Typically, an aircraft wing is supported by a single structural spar attached to the main fuselage at the wing root as shown. This arrangement can be idealized as a cantilever beam with a loading distribution characterizing wing pressure. In general, holes are introduced to the structural members to reduce the overall weight of the wing (observe the rib sections shown in 8). For the idealized beam arrangement (shown in the C), assume that the cross section of the spar is uniform and has a rectangular cross section (2" x 16"). The material is 2016-T6 Aluminum. If four 7" diameter holes are introduced to the beam (as shown in C, below), what is the maximum increase in normal stress? Ignore the effect of transverse shear.

Typically, an aircraft wing is supported by a single structural spar attached to the main fuselage at the wing root as shown. This arrangement can be idealized as a cantilever beam with a loading distribution characterizing wing pressure. In general, holes are introduced to the structural members to reduce the overall weight of the wing (observe the rib sections shown in 8). For the idealized beam arrangement (shown in the C), assume that the cross section of the spar is uniform and has a rectangular cross section (2" x 16"). The material is 2016-T6 Aluminum. If four 7" diameter holes are introduced to the beam (as shown in C, below), what is the maximum increase in normal stress? Ignore the effect of transverse shear.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Typically, an aircraft wing is supported by a single structural spar attached to the main fuselage at the wing root as
shown. This arrangement can be idealized as a cantilever beam with a loading distribution characterizing wing pressure.
In general, holes are introduced to the structural members to reduce the overall weight of the wing (observe the rib
sections shown in B). For the idealized beam arrangement (shown in the C), assume that the cross section of the spar is
uniform and has a rectangular cross section (2" x 16"). The material is 2016-T6 Aluminum.
If four 7" diameter holes are introduced to the beam (as shown in C, below), what is the maximum increase in normal
stress? Ignore the effect of transverse shear.
(A)
(C)
Wing Root
(Assumed Fixed)
80 lb/in
1.8'
1.8'
(B)
1.8'
9'
Wing Root
+
1.8'
W
Wing Tip
Fuel Tank
Wing Tip
(Assumed Free)

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Step 2: Calculate the bending moment at any distance x from the free end of the cantilever:

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Step 3: Calculate the maximum bending moment value and the moment of inertia:

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Step 4: Calculate the value of the maximum normal stress when there are no holes present:

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Step 5: Calculate the value of the moment of inertia of the cross-section when there are holes present:

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