Refer to the textbook or other references specified in the course syllabus, read about Newton's Method for One-Dimensional Unconstrained Optimization and solve the following problem: The deflection of a uniform beam subject to a linearly increasing distributed load can be computed as: Wo y : -x* + 2L?x³ – L*x) 120EIL 50,000 kN/cm?, I = 30,000 cm“, and wo = 2.0 kN/cm, Given that L = 500 cm, E determine the point of maximum deflection using the Newton's method until the approximate error falls below ɛs = 0.05% with initial guess of x = 100. %3D %3D

Refer to the textbook or other references specified in the course syllabus, read about Newton's Method for One-Dimensional Unconstrained Optimization and solve the following problem: The deflection of a uniform beam subject to a linearly increasing distributed load can be computed as: Wo y : -x* + 2L?x³ – L*x) 120EIL 50,000 kN/cm?, I = 30,000 cm“, and wo = 2.0 kN/cm, Given that L = 500 cm, E determine the point of maximum deflection using the Newton's method until the approximate error falls below ɛs = 0.05% with initial guess of x = 100. %3D %3D

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

One-Dimensional Unconstrained Optimization / Newton's Method
Refer to the textbook or other references specified in the course syllabus, read about
Newton's Method for One-Dimensional Unconstrained Optimization and solve the
following problem:
The deflection of a uniform beam subject to a linearly increasing distributed load can be
computed as:
wo
y =
-(-x° + 2L²x³ – L*x)
120EIL
Given that L = 500 cm, E = 50,000 kN/cm², I = 30,000 cm“, and wo = 2.0 kN/cm,
determine the point of maximum deflection using the Newton's method until the
approximate error falls below ɛs = 0.05% with initial guess of x = 100.

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