Explanation Given information: The stress along x direction is − 5700 psi , the stress along y direction is 950 psi , the shear stress is − 2100 psi and the angle θ is 65 ° Steps for construction of Mohr’s circle: The horizontal axis is taken as σ axis and the vertical axis is taken as τ axis. Locate the center of Mohr’s circle at a distance of − 2375 psi from the origin along the horizontal direction. Mark this point as C . Mark two points A and E on stress axis. These are marked from O . A represents σ y and E represents σ x . From E , line perpendicular to the axis upwards, up to a distance of τ x y from E is drawn. With C as a center and radius is the distance up to shear stress from C , draw a circle. Angle between the radius and horizontal is α . Write the expression for the center of the Mohr’s circle. C = σ x + σ y 2 .....(I) Here, the center of the circle is C , stress in x direction is σ x and stress in y direction is σ y . Write the expression for the average stress. σ a v g = σ x + σ y 2 .....(II) Here, average stress is σ a v g . Write the expression for the Mohr’s circle radius. R = ( σ x − σ a v g ) 2 + ( τ x y ) 2 .....(III) Here, the Mohr’s circle radius is R and the shear stress in x y plane is τ x y . Write the expression for angle α from the Mohr’s circle. α = tan − 1 ( | τ x y σ x − σ a v g | ) .....(IV) Here, α is the angle from the Mohr’s circle. Write the expression for the angle β from the Mohr’s circle. β = 180 ° − 2 θ + α .....(IV) Here, β is the angle from the Mohr’s circle and θ is the given angle. Write the expression for maximum stress. σ x 1 = σ a v g + R cos β .....(V) Here, the maximum stress is σ x 1 . Write the expression for the minimum stress. σ y ' = σ a v g − R cos β ……. (VI) Here, the minimum stress is σ y ' . Write the expression for the maximum shear stress. τ x ' y ' = − R sin β .....(VII) Here, the maximum shear stress is τ x ' y ' . Calculation: The figure below shows the diagram of Mohr’s circle. Figure (1) Substitute − 5700 psi for σ x and 950 psi for σ y in Equation (I). C = − 5700 psi + 950 psi 2 = − 2375 psi Substitute − 5700 psi for σ x and 950 psi for σ y in Equation (II)

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN: 9781337093347

Author: Barry J. Goodno, James M. Gere

Publisher: Cengage Learning

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Chapter 7, Problem 7.4.17P

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The stresses acting on an element at an angle θ from the x axis, using Mohr’s circle.

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The stresses acting on an element at an angle θ from the x axis, using Mohr’s circle.

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