and y vs. y (phase plot)4. Consider the deflection v of the beam to the right. The beam is supported at each end and sags due to its ownweight (a distributed load q = 50 kN/m). The equation describing the deflection isd'uqx (x- L)dx2EIwhere L=5.0 m, I = 0.0052 m* and E = 1.0x1010 Pa. Use the methodof your choosing (shooting or finite differences) to solve for: 1) theslope at each end of the beam; 2) the maximum deflection; and3) the location of maximum deflection.

Answered: Image /qna-images/answer/df1eedc7-ce18-48af-b82b-7a486b64a170.jpg

and y vs. y' (phase plot) 4. Consider the deflection v of the beam to the right. The beam is supported at each end and sags due to its own weight (a distributed load q = 50 kN/m). The equation describing the deflection is d'u qx (x-L) dx 2EI where L=5.0 m, 1 = 0.0052 m and E = 1.0x100 Pa. Use the method of your choosing (shooting or finite differences) to solve for: 1) the slope at each end of the beam; 2) the maximum deflection; and 3) the location of maximum deflection.

and y vs. y' (phase plot) 4. Consider the deflection v of the beam to the right. The beam is supported at each end and sags due to its own weight (a distributed load q = 50 kN/m). The equation describing the deflection is d'u qx (x-L) dx 2EI where L=5.0 m, 1 = 0.0052 m and E = 1.0x100 Pa. Use the method of your choosing (shooting or finite differences) to solve for: 1) the slope at each end of the beam; 2) the maximum deflection; and 3) the location of maximum deflection.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.4.10P: -10 Derive the equations of the deflection curve for beam AB with sliding support at A and roller...

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-22 Derive the equations of the deflection curve for a simple beam AB with a distributed load of peak intensity q0acting over the left-hand half of the span (see figure). Also, determine the deflection cat the midpoint of the beam. Use the second-order differential equation of the deflection curve.
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A heavy object of weight W is dropped onto the midpoint of a simple beam AB from a height h (see figure). Obtain a formula for the maximum bending stress ^ma* due to tne filing weight in terms of h, st, and 5st, where it is the maximum bending stress and Sstis the deflection at the midpoint when the weight W acts on the beam as a statically applied load. Plot a graph of the ratio o"max/ö"it (that is, the ratio of the dynamic stress to the static stress) versus the ratio iifS^r(Let h/S^ vary from 0 to 10.)
-6 Calculate the maximum deflection of a uniformly loaded simple beam if the span length L = 2.0 m, the intensity of the uniform load q = 2.0 kN/m, and the maximum bending stress = 60 MPa, The cross section of the beam is square, and the material is aluminum having modulus of elasticity E = 70 GPa. (Use the formulas of Example 9-1.)
A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap exists between the unloaded beam and the support at C. Assume that span length L = 40 in. and flexural rigidity of the beam EI = 04 x 109lb-in2. Plot a graph of the bending moment at B as a function of the load intensity q. Hint: See Example 9-9 for guidance on computing the deflection at C.