1. (a) A structural element is subjected to the stresses σx = a, σy = b, ɩxy = c, where the values a, b, and c are assigned in the table below. i) Write down the stress tensor S corresponding to this stress regime. (1%) ii) Use matrix methods to find the principal stresses acting on this element, using the information in the stress tensor. (6%) iii) Use your results from part (ii) to determine the maximum in-plane shear stress acting on this element. (2%) iv) Use matrix methods to find the direction in which the major principal stress (σmax) is acting. Express your answer as the angle (0) from the current x-axis to the direction of action of this stress. (7%)
1. (a) A structural element is subjected to the stresses σx = a, σy = b, ɩxy = c, where the values a, b, and c are assigned in the table below. i) Write down the stress tensor S corresponding to this stress regime. (1%) ii) Use matrix methods to find the principal stresses acting on this element, using the information in the stress tensor. (6%) iii) Use your results from part (ii) to determine the maximum in-plane shear stress acting on this element. (2%) iv) Use matrix methods to find the direction in which the major principal stress (σmax) is acting. Express your answer as the angle (0) from the current x-axis to the direction of action of this stress. (7%)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:1. (a)
A structural element is subjected to the stresses σx = a, σy = b, ɩxy = c, where the values
a, b, and c are assigned in the table below.
i) Write down the stress tensor S corresponding to this stress regime.
(1%)
ii) Use matrix methods to find the principal stresses acting on this element, using the
information in the stress tensor.
(6%)
iii) Use your results from part (ii) to determine the maximum in-plane shear stress acting
on this element.
(2%)
iv) Use matrix methods to find the direction in which the major principal stress (σmax) is
acting. Express your answer as the angle (0) from the current x-axis to the direction
of action of this stress.
(7%)
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