622_Mechanics Homework Mechanics of Materials Solution

622_Mechanics Homework Mechanics of Materials Solution -...

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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 built-up 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 = 21-1455): 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 250-91: .- ...
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