A machine of mass m = 100 kg is mounted on a simply supported beam of length l = 3 m, moment of inertia / = 1.5 x 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. ply Supported Beam P 1 ·b· y(x) = m Pbx - (1² - x²-b²); 6EIL Pa(1-x) 6EIL 0 ≤x≤a x²-a²); a ≤x≤l -(21x - x² -a²);

Elements Of Electromagnetics
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Use answer from first part without spring to build onto next part, thanks.

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.
Simply Supported Beam
P
X
1
·b·
y(x)
=
m
Pbx
6EIL
−(1²-x² - 6²); 0≤x≤ a
Pa(1x)
6EIL
(21xx²a²); a ≤ x ≤ 1
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. Simply Supported Beam P X 1 ·b· y(x) = m Pbx 6EIL −(1²-x² - 6²); 0≤x≤ a Pa(1x) 6EIL (21xx²a²); a ≤ x ≤ 1
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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