analysis Assumptions and Modeling Notes A nodal spacing of 22 inches is selected to match the discrete foundation locations upon which the stiffness is based. The beam le...
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