(a) Determine the principal stresses (σp1>σp2) and the maximum in-plane shear stress τmax acting at the point. (b) Find the smallest rotation angle θp

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 12 ksi, Sy = 35 ksi, and Sxy = 12 ksi. (a) Determine the principal stresses (σp1>σp2) and the maximum in-plane shear stress τmax acting at the point. (b) Find the smallest rotation angle θp (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch
Consider a point in a structural member that is
subjected to plane stress. Normal and shear
stress magnitudes acting on horizontal and
vertical planes at the point are Sx = 12 ksi, Sy =
35 ksi, and Sxy = 12 ksi.
(a) Determine the principal stresses (
Op1 > 0,2) and the maximum in-plane shear
stress Tmax acting at the point.
(b) Find the smallest rotation angle Op
(counterclockwise is positive, clockwise is
negative) that will rotate to principal directions.
Then show these stresses in an appropriate
sketch (e.g., see Figure 12.15 or Figure 12.16)
Sxy
||
Opl
Op2
Tmax =
=
||
Sx
O
ksi.
ksi.
ksi.
Transcribed Image Text:Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 12 ksi, Sy = 35 ksi, and Sxy = 12 ksi. (a) Determine the principal stresses ( Op1 > 0,2) and the maximum in-plane shear stress Tmax acting at the point. (b) Find the smallest rotation angle Op (counterclockwise is positive, clockwise is negative) that will rotate to principal directions. Then show these stresses in an appropriate sketch (e.g., see Figure 12.15 or Figure 12.16) Sxy || Opl Op2 Tmax = = || Sx O ksi. ksi. ksi.
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