Element A is subjected to the stress state shown in the x-y plane (+x is to the right, ty is up). Use Mohr's Circle to solve the following problems. You MUST draw Mohr's Circle to get credit for these problems! 75 MPa 25 MPa 105 MPa (a) Determine the complete state of stress on the element in the x-y coordinate system. (b) Determine the state of stress if this element is rotated 25° (c) Determine the values of the principal stresses. (d) Determine the value of the maximum in-plane shear stress, Tmax in plane. (e) Determine the absolute maximum shear stress, Tmax abcolute (by drawing circles from each principal stress to the origin). Is Tmax abcolutre in the x-y plane (i.e., is Tmax abcolute equal to Tmax in-plane)? ers: (a) ox = 105 MPa (T); oy = 75 MPa (T); T = +25 MPa; o; = T = Tz = 0 4570 1MR.
Element A is subjected to the stress state shown in the x-y plane (+x is to the right, ty is up). Use Mohr's Circle to solve the following problems. You MUST draw Mohr's Circle to get credit for these problems! 75 MPa 25 MPa 105 MPa (a) Determine the complete state of stress on the element in the x-y coordinate system. (b) Determine the state of stress if this element is rotated 25° (c) Determine the values of the principal stresses. (d) Determine the value of the maximum in-plane shear stress, Tmax in plane. (e) Determine the absolute maximum shear stress, Tmax abcolute (by drawing circles from each principal stress to the origin). Is Tmax abcolutre in the x-y plane (i.e., is Tmax abcolute equal to Tmax in-plane)? ers: (a) ox = 105 MPa (T); oy = 75 MPa (T); T = +25 MPa; o; = T = Tz = 0 4570 1MR.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:1. Element A is subjected to the stress state shown in the x-y plane
75 MPa
(+x is to the right, +y is up). Use Mohr's Circle to solve the
following problems. You MUST draw Mohr's Circle to get
credit for these problems!
25 MPa
105 MPa
(a) Determine the complete state of stress on the element in
the x-y coordinate system.
(b) Determine the state of stress if this element is rotated 25°
(c) Determine the values of the principal stresses.
(d) Determine the value of the maximum in-plane shear stress, Tmax in plans.
(e) Determine the absolute maximum shear stress, Tmax abzolute (by drawing circles from
each principal stress to the origin). Is Tmax abzoluts in the x-y plane (i.e., is Tmax absolute
equal to Tmax, in-plane)?
nswers: (a) ox = 105 MPa (T); oy = 75 MPa (T); Ty = +25 MPa; o; = Tx = Tyz = 0
(b) ox = 118.8 MPa (T); o, = 61.21 MPa (T); t = -4.579 MPa
(c) 01.2 =119.2 MPa (T), 60.8 MPa (T)
(d) Tmax in-plane = 29.15 MPa
(e) Tmax absolute = 59.58 MPa; no, Tmax, absolute is not in the x-y plane
All three circles must be drawn for part (e)!
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