1. The state of stress in a solid is defined by: 01 = 20, 02 = -40, ơ3 = -10, T12 = 0, t23 =-15, 713 = 15 (all stresses in ksi). 1.1. Find the direct stress, on, on an internal surface whose normal ī is at 60° to axis ī, and makes equal angles with axes i, and i3.

Structural Analysis
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Chapter2: Loads On Structures
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1. The state of stress in a solid is defined by: o, = 20, ơ2 = -40, 03 = -10, t12 = 0, T23 = -15, T13 =15 (all
stresses in ksi).
1.1. Find the direct stress, o,, on an internal surface whose normal ī is at 60° to axis ī, and makes equal angles
with axes i, and i3.
1.2. Find the principal stresses, opi, and their directions, ñī, (i = 1,2,3). HINT: you do NOT have to do this by
hand; use the eigenvalue function in MATLAB, Mathematica or Wolfram Alpha.
Transcribed Image Text:1. The state of stress in a solid is defined by: o, = 20, ơ2 = -40, 03 = -10, t12 = 0, T23 = -15, T13 =15 (all stresses in ksi). 1.1. Find the direct stress, o,, on an internal surface whose normal ī is at 60° to axis ī, and makes equal angles with axes i, and i3. 1.2. Find the principal stresses, opi, and their directions, ñī, (i = 1,2,3). HINT: you do NOT have to do this by hand; use the eigenvalue function in MATLAB, Mathematica or Wolfram Alpha.
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