9.5-40 The wing of a small plane is represented by asimplified prismatic cantilever beam model acted onby the distributed loads shown in the figure. Assumeconstant EI = 1200 kN m, Find the tip deflectionand rotation at B.1600 N/m90 N/m111.0 m2.6 m2.6 m1600 N/m90 N/mAPROBLEM 9.5-40

Answered: 1.0 m 2.6 m 2.6 m 1600 N/m 900 N/m

Engineering

Mechanical Engineering

1.0 m 2.6 m 2.6 m 1600 N/m 900 N/m

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter9: Deflections Of Beams

Section: Chapter Questions

Problem 9.5.40P: The wing of a small plane is represented by a simplified prismatic cantilever beam model acted on by...

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Question

9.5-40 The wing of a small plane is represented by a
simplified prismatic cantilever beam model acted on
by the distributed loads shown in the figure. Assume
constant EI = 1200 kN m, Find the tip deflection
and rotation at B.
1600 N/m
90 N/m
11
1.0 m
2.6 m
2.6 m
1600 N/m
90 N/m
A
PROBLEM 9.5-40

Expert Solution

Step 1

Prismatic cantilever beam

$E I = 1200 K N - m^{2}$

Taking section at a distance x from the free end.

By similar triangle,

$\frac{700}{2.6} = \frac{w_{x}}{x - 3.6} w_{x} = \frac{3500}{13} (x - 3.6)$

since,

$M x = [(\frac{900 x L}{2}) x (x - \frac{2}{3})] + [(900) x \{2.6 (x - 2.3)\}] + [\frac{900 {(x - 3.6)}^{2}}{2}] + [(\frac{3500 {(x - 3.6)}^{2}}{13 x 2}) (\frac{x - 3.6}{3})]$

$M x = [450 (x - \frac{2}{3})] + [2340 (x - 2.3)] + [450 {(x - 3.6)}^{2}] + [\frac{1750 {(x - 3.6)}^{2}}{13 x 3}]$

by double integration method,

$E I \frac{d y}{d x} = [\frac{450}{2} {(x - \frac{2}{3})}^{2}] + [\frac{2340}{2} {(x - 2.3)}^{2}] + [\frac{450}{2} {(x - 2.3)}^{3}] + [\frac{1750}{13 x 3 x 4} {(x - 2.3)}^{4}] + c_{1}$

where, $c_{1} = I n t e g r a t i o n c o n s \tan t$

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