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1. At a critical point on the free surface of a loaded beam, the strains are measured in three directions at 0, = 0°, 0, = 45, 0̟=90° (see Fig. 1). They are found to be -10, +5×10³, +10*, respectively. a) Calculate the magnitude and orientation of the principal strains at the point. b) If E = 120 GPa, v=0.3, find the magnitude of the principal stresses. c) Determine the directions of the principal planes. 90 45° Fig. 1 2.

1. At a critical point on the free surface of a loaded beam, the strains are measured in three directions at 0, = 0°, 0, = 45, 0̟=90° (see Fig. 1). They are found to be -10, +5×10³, +10*, respectively. a) Calculate the magnitude and orientation of the principal strains at the point. b) If E = 120 GPa, v=0.3, find the magnitude of the principal stresses. c) Determine the directions of the principal planes. 90 45° Fig. 1 2.

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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1. At a critical point on the free surface of a loaded beam, the strains are measured in three directions at 0, = 0°, 0,=45, 0̟=90° (see Fig. 1). They are found to be -10, +5×10³, +10´, respectively. a) Calculate the magnitude and orientation of the principal strains at the point. b) If E = 120 GPa, v=0.3, find the magnitude of the principal stresses. c) Determine the directions of the principal planes. 90 45° Fig. 1 2. A sheet of material is subjected to a two-dimensional stress system in the x-y plane. At a given point, an element with its sides parallel to x and y axes is found to have a shear strain of 1×10, while an element at 45° to the first has a shear strain of 4×10 (Fig. 2). a) Calculate the maximum shear strain at this point. b) If the shear modulus 100 MPa, find the difference between the two principal stresses. y =4x104 D F6 F8 F9 F10 F11 F12 & 69
Transcribed Image Text:1. At a critical point on the free surface of a loaded beam, the strains are measured in three directions at 0, = 0°, 0,=45, 0̟=90° (see Fig. 1). They are found to be -10, +5×10³, +10´, respectively. a) Calculate the magnitude and orientation of the principal strains at the point. b) If E = 120 GPa, v=0.3, find the magnitude of the principal stresses. c) Determine the directions of the principal planes. 90 45° Fig. 1 2. A sheet of material is subjected to a two-dimensional stress system in the x-y plane. At a given point, an element with its sides parallel to x and y axes is found to have a shear strain of 1×10, while an element at 45° to the first has a shear strain of 4×10 (Fig. 2). a) Calculate the maximum shear strain at this point. b) If the shear modulus 100 MPa, find the difference between the two principal stresses. y =4x104 D F6 F8 F9 F10 F11 F12 & 69
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