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(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

(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
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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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