Unformatted text preview: PROBLEM 5.146 11‘ 5.145. and 5.146 A preliminary design based on the use of a cantilever prismatic beam
indicated that a beam with a rectangular cross section 2 in. wide anle in. deep would
be required to safely support the‘load shown in part a of the ﬁgure. It was then decided to replace that beam with a builtup beam obtained by gluing together, as shown in part
b of the ﬁgure, ﬁve pieces of the same timber as the original beam and of 2 x 2 in. cross section. Determine the respective lengths [1 and 12 of the two inner and two outer pieces of timber that will yield the same factor of safety as the original design. SOLUTION [H‘Be ‘Hlﬂﬂa g.
‘ML’ inluw(Xt/€.1S")
[Mlor It’ll", (X, /6.25’) " A+c
MID M 'B 53 = 4w = 211455): 2 355* A +., c sq. Hum :50»? e 2%“ c it ‘D 55 = tub thaw: 353  £125 ___ ‘
c‘ 72?” 1.25 'FT' 1),: 6.257— 1.23' Pr = 5.00 +3. «in X9: M = 3.75131 W )2 = 6.25 3.7:Pr r 25091: . ...
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 Summer '10
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