Problem 5. Consider A Beam Supported By A Distributed Spring Foundation (Such As A Railroad Rail Or Grade-Beam); Such Supports Are Know As Winkler Foundations. Assume The Beam Is 100 Ft Long With A Young's Modulus Of E = 30 X 106 Psi And A Cross-Sectional Area Moment Of Inertia I = 77.4 In4. Assume A Foundation Stiffness Of K 100 Lb/In2 And Determine The

 

 

Problem 5. Consider a beam supported by a distributed spring foundation (such as a railroad rail or grade-beam); such supports are know as Winkler Foundations. Assume the beam is 100 ft long with a Young's modulus of E = 30 x 106 psi and a cross-sectional area moment of inertia I = 77.4 in. Assume a foundation stiffness of k = 100 lb/in and determine the maximum positive and negative moments in the beam for a 30 x 103 lb load distributed over 3 in around the beam's center. Note that for this exercise the governing equation is given by Elv(x)"" = q(x), where q(x) = Japplied(x) kv(x). For boundary conditions, assume zero moment and shear at each end. 3mm L/2 3". 30,000 lbf we we we < L/2