A machine of mass m = 100 kg is mounted on a simply supported beam of length 1 = 3 m, moment of inertia / = 1.5 × 10-4 m², and Young's modulus E = 3 × 10¹¹ N/m². Find the equivalent spring constant of the beam at the middle. What is the deflection of the beam at the middle? Assume the mass of the beam is negligible. ↓ m Simply supported beam with load at the middle keq = 48EI 13

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 9.5.4P: Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of...
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A machine of mass m = 100 kg is mounted on a simply supported beam of length 1 = 3 m,
moment of inertia / = 1.5 × 10-4 m², and Young's modulus E = 3 × 10¹¹ N/m². Find the equivalent
spring constant of the beam at the middle.
What is the deflection of the beam at the middle? Assume the mass of the beam is negligible.
m
Simply supported beam with load
at the middle
keq
=
48EI
13
Transcribed Image Text:A machine of mass m = 100 kg is mounted on a simply supported beam of length 1 = 3 m, moment of inertia / = 1.5 × 10-4 m², and Young's modulus E = 3 × 10¹¹ N/m². Find the equivalent spring constant of the beam at the middle. What is the deflection of the beam at the middle? Assume the mass of the beam is negligible. m Simply supported beam with load at the middle keq = 48EI 13
Now, let's suppose you attach a spring of stiffness k at mid-span to reduce the vertical deflection of
the beam. Is this a series or parallel connection? Why?
When k = 32 x
107 N/m, calculate the overall stiffness of the system at the middle of the beam. What is the deflection of
the beam at the middle? How much reduction in deflection has been achieved?
m
Transcribed Image Text:Now, let's suppose you attach a spring of stiffness k at mid-span to reduce the vertical deflection of the beam. Is this a series or parallel connection? Why? When k = 32 x 107 N/m, calculate the overall stiffness of the system at the middle of the beam. What is the deflection of the beam at the middle? How much reduction in deflection has been achieved? m
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