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9th Edition

Barry J. Goodno + 1 other

Publisher: Cengage Learning

ISBN: 9781337093347

Chapter 9, Problem 9.9.11P

Textbook Problem

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An overhanging beam *ABC *rests on a simple support at *A *and a spring support at *B *(see figure). A concentrated load *P *acts at the end of the overhang. Span *AB *has length /_, the overhang has length *a, *and the spring has stiffness *k.*

Determine the downward displacement *6 _{C}*of the end of the overhang. (Obtain the solution by using the modified form of Castigliano's theorem.)

To determine

Downward displacement

**Given:**

Bending moment and partial derivative for segment AB:

Bending moment and partial derivative for segment BC:

Strain energy of the spring:

Strain energy of the beam:

Total strain energy:

Apply Castigliano’s Theorem:

Mechanics of Materials (MindTap Course List)

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