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6. Airplane components often have a “stressed skin" construction, which consists of a thin sheet of aluminum in tension connected to the structure with rivets (i.e. pins that go through circular holes). a. If the aluminum skin is subject to a far-field biaxial tension of σ = 100 MPa and has a yield strength of σ = 210 MPa, will the rivet cause the sheet to yield? b. What is the strain through the thickness (z-direction) at the top-most edge of the hole? What does this mean is happening to the plate at that point? c. If a crack of length a = 1 mm forms at the side of the hole, will the plate fracture? How about if the crack is a = 3 mm? Take the aluminum to have a fracture toughness of K₁c = 15 MPa√m, and take the geometric stress concentration factor to be Y = 1.12. 50 = a

6. Airplane components often have a “stressed skin" construction, which consists of a thin sheet of aluminum in tension connected to the structure with rivets (i.e. pins that go through circular holes). a. If the aluminum skin is subject to a far-field biaxial tension of σ = 100 MPa and has a yield strength of σ = 210 MPa, will the rivet cause the sheet to yield? b. What is the strain through the thickness (z-direction) at the top-most edge of the hole? What does this mean is happening to the plate at that point? c. If a crack of length a = 1 mm forms at the side of the hole, will the plate fracture? How about if the crack is a = 3 mm? Take the aluminum to have a fracture toughness of K₁c = 15 MPa√m, and take the geometric stress concentration factor to be Y = 1.12. 50 = a

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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6. Airplane components often have a “stressed skin" construction, which consists of a thin sheet of aluminum in tension connected to the structure with rivets (i.e. pins that go through circular holes). a. If the aluminum skin is subject to a far-field biaxial tension of σ = 100 MPa and has a yield strength of σ = 210 MPa, will the rivet cause the sheet to yield? b. What is the strain through the thickness (z-direction) at the top-most edge of the hole? What does this mean is happening to the plate at that point? c. If a crack of length a = 1 mm forms at the side of the hole, will the plate fracture? How about if the crack is a = 3 mm? Take the aluminum to have a fracture toughness of K₁c = 15 MPa√m, and take the geometric stress concentration factor to be Y = 1.12. 50 = a
Transcribed Image Text:6. Airplane components often have a “stressed skin" construction, which consists of a thin sheet of aluminum in tension connected to the structure with rivets (i.e. pins that go through circular holes). a. If the aluminum skin is subject to a far-field biaxial tension of σ = 100 MPa and has a yield strength of σ = 210 MPa, will the rivet cause the sheet to yield? b. What is the strain through the thickness (z-direction) at the top-most edge of the hole? What does this mean is happening to the plate at that point? c. If a crack of length a = 1 mm forms at the side of the hole, will the plate fracture? How about if the crack is a = 3 mm? Take the aluminum to have a fracture toughness of K₁c = 15 MPa√m, and take the geometric stress concentration factor to be Y = 1.12. 50 = a
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