Problem Set 5 EMA 4714  Materials Selection and
Failure Analysis
Due Wednesday, February 20, 2008 – 8:30 am
1. The following 4 problems [lifted from Ashby, Materials Selection in
Mechanical Design] all involve cantilever beams, but with different
loading configurations or design objectives/constraints. Read
carefully
....
********************************************************
The constraint equation in all 4 cases is the same as is the 2nd area
moment [inertia];
δ
= FL
3
/[C
1
EI]
I = t
4
/12
a. Show that the best material for a cantilever beam of length L and
given [i.e. fixed] square section [t x t] which will deflect least under a
given end load F is that with the largest value of the index M = E,
where E is Young’s Modulus [neglect selfweight].
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L
3
/[2Et
4
]; m = Lt
2
?
; Substituting value for m into expression for
?
min
,
?
min
= [3/2][L
4
/t
2
][
?
/E]; M
δ
min
= 12FL
3
/[3Et
4
] = 4FL
3
/[Et
4
] = [4F]][L
3
/t
4
][1/E]; M
1
= E
QED
b. Show that the best material choice for a cantilever beam of a given
length L and with a given square section [t x t] which will deflect
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 Spring '08
 Staff
 Cantilever, Cantilever Beam, δmin, lightest cantilever beam

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