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A very thin rectangular plate (see figure (a)) is subjected to a biaxial plane stress state (σx, σy). The width and height of the plate are b = 7.5 [in] and h = 2.5 [in], respectively. The measures show that the strains in the (x, y) directions are εxx = 2.85x10−4 and εyy = −1.90x10−4, respectively. Figure (b) shows a 2D front view of the plate. Calculate i) The increment ΔL =  Lfinal - Linitial in the length of the diagonal Od. ii) The change ΔΦ = Φfinal - Φinitial of the angle formed between the diagonal Od and the x axis. iii) The change ΔΨ = Ψfinal - Ψinitial of the angle formed between the diagonal Od and the y axis. Note: remember that in a plane stress state we have σz = τxz = τyz = 0 and if it is also bi-axial we have τyx = 0.

A very thin rectangular plate (see figure (a)) is subjected to a biaxial plane stress state (σx, σy). The width and height of the plate are b = 7.5 [in] and h = 2.5 [in], respectively. The measures show that the strains in the (x, y) directions are εxx = 2.85x10−4 and εyy = −1.90x10−4, respectively. Figure (b) shows a 2D front view of the plate. Calculate i) The increment ΔL =  Lfinal - Linitial in the length of the diagonal Od. ii) The change ΔΦ = Φfinal - Φinitial of the angle formed between the diagonal Od and the x axis. iii) The change ΔΨ = Ψfinal - Ψinitial of the angle formed between the diagonal Od and the y axis. Note: remember that in a plane stress state we have σz = τxz = τyz = 0 and if it is also bi-axial we have τyx = 0.

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
Problem 1.1MA
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A very thin rectangular plate (see figure (a)) is subjected to a biaxial plane stress state (σx, σy). The width and height of the plate are b = 7.5 [in] and h = 2.5 [in], respectively. The measures show that the strains in the (x, y) directions are εxx = 2.85x10−4 and εyy = −1.90x10−4, respectively. Figure (b) shows a 2D front view of the plate.

Calculate

i) The increment ΔL =  Lfinal - Linitial in the length of the diagonal Od.

ii) The change ΔΦ = Φfinal - Φinitial of the angle formed between the diagonal Od and the x axis.

iii) The change ΔΨ = Ψfinal - Ψinitial of the angle formed between the diagonal Od and the y axis.

Note: remember that in a plane stress state we have σz = τxz = τyz = 0 and if it is also bi-axial
we have τyx = 0.

|y Ty Ox 9. (a)
Transcribed Image Text:|y Ty Ox 9. (a)
h (b)
Transcribed Image Text:h (b)
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