Explanation Given information: The normal stress along x-axis is 3500 psi , normal stress along y-axis is 12200 psi ,and shear stress along xy-plane is − 3300 MPa , orientation of element is − 51 ° . The following are the steps TO-Draw the Mohr’s circle Draw the horizontal line σ x -axis as a normal stress and vertical line τ x 1 y 1 -axis as shear stress and indicate the origin as point O ( 0 , 0 ) . Write the expression to locate the center point C of the circle from the origin O(ie., OC). OC = σ a v g = σ x + σ y 2 …… (I) Here, the normal stress along x-axis is σ x , normal stress along y-axis is σ y , and average stress is σ a v g . Mark the center point as C: ( σ a v g , 0 ) . Write the expression for the radius of Mohr’s circle. R = ( σ x − σ a v g ) 2 + τ x y 2 …… (II) Here, the radius of the Mohr’s circle is R and shear stress along xy-plane is τ x y . Mark point A: ( σ x , τ x y ) and point B: ( σ y , − τ x y ) and joint the point A and B. Write the expression for principle angle. α = tan − 1 ( τ x y σ x − σ a v g ) …… (III) Here, principle angle is α . Write the expression for the stress acting on element along x -direction. σ x ′ = σ a v g + R cos ( 2 θ − α ) …… (IV) Here, the stress acting on element along x -direction is σ x ′ and orientation of the plane is θ Write the expression for the stress acting on element along y -direction. σ y ′ = σ a v g − R cos ( 2 θ − α ) …… (V) Here, the stress acting on element along y -direction is σ y ' . The shear stress acting on element along x-y plane. τ x ′ y ′ = − R sin ( 2 θ − α ) ...... (VI) Here, shear stress acting on element along x-y plane is τ x ′ y ′ . Calculation: Substitute 3500 psi for σ x and 12200 psi for σ y in Equation (I). σ a v g = ( 3500 psi ) + ( 12200 psi ) 2 = 15700 psi 2 = 7850 psi Substitute 3500 psi for σ x and 12200 psi for σ y and − 3300 psi for τ x y in Equation (II). R = ( ( 3500 psi ) − ( 7850 psi ) ) 2 + ( − 3300 psi ) 2 = 29812500 ( psi ) 2 = 5460

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN: 9781337093347

Author: Barry J. Goodno, James M. Gere

Publisher: Cengage Learning

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Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain b…

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Chapter 7, Problem 7.4.13P

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The stresses on the element oriented at angle −51°from x-axis using Mohr’s circle.

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Chapter 7, Problem 7.4.12P

Chapter 7, Problem 7.4.14P

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Mechanics of Materials (MindTap Course List)

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The stresses on the element oriented at angle − 51 ° from x-axis using Mohr’s circle.

Solution Summary: The author explains the steps to draw the Mohr’s circle.

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