In guarding against excessive deflection due to an applied force F, the designer determined the maximum deflection of a cantilevered beam at its free end to be given by the following formula S FL³ 3EI and its mass to be given by the formula m = πr² Lp πη2 where the beam has a cross-sectional radius r, length L and moment of inertia / and its material has an elastic modulus E and density p. The beam is shown below.

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter11: Columns
Section: Chapter Questions
Problem 11.5.4P: A brass bar of a length L = 0.4 m is loaded at end B by force P = 10 kN with an eccentricity e =...
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Use the chart given in the textbook Shigley’s Mechanical Engineering Design, 10th Ed. Figure 2-16).
In guarding against excessive deflection due to
an applied force F, the designer determined the
maximum deflection of a cantilevered beam at
its free end to be given by the following formula
8 =
=
FL³
3EI
and its mass to be given by the formula
πη2 Lρ
m =
where the beam has a cross-sectional radius r,
length L and moment of inertia / and its material
has an elastic modulus E and density p. The
beam is shown below.
L
Transcribed Image Text:In guarding against excessive deflection due to an applied force F, the designer determined the maximum deflection of a cantilevered beam at its free end to be given by the following formula 8 = = FL³ 3EI and its mass to be given by the formula πη2 Lρ m = where the beam has a cross-sectional radius r, length L and moment of inertia / and its material has an elastic modulus E and density p. The beam is shown below. L
• Suggest an expression for the mass of
the beam in terms of the following:
1. Load and safety factor
2. Geometry
3. Material properties
• Give an expression for the stiffness-to-
weight performance index for this beam
• Select one material that:
1. exhibits ductile behavior,
2. satisfies the stiffness-to-weight
performance index of around P=2,
and
3. has an elastic modulus 100 GPa < E
< 200 GPa
Transcribed Image Text:• Suggest an expression for the mass of the beam in terms of the following: 1. Load and safety factor 2. Geometry 3. Material properties • Give an expression for the stiffness-to- weight performance index for this beam • Select one material that: 1. exhibits ductile behavior, 2. satisfies the stiffness-to-weight performance index of around P=2, and 3. has an elastic modulus 100 GPa < E < 200 GPa
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